# Cox Regression Analysis

Cox Regression builds a predictive model for time-to-event data. The model produces a survival function that predicts the probability that the event of interest has occurred at a given time t for given values of the predictor variables. The shape of the survival function and the regression coefficients for the predictors are estimated from observed subjects; the model can then be applied to new cases that have measurements for the predictor variables. Note that information from censored subjects, that is, those that do not experience the event of interest during the time of observation, contributes usefully to the estimation of the model.

Example. Do men and women have different risks of developing lung cancer based on cigarette smoking? By constructing a Cox Regression model, with cigarette usage (cigarettes smoked per day) and gender entered as covariates, you can test hypotheses regarding the effects of gender and cigarette usage on time-to-onset for lung cancer.

Statistics. For each model: –2LL, the likelihood-ratio statistic, and the overall chi-square. For variables in the model: parameter estimates, standard errors, and Wald statistics. For variables not in the model: score statistics and residual chi-square.

Cox Regression Data Considerations

Data. Your time variable should be quantitative, but your status variable can be categorical or continuous. Independent variables (covariates) can be continuous or categorical; if categorical, they should be dummy- or indicator-coded (there is an option in the procedure to recode categorical variables automatically). Strata variables should be categorical, coded as integers or short strings.

Assumptions. Observations should be independent, and the hazard ratio should be constant across time; that is, the proportionality of hazards from one case to another should not vary over time. The latter assumption is known as the proportional hazards assumption.

Related procedures. If the proportional hazards assumption does not hold (see above), you may need to use the Cox with Time-Dependent Covariates procedure. If you have no covariates, or if you have only one categorical covariate, you can use the Life Tables or Kaplan-Meier procedure to examine survival or hazard functions for your sample(s). If you have no censored data in your sample (that is, every case experienced the terminal event), you can use the Linear Regression procedure to model the relationship between predictors and time-to-event.

Obtaining a Cox Regression Analysis

This feature requires Custom Tables and Advanced Statistics.