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Using auxiliary data for parameter estimation with non‐ignorably missing outcomes

We propose a method for estimating parameters in generalized linear models when the outcome variable is missing for some subjects and the missing data mechanism is non‐ignorable. We assume throughout that the covariates are fully observed. One possible method for estimating the parameters is maximum likelihood with a non‐ignorable missing data model. However, caution must be used when fitting non‐ignorable missing data models because certain parameters may be inestimable for some models. Instead of fitting a non‐ignorable model, we propose the use of auxiliary information in a likelihood approach to reduce the bias, without having to specify a non‐ignorable model. The method is applied to a mental health study.