# hazardratio

Estimate Cox model hazard relative to baseline

## Syntax

``hazard = hazardratio(coxMdl,X)``
``hazard = hazardratio(coxMdl,X,Stratification)``
``hazard = hazardratio(___,'Baseline',baseline)``

## Description

example

````hazard = hazardratio(coxMdl,X)` returns the estimated hazard relative to the baseline for a fitted Cox proportional hazards model `coxMdl` using the predictors `X`.```

example

````hazard = hazardratio(coxMdl,X,Stratification)` returns the estimated hazard relative to the baseline using the predictors `X` and stratification levels `Stratification`. The number of rows in `X` and `Stratification` must be the same. NoteWhen you train `coxMdl` using stratification variables and pass predictor variables `X`, `hazardratio` also requires you to pass stratification variables. ```

example

````hazard = hazardratio(___,'Baseline',baseline)` estimates the hazard relative to the supplied baseline using any of the input argument combinations in the previous syntaxes.```

## Examples

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Perform a Cox proportional hazards regression on the `lightbulb` data set, which contains simulated lifetimes of light bulbs. The first column of the light bulb data contains the lifetime (in hours) of two different types of bulbs. The second column contains a binary variable indicating whether the bulb is fluorescent or incandescent; 0 indicates the bulb is fluorescent, and 1 indicates it is incandescent. The third column contains the censoring information, where 0 indicates the bulb was observed until failure, and 1 indicates the observation was censored.

Fit a Cox proportional hazards model for the lifetime of the light bulbs, accounting for censoring. The predictor variable is the type of bulb.

```load lightbulb coxMdl = fitcox(lightbulb(:,2),lightbulb(:,1), ... 'Censoring',lightbulb(:,3));```

View the default baseline for the fitted model.

`defaultBaseline = coxMdl.Baseline`
```defaultBaseline = 0.5000 ```

Compute the hazard ratio of an incandescent bulb (1) relative to this baseline.

`defaultHazard = hazardratio(coxMdl,1)`
```defaultHazard = 10.6238 ```

Compute the hazard ratio of an incandescent bulb relative to a fluorescent bulb (0).

`relHazard = hazardratio(coxMdl,1,'Baseline',0)`
```relHazard = 112.8646 ```

The hazard rate of an incandescent bulb is estimated to be over 100 times the hazard rate of a fluorescent bulb.

Create a Cox model from the `readmissiontimes` data. In this data, `0` indicates a male patient, and `1` indicates a female patient.

```load readmissiontimes coxMdl = fitcox([Age,Sex,Weight],ReadmissionTime,'Censoring',Censored);```

Calculate the relative hazard of a 40-year-old man weighing 200 lbs. relative to the baseline hazard.

`hazard = hazardratio(coxMdl,[40 0 200])`
```hazard = 4.3112 ```

Calculate the hazard of this same man relative to a 50-year-old woman weighing 150 lbs.

`hazard2 = hazardratio(coxMdl,[40 0 200],'Baseline',[50 1 150])`
```hazard2 = 5.2053 ```

Load the `coxModel` data. (This simulated data is generated in the example Cox Proportional Hazards Model Object.) The model named `coxMdl` has three stratification levels (1, 2, and 3) and a predictor `X` with three categorical values (1, 1/20, and 1/100).

`load coxModel`

Find the hazard ratio of the predictor value `categorical(1)` and stratification level 3 with respect to the baseline.

```X = categorical(1); stratification = 3; hazard = hazardratio(coxMdl,X,stratification)```
```hazard = 12.7096 ```

Calculate the ratio with respect to a baseline of 0.

`hazard = hazardratio(coxMdl,X,stratification,'Baseline',0)`
```hazard = 95.5127 ```

Calculate the ratio of a `categorical(1/100)` predictor with respect to a baseline of 0.

```X = categorical(1/100); hazard = hazardratio(coxMdl,X,stratification,'Baseline',0)```
```hazard = 1 ```

## Input Arguments

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Fitted Cox proportional hazards model, specified as a `CoxModel` object. Create `coxMdl` using `fitcox`.

Data for estimating the hazard, specified as a matrix or table. The data must be the same type as the data used to train `coxMdl`.

Data Types: `double` | `table` | `categorical`

Stratification level, specified as a variable or variables of the same type used for training `coxMdl`. Specify the same number of rows in `Stratification` as in `X`.

Data Types: `single` | `double` | `logical` | `char` | `string` | `table` | `cell` | `categorical`

Baseline hazard, specified as a real scalar or row vector.

• A scalar value applies to all predictors.

• A row vector value must have the same number of entries as the number of predictors.

The returned hazard ratio is relative to the baseline.

Example: `[1 20 100]`

Data Types: `single` | `double`

## Output Arguments

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Hazard ratio relative to the baseline, returned as a nonnegative vector. `hazard` gives the factor by which to multiply the baseline hazard, so you can obtain the relative hazard of an individual with predictor values `X` and, if applicable, stratification level `Stratification`.

## Version History

Introduced in R2021a