The Cox Model and 'Type 3' Tests

• Activity Number: 167
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Terry Therneau*+
• Companies: Mayo Clinic
• Keywords: Cox model ; type 3 tests ; software

Abstract

SAS recently added "type 3" to the phreg procedure; I am the author of the primary survival package for R so looked into it. I have suspicions whenever a linear model formula is grafted onto the Cox model. Sometimes the equations transfer (Wald tests) but more often they simply don't perform (adjusted variable plots). In population adjustment methods, popular in epidemiology, data are reweighted such that the two groups have a common distribution p for the confounder, followed by a simple summary of the reweighted data. The SAS "type 3" tests for linear models are a particular variant of this which use a uniform distribution for p. There are multiple approaches to compute the type 3 value, which give identical answers for linear models but not necessarily so for a Cox model. Key questions for survival models are a. whether a uniform distribution makes sense as the target distribution, b. how best to define "uniform", c. how different are the results of the different formulas when copied across to this new case, and d. which is best? Answers are a: almost never, b: "equal n" and "equal events" are both contenders, c: very different, and d: SAS phreg has used the worst.