Method table for Fit Cox Model in a Counting Process Form

Find definitions and interpretation guidance for every statistic in the Method table.

In This Topic

Cox model type
Categorical predictor coding
Tie adjustment
Covariance matrix for analysis
Stratification variables
Transformation for proportional hazards tests
Rows unused

Cox model type

Displays the type of Cox regression model that Minitab uses for the analysis. Minitab offers two types of models, a fixed predictors only model, and a counting process form model. If you have time-dependent repeated measures or time-dependent predictors, you have to use a counting process form model.

Categorical predictor coding

Minitab can use either the (0, 1) or (−1, 0, +1) coding scheme to include categorical variables in the model. The (0, 1) scheme is the default for regression and Cox regression analyses while the (−1, 0, +1) scheme is the default for ANOVA and DOE. The choice between these two schemes does not change the statistical significance of the categorical variables. However, the coding scheme does change the coefficients and how to interpret them.

Interpretation

Verify the coding scheme that is displayed to ensure that you performed the intended analysis. Interpret the coefficients for the categorical variables as follows:

With the (0, 1) coding scheme, the coefficient for a categorical level represents the logarithm of the risk that a subject with the level experiences the event relative to an individual in the reference level. The coefficient for the reference level is not displayed in the Coefficients table.
With the (−1, 0,+1) coding scheme, twice the coefficient for a categorical level represents the logarithm of the risk that a subject with the level experiences the event relative to an individual in another level.

Tie adjustment

Displays the method that Minitab uses for adjusting for ties. Usually the Efron method provides better estimates than the Breslow method when there many ties in the response data. The two methods yield the same estimates when there are no ties in the response data.

Covariance matrix for analysis

Minitab displays this row in the table if you selected to perform the analysis using the robust covariance matrix¹. All the tests and confidence intervals in the analysis use the robust covariance matrix. Minitab does not display anything in the Method table if the analysis uses the model variance-covariance matrix.

Stratification variables

Displays the stratification variables that Minitab uses in the analysis. A stratified model estimates a baseline hazard rate for each strata but uses the same estimates for the effects of the predictors. You can have up to two stratification variables.

Transformation for proportional hazards tests

Displays the transformation Minitab uses in the proportional hazards test. It is a test of linear association between the scaled Schoenfeld residuals and some function, g(t), of the event times. Minitab only displays the transformation if you select something other than the identity function.

Natural log function: The analysis uses the natural log function, g(t) = ln (t), to transform the event times for the tests of proportional hazards.
Rank function: The analysis uses the rank function, g(t) = Rank (t), to transform the event times for the tests of proportional hazards. The rank function is based on the ranks of the event times. Tied values are assigned their average ranks.
Kaplan-Meier survival function: The analysis uses the Kaplan-Meier's survival function to transform the event times for the tests of proportional hazards. The survival estimates are based on the response time.

Rows unused

Displays the number of rows that Minitab excludes from the analysis. The Method table does not display this row in the table if the analysis uses every row. Minitab excludes rows from the analysis if they have a missing value or if the response time is non positive. This exclusion does not depend on the data format. If the entry time is greater than the end time, you get an error and the analysis does not run.

¹ Lin, D.Y., and Wei, L.J. (1989). The robust inference for the Cox Proportional hazards model. Journal of the American Statistical Association, 84: 1074-1078