Journal of Data Science

Precision medicine is an innovative approach that aims to customize medical treatments and interventions to patients based on their individual characteristics. Several estimation techniques, including Q-learning, have been developed to determine optimal treatment rules. However, the applicability of these methods depends on the availability of precisely measured variables. This study extends the scope of Q-learning to incorporate compound outcomes, deviating from the commonly assumed univariate outcomes, and further accommodates data with mismeasurement in both binary and continuous covariates. Two methods are described to mitigate the impact of mismeasurement. Numerical studies reveal that mismeasurement in covariates leads to notable estimation bias in parameters indexing the optimal treatment, yet the methods addressing the mismeasured effects yield improved results.

Abstract: Of interest in this paper is the development of a model that uses inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false positive misclassification rate may be estimated. Also, three first-order likelihood based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the score and likelihood ratio intervals are generally preferable over the Wald interval. Lastly, the model is applied to a medical data set.

Abstract: Interval estimation for the proportion parameter in one-sample misclassified binary data has caught much interest in the literature. Re cently, an approximate Bayesian approach has been proposed. This ap proach is simpler to implement and performs better than existing frequen tist approaches. However, because a normal approximation to the marginal posterior density was used in this Bayesian approach, some efficiency may be lost. We develop a closed-form fully Bayesian algorithm which draws a posterior sample of the proportion parameter from the exact marginal posterior distribution. We conducted simulations to show that our fully Bayesian algorithm is easier to implement and has better coverage than the approximate Bayesian approach.