# linhyptest

Linear hypothesis tests on Cox model coefficients

## Syntax

``testTable = linhyptest(coxMdl)``

## Description

example

````testTable = linhyptest(coxMdl)` returns an ANOVA-style table with p-values for tests that determine if sequential combinations of Cox model coefficient estimates are zero. `linhyptest` tests successive null hypotheses, starting with the hypothesis that all the coefficients are 0. The function then tests to determine if all but the first coefficient are 0, all but the first two coefficients are zero, and so on, up to the number of coefficients minus one. A significant p-value indicates that you can reject the null hypothesis, meaning the assumption that all coefficients in a particular combination of coefficients are 0.```

## Examples

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Examine the result of `linhyptest` on the `readmissiontimes` data set.

```load readmissiontimes coxMdl = fitcox([Age,Sex,Weight],ReadmissionTime,... 'Censoring',Censored); testTable = linhyptest(coxMdl)```
```testTable=3×2 table Predictor pValue _______________ __________ {'Empty Model'} 2.5612e-07 {'X1' } 7.9753e-08 {'X1, X2' } 0.095973 ```
• The first row of the returned table indicates that you can reject the hypothesis that all model coefficients are 0 at the `.05` or `.01` significance levels.

• The second row indicates that you can reject the hypothesis that only the `Sex` and `Weight` coefficients are 0 at the `.05` or `.01` significance levels.

• The third row indicates that you cannot reject the hypothesis that only the `Weight` coefficient is 0 at the `.05` or `.01` significance levels.

## Input Arguments

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

## Output Arguments

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Significance levels of cumulative hypothesis tests, returned as a table. The tested coefficients are in the `Coefficients` property of the model. The table returns tests of successive null hypotheses, starting with the hypothesis that all the coefficients are 0. The second row tests whether all but the first coefficient is 0. The third row tests whether all but the first two coefficients are zero, and so on. The last row tests whether all coefficients but the last are zero. A significant p-value indicates that you can reject the null hypothesis, meaning the assumption that all coefficients in a particular combination of coefficients are 0. A significant p-value is one that is smaller than a specified significance level.