# 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 SPSS® Statistics Standard Edition or the Advanced Statistics Option.

- From the menus choose:
- Select a time variable. Cases whose time values are negative are not analyzed.
- Select a status variable, and then click Define Event.
- Select one or more covariates. To include interaction terms, select all of the variables involved in the interaction and then click >a*b>.

Optionally, you can compute separate models for different groups by defining a strata variable.

This procedure pastes COXREG command syntax.