Cox Proportional Hazards Model: Example 2 - Survival - Time-Dependent

The data set for this example, Pike.sta, is based on a set reported by Pike (1966) describing the survival times for two groups of rats that had been exposed to a carcinogen. Suppose that we suspect that the effect of treatment (exposure to carcinogen) on the underlying hazard is not constant, that is, the proportionality assumption is violated. To the assumption, a model will be fit that includes both the fixed covariate Group as well as the time-dependent covariate defined as Group * (Log(Time)-5.4), where 5.4 is the mean of the log of survival times.

Open the example data file Pike.sta, and start the Cox Proportional Hazards module. Following are instructions to do this from the ribbon bar and from the classic menus.

Ribbon bar. Select the Home tab. In the File group, click the Open arrow, and select Open Examples to display the Open a Statistica Data File dialog box. The data set is located in the Datasets folder.

Next, on the Statistics tab, in the Advanced/Multivariate group, click the Advanced Models arrow and select Cox Proportional Hazards to display the Cox Proportional Hazards Regression dialog box.

Classic menus. From the File menu, select Open Examples to display the Open a from the File menu Data File dialog box. Pike.sta is located in the Datasets folder.   

Next, from the Statistics - Advanced Linear/Nonlinear submenu, select Cox Proportional Hazards Models.

Starting the analysis

In the Cox Proportional Hazards Regression dialog box, on the Quick tab, in the Input type group box, select the Survival time, covariates, factors, censor, time-dependent covariates option button.

Click the Variables button, and in the variable selection dialog box, make the following variable selections.

Click the OK button. A message is displayed advising that some variables contain text values. Click the Continue with current selection button.

Double-click in the Code for complete responses field, select 0:complete, and click OK.

Specify censored as the Code for censored responses.

Click the Expression(s) button to display the Define Time-Dependent Covariates/Expressions dialog box.

Click the Add Time Covariate button to display the Enter expression for time dependent covariates dialog box, where you specify the formula for the time-dependent covariate. Enter the time-dependent expression/formula (as shown below) and enter the covariate name: TCOV.

Click OK. Note that the variable, TCOV, has been added to the Define Time-Dependent Covariates/Expressions dialog box.

Click OK.

In the Cox Proportional Hazards Regression dialog box, click OK to perform the analysis and display the Cox Proportional Hazards Results dialog box.

On the Quick tab, click the Parameter estimates button.

Notice that the time-dependent covariate is not significant with a p-value of 0.899912. This indicates that the time-dependent covariate should not be placed in the model and that the model with the single fixed covariate is not inappropriate.