Estimating restricted mean survival time and expected life-years lost in the presence of competing risks within flexible parametric survival models

DOI: https://doi.org/10.21203/rs.2.23839/v2

Abstract

We present various measures, specifically the expected life-years list due to a cause of death, that can be predicted for a specific covariate pattern to facilitate interpretation in observational studies. These can also be summarised at the population-level using standardisation to obtain marginal measures. The restricted mean survival time (RMST) measure can be obtained in the presence of competing risks using Royston-Parmar flexible parametric survival models (FPMs). Royston-Parmar FPMs can be fitted on either the cause-specific hazards or cumulative incidence scale in the presence of competing risks. An advantage of modelling within this framework for competing risks data is the ease at which other alternative predictions to the (cause-specific or subdistribution) hazard ratio can be obtained. The RMST estimate is one such measure. This has an attractive interpretation, especially when the proportionality assumption is violated. In addition to this, compared to similar measures, fewer assumptions are required and it does not require extrapolation. Furthermore, one can easily obtain the expected number of life-years lost, or gained, due to a particular cause of death, which is a further useful prognostic measure. We describe estimation of RMST after fitting a FPM on either the log-cumulative subdistribution, or cause-specific hazards scale. As an illustration of reporting such measures to facilitate interpretation of a competing risks analysis, models are fitted to English colorectal data.

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