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. ^

Identfying predictors of St. Louis encephalitis activity in Houston Texas

Generalized linear Poisson and logistic regression models were utilized to examine the relationship between temperature and precipitation and cases of Saint Louis encephalitis virus spread in the Houston metropolitan area. The models were investigated with and without repeated measures, with a first order autoregressive (AR1) correlation structure used for the repeated measures model. The two types of Poisson regression models, with and without correlation structure, showed that a unit increase in temperature measured in degrees Fahrenheit increases the occurrence of the virus 1.7 times and a unit increase in precipitation measured in inches increases the occurrence of the virus 1.5 times. Logistic regression did not show these covariates to be significant as predictors for encephalitis activity in Houston for either correlation structure. This discrepancy for the logistic model could be attributed to the small data set.^ Keywords: Saint Louis Encephalitis; Generalized Linear Model; Poisson; Logistic; First Order Autoregressive; Temperature; Precipitation. ^

Regression with autocorrelated data: A study of time trend of global infant mortality rate

The infant mortality rate (IMR) is considered to be one of the most important indices of a country's well-being. Countries around the world and other health organizations like the World Health Organization are dedicating their resources, knowledge and energy to reduce the infant mortality rates. The well-known Millennium Development Goal 4 (MDG 4), whose aim is to archive a two thirds reduction of the under-five mortality rate between 1990 and 2015, is an example of the commitment. ^ In this study our goal is to model the trends of IMR between the 1950s to 2010s for selected countries. We would like to know how the IMR is changing overtime and how it differs across countries. ^ IMR data collected over time forms a time series. The repeated observations of IMR time series are not statistically independent. So in modeling the trend of IMR, it is necessary to account for these correlations. We proposed to use the generalized least squares method in general linear models setting to deal with the variance-covariance structure in our model. In order to estimate the variance-covariance matrix, we referred to the time-series models, especially the autoregressive and moving average models. Furthermore, we will compared results from general linear model with correlation structure to that from ordinary least squares method without taking into account the correlation structure to check how significantly the estimates change.^

DEFINITION OF THE LANDSCAPE OF CHROMATIN STRUCTURE AT THE FRATAXIN GENE IN FRIEDREICH’S ATAXIA

Friedreich’s ataxia (FRDA) is caused by the transcriptional silencing of the frataxin (FXN) gene. FRDA patients have expansion of GAA repeats in intron 1 of the FXN gene in both alleles. A number of studies demonstrated that specific histone deacetylase inhibitors (HDACi) affect either histone modifications at the FXN gene or FXN expression in FRDA cells, indicating that the hyperexpanded GAA repeat may facilitate heterochromatin formation. However, the correlation between chromatin structure and transcription at the FXN gene is currently limited due to a lack of more detailed analysis. Therefore, I analyzed the effects of the hyperexpanded GAA repeats on transcription status and chromatin structure using lymphoid cell lines derived from FRDA patients. Using chromatin immunoprecipitation and quantitative PCR, I observed significant changes in the landscape of histone modifications in the vicinity of the GAA tract in FRDA cells relative to control cells. Similar epigenetic changes were observed in GFP reporter construct containing 560 GAA repeats. Further, I detected similar levels of FXN pre-mRNA at a region upstream of hyperexpanded GAA repeats in FRDA and control cells, indicating similar efficiency of transcription initiation in FRDA cells. I also showed that histone modifications associated with hyperexpanded GAA repeats are independent of transcription progression using the GFP reporter system. My data strongly support evidence that FXN deficiency in FRDA patients is consequence of defective transition from initiation to elongation of FXN transcription due to heterochromatin-like structures formed in the proximity of the hyperexpanded GAAs.

Structure-function relation in retinoid regulated gene expression

Retinoids are known to inhibit proliferation of and induce terminal differentiation of many normal and transformed cells. It has been postulated that retinoids exert their effect by altering gene expression. HL-60 cells and macrophages both respond to retinoic acid action by the rapid induction of the enzyme tissue transglutaminase. The induction has been shown to be due to increased transcription of the transglutaminase gene. The first part of the dissertation studied the structure-function relationship of retinoid-regulated transglutaminase induction, differentiation and proliferation in HL-60 cells using retinoid analogs. The results indicated strict structural constraints and a strong structure-function correlation between transglutaminase induction and differentiation; those retinoids that induced transglutaminase also induced differentiation, those analogs that did not induce transglutaminase could not induce differentiation. The ability of the retinoids to induce transglutaminase in HL-60 cells was paralleled in macrophages. However, the antiproliferative effect of the retinoids displayed less stringent structural constraints than their differentiation- and transglutaminase-inducing properties. Specifically all the retinoids were able to inhibit proliferation to varying extents. It is concluded that the induction of transglutaminase and of differentiation by retinoids is mediated by receptors. While receptor mediation cannot be entirely ruled out, with the current data no definitive statement can be made about the antiproliferative activity of retinoids. Also, the concordance in the ability of the retinoids to induce transglutaminase and the ability to induce differentiation of HL-60 cells suggests that the former is an early response of the cells to retinoids and differentiation a later consequence on the same pathway. Using the induction of transglutaminase as an index of the direct, or primary, effect of retinoids on gene expression, the second part of the dissertation investigates, by 2D gel electrophoresis, the alteration in the rates of synthesis of other proteins in macrophages and HL-60 cells in response to short incubations with retinoic acid. Any changes in parallel with transglutaminase were taken to indicate proteins directly under the control of retinoic acid. It is concluded that retinoic acid regulates the expression of a circumscribed set of genes in a cell-specific manner. The results support the hypothesis that retinoids exert their multiple effects on myeloid cells, in part, by receptor-mediated alternations in gene expression. ^

Structure-function analysis of human Integrator subunit-4

Structure-function analysis of human Integrator subunit 4 Anupama Sataluri Advisor: Eric. J. Wagner, Ph.D. Uridine-rich small nuclear RNAs (U snRNA) are RNA Polymerase-II (RNAPII) transcripts that are ubiquitously expressed and are known to be essential for gene expression. snRNAs play a key role in mRNA splicing and in histone mRNA expression. Inaccurate snRNA biosynthesis can lead to diseases related to defective splicing and histone mRNA expression. Although the 3′ end formation mechanism and processing machinery of other RNAPII transcripts such as mRNA has been well studied, the mechanism of snRNA 3′ end processing has remained a mystery until the recent discovery of the machinery that mediates this process. In 2005, a complex of 14 subunits (the Integrator complex) associated with RNA Polymerase-II was discovered. The 14subunits were annotated Integrator 1-14 based on their size. The subunits of this complex together were found to facilitate 3′ end processing of snRNA. Identification of the Integrator complex propelled research in the direction of understanding the events of snRNA 3’end processing. Recent studies from our lab confirmed that Integrator subunit (IntS) 9 and 11 together perform the endonucleolytic cleavage of the nascent snRNA 3′ end to generate mature snRNA. However, the role of other members of the Integrator complex remains elusive. Current research in our lab is focused on deciphering the role of each subunit within the Integrator complex This work specifically focuses on elucidating the role of human Integrator subunit 4 (IntS4) and understanding how it facilitates the overall function of the complex. IntS4 has structural similarity with a protein called “Symplekin”, which is part of the mRNA 3’end processing machinery. Symplekin has been thoroughly researched in recent years and structure-function correlation studies in the context of mRNA 3’end processing have reported a scaffold function for Symplekin due to the presence of HEAT repeat motifs in its N-terminus. Based upon the structural similarity between IntS4 and Symplekin, we hypothesized that Integrator subunit 4 may be behaving as a Symplekin-like scaffold molecule that facilitates the interaction between other members of the Integrator Complex. To answer this question, the two important goals of this study were to: 1) identify the region of IntS4, which is important for snRNA 3′ end processing and 2) determine binding partners of IntS4 which promote its function as a scaffold. IntS4 structurally consists of a highly conserved N-terminus with 8 HEAT repeats, followed by a nonconserved C- terminus. A series of siRNA resistant N and C-terminus deletion constructs as well as specific point mutants within its N-terminal HEAT repeats were generated for human IntS4 and, utilizing a snRNA transcriptional readthrough GFP-reporter assay, we tested their ability to rescue misprocessing. This assay revealed a possible scaffold like property of IntS4. To probe IntS4 for interaction partners, we performed co-immunoprecipitation on nuclear extracts of IntS4 expressing stable cell lines and identified IntS3 and IntS5 among other Integrator subunits to be binding partners which facilitate the scaffold like function of hIntS4. These findings have established a critical role for IntS4 in snRNA 3′ end processing, identified that both its N and C termini are essential for its function, and mapped putative interaction domains with other Integrator subunits.