The non-zero mean SIMEX: Improving estimation in the face of measurement error

Abstract

Abstract:The simulation extrapolation method developed by Cook and Stefanski (1995) is a simulation based technique for estimating and reducing bias due to additive measurement error armed only with knowledge of the variance of the measurement error distribution. However there are many instances in which validation data are not available, and measurement error is known not to have mean zero. For example, in assessing phylogenetic cluster size of HIV viruses, cluster size is systematically underestimated since clustering can only be performed on the viruses of those individuals who have presented for testing. In this setting, it is not possible to obtain validation data; however, using knowledge gleaned from the literature, the distribution of the errors may be estimated. In this work, we extend the simulation extrapolation procedure to accommodate errors with non-zero means, motivated by an interest in determining behavioural correlates of HIV phylogenetic cluster size. We provide theoretical justification for the generalization to the non-zero mean measurement error case, proving its consistency and demonstrating its performance via simulation. We then apply the result to data from a the province of Quebec in Canada to show that findings from a naïve analysis are robust to a substantial range of possible measurement error distributions.