Population genetics of VNTR loci and their applications in evolutionary studies

Variable number of tandem repeats (VNTR) are genetic loci at which short sequence motifs are found repeated different numbers of times among chromosomes. To explore the potential utility of VNTR loci in evolutionary studies, I have conducted a series of studies to address the following questions: (1) What are the population genetic properties of these loci? (2) What are the mutational mechanisms of repeat number change at these loci? (3) Can DNA profiles be used to measure the relatedness between a pair of individuals? (4) Can DNA fingerprint be used to measure the relatedness between populations in evolutionary studies? (5) Can microsatellite and short tandem repeat (STR) loci which mutate stepwisely be used in evolutionary analyses?^ A large number of VNTR loci typed in many populations were studied by means of statistical methods developed recently. The results of this work indicate that there is no significant departure from Hardy-Weinberg expectation (HWE) at VNTR loci in most of the human populations examined, and the departure from HWE in some VNTR loci are not solely caused by the presence of population sub-structure.^ A statistical procedure is developed to investigate the mutational mechanisms of VNTR loci by studying the allele frequency distributions of these loci. Comparisons of frequency distribution data on several hundreds VNTR loci with the predictions of two mutation models demonstrated that there are differences among VNTR loci grouped by repeat unit sizes.^ By extending the ITO method, I derived the distribution of the number of shared bands between individuals with any kinship relationship. A maximum likelihood estimation procedure is proposed to estimate the relatedness between individuals from the observed number of shared bands between them.^ It was believed that classical measures of genetic distance are not applicable to analysis of DNA fingerprints which reveal many minisatellite loci simultaneously in the genome, because the information regarding underlying alleles and loci is not available. I proposed a new measure of genetic distance based on band sharing between individuals that is applicable to DNA fingerprint data.^ To address the concern that microsatellite and STR loci may not be useful for evolutionary studies because of the convergent nature of their mutation mechanisms, by a theoretical study as well as by computer simulation, I conclude that the possible bias caused by the convergent mutations can be corrected, and a novel measure of genetic distance that makes the correction is suggested. In summary, I conclude that hypervariable VNTR loci are useful in evolutionary studies of closely related populations or species, especially in the study of human evolution and the history of geographic dispersal of Homo sapiens. (Abstract shortened by UMI.) ^

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

Simulation study of joint transition and Weibull survival model with shared parameters

This study investigates a theoretical model where a longitudinal process, that is a stationary Markov-Chain, and a Weibull survival process share a bivariate random effect. Furthermore, a Quality-of-Life adjusted survival is calculated as the weighted sum of survival time. Theoretical values of population mean adjusted survival of the described model are computed numerically. The parameters of the bivariate random effect do significantly affect theoretical values of population mean. Maximum-Likelihood and Bayesian methods are applied on simulated data to estimate the model parameters. Based on the parameter estimates, predicated population mean adjusted survival can then be calculated numerically and compared with the theoretical values. Bayesian method and Maximum-Likelihood method provide parameter estimations and population mean prediction with comparable accuracy; however Bayesian method suffers from poor convergence due to autocorrelation and inter-variable correlation. ^

An ordinal logistic regression model with misclassification of the outcome variable and categorical covariate

Ordinal outcomes are frequently employed in diagnosis and clinical trials. Clinical trials of Alzheimer's disease (AD) treatments are a case in point using the status of mild, moderate or severe disease as outcome measures. As in many other outcome oriented studies, the disease status may be misclassified. This study estimates the extent of misclassification in an ordinal outcome such as disease status. Also, this study estimates the extent of misclassification of a predictor variable such as genotype status. An ordinal logistic regression model is commonly used to model the relationship between disease status, the effect of treatment, and other predictive factors. A simulation study was done. First, data based on a set of hypothetical parameters and hypothetical rates of misclassification was created. Next, the maximum likelihood method was employed to generate likelihood equations accounting for misclassification. The Nelder-Mead Simplex method was used to solve for the misclassification and model parameters. Finally, this method was applied to an AD dataset to detect the amount of misclassification present. The estimates of the ordinal regression model parameters were close to the hypothetical parameters. β1 was hypothesized at 0.50 and the mean estimate was 0.488, β2 was hypothesized at 0.04 and the mean of the estimates was 0.04. Although the estimates for the rates of misclassification of X1 were not as close as β1 and β2, they validate this method. X 1 0-1 misclassification was hypothesized as 2.98% and the mean of the simulated estimates was 1.54% and, in the best case, the misclassification of k from high to medium was hypothesized at 4.87% and had a sample mean of 3.62%. In the AD dataset, the estimate for the odds ratio of X 1 of having both copies of the APOE 4 allele changed from an estimate of 1.377 to an estimate 1.418, demonstrating that the estimates of the odds ratio changed when the analysis includes adjustment for misclassification. ^

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

A Bayesian analysis for spatial processes with application to mapping

In geographical epidemiology, maps of disease rates and disease risk provide a spatial perspective for researching disease etiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. Empirical Bayesian (EB) methods have been used to spatially smooth the estimates by permitting an area estimate to "borrow strength" from its neighbors. Such EB methods include the use of a Gamma model, of a James-Stein estimator, and of a conditional autoregressive (CAR) process. A fully Bayesian analysis of the CAR process is proposed. One advantage of this fully Bayesian analysis is that it can be implemented simply by using repeated sampling from the posterior densities. Use of a Markov chain Monte Carlo technique such as Gibbs sampler was not necessary. Direct resampling from the posterior densities provides exact small sample inferences instead of the approximate asymptotic analyses of maximum likelihood methods (Clayton & Kaldor, 1987). Further, the proposed CAR model provides for covariates to be included in the model. A simulation demonstrates the effect of sample size on the fully Bayesian analysis of the CAR process. The methods are applied to lip cancer data from Scotland, and the results are compared. ^

Logistic regression with Markov chains as covariates

The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^

Age -period -cohort analysis: An extension of Cox's lifetable regression with time -dependent covariates

It is well known that an identification problem exists in the analysis of age-period-cohort data because of the relationship among the three factors (date of birth + age at death = date of death). There are numerous suggestions about how to analyze the data. No one solution has been satisfactory. The purpose of this study is to provide another analytic method by extending the Cox's lifetable regression model with time-dependent covariates. The new approach contains the following features: (1) It is based on the conditional maximum likelihood procedure using a proportional hazard function described by Cox (1972), treating the age factor as the underlying hazard to estimate the parameters for the cohort and period factors. (2) The model is flexible so that both the cohort and period factors can be treated as dummy or continuous variables, and the parameter estimations can be obtained for numerous combinations of variables as in a regression analysis. (3) The model is applicable even when the time period is unequally spaced.^ Two specific models are considered to illustrate the new approach and applied to the U.S. prostate cancer data. We find that there are significant differences between all cohorts and there is a significant period effect for both whites and nonwhites. The underlying hazard increases exponentially with age indicating that old people have much higher risk than young people. A log transformation of relative risk shows that the prostate cancer risk declined in recent cohorts for both models. However, prostate cancer risk declined 5 cohorts (25 years) earlier for whites than for nonwhites under the period factor model (0 0 0 1 1 1 1). These latter results are similar to the previous study by Holford (1983).^ The new approach offers a general method to analyze the age-period-cohort data without using any arbitrary constraint in the model. ^

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^

Detection of nonrandom association of alleles from the distribution of the number of heterozygous loci in a sample.

The distribution of the number of heterozygous loci in two randomly chosen gametes or in a random diploid zygote provides information regarding the nonrandom association of alleles among different genetic loci. Two alternative statistics may be employed for detection of nonrandom association of genes of different loci when observations are made on these distributions: observed variance of the number of heterozygous loci (s2k) and a goodness-of-fit criterion (X2) to contrast the observed distribution with that expected under the hypothesis of random association of genes. It is shown, by simulation, that s2k is statistically more efficient than X2 to detect a given extent of nonrandom association. Asymptotic normality of s2k is justified, and X2 is shown to follow a chi-square (chi 2) distribution with partial loss of degrees of freedom arising because of estimation of parameters from the marginal gene frequency data. Whenever direct evaluations of linkage disequilibrium values are possible, tests based on maximum likelihood estimators of linkage disequilibria require a smaller sample size (number of zygotes or gametes) to detect a given level of nonrandom association in comparison with that required if such tests are conducted on the basis of s2k. Summarization of multilocus genotype (or haplotype) data, into the different number of heterozygous loci classes, thus, amounts to appreciable loss of information.

Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^