Bayesian analysis of case control polygenic etiology studies with missing data

Many genetic studies are based on analysing multiple DNA regions of cases and controls. Usually each is tested separately for association with disease. However, some diseases may require interacting polymorphisms at several regions, and most disease susceptibility is polygenic. In this paper, we develop new methods for determining combinations of polymorphisms that affect the risk of disease. For example, two different genes might produce normal proteins, but these proteins improperly function when they occur together. We consider a Bayesian approach to analyse studies where DNA data from cases and controls have been analysed for polymorphisms at multiple regions and a polygenic etiology is suspected. The method of Gibbs sampling is used to incorporate data from individuals who have not had every region analysed at the DNA sequence or amino acid level. The Gibbs sampling algorithm alternatively generates a sample from the posterior distribution of the sequence of combinations of polymorphisms in cases and controls and then uses this sample to impute the data that are missing. After convergence the algorithm is used to generate a sample from the posterior distribution for the probability of each combination in order to identify groups of polymorphisms that best discriminate cases from controls. We apply the methods to a genetic study of type I diabetes. The protein encoded by the TAP2 gene is important in T cell function, and thus may affect the development of autoimmune diseases such as insulin dependent diabetes mellitus (IDDM). We determine pairs of polymorphisms of genetic fragments in the coding regions of linked HLA genes that may impact the risk of IDDM.     

Maximum likelihood estimation in random effects cure rate models with nonignorable missing covariates

We introduce a method of parameter estimation for a random effects cure rate model. We also propose a methodology that allows us to account for nonignorable missing covariates in this class of models. The proposed method corrects for possible bias introduced by complete case analysis when missing data are not missing completely at random and is motivated by data from a pair of melanoma studies conducted by the Eastern Cooperative Oncology Group in which clustering by cohort or time of study entry was suspected. In addition, these models allow estimation of cure rates, which is desirable when we do not wish to assume that all subjects remain at risk of death or relapse from disease after sufficient follow-up. We develop an EM algorithm for the model and provide an efficient Gibbs sampling scheme for carrying out the E-step of the algorithm.     

Optimal estimator for the survival distribution and related quantities for treatment policies in two-stage randomization designs in clinical trials

Two-stage designs, where patients are initially randomized to an induction therapy and then depending upon their response and consent, are randomized to a maintenance therapy, are common in cancer and other clinical trials. The goal is to compare different combinations of primary and maintenance therapies to find the combination that is most beneficial. In practice, the analysis is usually conducted in two separate stages which does not directly address the major objective of finding the best combination. Recently Lunceford, Davidian, and Tsiatis (2002, Biometrics58, 48-57) introduced ad hoc estimators for the survival distribution and mean restricted survival time under different treatment policies. These estimators are consistent but not efficient, and do not include information from auxiliary covariates. In this article we derive estimators that are easy to compute and are more efficient than previous estimators. We also show how to improve efficiency further by taking into account additional information from auxiliary variables. Large sample properties of these estimators are derived and comparisons with other estimators are made using simulation. We apply our estimators to a leukemia clinical trial data set that motivated this study.     

A class of Bayesian shared gamma frailty models with multivariate failure time data

For multivariate failure time data, we propose a new class of shared gamma frailty models by imposing the Box-Cox transformation on the hazard function, and the product of the baseline hazard and the frailty. This novel class of models allows for a very broad range of shapes and relationships between the hazard and baseline hazard functions. It includes the well-known Cox gamma frailty model and a new additive gamma frailty model as two special cases. Due to the nonnegative hazard constraint, this shared gamma frailty model is computationally challenging in the Bayesian paradigm. The joint priors are constructed through a conditional-marginal specification, in which the conditional distribution is univariate, and it absorbs the nonlinear parameter constraints. The marginal part of the prior specification is free of constraints. The prior distributions allow us to easily compute the full conditionals needed for Gibbs sampling, while incorporating the constraints. This class of shared gamma frailty models is illustrated with a real dataset.     

Nonparametric estimation of age-at-onset distributions from censored kin-cohort data

We present a nonparametric estimator of genotype-specific age-at-onsetdistributions from kin-cohort data. Standard error calculationsare derived and the methodology is illustrated through an analysisof the influence of mutations of the Parkin gene on Parkinson'sdisease. Semiparametric efficiency considerations are brieflydiscussed.     

A Bayesian analysis of colonic crypt structure and coordinated response to carcinogen exposure incorporating missing crypts

This paper is concerned with modeling the architecture of colonic crypts and the implications of this modeling for understanding possible coordinated response of carcinogen-induced DNA damage between various regions of the colon. The methods we develop to address these two issues are applied to a particular important example in colon carcinogenesis. We cast the problem as an unusual and not previously studied hierarchical mixed-effects model characterized by completely missing covariates in units at a structurally base level, except for some randomly selected units. Information concerning the missing covariates is available through certain known ordering constraints and surrogate measures. Our methods use Bayesian machinery. We exploit the biological structure of this problem to generate the missing covariates simultaneously and efficiently at the base levels, as opposed to the naive practice of generating units at the base levels one-at-a-time with Metropolis-Hastings steps. We apply our methods to show that different regions of the colon have different architectures, and to estimate an important but non-standard function that measures the interrelationship of DNA damage mechanisms in different regions of the colon.     

A simulation study of three methods for estimating selective values and survival rates from recapture data

The methods ofManly (1973),Manly (1975) andManly (1977) for estimating survival rates and relative survival rates from recapture data have been compared by computer simulation. In the simulations batches of two types of animal were “released” at one point in “time” and recapture samples were taken at “daily” intervals from then on. The various methods of estimation were then used to estimate, the daily survival rates of type 1 and type 2 animals, and also the survival rate of the type 2 animals relative to the type 1 animals. Simulation experiments were designed to examine (a) the bias in estimates, (b) the relative precision of different methods of estimation, (c) the validity of confidence intervals for true parameter values, and (d) the effect on estimates of the failure of certain assumptions.     

Electrochemical potentials and pressures of biofluids from common experimental data

Many biosystems are complex mixtures of disparate biofluids. To study contact and transport phenomena in these mixtures, one has to apply much information on the biofluids which are components of the mixtures. A lot of the corresponding data can be extracted by means of experiments. However, it is not always easy to obtain experimental results on rather deep physical characteristics of biofluids, especially if the bioparticles are complicated systems and the fluid coexists in the mixture with a large number of other fluids. In these cases, the necessary data can, in principle, be extracted from those results which are easier to obtain experimentally. The present work proposes a method to evaluate the biofluid equilibrium pressure and electrochemical potential from common experimental values of the fluid concentration and absolute temperature as well as the fluid-particle mass, volume and spin. In so doing, the nonzero values of the particle volume are accounted for. The procedure is illustrated with a numerical example on the fluid of red blood cells (or erythrocytes) in human blood. The pressure values obtained are 49.1 and 38.8 micropascals for men and women respectively whereas the electrochemical-potential values are –2.124 and –2.130 electronvolts for men and women respectively.     

Electrolyte effects on the intervalence transition within discrete binuclear cyano-bridged complexes. An estimation of activation free energy from static, optical and electrochemical data

A study of the metal-to-metal charge-transfer (MMCT) transition within the binuclear cyano-bridged complexes cis-[L¹³Co^III(μ-NC)Fe^II(CN)₅]⁻ (L¹³ = 12-methyl-1,4,7,10-tetraazacyclotridecan-12-amine), trans-[L¹⁴Co^III(μ-NC)Fe^II(CN)₅]⁻ (L¹⁴ = 6-methyl-1,4,8,11-tetraazacyclotetradecan-6-amine) and trans-[L¹⁵Co^III(μ-NC)Fe^II(CN)₅]⁻ (L¹⁵ = 10-methyl-1,4,8,12-tetraazacyclopentadecan-10-amine) has been carried out in electrolyte solutions at varying concentrations. Using these data, as well as the reaction free energies obtained from electrochemical measurements, the reorganisation and activation free energies for the forward and reverse thermal electron-transfer processes have been estimated. The changes of these parameters with the electrolyte concentration, as well as those of the energy of the maximum MMCT band and the reaction free energy, are mainly due to ion-pairing effects.