Tests for Proportional Hazards table for Fit Cox Model in a Counting Process Form

Find definitions and interpretations for every statistic in the Tests for Proportional Hazards table.

In This Topic

DF
Correlation
Chi-square
P-value

The footnote to the table identifies the transformation of the event times for the test. Consider whether to try additional transformations for your analysis, especially if the residual plots show outliers in the data.

DF

Each coefficient in the model uses 1 degree of freedom. The degrees of freedom for the overall test for the proportional hazards are equal to the sum of the degrees of freedom for the coefficients in the model.

Correlation

The correlation measures the strength of the linear association between the scaled Schoenfeld residuals for a coefficient and the function of event times for the test. Larger correlations indicate more evidence against the proportional hazards assumption. Use the p-value to formally interpret the test with respect to the uncertainty in the data.

Chi-square

Each term in the table has a chi-square value. The overall test also has a chi-square value. The chi-square value is the test statistic that assesses the proportional hazards assumption. A sufficiently large chi-square statistic results in a small p-value, which indicates a violation of the proportional hazards assumption.

P-value

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

Interpretation

Use the tests to determine whether the model meets the proportional hazards assumption. The null hypothesis is that the model meets the assumption for all the predictors. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the model meets the assumption when it actually does not.

Overall test: The null hypothesis is that the effect of all terms in the model meets the proportional hazards assumption. If the p-value is less than your significance level, then there is statistical evidence that at least one term violates the proportional hazards assumption. Examine the tests of the individual terms to determine which terms are responsible for the violation.
Test for a term: The null hypothesis is that the effect of the term meets the proportional hazards assumption. If the p-value is less than your significance level, then you can conclude that there is statistical evidence that the term violates the proportional hazards assumption. If the test identifies a violation, consider storing the scaled Schoenfeld residuals to plot against the event times and transformed event times. Use plots of the scaled Schoenfeld residuals to identify causes of the nonproportionality, such as a decreasing or increasing effect. In some cases, the nonproportionality disappears through the addition of interaction terms or the use of terms to form strata.