User Guide

99
Chapter
11
Cox Regression Analysis
Like Life Tables and Kaplan-Meier survival analysis, Cox Regression is a method for
modeling time-to-event data in the presence of censored cases. However, Cox
Regression allows you to include predictor variables (covariates) in your models. For
example, you could construct a model of length of employment based on educational
level and job category. Cox Regression will handle the censored cases correctly, and
it will provide estimated coefficients for each of the covariates, allowing you to assess
the impact of multiple covariates in the same model. You can also use Cox Regression
to examine the effect of continuous covariates.
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.
Data. Your time variable should be quantitative and 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.