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Paper No. 05-1

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JB Copas and S Eguchi

Local Model Uncertainty and Incomplete Data bias

Date: February 2005

Abstract: Problems of the analysis of data with incomplete observations are all too familiar in statistics. They are doubly difficult if we are also uncertain about the choice of model. We propose a general formulation for the discussion of such problems, and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small. Loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation: the increase in variance when an assumed model is correct, the bias in estimation when the model is incorrect. Examples include non-ignorable missing data, hidden confounders in observational studies, and publication bias in meta analysis. Doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of un-detectably small model departures. The problem of assessing the risk of lung cancer from passive smoking is used as a motivating example.

Keywords: Missing data; Selection bias; Ignorable; Missing at random; Coarsening; Misspecified models; Hidden confounders; Publication bias