A special case of reduced rank models for identification and modelling of time varying effects in survival analysis

<jats:p>Flexible survival models are in need when modelling data from long term follow‐up studies. In many cases, the assumption of proportionality imposed by a Cox model will not be valid. Instead, a model that can identify time varying effects of fixed covariates can be used. Although there are several approaches that deal with this problem, it is not always straightforward how to choose which covariates should be modelled having time varying effects and which not. At the same time, it is up to the researcher to define appropriate time functions that describe the dynamic pattern of the effects. In this work, we suggest a model that can deal with both fixed and time varying effects and uses simple hypotheses tests to distinguish which covariates do have dynamic effects. The model is an extension of the parsimonious reduced rank model of rank 1. As such, the number of parameters is kept low, and thus, a flexible set of time functions, such as b‐splines, can be used. The basic theory is illustrated along with an efficient fitting algorithm. The proposed method is applied to a dataset of breast cancer patients and compared with a multivariate fractional polynomials approach for modelling time‐varying effects. Copyright © 2016 John Wiley &amp; Sons, Ltd.</jats:p>