Extension of k-ratio methods to rank-based analyses

An extension of k-ratio multiple comparison methods to rank-based analyses is described. The new method is analogous to the Duncan-Godbold approximate k-ratio procedure for unequal sample sizes or correlated means. The close parallel of the new methods to the Duncan-Godbold approach is shown by demonstrating that they are based upon different parameterizations as starting points.^ A semi-parametric basis for the new methods is shown by starting from the Cox proportional hazards model, using Wald statistics. From there the log-rank and Gehan-Breslow-Wilcoxon methods may be seen as score statistic based methods.^ Simulations and analysis of a published data set are used to show the performance of the new methods. ^

A Bayesian approach to estimating the intraclass correlation coefficient

A Bayesian approach to estimating the intraclass correlation coefficient was used for this research project. The background of the intraclass correlation coefficient, a summary of its standard estimators, and a review of basic Bayesian terminology and methodology were presented. The conditional posterior density of the intraclass correlation coefficient was then derived and estimation procedures related to this derivation were shown in detail. Three examples of applications of the conditional posterior density to specific data sets were also included. Two sets of simulation experiments were performed to compare the mean and mode of the conditional posterior density of the intraclass correlation coefficient to more traditional estimators. Non-Bayesian methods of estimation used were: the methods of analysis of variance and maximum likelihood for balanced data; and the methods of MIVQUE (Minimum Variance Quadratic Unbiased Estimation) and maximum likelihood for unbalanced data. The overall conclusion of this research project was that Bayesian estimates of the intraclass correlation coefficient can be appropriate, useful and practical alternatives to traditional methods of estimation. ^

Multivariate methods for correlated effects sizes

Current statistical methods for estimation of parametric effect sizes from a series of experiments are generally restricted to univariate comparisons of standardized mean differences between two treatments. Multivariate methods are presented for the case in which effect size is a vector of standardized multivariate mean differences and the number of treatment groups is two or more. The proposed methods employ a vector of independent sample means for each response variable that leads to a covariance structure which depends only on correlations among the $p$ responses on each subject. Using weighted least squares theory and the assumption that the observations are from normally distributed populations, multivariate hypotheses analogous to common hypotheses used for testing effect sizes were formulated and tested for treatment effects which are correlated through a common control group, through multiple response variables observed on each subject, or both conditions.^ The asymptotic multivariate distribution for correlated effect sizes is obtained by extending univariate methods for estimating effect sizes which are correlated through common control groups. The joint distribution of vectors of effect sizes (from $p$ responses on each subject) from one treatment and one control group and from several treatment groups sharing a common control group are derived. Methods are given for estimation of linear combinations of effect sizes when certain homogeneity conditions are met, and for estimation of vectors of effect sizes and confidence intervals from $p$ responses on each subject. Computational illustrations are provided using data from studies of effects of electric field exposure on small laboratory animals. ^

A multiplicative model for standardizing vital rates without using external standards

Standardization is a common method for adjusting confounding factors when comparing two or more exposure category to assess excess risk. Arbitrary choice of standard population in standardization introduces selection bias due to healthy worker effect. Small sample in specific groups also poses problems in estimating relative risk and the statistical significance is problematic. As an alternative, statistical models were proposed to overcome such limitations and find adjusted rates. In this dissertation, a multiplicative model is considered to address the issues related to standardized index namely: Standardized Mortality Ratio (SMR) and Comparative Mortality Factor (CMF). The model provides an alternative to conventional standardized technique. Maximum likelihood estimates of parameters of the model are used to construct an index similar to the SMR for estimating relative risk of exposure groups under comparison. Parametric Bootstrap resampling method is used to evaluate the goodness of fit of the model, behavior of estimated parameters and variability in relative risk on generated sample. The model provides an alternative to both direct and indirect standardization method. ^

Bayesian inference and its application to meta-analysis of epidemiologic data

In Part One, the foundations of Bayesian inference are reviewed, and the technicalities of the Bayesian method are illustrated. Part Two applies the Bayesian meta-analysis program, the Confidence Profile Method (CPM), to clinical trial data and evaluates the merits of using Bayesian meta-analysis for overviews of clinical trials.^ The Bayesian method of meta-analysis produced similar results to the classical results because of the large sample size, along with the input of a non-preferential prior probability distribution. These results were anticipated through explanations in Part One of the mechanics of the Bayesian approach. ^

Mitral valve prolapse and its relationship with stroke

The purpose of this study was to elucidate the relationship between mitral valve prolapse and stroke. A population-based historical cohort investigation was conducted among residents of Olmsted County, Minnesota who had an initial echocardiographic diagnosis of mitral valve prolapse from 1975 through 1989. This cohort (N = 1085) was followed for stroke outcomes using the resources of an operational medical record linkage system. There was an overall two-fold increase in the incidence of stroke among individuals with mitral valve prolapse relative to a standard population (standardized morbidity ratio = 2.12, 95% confidence limits = 1.33-3.21). When the data were partitioned by duration of follow-up from the diagnosis of mitral valve prolapse, or by the calendar years at echocardiographic diagnosis, respectively, the association between mitral valve prolapse and stroke was not modified. Mitral valve prolapse subjects 85 years and older were at highest increased risk of developing strokes relative to the general population (standardized morbidity ratio = 5.47, 95% confidence limits = 2.20-11.24). Coronary heart disease, atrial fibrillation, diabetes mellitus and hypertension, were unlikely to have confounded the association between mitral valve prolapse and stroke.^ The cumulative risk of first stroke among individuals initially diagnosed with mitral valve prolapse age 15 to 64 years, given survival to 15.2 years of follow-up, was 4.0%. The cumulative risk of first stroke among individuals initially diagnosed with mitral valve prolapse age 65 to 74 years, given survival to 11.2 years of follow-up, was 13.2%. The cumulative risk of first stroke among individuals initially diagnosed with mitral valve prolapse age 75 years and older, given survival to 6.7 years of follow-up, was 30.6%.^ Among individuals with mitral valve prolapse, age, diabetes, and atrial fibrillation were associated with an increased risk of stroke. Atrial fibrillation was associated with a four-fold rate of stroke and diabetes associated with a seven-fold rate of stroke.^ Findings from this research support the hypothesis that mitral valvular heart prolapse is linked with a stroke sequela. ^

Design of mixed-longitudinal studies

Cross-sectional designs, longitudinal designs in which a single cohort is followed over time, and mixed-longitudinal designs in which several cohorts are followed for a shorter period are compared by their precision, potential for bias due to age, time and cohort effects, and feasibility. Mixed longitudinal studies have two advantages over longitudinal studies: isolation of time and age effects and shorter completion time. Though the advantages of mixed-longitudinal studies are clear, choosing an optimal design is difficult, especially given the number of possible combinations of the number of cohorts and number of overlapping intervals between cohorts. The purpose of this paper is to determine the optimal design for detecting differences in group growth rates.^ The type of mixed-longitudinal study appropriate for modeling both individual and group growth rates is called a "multiple-longitudinal" design. A multiple-longitudinal study typically requires uniform or simultaneous entry of subjects, who are each observed till the end of the study.^ While recommendations for designing pure-longitudinal studies have been made by Schlesselman (1973b), Lefant (1990) and Helms (1991), design recommendations for multiple-longitudinal studies have never been published. It is shown that by using power analyses to determine the minimum number of occasions per cohort and minimum number of overlapping occasions between cohorts, in conjunction with a cost model, an optimal multiple-longitudinal design can be determined. An example of systolic blood pressure values for cohorts of males and cohorts of females, ages 8 to 18 years, is given. ^

Assessing time-by-covariate interactions in Cox proportional hazards regression models using cubic spline functions

This dissertation develops and explores the methodology for the use of cubic spline functions in assessing time-by-covariate interactions in Cox proportional hazards regression models. These interactions indicate violations of the proportional hazards assumption of the Cox model. Use of cubic spline functions allows for the investigation of the shape of a possible covariate time-dependence without having to specify a particular functional form. Cubic spline functions yield both a graphical method and a formal test for the proportional hazards assumption as well as a test of the nonlinearity of the time-by-covariate interaction. Five existing methods for assessing violations of the proportional hazards assumption are reviewed and applied along with cubic splines to three well known two-sample datasets. An additional dataset with three covariates is used to explore the use of cubic spline functions in a more general setting. ^

The effect of life events on blood pressure and body mass index in children

In Conroe, Texas, 492 students ages 5 to 15 participated in a screening examination for cardiovascular risk factor study. Among 492 students, 141 elementary and junior high students participated in the present sub-study to investigate the effect of the number of recent life events on blood pressure and on body mass index. Using the elementary and junior high school Coddington scales, life events occurring in the past 12 months were measured for students ages 9 to 14 years, no significant differences in life events were observed by age and sex. The number of life events was not related to blood pressure but was positively correlated to body mass index in children and adolescents. ^

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. ^

Modeling the survival of T-cell lymphocytes using compound branching processes

Radiotherapy has been a method of choice in cancer treatment for a number of years. Mathematical modeling is an important tool in studying the survival behavior of any cell as well as its radiosensitivity. One particular cell under investigation is the normal T-cell, the radiosensitivity of which may be indicative to the patient's tolerance to radiation doses.^ The model derived is a compound branching process with a random initial population of T-cells that is assumed to have compound distribution. T-cells in any generation are assumed to double or die at random lengths of time. This population is assumed to undergo a random number of generations within a period of time. The model is then used to obtain an estimate for the survival probability of T-cells for the data under investigation. This estimate is derived iteratively by applying the likelihood principle. Further assessment of the validity of the model is performed by simulating a number of subjects under this model.^ This study shows that there is a great deal of variation in T-cells survival from one individual to another. These variations can be observed under normal conditions as well as under radiotherapy. The findings are in agreement with a recent study and show that genetic diversity plays a role in determining the survival of T-cells. ^

Prospective run theory for multinomial outcomes

The focus of this study was to generalize the theory of runs to multinomial outcomes using the generating function approach. Detailed discussion is provided for determining the probability distributions for all runs of length i in a sequence of n trials for the binomial and trinomial cases. The generalization to multinomial case is also presented. Application to data for patients from a long term disability care facility is presented to illustrate the use of Run Theory in determining the probability of a dominant state of treatment associated with a patient during his/her hospitalization. ^

Maximal exercise hemodynamics and risk of mortality in apparently healthy men and women

The use of exercise electrocardiography (ECG) to detect latent coronary heart disease (CHD) is discouraged in apparently healthy populations because of low sensitivity. These recommendations however, are based on the efficacy of evaluation of ischemia (ST segment changes) with little regard for other measures of cardiac function that are available during exertion. The purpose of this investigation was to determine the association of maximal exercise hemodynamic responses with risk of mortality due to all-causes, cardiovascular disease (CVD), and coronary heart disease (CHD) in apparently healthy individuals. Study participants were 20,387 men (mean age = 42.2 years) and 6,234 women (mean age = 41.9 years) patients of a preventive medicine center in Dallas, TX examined between 1971 and 1989. During an average of 8.1 years of follow-up, there were 348 deaths in men and 66 deaths in women. In men, age-adjusted all-cause death rates (per 10,000 person years) across quartiles of maximal systolic blood pressure (SBP) (low to high) were: 18.2, 16.2, 23.8, and 24.6 (p for trend $<$0.001). Corresponding rates for maximal heart rate were: 28.9, 15.9, 18.4, and 15.1 (p trend $<$0.001). After adjustment for confounding variables including age, resting systolic pressure, serum cholesterol and glucose, body mass index, smoking status, physical fitness and family history of CVD, risks (and 95% confidence interval (CI)) of all-cause mortality for quartiles of maximal SBP, relative to the lowest quartile, were: 0.96 (0.70-1.33), 1.36 (1.01-1.85), and 1.37 (0.98-1.92) for quartiles 2-4 respectively. Similar risks for maximal heart rate were: 0.61 (0.44-0.85), 0.69 (0.51-0.93), and 0.60 (0.41-0.87). No associations were noted between maximal exercise rate-pressure product mortality. Similar results were seen for risk of CVD and CHD death. In women, similar trends in age-adjusted all-cause and CVD death rates across maximal SBP and heart rate categories were observed. Sensitivity of the exercise test in predicting mortality was enhanced when ECG results were evaluated together with maximal exercise SBP or heart rate with a concomitant decrease in specificity. Positive predictive values were not improved. The efficacy of the exercise test in predicting mortality in apparently healthy men and women was not enhanced by using maximal exercise hemodynamic responses. These results suggest that an exaggerated systolic blood pressure or an attenuated heart rate response to maximal exercise are risk factors for mortality in apparently healthy individuals. ^

The use of the computerized and revised vital record in conducting etiologic studies on neural tube defects

The purpose of this study was to evaluate the adequacy of computerized vital records in Texas for conducting etiologic studies on neural tube defects (NTDs), using the revised and expanded National Centers for Health Statistics vital record forms introduced in Texas in 1989.^ Cases of NTDs (anencephaly and spina bifida) among Harris County (Houston) residents were identified from the computerized birth and death records for 1989-1991. The validity of the system was then measured against cases ascertained independently through medical records and death certificates. The computerized system performed poorly in its identification of NTDs, particularly for anencephaly, where the false positive rate was 80% with little or no improvement over the 3-year period. For both NTDs the sensitivity and predictive value positive of the tapes were somewhat higher for Hispanic than non-Hispanic mothers.^ Case control studies were conducted utilizing the tape set and the independently verified data set, using controls selected from the live birth tapes. Findings varied widely between the data sets. For example, the anencephaly odds ratio for Hispanic mothers (vs. non-Hispanic) was 1.91 (CI = 1.38-2.65) for the tape file, but 3.18 (CI = 1.81-5.58) for verified records. The odds ratio for diabetes was elevated for the tape set (OR = 3.33, CI = 1.67-6.66) but not for verified cases (OR = 1.09, CI = 0.24-4.96), among whom few mothers were diabetic. It was concluded that computerized tapes should not be solely relied on for NTD studies.^ Using the verified cases, Hispanic mother was associated with spina bifida, and Hispanic mother, teen mother, and previous pregnancy terminations were associated with anencephaly. Mother's birthplace, education, parity, and diabetes were not significant for either NTD.^ Stratified analyses revealed several notable examples of statistical interaction. For anencephaly, strong interaction was observed between Hispanic origin and trimester of first prenatal care.^ The prevalence was 3.8 per 10,000 live births for anencephaly and 2.0 for spina bifida (5.8 per 10,000 births for the combined categories). ^

Genetic epidemiologic methods in risk determination in Li-Fraumeni syndrome

Li-Fraumeni syndrome (LFS) is characterized by a variety of neoplasms occurring at a young age with an apparent autosomal dominant transmission. Individuals in pedigrees with LFS have high incidence of second malignancies. Recently LFS has been found to be associated with germline mutations of a tumor-suppressor gene, p53. Because LFS is rare and indeed not a clear-cut disease, it is not known whether all cases of LFS are attributable to p53 germline mutations and how p53 plays in cancer occurrence in such cancer syndrome families. In the present study, DNAs from constitutive cells of two-hundred and thirty-three family members from ten extended pedigrees were screened for p53 mutations. Six out of the ten LFS families had germline mutations at the p53 locus, including point and deletion mutations. In these six families, 55 out of 146 members were carriers of p53 mutations. Except one, all mutations occurred in exons 5 to 8 (i.e., the "hot spot" region) of the p53 gene. The age-specific penetrance of cancer was estimated after the genotype for each family member at risk was determined. The penetrance was 0.15, 0.29, 0.35, 0.77, and 0.91 by 20, 30, 40, 50 and 60 year-old, respectively, in male carriers; 0.19, 0.44, 0.76, and 0.90 by 20, 30, 40, and 50 year-old, respectively, in female carriers. These results indicated that one cannot escape from tumorigenesis if one inherits a p53 mutant allele; at least ninety percent of p53 carriers will develop cancer by the age of 60. To evaluate the possible bias due to the unexamined blood-relatives in LFS families, I performed a simulation analysis in which a p53 genotype was assigned to each unexamined person based on his cancer status and liability to cancer. The results showed that the penetrance estimates were not biased by the unexamined relatives. I also determined the sex, site, and age-specific penetrance of breast cancer in female carriers and lung cancer in male carriers. The penetrance of breast cancer in female carriers was 0.81 by age 45; the penetrance of lung cancer in male carriers was 0.78 by age 60, indicating that p53 play a key role for tumorigenesis in common cancers. ^