4.5 Article

Impact of the model-building strategy on inference about nonlinear and time-dependent covariate effects in survival analysis

Journal

STATISTICS IN MEDICINE
Volume 33, Issue 19, Pages 3318-3337

Publisher

WILEY
DOI: 10.1002/sim.6178

Keywords

Cox's proportional hazards model; flexible modeling; hypothesis testing; model-building strategy; residual confounding

Funding

  1. Canadian Institutes for Health Research (CIHR) [81275]
  2. Natural Sciences and Engineering Research Council of Canada (NSERC) [228203]
  3. CIHR [ETG 92246]
  4. Terry Fox Research Institute

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Cox's proportional hazards (PH) model assumes constant-over-time covariate effects. Furthermore, most applications assume linear effects of continuous covariates on the logarithm of the hazard. Yet, many prognostic factors have time-dependent (TD) and/or nonlinear (NL) effects, that is, violate these conventional assumptions. Detection of such complex effects could affect prognosis and clinical decisions. However, assessing the effects of each of the multiple, often correlated, covariates in flexible multivariable analyses is challenging. In simulations, we investigated the impact of the approach used to build the flexible multivariable model on inference about the TD and NL covariate effects. Results demonstrate that the conclusions regarding the statistical significance of the TD/NL effects depend heavily on the strategy used to decide which effects of the other covariates should be adjusted for. Both a failure to adjust for true TD and NL effects of relevant covariates and inclusion of spurious effects of covariates that conform to the PH and linearity assumptions increase the risk of incorrect conclusions regarding other covariates. In this context, iterative backward elimination of nonsignificant NL and TD effects from the multivariable model, which initially includes all these effects, may help discriminate between true and spurious effects. The practical importance of these issues was illustrated in an example that reassessed the predictive ability of selected biomarkers for survival in advanced non-small-cell lung cancer. In conclusion, a careful model-building strategy and flexible modeling of multivariable survival data can yield new insights about predictors' roles and improve the validity of analyses. Copyright (C) 2014 John Wiley & Sons, Ltd.

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