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.