A BAYESIAN APPROACH TO DOSE-RESPONSE ASSESSMENT AND DRUG-DRUG INTERACTION ANALYSIS: APPLICATION TO IN VITRO STUDIES

The considerable search for synergistic agents in cancer research is motivated by the therapeutic benefits achieved by combining anti-cancer agents. Synergistic agents make it possible to reduce dosage while maintaining or enhancing a desired effect. Other favorable outcomes of synergistic agents include reduction in toxicity and minimizing or delaying drug resistance. Dose-response assessment and drug-drug interaction analysis play an important part in the drug discovery process, however analysis are often poorly done. This dissertation is an effort to notably improve dose-response assessment and drug-drug interaction analysis. The most commonly used method in published analysis is the Median-Effect Principle/Combination Index method (Chou and Talalay, 1984). The Median-Effect Principle/Combination Index method leads to inefficiency by ignoring important sources of variation inherent in dose-response data and discarding data points that do not fit the Median-Effect Principle. Previous work has shown that the conventional method yields a high rate of false positives (Boik, Boik, Newman, 2008; Hennessey, Rosner, Bast, Chen, 2010) and, in some cases, low power to detect synergy. There is a great need for improving the current methodology. We developed a Bayesian framework for dose-response modeling and drug-drug interaction analysis. First, we developed a hierarchical meta-regression dose-response model that accounts for various sources of variation and uncertainty and allows one to incorporate knowledge from prior studies into the current analysis, thus offering a more efficient and reliable inference. Second, in the case that parametric dose-response models do not fit the data, we developed a practical and flexible nonparametric regression method for meta-analysis of independently repeated dose-response experiments. Third, and lastly, we developed a method, based on Loewe additivity that allows one to quantitatively assess interaction between two agents combined at a fixed dose ratio. The proposed method makes a comprehensive and honest account of uncertainty within drug interaction assessment. Extensive simulation studies show that the novel methodology improves the screening process of effective/synergistic agents and reduces the incidence of type I error. We consider an ovarian cancer cell line study that investigates the combined effect of DNA methylation inhibitors and histone deacetylation inhibitors in human ovarian cancer cell lines. The hypothesis is that the combination of DNA methylation inhibitors and histone deacetylation inhibitors will enhance antiproliferative activity in human ovarian cancer cell lines compared to treatment with each inhibitor alone. By applying the proposed Bayesian methodology, in vitro synergy was declared for DNA methylation inhibitor, 5-AZA-2'-deoxycytidine combined with one histone deacetylation inhibitor, suberoylanilide hydroxamic acid or trichostatin A in the cell lines HEY and SKOV3. This suggests potential new epigenetic therapies in cell growth inhibition of ovarian cancer cells.

A cladistic analysis of apolipoprotein B gene variation and plasma lipid and apolipoprotein B levels, using familial data

Any functionally important mutation is embedded in an evolutionary matrix of other mutations. Cladistic analysis, based on this, is a method of investigating gene effects using a haplotype phylogeny to define a set of tests which localize causal mutations to branches of the phylogeny. Previous implementations of cladistic analysis have not addressed the issue of analyzing data from related individuals, though in human studies, family data are usually needed to obtain unambiguous haplotypes. In this study, a method of cladistic analysis is described in which haplotype effects are parameterized in a linear model which accounts for familial correlations. The method was used to study the effect of apolipoprotein (Apo) B gene variation on total-, LDL-, and HDL-cholesterol, triglyceride, and Apo B levels in 121 French families. Five polymorphisms defined Apo B haplotypes: the signal peptide Insertion/deletion, Bsp 1286I, XbaI, MspI, and EcoRI. Eleven haplotypes were found, and a haplotype phylogeny was constructed and used to define a set of tests of haplotype effects on lipid and apo B levels.^ This new method of cladistic analysis, the parametric method, found significant effects for single haplotypes for all variables. For HDL-cholesterol, 3 clusters of evolutionarily-related haplotypes affecting levels were found. Haplotype effects accounted for about 10% of the genetic variance of triglyceride and HDL-cholesterol levels. The results of the parametric method were compared to those of a method of cladistic analysis based on permutational testing. The permutational method detected fewer haplotype effects, even when modified to account for correlations within families. Simulation studies exploring these differences found evidence of systematic errors in the permutational method due to the process by which haplotype groups were selected for testing.^ The applicability of cladistic analysis to human data was shown. The parametric method is suggested as an improvement over the permutational method. This study has identified candidate haplotypes for sequence comparisons in order to locate the functional mutations in the Apo B gene which may influence plasma lipid levels. ^

Secondary data analysis of lead screening compliance in high-risk children

Introduction. Despite the ban of lead-containing gasoline and paint, childhood lead poisoning remains a public health issue. Furthermore, a Medicaid-eligible child is 8 times more likely to have an elevated blood lead level (EBLL) than a non-Medicaid child, which is the primary reason for the early detection lead screening mandate for ages 12 and 24 months among the Medicaid population. Based on field observations, there was evidence that suggested a screening compliance issue. Objective. The purpose of this study was to analyze blood lead screening compliance in previously lead poisoned Medicaid children and test for an association between timely lead screening and timely childhood immunizations. The mean months between follow-up tests were also examined for a significant difference between the non-compliant and compliant lead screened children. Methods. Access to the surveillance data of all childhood lead poisoned cases in Bexar County was granted by the San Antonio Metropolitan Health District. A database was constructed and analyzed using descriptive statistics, logistic regression methods and non-parametric tests. Lead screening at 12 months of age was analyzed separately from lead screening at 24 months. The small portion of the population who were also related were included in one analysis and removed from a second analysis to check for significance. Gender, ethnicity, age of home, and having a sibling with an EBLL were ruled out as confounders for the association tests but ethnicity and age of home were adjusted in the nonparametric tests. Results. There was a strong significant association between lead screening compliance at 12 months and childhood immunization compliance, with or without including related children (p<0.00). However, there was no significant association between the two variables at the age of 24 months. Furthermore, there was no significant difference between the median of the mean months of follow-up blood tests among the non-compliant and compliant lead screened population for at the 12 month screening group but there was a significant difference at the 24 month screening group (p<0.01). Discussion. Descriptive statistics showed that 61% and 56% of the previously lead poisoned Medicaid population did not receive their 12 and 24 month mandated lead screening on time, respectively. This suggests that their elevated blood lead level may have been diagnosed earlier in their childhood. Furthermore, a child who is compliant with their lead screening at 12 months of age is 2.36 times more likely to also receive their childhood immunizations on time compared to a child who was not compliant with their 12 month screening. Even though there was no statistical significant association found for the 24 month group, the public health significance of a screening compliance issue is no less important. The Texas Medicaid program needs to enforce lead screening compliance because it is evident that there has been no monitoring system in place. Further recommendations include a need for an increased focus on parental education and the importance of taking their children for wellness exams on time.^

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Slope estimation in a parametric measurement error model: A simulation study

In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^