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Assessment of time-varying long-term effects of therapies and prognostic factors

Duration: 2004-2010

Principal investigator: Prof. Dr. Willi Sauerbrei (IMBI)

Researchers: Prof. Dr. Willi Sauerbrei (IMBI), Dr. Anika Buchholz (IMBI)



With longer follow-up the proportional hazards (PH) assumption may become questionable in the Cox model. Extension by including an interaction between a covariate and a prespecified parametric function of time may be sensible. Using step functions by categorizing the time in two to four parts is a simple approach, but with several important disadvantages. No traditional approach has gained general popularity. At least seven approaches based on more elaborated procedures have been published in the last five years. In many respects they are very different, all lack detailed investigation of properties and hardly any comparisons are published.
We developed a new procedure called MFPT, which is an extension of the multivariable fractional polynomial (MFP) approach. Only one of the other six new approaches considers all 4 steps of MFPT: (1) select influential variables; (2) determine a sensible dose-response function for continuous variables; (3) investigate time-varying effects; (4) model such time-varying effects on a continuous scale. Results of the first two steps have an influence on the time-varying effect part in steps (3) and (4). To improve the first part we proposed a preliminary transformation making MFP more robust. For practical applicability of the MFP part we made programs available.
The Rotterdam breast cancer series (about 3000 patients, up-to 20 years follow-up) guided the development of MFPT as the main example. Eight of the ten variables were included in the final model, two of them with a time-varying effect. Instability is a serious issue of all multi--variable models derived data-dependently. Using bootstrap resampling we investigated it in the Rotterdam data. External validation of the model was started by considering some aspects of the Rotterdam MFPT model in the GBSG data. Differences in the structure of the two data sets complicate these investigations.
We started collaboration with the six groups who proposed procedures to investigate time-varying effects. For some of the approaches we used the models derived with MFPT in the Rotterdam data and gained first experiences with these approaches. In this way we combined the first two (time-fixed) steps from our approach with time-varying steps from other approaches.
Computational aspects may be one of the most important reasons that time-varying effects are hardly investigated. A substantial enlargement of the data set is often required and may cause severe computational difficulties, it may even be impossible to fit a model. In the Rotterdam data we could show that 'simplifying' survival time by categorization in small intervals is a sensible way to cope with it. Using six months intervals resulted in 35698 pseudo-observations, a split at each event-time gives about 2.2 million. Categorizing survival time makes specific analyses much easier and simulation studies possible.