The Short-Term and Long-Term Hazard Ratio Model: Parameterization Inconsistency

The test of Yang and Prentice, based on the short-term and long-term hazard ratio model for the presence of a regression effect appears to be an attractive one, being able to detect departures from a null hypothesis of no effect against quite broad alternatives. We recall the model on which this test is based and the test itself. In simulations, the test has shown good performance and is judged to be of potential value when alternatives to the null may be of a nonproportional hazards nature. However, the model, even when valid, suffers from a parameterization inconsistency in the sense that parameter estimates can violate the model’s assumed parametric structure even when true. This leads to awkward behavior in some situations. For example, this inconsistency implies that inference will not be invariant to the coding of treatment allocation. While this is a theoretical observation, we provide real examples that highlight the difficulty in making clear cut inferences from the model. Potential solutions are available and we provide some discussion on this.