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Outcome-dependent sampling probabilities can be used to increase efficiency in observational studies. For continuous outcomes, appropriate consideration of sampling design in estimating parameters of interest is often computationally cumbersome. In this article, we suggest a Stochastic EM type algorithm for estimation when ascertainment probabilities are known or estimable. The computational complexity of the likelihood is avoided by filling in missing data so that an approximation of the full data likelihood can be used. The method is not restricted to any specific distribution of the data and can be used for a broad range of statistical models.

A Stochastic EM Type Algorithm for Parameter Estimation in Models with Continuous Outcomes, under Complex Ascertainment