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Optimization of clinical trial designs can help investigators achieve higher quality results for the given resource constraints. The present paper gives an overview of optimal designs for various important problems that arise in different stages of clinical drug development, including phase I dose-toxicity studies; phase I/II studies that consider early efficacy and toxicity outcomes simultaneously; phase II dose-response studies driven by multiple comparisons (MCP), modeling techniques (Mod), or their combination (MCP-Mod); phase III randomized controlled multi-arm multi-objective clinical trials to test difference among several treatment groups; and population pharmacokinetics-pharmacodynamics experiments. We find that modern literature is very rich with optimal design methodologies that can be utilized by clinical researchers to improve efficiency of drug development.

Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple-objective LQAS plans that meet user-specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use Mixed Integer Nonlinear Programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique.

Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studyingtheir properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariablyapplicable to the particular problem only.We propose a systematic approach to construct optimal exact designs by incorporatingthe Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. Asexamples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global orlocal optimizers. Our examples include design problems with constraints on the locations or the number of replicates at theoptimal design points.

Thresholding variable plays a crucial role in subgroup identification for personalizedmedicine. Most existing partitioning methods split the sample basedon one predictor variable. In this paper, we consider setting the splitting rulefrom a combination of multivariate predictors, such as the latent factors, principlecomponents, and weighted sum of predictors. Such a subgrouping methodmay lead to more meaningful partitioning of the population than using a singlevariable. In addition, our method is based on a change point regression modeland thus yields straight forward model-based prediction results. After choosinga particular thresholding variable form, we apply a two-stage multiple changepoint detection method to determine the subgroups and estimate the regressionparameters. We show that our approach can produce two or more subgroupsfrom the multiple change points and identify the true grouping with high probability.In addition, our estimation results enjoy oracle properties. We design asimulation study to compare performances of our proposed and existing methodsand apply them to analyze data sets from a Scleroderma trial and a breastcancer study.

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs.

Objective Patients with SLE have an increased risk ofatherosclerosis (ATH) that is not adequately explainedby traditional risk factors. We previously described thePredictors of Risk for Elevated Flares, Damage Progression,and Increased Cardiovascular disease in PaTients withSLE (PREDICTS) atherosclerosis-risk panel, which includesproinflammatory HDL (piHDL), leptin, soluble tumournecrosis factor-like weak inducer of apoptosis (sTWEAK)and homocysteine, as well as age and diabetes. A highPREDICTS score confers 28-fold increased odds forfuture atherosclerosis in SLE. The aim of this study is todetermine whether PREDICTS biomarkers are modifiable bycommon lupus therapies.Methods This prospective observational study includedSLE subjects started on new lupus treatments. Leptin,sTWEAK, homocysteine and antioxidant function of HDLwere measured at baseline (prior to drug initiation), 6weeks and 12 weeks.Results 16 subjects started mycophenolate (MMF), 18azathioprine (AZA) and 25 hydroxychloroquine (HCQ).In MMF-treated subjects, HDL function progressivelyimproved from 2.23 ± 1.32 at baseline to 1.37±0.81at 6 weeks (p=0.02) and 0.93±0.54 at 12 weeks(p=0.009). sTWEAK levels also improved in MMF-treatedsubjects from 477.5±447.1 to 290.3±204.6 pg/mLafter 12 weeks (p=0.04), but leptin and homocysteinelevels were not significantly changed. In HCQ-treatedsubjects, only HDL function improved from 1.80±1.29 atbaseline to 1.03±0.74 after 12 weeks (p=0.05). Therewere no changes in the AZA group. MMF treatmentwas still associated with significant improvements inHDL function after accounting for potential confounderssuch as total prednisone dose and changes in diseaseactivity. Overall, the mean number of high-risk PREDICTSbiomarkers at week 12 significantly decreased in theentire group of patients started on a new lupus therapy(2.1±0.9 to 1.8±0.9, p=0.02) and in the MMF-treatedgroup (2.4±0.8 vs 1.8±0.9, p=0.003), but not in theAZA or HCQ groups. In multivariate analysis, the odds ofhaving