We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

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In bioequivalence studies, drug formulations are compared in terms of bioavailability parameters such as the area under the concentration-time curve (AUC), the maximum concentration (Cmax), and the time to maximum concentration (t(max)). Accuracy in measuring these parameters directly affects the accuracy of bioequivalence tests. Because the number of blood draws per patient is limited, the blood collection times must be spaced so that concentration-time curve measurements can produce accurate bioavailability parameter estimates. This paper describes an optimization approach for calculating optimal time designs for one-compartment models, but is sufficiently general for other compartmental models. Simulation indicates that the optimal design improves the accuracy of AUC estimation.