Often repeated measures data are summarized into pre-post-treatment measurements. Various methods exist in the literature for estimating and testing treatment effect, including ANOVA, analysis of covariance (ANCOVA), and linear mixed modeling (LMM). Under the first two methods, outcomes can either be modeled as the post treatment measurement (ANOVA-POST or ANCOVA-POST), or a change score between pre and post measurements (ANOVA-CHANGE, ANCOVA-CHANGE). In LMM, the outcome is modeled as a vector of responses with or without Kenward-Rogers adjustment. We consider five methods common in the literature, and discuss them in terms of supporting simulations and theoretical derivations of variance. Consistent with existing literature, our results demonstrate that each method leads to unbiased treatment effect estimates, and based on precision of estimates, 95% coverage probability, and power, ANCOVA modeling of either change scores or post-treatment score as the outcome, prove to be the most effective. We further demonstrate each method in terms of a real data example to exemplify comparisons in real clinical context.
The reasons for the ethnic disparities in the prevalence of systemic lupus erythematosus (SLE) and the relative high frequency of SLE risk alleles in the population are not fully understood. Population genetic factors such as natural selection alter allele frequencies over generations and may help explain the persistence of such common risk variants in the population and the differential risk of SLE. In order to better understand the genetic basis of SLE that might be due to natural selection, a total of 74 genomic regions with compelling evidence for association with SLE were tested for evidence of recent positive selection in the HapMap and HGDP populations, using population differentiation, allele frequency, and haplotype-based tests. Consistent signs of positive selection across different studies and statistical methods were observed at several SLE-associated loci, including PTPN22, TNFSF4, TET3-DGUOK, TNIP1, UHRF1BP1, BLK, and ITGAM genes. This study is the first to evaluate and report that several SLE-associated regions show signs of positive natural selection. These results provide corroborating evidence in support of recent positive selection as one mechanism underlying the elevated population frequency of SLE risk loci and supports future research that integrates signals of natural selection to help identify functional SLE risk alleles.
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