# coefci

## Description

## Examples

### Cox Model Confidence Interval

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

### Confidence Intervals for Multiple Predictors

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 the data.

`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

`level`

— Level of significance for confidence interval

`0.05`

(default) | positive number less than `1`

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

`ci`

— Confidence interval

real two-column matrix

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**

## See Also

`CoxModel`

| `linhyptest`

| `fitcox`

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