Cost and power analysis of linkage disequilibrium methods for locating genes influencing quantitative traits in humans

Linkage disequilibrium methods can be used to find genes influencing quantitative trait variation in humans. Linkage disequilibrium methods can require smaller sample sizes than linkage equilibrium methods, such as the variance component approach to find loci with a specific effect size. The increase in power is at the expense of requiring more markers to be typed to scan the entire genome. This thesis compares different linkage disequilibrium methods to determine which factors influence the power to detect disequilibrium. The costs of disequilibrium and equilibrium tests were compared to determine whether the savings in phenotyping costs when using disequilibrium methods outweigh the additional genotyping costs.^ Nine linkage disequilibrium tests were examined by simulation. Five tests involve selecting isolated unrelated individuals while four involved the selection of parent child trios (TDT). All nine tests were found to be able to identify disequilibrium with the correct significance level in Hardy-Weinberg populations. Increasing linked genetic variance and trait allele frequency were found to increase the power to detect disequilibrium, while increasing the number of generations and distance between marker and trait loci decreased the power to detect disequilibrium. Discordant sampling was used for several of the tests. It was found that the more stringent the sampling, the greater the power to detect disequilibrium in a sample of given size. The power to detect disequilibrium was not affected by the presence of polygenic effects.^ When the trait locus had more than two trait alleles, the power of the tests maximized to less than one. For the simulation methods used here, when there were more than two-trait alleles there was a probability equal to 1-heterozygosity of the marker locus that both trait alleles were in disequilibrium with the same marker allele, resulting in the marker being uninformative for disequilibrium.^ The five tests using isolated unrelated individuals were found to have excess error rates when there was disequilibrium due to population admixture. Increased error rates also resulted from increased unlinked major gene effects, discordant trait allele frequency, and increased disequilibrium. Polygenic effects did not affect the error rates. The TDT, Transmission Disequilibrium Test, based tests were not liable to any increase in error rates.^ For all sample ascertainment costs, for recent mutations ($<$100 generations) linkage disequilibrium tests were less expensive than the variance component test to carry out. Candidate gene scans saved even more money. The use of recently admixed populations also decreased the cost of performing a linkage disequilibrium test. ^

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. ^

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

Evaluation of risk factors for long term changes in refractive error among adult patients at a Dallas Texas private setting A retrospective chart-review study

Background. Over 39.9% of the adult population forty or older in the United States has refractive error, little is known about the etiology of this condition and associated risk factors and their entailed mechanism due to the paucity of data regarding the changes of refractive error for the adult population over time.^ Aim. To evaluate risk factors over a long term, 5-year period, in refractive error changes among persons 43 or older by testing the hypothesis that age, gender, systemic diseases, nuclear sclerosis and baseline refractive errors are all significantly associated with refractive errors changes in patients at a Dallas, Texas private optometric office.^ Methods. A retrospective chart review of subjective refraction, eye health, and self-report health history was done on patients at a private optometric office who were 43 or older in 2000 who had eye examinations both in 2000 and 2005. Aphakic and pseudophakic eyes were excluded as well as eyes with best corrected Snellen visual acuity of 20/40 and worse. After exclusions, refraction was obtained on 114 right eyes and 114 left eyes. Spherical equivalent (sum of sphere + ½ cylinder) was used as the measure of refractive error.^ Results. Similar changes in refractive error were observed for the two eyes. The 5-year change in spherical power was in a hyperopic direction for younger age groups and in a myopic direction for older subjects, P<0.0001. The gender-adjusted mean change in refractive error in right eyes of persons aged 43 to 54, 55 to 64, 65 to 74, and 75 or older at baseline was +0.43D, +0.46 D, -0.09 D, and -0.23D, respectively. Refractive change was strongly related to baseline nuclear cataract severity; grades 4 to 5 were associated with a myopic shift (-0.38 D, P< 0.0001). The mean age-adjusted change in refraction was +0.27 D for hyperopic eyes, +0.56 D for emmetropic eyes, and +0.26 D for myopic eyes.^ Conclusions. This report has documented refractive error changes in an older population and confirmed reported trends of a hyperopic shift before age 65 and a myopic shift thereafter associated with the development of nuclear cataract.^