In This Topic
The tests of the proportional hazards assumption in Minitab Statistical Software use the approach from Grambsch and Therneau (1994)1.
DF
The degrees of freedom are 1 for each estimated coefficient. For the overall test, the degrees of freedom are the sum of the degrees of freedom for the coefficients.
Chi-square
Global test for all predictors
The tests assesses the null hypothesis that the slopes for all of the terms in the model are zero for the relationship between the scaled Schoenfeld residuals and a time-scaled transformation of the event times against the alternative hypothesis that at least one slope is nonzero.
The test statistic for the simultaneous test of all predictors in the model has the following form:
Under the null hypothesis that the assumption of proportional hazards is
true for all predictors, 
asymptotically follows a chi-square distribution with
p degrees of freedom.
Test for individual predictors
The tests assess the null hypothesis that the slope is zero for the relationship between the scaled Schoenfeld residuals for a term and a time-scaled transformation of the event times against the alternative hypothesis that the slope is nonzero.
The test statistic with respect to an individual predictor has the following form:
Under the null hypothesis that the assumption of proportional hazards is
true for the predictor, 
asymptotically follows a chi-square distribution with 1 degree of freedom.
Notation
| Term | Description |
|---|---|
 | the event times |
| d | the number of event times |
| p | the number of estimated parameters in the model |
 | A time scale transformation of the event times. The following functions are
in Minitab Statistical Software:
|
 | the variance-covariance matrix of  |
| S | the d × p matrix of the Schoenfeld residuals |
| S* | the d × p matrix of the scaled Schoenfeld residuals |
 | a
d-dimensional vector whose components are the centered values of
where  |
 |  |
 | the sample variance of the components of  |
 | the sample mean of the components of  |
 | the standard error of the
jth component of the vector
of estimated parameters from the Cox proportional hazard model |
 | the correlation coefficient between the scaled Schoenfeld residuals for the
jth predictor and the time-transformed functional values,
 |
P-value
where 
is a random variable that follows a chi-square distribution with
degrees of freedom. 
is the test statistic.
