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Modeling Biomedical Data and the Foundations of Bioequivalence

 Leena Choi,  PhD Candidate, Johns Hopkins Department of Biostatistics

This thesis covers three important problems in statistical applications related to the study of concentrations in the human body; representing data as evidence, study design and structural modelling. First, we proposed a new paradigm to represent data as evidence with application to bioequivalence trials. Bioequivalence trials are abbreviated clinical trials where a generic drug or a new formulation attempts to demonstrate bioequivalence to a corresponding brand-name drug or pre-approved formulation. Bioequivalence trials are a crucial aspect of public health, since the efficacy and safety of generic drugs or new formulations need to be guaranteed while also allowing cheaper generic drugs to be made available to the public. There exists confusion between hypothesis testings and confidence intervals in this area, which is indicative of the existence of systemic defects in the frequentist approach. The proposed likelihood paradigm avoids these problems. We used profile likelihoods to represent data as evidence. Furthermore, we examined the main properties of profile likelihoods and estimated likelihoods under simulation. Our simulation study showed that profile likelihoods are a very good alternative to the true likelihood, as long as the sample size is moderate. Our study also showed that the standard method in current practice of bioequivalence trials only generates weak evidence from the evidential point of view.

Secondly, we discussed the selection of optimal sampling times in the design of bioequivalence studies. Finding optimal sampling times is critical to estimating the area under the blood concentration-time curve, which is a or the fundamental metric in bioequivalence trials. We proposed a new objective function and a simulated annealing algorithm to perform the optimization. The results showed that our new objective function and algorithm worked very well in finding optimal sampling times where established algorithms fail.

Thirdly, we developed a structural model based on underlying physiological theory for fractionately collected ejaculates. This proposed method does not suffer from the statistical limitations of current practices. The model also provides population-average estimates in addition to subject-specific estimates. We performed sensitivity analysis using several choices of distributions for random effects along with several choices of priors. We found that the estimates were insensitive to the distributional assumptions for the random effects and priors.  In addition, the model was not affected by a form of outlier that negatively impacted the other methods.

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