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In this thesis, I am interested in estimating the difference between dependent proportions from a 2 × 2 contingency table when there are missing data. The Expectation-Maximization (EM) algorithm is used to obtain an estimate for the difference between correlated proportions. To obtain the standard error of this difference I employ a resampling technique known as bootstrapping. The performance of the bootstrap standard error is evaluated for different sample sizes and different fractions of missing information. Finally, a 100(1-α)% bootstrap confidence interval is proposed and its coverage is evaluated through simulation.

Missing data are ubiquitous in many domains such as healthcare. Depending on how they are missing, the (conditional) independence relations in the observed data may be different from those for the complete data generated by the underlying causal process (which are not fully observable) and, as a consequence, simply applying existing causal discovery methods to the observed data may give wrong conclusions. It is then essential to extend existing causal discovery approaches to find true underlying causal structure from such incomplete data. In this thesis, we aim at solving this problem for data that are missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). With missingness mechanisms represented by the Missingness Graph, we present conditions under which addition corrected to derive conditional independence/dependence relations in the complete data. Combined with the correction method that gives closed-form, consistent tests of conditional independence, the proposed causal discovery method, as an extension of the PC algorithm, is shown to give asymptotically correct results. Experiment results illustrate that with further reasonable assumptions, the proposed algorithm can correct the conditional independence for values MCAR, MAR and rather general cases of values MNAR. / Saknade data är allestädes närvarande på många områden, t.ex. sjukvård. Beroende på hur de saknas kan de (villkorliga) oberoende förhållandena i de observerade uppgifterna skilja sig från de för de fullständiga data som genereras av den underliggande orsaksprocessen (som inte är fullt observerbara) och som en följd av att helt enkelt tillämpa befintlig kausal upptäckt metoder för de observerade data kan ge felaktiga slutsatser. Det är då viktigt att förlänga befintliga metoder för kausala upptäckter för att hitta en sann underliggande kausalstruktur från sådana ofullständiga data. I denna avhandling strävar vi efter att lösa detta problem för data som saknas helt slumpmässigt (MCAR), saknas slumpmässigt (MAR) eller saknas inte slumpmässigt (MNAR). Med missmekanismer representerade av Missfallsgrafen presenterar vi förhållanden under vilka tillägg korrigerade för att härleda villkorliga oberoende/beroendeförhållanden i de fullständiga uppgifterna.Kombinerad med korrigeringsmetoden som ger sluten form, konsekventa test av villkorligt oberoende, visas att den föreslagnaorsaks-sökningsmetoden, som en förlängning av PC-algoritmen, ger asymptotiskt korrekta resultat. Experimentresultat illustrera att med ytterligare rimliga antaganden kan den föreslagna algoritmen korrigera det villkorliga oberoende för värdena MCAR, MAR och ganska generella fall av värden MNAR.

The recent call to reconstruct a detailed picture of the tree of life for all organisms has forever changed the field of molecular phylogenetics. Sequencing technology has improved to the point that scientics can now routinely sequence complete plastid/mitochondrial genomes and thus, vast amounts of data can be used to reconstruct phylogenies. These data are accumulating in DNA sequence repositories, such as GenBank, where everyone can benefit from the vast growth of information. The trend of generating genomic-region rich datasets has far outpaced the expasion of datasets by sampling a broader array of taxa. We show here that expanding a dataset both by increasing genomic regions and species sampled using GenBank data, despite the inherent missing DNA that comes with GenBank data, can provide a robust phylogeny for the plant order Caryophyllales (angiosperms). We also investigate the utility of trnK intron in phylogeny reconstruction at relativley deep evolutionary history (the caryophyllid order) by comparing it with rapidly evolving matK. We show that trnK intron is comparable to matK in terms of the proportion of variable sites, parsimony informative sites, the distribution of those sites among rate classes, and phylogenetic informativness across the history of the order. This is especailly useful since trnK intron is often sequenced concurrently with matK which saves on time and resources by increasing the phylogenetic utility of a single genomic region (rapidly evolving matK/trnK). Finally, we show that the inclusion of RNA edited sites in datasets for phylogeny reconstruction did not appear to impact resolution or support in the Gnetales indicating that edited sites in such low proportions do not need to be a consideration when building datasets. We also propose an alternate start codon for matK in Ephedra based on the presense of a 38 base pair indel in several species that otherwise result in pre-mature stop codons, and present 20 RNA edited sites in two Zamiaceae and three Pinaceae species. / Ph. D.

Missing data continues to be one of the main problems in data analysis as it reduces sample representativeness and consequently, causes biased estimates. Multiple imputation methods have been established as an effective method of handling missing data. In this study, we examined multiple imputation methods for quantitative variables on twelve data sets with varied sizes and variability that were pseudo generated from an original data. The multiple imputation methods examined are the predictive mean matching, Bayesian linear regression and linear regression, non-Bayesian in the MICE (Multiple Imputation Chain Equation) package in the statistical software, R. The parameter estimates generated from the linear regression on the imputed data were compared to the closest parameter estimates from the complete data across all twelve data sets.

The Conover Solution is a nonparametric method used to analyze relative growth in students' achievement on state tests administered on two or more occasions. However, there has been very little research assessing the robustness of this method in the presence of missing data. Using vertically scaled and non-vertically scaled data from the math portion of a statewide assessment for grades 4-7, I compare results from listwise deletion and multiple imputation across the residual gain score model, the simple gain score model, and the HLM-NPAR model. In these approaches, I study differences by gender and race in two-level models and then extend the modeling to a three-level model that incorporates school-level random effects. The results are similar across missing data and the modeling approaches for both gender and race. These results hold across multiple cohorts. In addition, there are school-level effects. The results do not vary across missing data or modeling approaches. I discuss implications for these findings and guidelines for practitioners.

A globular cluster is a collection of stars that orbits the center of its galaxy as a single satellite. Understanding what influences the formations of these clusters provides understanding of galaxy structure and insight into their early development. We continue the work of Harris et al. (2013), who identified a set of predictors that accurately determined the number of clusters Ngc, through analysis of an incomplete dataset. We aimed to improve upon these results through imputation of the missing data. A small amount of precision was gained for the slope of Ngc~ R_e*sigma_ e, while the intercept suffered a small loss of precision. Estimates of intrinsic variance also increased with the addition of imputed data. We also found galaxy morphological type to be a significant predictor of Ngc in a model with R_e*sigma_ e. Although it increased precision of the slope and reduced the residual variance, its overall contribution was negligible. / Thesis / Master of Science (MSc)

PhD Thesis / Older adults are a rapidly growing segment of the population with unique healthcare needs. As people age, they are more likely to become susceptible to diseases and develop complex health conditions that require tailored strategies to address. These vulnerabilities could also impact different stages of the research process to generate evidence that promote healthy aging and better quality of life for this population. Attrition and missing data are some of the common methodological challenges in research with older adults. These issues could affect the quality of evidence generated if not properly addressed. There is also limited evidence to guide the development of interventions in specific populations of older adults with frailty, who have reduced function and are at higher risk for poor health outcomes. Across six chapters, this thesis addresses these methodological and interventional gaps in research with older adults. Using different research methodologies including a systematic literature survey, secondary data analysis of a cohort study, and two randomized feasibility trials, this thesis provides some important considerations for practice. In particular, we (i) evaluated the magnitude, pattern, and factors associated with attrition in the Global Longitudinal Study of Osteoporosis in Women (GLOW) Hamilton cohort of older adults; (ii) performed a systematic survey of the reporting and handling of missing data in longitudinal observational studies of older adults; (iii) conducted a randomized controlled feasibility trial of the Geras virtual frailty rehabilitation program to build resilience in vulnerable older adults during the COVID-19 pandemic; and (iv) evaluated the feasibility of the FitJoints randomized controlled trial of a multimodal intervention in frail older patients with osteoarthritis awaiting hip and knee replacement. / Thesis / Doctor of Philosophy (PhD) / The number of people who are old is increasing by the day and so is the need to understand how to ensure they are aging well. Old age makes people more prone to diseases. The risks of becoming ill could make the efforts to generate knowledge that can help them thrive challenging. They could drop out of a study making it difficult to collect enough information for data analysis. For some older adults who are frail and have higher risk for diseases, there is little known about how to design programs that will enable them stay active and healthier during the COVID-19 pandemic or before they have hip or knee replacement surgery. This thesis contributes to the knowledge on how to improve the quality of research involving older adults and bridge the gap in the knowledge about how to support those who are frail among them.

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