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# Analysis of Lifetime Data

Nonparametric and semiparametric methods for analyzing reliability and survival data

Survival analysis is time-to-event analysis, that is, when the outcome of interest is the time until an event occurs. Examples of time-to-events are the time until infection, reoccurrence of a disease, or recovery in health sciences; the duration of unemployment in economics; the time until the failure of a machine part or the lifetime of light bulbs in engineering, and so on.

To perform survival analysis:

• Fit a model to your data. Use one or more of the functions listed on this page under Lifetime Data Analysis or Cox Proportional Hazards Models.

• Plot or otherwise analyze the fitted model using the methods in the examples listed on this page under Topics, or using Cox Proportional Hazards Models functions.

The `fitcox` function provides an object-oriented way to fit a Cox proportional hazards model. The resulting `CoxModel` object contains many statistics and methods for analysis. `coxphfit` is an older function for fitting Cox models that also enables code generation.

## Functions

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 `ksdensity` Kernel smoothing function estimate for univariate and bivariate data `mle` Maximum likelihood estimates `mlecov` Asymptotic covariance of maximum likelihood estimators `evfit` Extreme value parameter estimates `expfit` Exponential parameter estimates `gamfit` Gamma parameter estimates `lognfit` Lognormal parameter estimates `normfit` Normal parameter estimates `wblfit` Weibull parameter estimates `fitdist` Fit probability distribution object to data `dfittool` Open Distribution Fitter app
 `ecdf` Empirical cumulative distribution function `ecdfhist` Histogram based on empirical cumulative distribution function `plotSurvival` Plot survival function of Cox proportional hazards model `probplot` Probability plots `wblplot` Weibull probability plot

#### Fit Cox Proportional Hazards Model

 `coxphfit` Cox proportional hazards regression

#### Fit `CoxModel` Object

 `fitcox` Create Cox proportional hazards model

#### `CoxModel` Methods

 `coefci` Confidence interval for Cox proportional hazards model coefficients `hazardratio` Estimate Cox model hazard relative to baseline `linhyptest` Linear hypothesis tests on Cox model coefficients `plotSurvival` Plot survival function of Cox proportional hazards model `survival` Calculate survival of Cox proportional hazards model

## Objects

 `CoxModel` Cox proportional hazards model

## Topics

What Is Survival Analysis?

Learn about censoring, survival data, and the survivor and hazard functions.

Survivor Functions for Two Groups

Find the empirical survivor functions and the parametric survivor functions using the Burr type XII distribution fit on data for two groups.

Hazard and Survivor Functions for Different Groups

Estimate and plot the cumulative hazard and survivor functions for different groups.

Kaplan-Meier Method

Estimate the empirical hazard, survivor, and cumulative distribution functions.

Cox Proportional Hazards Model

Adjust survival rate estimates to quantify the effect of predictor variables.

Cox Proportional Hazards Model Object

Create data for a Cox model with three stratification levels, then fit and analyze the resulting model.

Cox Proportional Hazards Model for Censored Data

Create a Cox proportional hazards model, and assess the significance of the predictor variables.

Cox Proportional Hazards Model with Time-Dependent Covariates

Convert survival data to counting process form, and then construct a Cox proportional hazards model with time-dependent covariates.

Analyzing Survival or Reliability Data

Analyze lifetime data with censoring by modeling the time to failure of a throttle from an automobile fuel injection system.

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