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Abstract:
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To minimize cost and maximize information about expensive-to-evaluate outcomes, longitudinal studies must carefully select observations. We will often have auxiliary variables (that are related to the outcome) and covariates on which to base the selection. For example, in the Osteoarthritis Initiative investigators collected, but did not read MRI outcomes but selection can be based on less expensive X-ray information and covariates. Optimal designs to conduct such sampling are poorly developed. We describe an approach to construct auxiliary-variable-based sampling designs that are substantially more efficient than standard designs and quantify efficiency gains. Our approach exploits the fact that unmeasured expensive-to-evaluate outcomes are missing at random (MAR). We identify efficient designs by minimizing the variance of estimated parameters of interest from a joint, shared random effects model for the auxiliary variable and outcome over a class of subsampling designs, with sampling probabilities that follow a logistic model.
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