Bayesian two-component measurement error modelling for survival analysis using INLA-A case study on cardiovascular disease mortality in Switzerland

Measurement error (ME) in explanatory variables is a common problem in regression and survival analysis, as it may cause bias in the estimated parameters. It is shown how the integrated nested Laplace approximations (INLA) method can handle classical and Berkson ME in a single explanatory variable, illustrated for the case of a Weibull regression model. To this end, a two-component error model to account for a mix of Berkson and classical ME in a single covariate is introduced and applied to a study on cardiovascular disease (CVD) mortality in Switzerland. In particular, the model was used to correct for error in the self-reported mean daily number of cigarettes smoked, as well as in reportings of systolic blood pressure (SBP). Both variables suffer from classical error induced by an imprecision, either due to misremembering of study participants (cigarettes), or due to practical difficulties in obtaining accurate measurements (SBP), but also from a Berkson-type error that is induced by a rounding behaviour, also known as digit preference. In both cases, the effect estimates increased when the error was taken into account. Therefore, an important conclusion is that ME modelling in survival analysis is relevant, and a ready-to-use Bayesian solution including R-code is provided.