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GH531/EPI539

Computer Lab Module: Session 3

2012

StatCalc - Calculating a Sample Size with Epi-Info In this lesson, you will learn how to use the StatCalc feature of Epi-Info to calculate the sample size of a study you may design. StatCalc is a tool that automatically generates a range of sample sizes for different confidence and precision levels. You will learn how to use StatCalc to determine sample sizes for different types of studies, experiment with changes in study design parameters for understanding the relationship between these parameters and sample size, and become familiar with StatCalc’s limitations as a tool. LESSON ACTIVITIES

Use StatCalc to calculate sample sizes for descriptive cross-sectional, cohort, and case-control studies. Input different parameters into StatCalc’s calculator for viewing relationship between certain parameters and the sample size calculation.

WHAT YOU NEED

Epi-Info downloaded on your machine. If you do not have it, go to the main page on the Moodle Web site to access the CDC’s download page for Epi-Info.

Getting Started with StatCalc Other Epi-Info sessions in this course use the major modules of Epi-Info such as Form Designer and Analyze Data. StatCalc is one of the most useful parts of Epi-Info. It is used by researchers who prefer as well as have the resources to analyze their data with software programs such as STATA or SPSS. StatCalc is also one of the easiest tools to use. You input your parameters such as expected outcome value and desired precision, and then StatCalc determines the sample size. No memorization of formulas or mathematical equations is necessary! StatCalc has several tools: Sample Size and Power, Chi Square for Trend, and Tables (2X2, 2XN). We will be only learning to use the Sample Size and Power tool in this module. This module will not describe the equations used to calculate sample size or the terminology since these will be covered by the professors in the Sample Size lecture.

Choosing the Type of Study Design to Use Within the Sample Size and Power tool there are 3 choices: Population survey, Cohort or cross-sectional, and Unmatched case-control. Each study type uses a different formula for calculating sample size so you need to think carefully about which type is yours. You may notice that StatCalc does not offer an exhaustive list of study design types so you may find that your specific study type may not be listed here. If your study really does not fall within the specifications of these designs, you will need to use another program or tool to make your calculations since it is imperative to use the correct equation to obtain these numbers. Other sample size or power calculation tools may be more useful for non-Epidemiological studies. One free example is PS, which can be downloaded at http://biostat.mc.vanderbilt.edu/wiki/Main/PowerSampleSize. There is also a link within the Epi Info program 1

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to a website called OpenEpi (http://openepi.com/OE2.3/Menu/OpenEpiMenu.htm) that is full of useful calculators for more types of study designs. There are several pay options that can be found at the UCSF’s Department of Epidemiology and Biostatistics website, although much of the documentation is more technical than what you’ll find in this tutorial. Go to http://www.biostat.ucsf.edu/sampsize.html to see the list of possibilities. Note: You cannot use StatCalc to determine means, such as the average number of days a child stricken with malaria stayed at the hospital or the average cost of bednets in a region. Means use continuous variables, yielding values such as 51.34 as opposed to dichotomous variables (yes/no, seropositive/seronegative) which yield proportions (51%). If your outcome is a mean: You'll need to use an online sample size and power calculator such as those you can find on the UCSF site. Some recommendations are PS, PC-Size, and Rollin Brant’s Sample Size Calculators from the University of Calgary to be simple to follow. Now, assuming that you can use StatCalc for your needs, let's look at the types of studies that you can calculate sample sizes from. Each of the three types below requires a different sample size formula, so while you may detect similarities between them, remember that StatCalc will treat each differently. The workings "under the hood" will be completely different.

Making Your Study Design Choice in StatCalc Once you know which study design type you would like to use, navigate to StatCalc on the Epi Info navigation bar and select “Sample Size and Power” and the study design you would like to use.

Population Survey refers to a non-comparative cross-sectional survey, a descriptive study that provides a picture of a specific population's characteristics at a certain point in time. This picture is based on dichotomous variables such as gender, infected/not infected with a disease, etc. In Epi-Info, it assumes you are using random (not cluster) sampling, although many researchers use StatCalc even if they are not using a truly random sampling procedure (e.g. convenience sampling), being sure to note the limitations in the methods. Your population does not need to be large such as the population of a country; instead, it can mean village women in a certain area or all district households with children under 5 years old. In a study such as this one, you are not planning to compare two groups in the data collection phase, either before or after, or between those who are exposed and those who are not exposed. Instead, you are simply trying to find out information such as the number of days one may adhere to a new treatment plan/behavior change activity, the number of women who utilize traditional birth attendants at their home births, or the proportion of physicians and nurses who leave their posts for lucrative overseas jobs after 3 years of service in their nation's healthcare system.

Cohort or Cross Sectional Survey refers to the types of studies that compare two groups with dichotomous – not continuous – variables (comparing proportions not means), one of which is exposed and the other which is non-exposed. The cross-sectional survey in this case is a comparative survey, not the descriptive type of cross-sectional survey described above under Population Survey. So, in studies such as these, you may be interested in the amount of improvement in infant's Z-scores at monthly baby weighings after a soy food intervention (soy milk, tofu, soy-based porridge). Or, maybe you are interested in the difference in DOTS therapy drop-off rate at health clinics that lose significant numbers of staff to funding cuts versus clinics who retain their community health workers that assist with DOTS. 2

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2012

Unmatched Case Control refers to studies that compare two groups, one of which has a certain condition X or has experienced a specific outcome, and another which has not. Your study aims to determine whether the proportion of exposure in the two groups differs. So, you identify the outcome first and then look for the exposure. You typically use this type of study when you think the outcome is so unlikely that it would require a very large cohort study to enroll enough subjects who meet your selection criteria – those who have the outcome. So, in this type of study, you plan to determine the risk factors for mercury poisoning in a village in South China as you have identified a number of cases there. You have already identified some who are cases and some who are controls; your study focuses on determining the proportion of cases that share risk factors X, Y, and Z.

Entering Your Study Parameters for StatCalc to Use in Its Sample Size Calculation Calculating Sample Size for a Population Survey 1. Select Population Survey

The Population Survey Parameters Box should open.

2. Enter the size of the total population in your study area.

Notice that you can enter up to 9 digits.

Note that this number is not necessarily the total population as found through a national census. Rather, it is the total population under study — all of those possible study subjects who meet the inclusion criteria for the study and thus, are a part of your "denominator" in public health lingo. 3

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Your total population is not the number of subjects you believe you have the resources to enroll or the number of subjects you believe exhibit the behavior or the biological factor that you are planning to study.

For example, if you are interested in the level of Vitamin A deficiency among pregnant and breastfeeding women in the Collines region of Benin, your total population is all the women of childbearing age (given that most women are usually preparing to be pregnant, pregnant, or in the postpartum stage). It is not the entire population residing in the Collines region. Refer to the lectures on Indicators and Outcomes to refresh your memory about this if it does not make sense.

For this example, you will be examining the percentage of a region's households that regularly use bednets to protect expectant and breastfeeding mothers as well as children under 5 years old. So, enter 40,000 as the population and hit Tab to go to the next field.

3. You now need to enter the Expected Frequency.

The Expected Frequency is your estimate of the result. In statistical terms, this is your estimated proportion of the main variable in your study. It is your outcome that you expect from the intervention you plan or the information that you aim to gather and report on. Determining the value of this factor is where some of the guesswork will enter your study design. It is the part that may seem arbitrary, and may often be if one is researching a new field of study.

NOTE: If you are making a calculation from an epidemiological statistic such as mortality rate, be sure to express it correctly. For example, 60 per 100,000 IMR would be input as 0.06% into StatCalc, not 60% or 6%. Once again, refer to the Indicators & Outcomes lectures.

In this example, you know from discussions with key informants that only about 30% use bednets. Enter 30 and hit Tab to go to the next field.

4. Enter Confidence Limits.

The Confidence Limits is the outer limit in the range (+ or – your expected frequency) of results that you are comfortable seeing. It is a value that is either lower or higher than the number you input above under Expected Frequency of Factor Under Study. This field is where you will enter your desired precision — the value that determines how accurate your study will be in discovering the actual answer to your research question. In statistical parlance, this value will be an expression of your margin of error. Since you are not sure what your study outcomes will be, you must give yourself a range in which your data will fall. This range is the margin of error (+/- 9 points or +/- 2.5% that you see in the fine print in polls). In statistical theory, your expected value will lie within the range for a certain percentage of samples if you use your study methodology over and over again. (But, don't worry about setting your confidence level here StatCalc will do this for you soon.) 4

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Computer Lab Module: Session 3

2012

So, while you are hoping that the number you chose above for the Expected is the actual result, you know it may not be. Thus, you choose your Confidence Limit — the outer limit for the value that will still be an acceptable outcome for your study.

NOTE: You want to choose a Confidence Limit that provides you with enough room for error, but which is also precise enough to deliver results that are meaningful. If your possible range of results is too large, it will show that you lack confidence in your methodology's ability to find the actual answer to your question. If it is too small, the sample size is too big and the study is no longer feasible.

In this example, you decide that +/- 10% for the proportion of women that use bednets is acceptable. So, you type 10% into Confidence Lmits. Your window should now look like this:

The results are presented in the table next to the entry fields. You should now have a table of potential sample sizes for your study, each corresponding to a different confidence level that you can select. You should have a sample size of 57 study subjects for a 90% confidence interval, 81 for a 95% C.I., and 139 for a 99% C.I. A confidence level (or interval) is the probability that your study methodology will yield your expected results. It shows how certain you are that your expected results will appear if you were to repeat your study methodology on multiple samples. Typically, public health researchers use 90%, 95%, or 99% confidence intervals. Confidence interval is often abbreviated as C.I. 5

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Computer Lab Module: Session 3

2012

Notice that the size of the sample size increases as the confidence level increases. You need to get data from a larger number of subjects in order to have more precision (There is less variation in the data, so you know that your answer is more likely to be correct — the true value). At this point, you could choose the confidence level and thus, the sample size, for your study. If you are satisfied with the results and the parameters you enter are fixed, you now have finished the task of calculating a sample size. In this case, your parameters are not fixed. You would like to see the needed sample sizes if you change your Expected Frequency of Factor or if you change your Confidence Limits Result.

5. Input new values into the Confidence Limits. In other words, decrease your margin of error which will mean that you are expecting your study results to be more precise. Change 10% to 5%.

Notice how the results in the sample size table automatically change.

Did the sample size for a 95% confidence interval (Confidence Level = 95%) increase or decrease as the margin of error decreased? It should have increased substantially from 81 to 320 subjects needed for the study. You need a larger sample (more study subjects) when you want more precision.

Now, change from 5% to 18%. (NOTE: You may need to use the arrow keys or the Tab key to return to the Confidence Limits Result box.) What has happened to the sample sizes now?

Notice how the results in the sample size table automatically change.

Did the sample size for a 95% confidence interval increase or decrease as the margin of error decreased? It should have decreased substantially from your original result of 81 to 25 subjects needed for the study. You need a smaller sample (less study subjects) when you desire less precision and are comfortable with more variability in your data.

6. Return to your original parameters: 40,000 Population Size, 30% Expected Frequency, and 10% Confidence Limits. Now you will change your population size.

7. Experiment with changing your population size. Increase and decrease the study population size and then view your sample size results. You should notice that changing the population size does not have the same magnitude of effect as when you change your other sample size calculation parameters.

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For example, if your Expected Frequency is 30%, your Confidence Limits is 40%, and you reduce your Population Size from 40,000 to 10,000, your sample size using a 95% C.I. reduces by only 1 person. Sample size calculations depend much more on the variability in your data or the size of the change you expect to see than on the size of your base study population.

8. Exit out of the Population Survey mode by closing the window. We are now going to switch to designs where you are comparing two groups or two sets of data (e.g. before/after). These designs require slightly different inputs into StatCalc's sample size calculator. First, we'll use a Cohort Design.

Calculating Sample Size for a Cohort Study 1. Select Cohort or Cross-Sectional Study from the study design menu by typing C or moving the cursor over Unmatched Cohort and Cross-Sectional Study. Hit Enter/Return on the keyboard.

You should now enter the Cohort Study Parameters Box.

2. Choose your Two-Sided Confidence Level. The Confidence Level indicates how certain you are that your expected results will appear if you were to repeat your study methodology on multiple samples. As a Cohort Study compares two groups of data, your Confidence Level is the probability that you will find a difference between the two groups. 7

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Typically, one uses a 95% Confidence Level, though a higher level may be preferable for studies where there are repeated tests (like epigenetic studies).

So, select the confidence level of 95%. 3. Select the “Power” for your study. In statistical parlance, power expresses the probability that your statistical test will reject the alternative hypothesis in your study. In other words, it is the likelihood that your study results will demonstrate a significant difference between the two groups if there really is one. So, there will be a change from your baseline data to your post-intervention data or there will be a difference in how two distinct groups in your study (e.g. men and women) exhibit a disease or a behavior.

Remember that the size of your sample will increase as you increase your power in the study. In theory, more power is good as it should yield stronger, more significant results. However, more power can also be unnecessary causing you to utilize more resources (time, money). Thus, more can actually be less. The trick is to have enough power to produce meaningful results, but not so much that your study is not feasible.

Typically, researchers use 80% as their power when engaging in study planning.

So, enter a power level of 80% and hit Tab.

Your cursor should move to the next field. In this case, it is Ratio (Number of Unexposed: Number of Exposed).

4. Select the “Ratio (Unexposed : Exposed)” of your two groups,. This proportion expresses the number of study subjects you expect in your two groups that you will be comparing. If you do not expect your study enrollment numbers to be equal, input the expected ratio. For example, if you expect that 40% of your subjects will be vaccinated against HepB and 60% will not be, then your ratio will be 3:2, unexposed: exposed, 60%:40%. Of course, you could design a study in which you enroll equal numbers from each group; in this case, your ratio will be 1:1. It all depends on your study design. For this example, we will keep it simple so we will compare data from two groups of equal size. So, enter a ratio of 1. The entry for this field is not intuitive unfortunately; you do not enter 1:1, you only need to enter in the number of unexposed subjects per exposed, so you enter in the decimal number. For example, if the ratio is 3:2, then enter in 1.5. If it is 4:3, enter in 1.33. 5. Select your “% outcome in unexposed group” (your expected result for those who are unexposed in your study. If you are doing a program evaluation and comparing baseline data with post-intervention data, determining this value is easy. It is the number you gathered at baseline. Or, if you know that only 25% of pregnant women during ANC visits are agreeing to visit a VCT for HIV testing (and your study aims to increase the number who visit a VCT), then your expected result for the unexposed is also readily 8

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available. (It's 25%). You or someone else may have also have done a pilot study where this number may be available. If you do not know how many are actually unexposed, once again, you will need to make an educated guess using your expertise, knowledge, and published literature and reports on your outcome or similar outcomes. For this example, we will use 25% so type this into the Expected Frequency of Disease in the Unexposed field. Select Enter/Return, Tab, or the Down arrow to move to the next field.

Your cursor should move to the next field. In this case, it is a section for your Expected Results.

6. Choose your expected results (Risk ratio, Odds ratio, or % outcome in exposed group) from the study — the change you expect to see or the strength of the relationship you expect to find between the exposed and the unexposed. The expected outcome is the minimum difference that will be statistically significant in your study—in other words, it will have enough Power to show this difference but no more. Of course, you could show more, but this would merely demand a higher sample size, thereby requiring greater resources for little to no benefit. This outcome is what you use to judge whether your intervention was effective or not. As you would like an outcome to be persuasive enough to change policy or to improve a program, you need an outcome that will be significant enough. You will see three choices for expressing your expected results: Risk Ratio (RR), Odds Ratio (OR), and “% outcome in exposed group.” You can only choose one, so choose the one that is in the form that you plan on using for analyzing your results. If you plan on reporting a RR, then you should enter in the minimum detectable RR. If you do not have a good idea of what this number should be, you can examine the measures used by previous studies and input their values to get an idea of what size sample is needed. For example, if similar studies yielded a Risk Ratio of 2.45 then you might input data for RR. Or, if you have no idea what the RR and OR might be, you can use information from key informants, previous studies, or your own sense of reason and intuition to "guesstimate" the “% outcome in exposed group.” If you are writing a grant for the NIH or other such organizations, you will need to report sample sizes based on the measure you will use to analyze your results. Once you input data for one value, StatCalc will automatically calculate the values for the other two measures, so go ahead and input one to see what StatCalc calculates. Seeing all three figures may be helpful in fine-tuning your initial input. As you can see, it is very easy to change your parameters and input (Yes, the idea about your result being the minimum difference was repeated a few times above – it’s a good mantra to remember!) See the screenshot below to see how your window will look with a 95% Confidence Level of 95%, power of 80%, ratio of 1:1, 25% outcome in unexposed, and a RR of 1.50. 9

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Risk Ratio (RR) refers to Relative Risk or Risk Ratio, the epidemiological term denoting the risk of an outcome relative to exposure. RR shows the probability of the event occurring in the exposed group versus the control (non-exposed) group.

A relative risk of 1 means there is no difference in risk between the two groups.

A RR of < 1 means the outcome is less likely to occur in the experimental or exposed group than in the control group.

A RR of > 1 means the outcome is more likely to occur in the experimental or exposed group than in the control group.

Typically, RR is used for randomized control trials or prospective cohort studies, although one can use Odds Ratio (OR) as a measure as well in these types of studies (see below for more about the OR). If you are using results from a previous study that produced a range for the RR, use the RR that is closest to 1.00. Always input the value that shows the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources. As 1 indicates that there is no difference between your experimental and control groups, the RR closest to 1 will be the minimum difference. For this example, you don't know of any similar studies' results so you choose to input a value for the Percent Diseased among the Exposed. You would like to double the percentage of pregnant women

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attending VCTs so you decide 50% is your expected outcome value. (Above we had already determined that 25% was the value among the unexposed.) So, use the Tab key or mouse to move the cursor into the “% outcome in exposed group” field and type 50%.

Notice how the Odds Ratio and Relative Risk fields populate with estimates. Did Epi Info calculate a RR of 2.00 and an OR of 3.00?

7. Change your expected outcome value to 40%. See how the RR and OR change accordingly. You should now have an RR of 1.60 and an OR of 2.00 (and you did not even need to set up a 2x2 table!). 8. Change the RR to 3.56. You may need to use the Up/Down arrow keys or the Tab key to move to the RR field. Did you get an OR of 24.27 and 89% for the proportion of exposed who are diseased? 9. Change the RR to 17.00. You should notice that the OR is a negative value.

Odds Ratio (OR)

is also a measure of your intervention's effect, but it represents the odds of an outcome occurring in your exposed group versus the odds of producing the same outcome in your unexposed group. OR is an estimate of your Relative Risk, but it is not as reliable as Relative Risk.

An Odds Ratio of 1 means there is no difference between the two groups in the likelihood of producing a certain outcome.

An OR of < 1 means the outcome is less likely to occur in the experimental group than in the control group.

A RR of > 1 means the outcome is more likely to occur in the experimental group than in the control group.

OR can be used for both cohort and case-control studies, whereas RR is only possible for cohort studies in most cases. If you are using results from a previous study that produced a range for the OR, use the OR that is closest to 1.00. Always input the value that shows the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources. As 1 indicates that there is no difference between your experimental and control groups, the OR closest to 1 will be the minimum difference. Now, let’s return to determining a sample size for a cohort study. 10. Change the Percent Disease Among the Exposed field back to 50%.

The screen should change and a results table should appear.

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Notice that various sample sizes are calculated depending upon different values for power and confidence level.

Notice also that various sample sizes are calculated depending upon different ratios of unexposed : exposed in the study population.

Percent Diseased among the Exposed

refers to your expected results in the group that is of interest to you in the study. This group could be your experimental group that you have followed from baseline until the post-intervention evaluation, or it could be the group you are most interested in detecting a difference about (e.g. nurses, if your study seeks to determine if their proclivity to leave the government healthcare system after 5 years is greater than that of doctors'.) When you choose this value, you may consider that your results will produce a range of values (e.g. 25-30% are diseased) as you are not sure (hence, the study). Again, always input the value that is closest to the value for the unexposed group which you had entered above. Doing so will ensure that your Desired Result is the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources.

11. You can now see the sample size for your study.

How many subjects will you need to enroll in your study according to the parameters you input (95% C.I., 80% power, 1:1 ratio, % outcome unexposed 25%, %outcome exposed 50% )? You should answer 132 subjects (66 in each group) or 118 or 116 total.

What’s the smallest sample size that you can choose based on these results? At what level of confidence? At 80% confidence level you should have a total sample size of 68, 66, or 82 (depending on the equation you prefer).

If you demand more precision from your results (a higher C.I. of 99%), does your sample size increase or decrease? It should increase to 176, 174, or 188 total subjects.

NOTE: You do not want to choose too small of a sample size as it may not be as possible to exclude chance as the reason for why your results occurred. After all, you want to show that it was your intervention or that it was your particular inputs under study (e.g. risk factors) that made the difference. Typically, 90% is the lowest C.I. one uses to ensure that results are viable, but 95% is what is generally what you need for most scientific publications. Now, experiment with changing your study parameters and see the impact on your sample size results.

Increase your power to 85%.

Decrease your confidence level to 80%. 12

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Change your expected outcome to 33%.

Your sample sizes should be 692, 690, and 740.

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12. Once you input your changes, and StatCalc will recalculate the results. Notice that your sample size increases when your power increases. You need more samples to demonstrate that your results were significant. Notice that your sample size decreases as your confidence level decreases. You require less precision so you do not need as many samples to show that you have found the true value. Notice that your sample size increases considerably when you reduce the size of the difference between the Unexposed and the Exposed. You need more samples to show that there is a true difference.

This idea can be a bit counterintuitive, but it’s the relationship that statisticians have proven. The key concept to remember is that your estimated effect size – the size of the difference between your two groups – is inversely related to your sample size. As the difference decreases, your sample size will increase. Conversely, as the difference increases, your sample size will decrease. So, if you only have enough resources to study a certain number of subjects, you may need to change your input for the size of the difference between the two groups, perhaps significantly increasing the size of this difference. In the end, your trade-off is that you now may not have enough power in the study to show that your results are significant because your sample size has become too small for the effect that you are trying to show.

13. Close the StatCalc window to return to the main program window. You will notice that you get several sample sizes that slightly vary in size called Kelsey, Fleiss, and Fleiss w/CC. Basically these 3 sample sizes use 3 different equations to get to the sample size. The Kelsey and Fleiss equations will essentially give you the same numbers, but diverge slightly on the number of unexposed you need, especially as you add more controls. Either one for most purposes will probably be fine for most of the work you do. The Fleiss w/CC is a special modification of the Fleiss equation to assure that sufficient samples are obtained where it is expected that you will have a low prevalence of your condition among the unexposed (usually less than 5%). This is to help ensure that cell sizes in your 2X2 analysis tables do not have any 0s (i.e., no subjects), which would make it difficult to calculate your RR or OR. It is also useful if you know you will have very small numbers in one of your cells (like less than 10) of your 2X2 table. The sample size table gives you the number of exposed, number of unexposed, and total number needed to meet your inputted criteria. Now we will choose a Case Control study.

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Calculating Sample Size for a Case Control Study (Unmatched) Most of the instructions for calculating the sample size for this type of study design are the same. The big difference is the measure used for your expected outcome value. Also, your two groups are still exposed and unexposed, but because Case Control Studies start with outcomes and research the exposure, StatCalc indicates that you are comparing the ill and not ill. Note that Epi-Info calculates sample sizes for unmatched case control studies only. Matched studies use different, much more complicated equations that require you to know the Correlation Coefficient, i.e., the correlation between your exposure and being matched. If you are using a matched study design, you will need to use a different tool for determining sample size. See the resources provided by UCSF’s Department of Epidemiology and Biostatistics for possible tools that you can use: http://www.biostat.ucsf.edu/sampsize.html. The previously mentioned PS will do it. 1. Select Unmatched Case Control from the study design menu.

You should now enter the Unmatched Case-Control Study Parameters Box.

You should notice that this parameters box looks remarkably similar to the one you just used for the Cohort study. It is. Terminology has changed from UNEXPOSED/EXPOSED to NOT ILL/ILL, and the Desired Result section at the bottom no longer includes Relative Risk as a measure. Case Control studies do not usually use RR as a measure.

2. Choose your Confidence Level. The Confidence Level indicates how certain you are that your expected results will appear if you were to repeat your study methodology on multiple samples. As a Case Control Study compares two groups of data, your Confidence Level is the probability that you will find a difference between the two groups.

Typically, one uses a 95% Confidence Level.

3. Select the Power for your study. As noted previously, power expresses the probability that your statistical test will reject the alternative hypothesis in your study. In other words, it is the likelihood that your study results will demonstrate a significant difference between the two groups if there really is one. So, there will be a difference in how two distinct groups in your study (e.g. men and women) exhibit risk factors for a disease or behavior.

Once again, remember that the size of your sample will increase as you increase your power in the study. In theory, more power is good as it should yield stronger, more significant results. However, more power can also be unnecessary causing you to utilize more resources (time, money). Thus, more can actually be less. The trick is to have enough power to produce meaningful results, but not so much that your study is not feasible.

Typically, researchers use 80% as their power when engaging in study planning, so enter this number. 14

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4. Select the ratio of your two groups, not ill and ill, or those you know have the outcome and those who do not. This proportion expresses the number of study subjects you expect in your two groups that you will be comparing. For this example, we have 60 controls and 30 cases so we won't use a 1:1 ratio. Instead, it is a 2:1 ratio, number of controls per cases, or unexposed to exposed. So, input 2 into the Ratio field. 5. Enter in the % of controls exposed – the NOT ILL group. As noted earlier, if you do not know how many are actually unexposed, once again, you will need to make an educated guess. In this example, you are interested in determining if prolonged contact with river water (e.g. while doing laundry) is a risk factor for Buruli Ulcer. You believe that 20% of your controls – the NOT ILL – have been exposed. So type 20% into the % of controls exposed field.

6. Choose your expected results from the study (an Odds Ratio or % of cases exposed) — the change you expect to see or the strength of the relationship you expect to find between the exposed and the unexposed, the ILL and NOT ILL. Once again, we want to input the minimum difference that will be statistically significant in your study—in other words, it will have enough Power to show this difference but no more. It is what you use to judge whether your intervention was effective or not. As you would like an outcome to be persuasive enough to change policy or to improve a program, you need an outcome that will be significant enough. You will see only two choices for expressing your expected results: Odds Ratio, and % of cases with exposure.

Notice that Relative Risk is not included as this measure is not used for Case-Control Studies.

Again, you can only choose one parameter so choose the one that is easiest for you to predict - the one that you might already have information about. You may need to use your own sense of reason and intuition to "guesstimate" the percent of cases with exposure.

Remember to always choose the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources.

Once you input data for one value, StatCalc will automatically calculate the values for the other measure, so go ahead and input one to see what StatCalc calculates. Seeing both figures may be helpful in fine-tuning your initial input. And yes, you can change your mind on the size of your parameters! 15

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For this example, you know of a 2004 study in Ghana that found a positive association between frequent swimming in rivers and Buruli Ulcer. The Odds Ratio was 18.00. So, you choose to use this value for the Percent Exposed among the ILL. You’re not sure if there is a correspondence between the risk factor of swimming and regularly doing laundry in the river, but you think that the skin exposure might be similar. So, type 18.00 into the Odds Ratio Field.

Notice how the Percent Exposure among the ILL field populates with an estimate. You should see 81.8% in this field.

7. Change your expected exposure among ILL to 75% as you believe that 81.82% is just too high. See how the OR changes accordingly. You should now have an OR of 12.00.

The screen should change and sample sizes will appear in the table to the right of the parameters.

Notice that various sample sizes are calculated depending upon different values for power and confidence level as well as the different ratios of unexposed : exposed in the study population.

8. You can now choose the sample size for your study.

How many subjects will you need to enroll in your study according to the parameters you input (95% C.I., 80% power, 2:1 ratio)? You should answers should be 29 (10 cases, 19 controls), 26 (9 cases, 17 controls), and 35 (12 cases, 23 controls).

According to these results, what’s the smallest sample size that you can choose? At what level of confidence? According to these results, 15 subjects at a 80% C.I. is the smallest sample size.

If you demand more precision from your results (a higher C.I. of 99%), does your sample size increase or decrease? It should increase to 42, 39, or 47 total subjects.

Now, experiment with changing your study parameters and see the impact on your sample size results.

Decrease your power to 75%.

Decrease your confidence level to 90%

Change your cases with exposure 80%.

Change your ratio to 3:1.

Your sample sizes should now be 14, 12 and 20

As in the Cohort Study, notice how the sample size increases or decreases depending upon how you change the study parameters. As described for Cohort Studies, Unmatched Case Control studies also provide the same 3 types of sample sizes. 16

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Saving your Results in StatCalc Please note that there is not a direct way to save your results in StatCalc. Unfortunately, you cannot use the mouse to select the results table and copy/paste into a Word document. What I recommend is creating a table in Microsoft Word or Excel to input your results. You will likely need to do this anyway for any grant application. You can save your results by saving an image or printout of your window. Right click anywhere within the window and you can save it as an image or print it.

WHAT YOU HAVE LEARNED

How to navigate in Epi-Info’s StatCalc utility for calculating sample sizes.

How to use StatCalc for determining sample sizes in basic descriptive, population studies, cohort studies, and unmatched case control studies.

How the study design parameters impact the sample size calculation and what to consider when making choices about these parameters.

Practice! (as part of the Assignment) Go to the web site and answer the questions in the Assignment for Session 3. The questions are sample size problems that you will solve by using StatCalc. Thanks!

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StatCalc - Calculating a Sample Size with Epi-Info In this lesson, you will learn how to use the StatCalc feature of Epi-Info to calculate the sample size of a study you may design. StatCalc is a tool that automatically generates a range of sample sizes for different confidence and precision levels. You will learn how to use StatCalc to determine sample sizes for different types of studies, experiment with changes in study design parameters for understanding the relationship between these parameters and sample size, and become familiar with StatCalc’s limitations as a tool. LESSON ACTIVITIES

Use StatCalc to calculate sample sizes for descriptive cross-sectional, cohort, and case-control studies. Input different parameters into StatCalc’s calculator for viewing relationship between certain parameters and the sample size calculation.

WHAT YOU NEED

Epi-Info downloaded on your machine. If you do not have it, go to the main page on the Moodle Web site to access the CDC’s download page for Epi-Info.

Getting Started with StatCalc Other Epi-Info sessions in this course use the major modules of Epi-Info such as Form Designer and Analyze Data. StatCalc is one of the most useful parts of Epi-Info. It is used by researchers who prefer as well as have the resources to analyze their data with software programs such as STATA or SPSS. StatCalc is also one of the easiest tools to use. You input your parameters such as expected outcome value and desired precision, and then StatCalc determines the sample size. No memorization of formulas or mathematical equations is necessary! StatCalc has several tools: Sample Size and Power, Chi Square for Trend, and Tables (2X2, 2XN). We will be only learning to use the Sample Size and Power tool in this module. This module will not describe the equations used to calculate sample size or the terminology since these will be covered by the professors in the Sample Size lecture.

Choosing the Type of Study Design to Use Within the Sample Size and Power tool there are 3 choices: Population survey, Cohort or cross-sectional, and Unmatched case-control. Each study type uses a different formula for calculating sample size so you need to think carefully about which type is yours. You may notice that StatCalc does not offer an exhaustive list of study design types so you may find that your specific study type may not be listed here. If your study really does not fall within the specifications of these designs, you will need to use another program or tool to make your calculations since it is imperative to use the correct equation to obtain these numbers. Other sample size or power calculation tools may be more useful for non-Epidemiological studies. One free example is PS, which can be downloaded at http://biostat.mc.vanderbilt.edu/wiki/Main/PowerSampleSize. There is also a link within the Epi Info program 1

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to a website called OpenEpi (http://openepi.com/OE2.3/Menu/OpenEpiMenu.htm) that is full of useful calculators for more types of study designs. There are several pay options that can be found at the UCSF’s Department of Epidemiology and Biostatistics website, although much of the documentation is more technical than what you’ll find in this tutorial. Go to http://www.biostat.ucsf.edu/sampsize.html to see the list of possibilities. Note: You cannot use StatCalc to determine means, such as the average number of days a child stricken with malaria stayed at the hospital or the average cost of bednets in a region. Means use continuous variables, yielding values such as 51.34 as opposed to dichotomous variables (yes/no, seropositive/seronegative) which yield proportions (51%). If your outcome is a mean: You'll need to use an online sample size and power calculator such as those you can find on the UCSF site. Some recommendations are PS, PC-Size, and Rollin Brant’s Sample Size Calculators from the University of Calgary to be simple to follow. Now, assuming that you can use StatCalc for your needs, let's look at the types of studies that you can calculate sample sizes from. Each of the three types below requires a different sample size formula, so while you may detect similarities between them, remember that StatCalc will treat each differently. The workings "under the hood" will be completely different.

Making Your Study Design Choice in StatCalc Once you know which study design type you would like to use, navigate to StatCalc on the Epi Info navigation bar and select “Sample Size and Power” and the study design you would like to use.

Population Survey refers to a non-comparative cross-sectional survey, a descriptive study that provides a picture of a specific population's characteristics at a certain point in time. This picture is based on dichotomous variables such as gender, infected/not infected with a disease, etc. In Epi-Info, it assumes you are using random (not cluster) sampling, although many researchers use StatCalc even if they are not using a truly random sampling procedure (e.g. convenience sampling), being sure to note the limitations in the methods. Your population does not need to be large such as the population of a country; instead, it can mean village women in a certain area or all district households with children under 5 years old. In a study such as this one, you are not planning to compare two groups in the data collection phase, either before or after, or between those who are exposed and those who are not exposed. Instead, you are simply trying to find out information such as the number of days one may adhere to a new treatment plan/behavior change activity, the number of women who utilize traditional birth attendants at their home births, or the proportion of physicians and nurses who leave their posts for lucrative overseas jobs after 3 years of service in their nation's healthcare system.

Cohort or Cross Sectional Survey refers to the types of studies that compare two groups with dichotomous – not continuous – variables (comparing proportions not means), one of which is exposed and the other which is non-exposed. The cross-sectional survey in this case is a comparative survey, not the descriptive type of cross-sectional survey described above under Population Survey. So, in studies such as these, you may be interested in the amount of improvement in infant's Z-scores at monthly baby weighings after a soy food intervention (soy milk, tofu, soy-based porridge). Or, maybe you are interested in the difference in DOTS therapy drop-off rate at health clinics that lose significant numbers of staff to funding cuts versus clinics who retain their community health workers that assist with DOTS. 2

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Unmatched Case Control refers to studies that compare two groups, one of which has a certain condition X or has experienced a specific outcome, and another which has not. Your study aims to determine whether the proportion of exposure in the two groups differs. So, you identify the outcome first and then look for the exposure. You typically use this type of study when you think the outcome is so unlikely that it would require a very large cohort study to enroll enough subjects who meet your selection criteria – those who have the outcome. So, in this type of study, you plan to determine the risk factors for mercury poisoning in a village in South China as you have identified a number of cases there. You have already identified some who are cases and some who are controls; your study focuses on determining the proportion of cases that share risk factors X, Y, and Z.

Entering Your Study Parameters for StatCalc to Use in Its Sample Size Calculation Calculating Sample Size for a Population Survey 1. Select Population Survey

The Population Survey Parameters Box should open.

2. Enter the size of the total population in your study area.

Notice that you can enter up to 9 digits.

Note that this number is not necessarily the total population as found through a national census. Rather, it is the total population under study — all of those possible study subjects who meet the inclusion criteria for the study and thus, are a part of your "denominator" in public health lingo. 3

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Your total population is not the number of subjects you believe you have the resources to enroll or the number of subjects you believe exhibit the behavior or the biological factor that you are planning to study.

For example, if you are interested in the level of Vitamin A deficiency among pregnant and breastfeeding women in the Collines region of Benin, your total population is all the women of childbearing age (given that most women are usually preparing to be pregnant, pregnant, or in the postpartum stage). It is not the entire population residing in the Collines region. Refer to the lectures on Indicators and Outcomes to refresh your memory about this if it does not make sense.

For this example, you will be examining the percentage of a region's households that regularly use bednets to protect expectant and breastfeeding mothers as well as children under 5 years old. So, enter 40,000 as the population and hit Tab to go to the next field.

3. You now need to enter the Expected Frequency.

The Expected Frequency is your estimate of the result. In statistical terms, this is your estimated proportion of the main variable in your study. It is your outcome that you expect from the intervention you plan or the information that you aim to gather and report on. Determining the value of this factor is where some of the guesswork will enter your study design. It is the part that may seem arbitrary, and may often be if one is researching a new field of study.

NOTE: If you are making a calculation from an epidemiological statistic such as mortality rate, be sure to express it correctly. For example, 60 per 100,000 IMR would be input as 0.06% into StatCalc, not 60% or 6%. Once again, refer to the Indicators & Outcomes lectures.

In this example, you know from discussions with key informants that only about 30% use bednets. Enter 30 and hit Tab to go to the next field.

4. Enter Confidence Limits.

The Confidence Limits is the outer limit in the range (+ or – your expected frequency) of results that you are comfortable seeing. It is a value that is either lower or higher than the number you input above under Expected Frequency of Factor Under Study. This field is where you will enter your desired precision — the value that determines how accurate your study will be in discovering the actual answer to your research question. In statistical parlance, this value will be an expression of your margin of error. Since you are not sure what your study outcomes will be, you must give yourself a range in which your data will fall. This range is the margin of error (+/- 9 points or +/- 2.5% that you see in the fine print in polls). In statistical theory, your expected value will lie within the range for a certain percentage of samples if you use your study methodology over and over again. (But, don't worry about setting your confidence level here StatCalc will do this for you soon.) 4

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So, while you are hoping that the number you chose above for the Expected is the actual result, you know it may not be. Thus, you choose your Confidence Limit — the outer limit for the value that will still be an acceptable outcome for your study.

NOTE: You want to choose a Confidence Limit that provides you with enough room for error, but which is also precise enough to deliver results that are meaningful. If your possible range of results is too large, it will show that you lack confidence in your methodology's ability to find the actual answer to your question. If it is too small, the sample size is too big and the study is no longer feasible.

In this example, you decide that +/- 10% for the proportion of women that use bednets is acceptable. So, you type 10% into Confidence Lmits. Your window should now look like this:

The results are presented in the table next to the entry fields. You should now have a table of potential sample sizes for your study, each corresponding to a different confidence level that you can select. You should have a sample size of 57 study subjects for a 90% confidence interval, 81 for a 95% C.I., and 139 for a 99% C.I. A confidence level (or interval) is the probability that your study methodology will yield your expected results. It shows how certain you are that your expected results will appear if you were to repeat your study methodology on multiple samples. Typically, public health researchers use 90%, 95%, or 99% confidence intervals. Confidence interval is often abbreviated as C.I. 5

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Notice that the size of the sample size increases as the confidence level increases. You need to get data from a larger number of subjects in order to have more precision (There is less variation in the data, so you know that your answer is more likely to be correct — the true value). At this point, you could choose the confidence level and thus, the sample size, for your study. If you are satisfied with the results and the parameters you enter are fixed, you now have finished the task of calculating a sample size. In this case, your parameters are not fixed. You would like to see the needed sample sizes if you change your Expected Frequency of Factor or if you change your Confidence Limits Result.

5. Input new values into the Confidence Limits. In other words, decrease your margin of error which will mean that you are expecting your study results to be more precise. Change 10% to 5%.

Notice how the results in the sample size table automatically change.

Did the sample size for a 95% confidence interval (Confidence Level = 95%) increase or decrease as the margin of error decreased? It should have increased substantially from 81 to 320 subjects needed for the study. You need a larger sample (more study subjects) when you want more precision.

Now, change from 5% to 18%. (NOTE: You may need to use the arrow keys or the Tab key to return to the Confidence Limits Result box.) What has happened to the sample sizes now?

Notice how the results in the sample size table automatically change.

Did the sample size for a 95% confidence interval increase or decrease as the margin of error decreased? It should have decreased substantially from your original result of 81 to 25 subjects needed for the study. You need a smaller sample (less study subjects) when you desire less precision and are comfortable with more variability in your data.

6. Return to your original parameters: 40,000 Population Size, 30% Expected Frequency, and 10% Confidence Limits. Now you will change your population size.

7. Experiment with changing your population size. Increase and decrease the study population size and then view your sample size results. You should notice that changing the population size does not have the same magnitude of effect as when you change your other sample size calculation parameters.

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For example, if your Expected Frequency is 30%, your Confidence Limits is 40%, and you reduce your Population Size from 40,000 to 10,000, your sample size using a 95% C.I. reduces by only 1 person. Sample size calculations depend much more on the variability in your data or the size of the change you expect to see than on the size of your base study population.

8. Exit out of the Population Survey mode by closing the window. We are now going to switch to designs where you are comparing two groups or two sets of data (e.g. before/after). These designs require slightly different inputs into StatCalc's sample size calculator. First, we'll use a Cohort Design.

Calculating Sample Size for a Cohort Study 1. Select Cohort or Cross-Sectional Study from the study design menu by typing C or moving the cursor over Unmatched Cohort and Cross-Sectional Study. Hit Enter/Return on the keyboard.

You should now enter the Cohort Study Parameters Box.

2. Choose your Two-Sided Confidence Level. The Confidence Level indicates how certain you are that your expected results will appear if you were to repeat your study methodology on multiple samples. As a Cohort Study compares two groups of data, your Confidence Level is the probability that you will find a difference between the two groups. 7

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Typically, one uses a 95% Confidence Level, though a higher level may be preferable for studies where there are repeated tests (like epigenetic studies).

So, select the confidence level of 95%. 3. Select the “Power” for your study. In statistical parlance, power expresses the probability that your statistical test will reject the alternative hypothesis in your study. In other words, it is the likelihood that your study results will demonstrate a significant difference between the two groups if there really is one. So, there will be a change from your baseline data to your post-intervention data or there will be a difference in how two distinct groups in your study (e.g. men and women) exhibit a disease or a behavior.

Remember that the size of your sample will increase as you increase your power in the study. In theory, more power is good as it should yield stronger, more significant results. However, more power can also be unnecessary causing you to utilize more resources (time, money). Thus, more can actually be less. The trick is to have enough power to produce meaningful results, but not so much that your study is not feasible.

Typically, researchers use 80% as their power when engaging in study planning.

So, enter a power level of 80% and hit Tab.

Your cursor should move to the next field. In this case, it is Ratio (Number of Unexposed: Number of Exposed).

4. Select the “Ratio (Unexposed : Exposed)” of your two groups,. This proportion expresses the number of study subjects you expect in your two groups that you will be comparing. If you do not expect your study enrollment numbers to be equal, input the expected ratio. For example, if you expect that 40% of your subjects will be vaccinated against HepB and 60% will not be, then your ratio will be 3:2, unexposed: exposed, 60%:40%. Of course, you could design a study in which you enroll equal numbers from each group; in this case, your ratio will be 1:1. It all depends on your study design. For this example, we will keep it simple so we will compare data from two groups of equal size. So, enter a ratio of 1. The entry for this field is not intuitive unfortunately; you do not enter 1:1, you only need to enter in the number of unexposed subjects per exposed, so you enter in the decimal number. For example, if the ratio is 3:2, then enter in 1.5. If it is 4:3, enter in 1.33. 5. Select your “% outcome in unexposed group” (your expected result for those who are unexposed in your study. If you are doing a program evaluation and comparing baseline data with post-intervention data, determining this value is easy. It is the number you gathered at baseline. Or, if you know that only 25% of pregnant women during ANC visits are agreeing to visit a VCT for HIV testing (and your study aims to increase the number who visit a VCT), then your expected result for the unexposed is also readily 8

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available. (It's 25%). You or someone else may have also have done a pilot study where this number may be available. If you do not know how many are actually unexposed, once again, you will need to make an educated guess using your expertise, knowledge, and published literature and reports on your outcome or similar outcomes. For this example, we will use 25% so type this into the Expected Frequency of Disease in the Unexposed field. Select Enter/Return, Tab, or the Down arrow to move to the next field.

Your cursor should move to the next field. In this case, it is a section for your Expected Results.

6. Choose your expected results (Risk ratio, Odds ratio, or % outcome in exposed group) from the study — the change you expect to see or the strength of the relationship you expect to find between the exposed and the unexposed. The expected outcome is the minimum difference that will be statistically significant in your study—in other words, it will have enough Power to show this difference but no more. Of course, you could show more, but this would merely demand a higher sample size, thereby requiring greater resources for little to no benefit. This outcome is what you use to judge whether your intervention was effective or not. As you would like an outcome to be persuasive enough to change policy or to improve a program, you need an outcome that will be significant enough. You will see three choices for expressing your expected results: Risk Ratio (RR), Odds Ratio (OR), and “% outcome in exposed group.” You can only choose one, so choose the one that is in the form that you plan on using for analyzing your results. If you plan on reporting a RR, then you should enter in the minimum detectable RR. If you do not have a good idea of what this number should be, you can examine the measures used by previous studies and input their values to get an idea of what size sample is needed. For example, if similar studies yielded a Risk Ratio of 2.45 then you might input data for RR. Or, if you have no idea what the RR and OR might be, you can use information from key informants, previous studies, or your own sense of reason and intuition to "guesstimate" the “% outcome in exposed group.” If you are writing a grant for the NIH or other such organizations, you will need to report sample sizes based on the measure you will use to analyze your results. Once you input data for one value, StatCalc will automatically calculate the values for the other two measures, so go ahead and input one to see what StatCalc calculates. Seeing all three figures may be helpful in fine-tuning your initial input. As you can see, it is very easy to change your parameters and input (Yes, the idea about your result being the minimum difference was repeated a few times above – it’s a good mantra to remember!) See the screenshot below to see how your window will look with a 95% Confidence Level of 95%, power of 80%, ratio of 1:1, 25% outcome in unexposed, and a RR of 1.50. 9

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Risk Ratio (RR) refers to Relative Risk or Risk Ratio, the epidemiological term denoting the risk of an outcome relative to exposure. RR shows the probability of the event occurring in the exposed group versus the control (non-exposed) group.

A relative risk of 1 means there is no difference in risk between the two groups.

A RR of < 1 means the outcome is less likely to occur in the experimental or exposed group than in the control group.

A RR of > 1 means the outcome is more likely to occur in the experimental or exposed group than in the control group.

Typically, RR is used for randomized control trials or prospective cohort studies, although one can use Odds Ratio (OR) as a measure as well in these types of studies (see below for more about the OR). If you are using results from a previous study that produced a range for the RR, use the RR that is closest to 1.00. Always input the value that shows the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources. As 1 indicates that there is no difference between your experimental and control groups, the RR closest to 1 will be the minimum difference. For this example, you don't know of any similar studies' results so you choose to input a value for the Percent Diseased among the Exposed. You would like to double the percentage of pregnant women

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attending VCTs so you decide 50% is your expected outcome value. (Above we had already determined that 25% was the value among the unexposed.) So, use the Tab key or mouse to move the cursor into the “% outcome in exposed group” field and type 50%.

Notice how the Odds Ratio and Relative Risk fields populate with estimates. Did Epi Info calculate a RR of 2.00 and an OR of 3.00?

7. Change your expected outcome value to 40%. See how the RR and OR change accordingly. You should now have an RR of 1.60 and an OR of 2.00 (and you did not even need to set up a 2x2 table!). 8. Change the RR to 3.56. You may need to use the Up/Down arrow keys or the Tab key to move to the RR field. Did you get an OR of 24.27 and 89% for the proportion of exposed who are diseased? 9. Change the RR to 17.00. You should notice that the OR is a negative value.

Odds Ratio (OR)

is also a measure of your intervention's effect, but it represents the odds of an outcome occurring in your exposed group versus the odds of producing the same outcome in your unexposed group. OR is an estimate of your Relative Risk, but it is not as reliable as Relative Risk.

An Odds Ratio of 1 means there is no difference between the two groups in the likelihood of producing a certain outcome.

An OR of < 1 means the outcome is less likely to occur in the experimental group than in the control group.

A RR of > 1 means the outcome is more likely to occur in the experimental group than in the control group.

OR can be used for both cohort and case-control studies, whereas RR is only possible for cohort studies in most cases. If you are using results from a previous study that produced a range for the OR, use the OR that is closest to 1.00. Always input the value that shows the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources. As 1 indicates that there is no difference between your experimental and control groups, the OR closest to 1 will be the minimum difference. Now, let’s return to determining a sample size for a cohort study. 10. Change the Percent Disease Among the Exposed field back to 50%.

The screen should change and a results table should appear.

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Notice that various sample sizes are calculated depending upon different values for power and confidence level.

Notice also that various sample sizes are calculated depending upon different ratios of unexposed : exposed in the study population.

Percent Diseased among the Exposed

refers to your expected results in the group that is of interest to you in the study. This group could be your experimental group that you have followed from baseline until the post-intervention evaluation, or it could be the group you are most interested in detecting a difference about (e.g. nurses, if your study seeks to determine if their proclivity to leave the government healthcare system after 5 years is greater than that of doctors'.) When you choose this value, you may consider that your results will produce a range of values (e.g. 25-30% are diseased) as you are not sure (hence, the study). Again, always input the value that is closest to the value for the unexposed group which you had entered above. Doing so will ensure that your Desired Result is the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources.

11. You can now see the sample size for your study.

How many subjects will you need to enroll in your study according to the parameters you input (95% C.I., 80% power, 1:1 ratio, % outcome unexposed 25%, %outcome exposed 50% )? You should answer 132 subjects (66 in each group) or 118 or 116 total.

What’s the smallest sample size that you can choose based on these results? At what level of confidence? At 80% confidence level you should have a total sample size of 68, 66, or 82 (depending on the equation you prefer).

If you demand more precision from your results (a higher C.I. of 99%), does your sample size increase or decrease? It should increase to 176, 174, or 188 total subjects.

NOTE: You do not want to choose too small of a sample size as it may not be as possible to exclude chance as the reason for why your results occurred. After all, you want to show that it was your intervention or that it was your particular inputs under study (e.g. risk factors) that made the difference. Typically, 90% is the lowest C.I. one uses to ensure that results are viable, but 95% is what is generally what you need for most scientific publications. Now, experiment with changing your study parameters and see the impact on your sample size results.

Increase your power to 85%.

Decrease your confidence level to 80%. 12

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Change your expected outcome to 33%.

Your sample sizes should be 692, 690, and 740.

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12. Once you input your changes, and StatCalc will recalculate the results. Notice that your sample size increases when your power increases. You need more samples to demonstrate that your results were significant. Notice that your sample size decreases as your confidence level decreases. You require less precision so you do not need as many samples to show that you have found the true value. Notice that your sample size increases considerably when you reduce the size of the difference between the Unexposed and the Exposed. You need more samples to show that there is a true difference.

This idea can be a bit counterintuitive, but it’s the relationship that statisticians have proven. The key concept to remember is that your estimated effect size – the size of the difference between your two groups – is inversely related to your sample size. As the difference decreases, your sample size will increase. Conversely, as the difference increases, your sample size will decrease. So, if you only have enough resources to study a certain number of subjects, you may need to change your input for the size of the difference between the two groups, perhaps significantly increasing the size of this difference. In the end, your trade-off is that you now may not have enough power in the study to show that your results are significant because your sample size has become too small for the effect that you are trying to show.

13. Close the StatCalc window to return to the main program window. You will notice that you get several sample sizes that slightly vary in size called Kelsey, Fleiss, and Fleiss w/CC. Basically these 3 sample sizes use 3 different equations to get to the sample size. The Kelsey and Fleiss equations will essentially give you the same numbers, but diverge slightly on the number of unexposed you need, especially as you add more controls. Either one for most purposes will probably be fine for most of the work you do. The Fleiss w/CC is a special modification of the Fleiss equation to assure that sufficient samples are obtained where it is expected that you will have a low prevalence of your condition among the unexposed (usually less than 5%). This is to help ensure that cell sizes in your 2X2 analysis tables do not have any 0s (i.e., no subjects), which would make it difficult to calculate your RR or OR. It is also useful if you know you will have very small numbers in one of your cells (like less than 10) of your 2X2 table. The sample size table gives you the number of exposed, number of unexposed, and total number needed to meet your inputted criteria. Now we will choose a Case Control study.

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Computer Lab Module: Session 3

2012

Calculating Sample Size for a Case Control Study (Unmatched) Most of the instructions for calculating the sample size for this type of study design are the same. The big difference is the measure used for your expected outcome value. Also, your two groups are still exposed and unexposed, but because Case Control Studies start with outcomes and research the exposure, StatCalc indicates that you are comparing the ill and not ill. Note that Epi-Info calculates sample sizes for unmatched case control studies only. Matched studies use different, much more complicated equations that require you to know the Correlation Coefficient, i.e., the correlation between your exposure and being matched. If you are using a matched study design, you will need to use a different tool for determining sample size. See the resources provided by UCSF’s Department of Epidemiology and Biostatistics for possible tools that you can use: http://www.biostat.ucsf.edu/sampsize.html. The previously mentioned PS will do it. 1. Select Unmatched Case Control from the study design menu.

You should now enter the Unmatched Case-Control Study Parameters Box.

You should notice that this parameters box looks remarkably similar to the one you just used for the Cohort study. It is. Terminology has changed from UNEXPOSED/EXPOSED to NOT ILL/ILL, and the Desired Result section at the bottom no longer includes Relative Risk as a measure. Case Control studies do not usually use RR as a measure.

2. Choose your Confidence Level. The Confidence Level indicates how certain you are that your expected results will appear if you were to repeat your study methodology on multiple samples. As a Case Control Study compares two groups of data, your Confidence Level is the probability that you will find a difference between the two groups.

Typically, one uses a 95% Confidence Level.

3. Select the Power for your study. As noted previously, power expresses the probability that your statistical test will reject the alternative hypothesis in your study. In other words, it is the likelihood that your study results will demonstrate a significant difference between the two groups if there really is one. So, there will be a difference in how two distinct groups in your study (e.g. men and women) exhibit risk factors for a disease or behavior.

Once again, remember that the size of your sample will increase as you increase your power in the study. In theory, more power is good as it should yield stronger, more significant results. However, more power can also be unnecessary causing you to utilize more resources (time, money). Thus, more can actually be less. The trick is to have enough power to produce meaningful results, but not so much that your study is not feasible.

Typically, researchers use 80% as their power when engaging in study planning, so enter this number. 14

GH531/EPI539

Computer Lab Module: Session 3

2012

4. Select the ratio of your two groups, not ill and ill, or those you know have the outcome and those who do not. This proportion expresses the number of study subjects you expect in your two groups that you will be comparing. For this example, we have 60 controls and 30 cases so we won't use a 1:1 ratio. Instead, it is a 2:1 ratio, number of controls per cases, or unexposed to exposed. So, input 2 into the Ratio field. 5. Enter in the % of controls exposed – the NOT ILL group. As noted earlier, if you do not know how many are actually unexposed, once again, you will need to make an educated guess. In this example, you are interested in determining if prolonged contact with river water (e.g. while doing laundry) is a risk factor for Buruli Ulcer. You believe that 20% of your controls – the NOT ILL – have been exposed. So type 20% into the % of controls exposed field.

6. Choose your expected results from the study (an Odds Ratio or % of cases exposed) — the change you expect to see or the strength of the relationship you expect to find between the exposed and the unexposed, the ILL and NOT ILL. Once again, we want to input the minimum difference that will be statistically significant in your study—in other words, it will have enough Power to show this difference but no more. It is what you use to judge whether your intervention was effective or not. As you would like an outcome to be persuasive enough to change policy or to improve a program, you need an outcome that will be significant enough. You will see only two choices for expressing your expected results: Odds Ratio, and % of cases with exposure.

Notice that Relative Risk is not included as this measure is not used for Case-Control Studies.

Again, you can only choose one parameter so choose the one that is easiest for you to predict - the one that you might already have information about. You may need to use your own sense of reason and intuition to "guesstimate" the percent of cases with exposure.

Remember to always choose the minimum difference that you want to detect to yield significant results, no more and no less. Thus, you will have enough Power, but you won’t waste resources.

Once you input data for one value, StatCalc will automatically calculate the values for the other measure, so go ahead and input one to see what StatCalc calculates. Seeing both figures may be helpful in fine-tuning your initial input. And yes, you can change your mind on the size of your parameters! 15

GH531/EPI539

Computer Lab Module: Session 3

2012

For this example, you know of a 2004 study in Ghana that found a positive association between frequent swimming in rivers and Buruli Ulcer. The Odds Ratio was 18.00. So, you choose to use this value for the Percent Exposed among the ILL. You’re not sure if there is a correspondence between the risk factor of swimming and regularly doing laundry in the river, but you think that the skin exposure might be similar. So, type 18.00 into the Odds Ratio Field.

Notice how the Percent Exposure among the ILL field populates with an estimate. You should see 81.8% in this field.

7. Change your expected exposure among ILL to 75% as you believe that 81.82% is just too high. See how the OR changes accordingly. You should now have an OR of 12.00.

The screen should change and sample sizes will appear in the table to the right of the parameters.

Notice that various sample sizes are calculated depending upon different values for power and confidence level as well as the different ratios of unexposed : exposed in the study population.

8. You can now choose the sample size for your study.

How many subjects will you need to enroll in your study according to the parameters you input (95% C.I., 80% power, 2:1 ratio)? You should answers should be 29 (10 cases, 19 controls), 26 (9 cases, 17 controls), and 35 (12 cases, 23 controls).

According to these results, what’s the smallest sample size that you can choose? At what level of confidence? According to these results, 15 subjects at a 80% C.I. is the smallest sample size.

If you demand more precision from your results (a higher C.I. of 99%), does your sample size increase or decrease? It should increase to 42, 39, or 47 total subjects.

Now, experiment with changing your study parameters and see the impact on your sample size results.

Decrease your power to 75%.

Decrease your confidence level to 90%

Change your cases with exposure 80%.

Change your ratio to 3:1.

Your sample sizes should now be 14, 12 and 20

As in the Cohort Study, notice how the sample size increases or decreases depending upon how you change the study parameters. As described for Cohort Studies, Unmatched Case Control studies also provide the same 3 types of sample sizes. 16

GH531/EPI539

Computer Lab Module: Session 3

2012

Saving your Results in StatCalc Please note that there is not a direct way to save your results in StatCalc. Unfortunately, you cannot use the mouse to select the results table and copy/paste into a Word document. What I recommend is creating a table in Microsoft Word or Excel to input your results. You will likely need to do this anyway for any grant application. You can save your results by saving an image or printout of your window. Right click anywhere within the window and you can save it as an image or print it.

WHAT YOU HAVE LEARNED

How to navigate in Epi-Info’s StatCalc utility for calculating sample sizes.

How to use StatCalc for determining sample sizes in basic descriptive, population studies, cohort studies, and unmatched case control studies.

How the study design parameters impact the sample size calculation and what to consider when making choices about these parameters.

Practice! (as part of the Assignment) Go to the web site and answer the questions in the Assignment for Session 3. The questions are sample size problems that you will solve by using StatCalc. Thanks!

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