# coefci

Confidence interval for Cox proportional hazards model coefficients

Since R2021a

## Syntax

``ci = coefci(coxMdl)``
``ci = coefci(coxMdl,level)``

## Description

example

````ci = coefci(coxMdl)` returns a 95% confidence interval for the coefficients of a trained Cox proportional hazards model.```

example

````ci = coefci(coxMdl,level)` returns a 100(1 – `level`)% confidence interval for the coefficients.```

## 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))```
```coxMdl = Cox Proportional Hazards regression model Beta SE zStat pValue ______ ______ ______ __________ X1 4.7262 1.0372 4.5568 5.1936e-06 Log-likelihood: -212.638 ```

Find a 95% confidence interval for the returned `Beta` estimate.

`ci = coefci(coxMdl)`
```ci = 1×2 2.6934 6.7590 ```

Find a 99% confidence interval for the `Beta` estimate.

`ci99 = coefci(coxMdl,0.01)`
```ci99 = 1×2 2.0546 7.3978 ```

Find confidence intervals for predictors of the `readmissiontimes` data set. The response variable is `ReadmissionTime`, which shows the readmission times for 100 patients. The predictor variables are `Age`, `Sex`, `Weight`, and `Smoker`, the smoking status of each patient. A 1 indicates the patient is a smoker, and a 0 indicates the patient does not smoke. The column vector `Censored` contains the censorship information for each patient, where 1 indicates censored data, and 0 indicates the exact readmission times are observed. (This data is simulated.)

`load readmissiontimes`

Use all four predictors for fitting a model.

`X = [Age Sex Weight Smoker];`

Fit the model using the censoring information.

`coxMdl = fitcox(X,ReadmissionTime,'censoring',Censored);`

View the point estimates for the `Age`, `Sex`, `Weight`, and `Smoker` coefficients.

`coxMdl.Coefficients.Beta`
```ans = 4×1 0.0184 -0.0676 0.0343 0.8172 ```

Find 95% confidence intervals for these estimates.

`ci = coefci(coxMdl)`
```ci = 4×2 -0.0139 0.0506 -1.6488 1.5136 0.0042 0.0644 0.2767 1.3576 ```

The `Sex` coefficient (second row) has a large confidence interval, and the first two coefficients bracket the value 0. Therefore, you cannot reject the hypothesis that the `Age` and `Sex` predictors are zero.

## Input Arguments

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

Level of significance for the confidence interval, specified as a positive number less than `1`. The resulting percentage is 100(1 – `level`)%. For example, for a 99% confidence interval, specify `level` as `0.01`.

Example: `0.01`

Data Types: `double`

## Output Arguments

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Confidence interval, returned as a real two-column matrix. Each row of the matrix is a confidence interval for the corresponding predictor. The probability that the true predictor coefficient lies in its confidence interval is 100(1 – `level`)%. For example, the default value of `level` is `0.05`, so with no `level` specified, the probability that each predictor lies in its row of `ci` is 95%.

## Version History

Introduced in R2021a