Preclinical modeling of multi-drug cancer therapies

Anticancer drugs typically are administered in the clinic in the form of mixtures, sometimes called combinations. Only in rare cases, however, are mixtures approved as drugs. Rather, research on mixtures tends to occur after single drugs have been approved. The goal of this research project was to develop modeling approaches that would encourage rational preclinical mixture design. To this end, a series of models were developed. First, several QSAR classification models were constructed to predict the cytotoxicity, oral clearance, and acute systemic toxicity of drugs. The QSAR models were applied to a set of over 115,000 natural compounds in order to identify promising ones for testing in mixtures. Second, an improved method was developed to assess synergistic, antagonistic, and additive effects between drugs in a mixture. This method, dubbed the MixLow method, is similar to the Median-Effect method, the de facto standard for assessing drug interactions. The primary difference between the two is that the MixLow method uses a nonlinear mixed-effects model to estimate parameters of concentration-effect curves, rather than an ordinary least squares procedure. Parameter estimators produced by the MixLow method were more precise than those produced by the Median-Effect Method, and coverage of Loewe index confidence intervals was superior. Third, a model was developed to predict drug interactions based on scores obtained from virtual docking experiments. This represents a novel approach for modeling drug mixtures and was more useful for the data modeled here than competing approaches. The model was applied to cytotoxicity data for 45 mixtures, each composed of up to 10 selected drugs. One drug, doxorubicin, was a standard chemotherapy agent and the others were well-known natural compounds including curcumin, EGCG, quercetin, and rhein. Predictions of synergism/antagonism were made for all possible fixed-ratio mixtures, cytotoxicities of the 10 best-scoring mixtures were tested, and drug interactions were assessed. Predicted and observed responses were highly correlated (r2 = 0.83). Results suggested that some mixtures allowed up to an 11-fold reduction of doxorubicin concentrations without sacrificing efficacy. Taken together, the models developed in this project present a general approach to rational design of mixtures during preclinical drug development. ^

Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^