The primary aim of this thesis is the elucidation of covariate effects on the dependence structure of random variables in bivariate or multivariate models. We develop a unified approach via a conditional copula model in which the copula is parametric and its parameter varies as the covariate. We propose a nonparametric procedure based on local likelihood to estimate the functional relationship between the copula parameter and the covariate, derive the asymptotic properties of the proposed estimator and outline the construction of pointwise confidence intervals. We also contribute a novel conditional copula selection method based on cross-validated prediction errors and a generalized likelihood ratio-type test to determine if the copula parameter varies significantly. We derive the asymptotic null distribution of the formal test. Using subsets of the Matched Multiple Birth and Framingham Heart Study datasets, we demonstrate the performance of these procedures via analyses of gestational age-specific twin birth weights and the impact of change in body mass index on the dependence between two consequent pulse pressures taken from the same subject.

The main objective of the thesis was to compare two methods of calculating adjusted attributable fractions and deaths as applied to smoking exposure and four health outcomes, lung cancer, ischaemic heart disease, chronic obstructive pulmonary disease, and cerebrovascular disease, for Canadians 30 years or older in the year 2005. An additional objective was to calculate variance estimates for the evaluation of precision. Such estimates have not been published for Canada to date. Attributable fractions were calculated using the fully adjusted method and the partial adjustment method. This method requires confounder strata specific (stratified) estimates of relative risk, along with accompanying estimates of variance. These estimates have not previously been published, and were derived from the Cancer Prevention Study II cohort. Estimates of the prevalence of smoking in Canada were obtained from the Canadian Community Health Survey 2005. Variance estimates were calculated using a Monte Carlo simulation. The fully adjusted method produced smaller attributable fractions in each of the eight disease-sex-specific categories than the partially adjusted method. This suggests an upwards bias when using the partial adjustment method in the attributable fraction for the relationship between cigarette smoking and cause-specific mortality in Canadian men and women. Summed across both sexes and the four smoking related causes of death, the number of deaths attributable to smoking was estimated to be 25,684 using the fully adjusted method and 28,466 using the partial adjustment method, an upward bias of over ten percent, or 2,782 deaths. It is desirable, theoretically, to use methods which can fully adjust for the effect of confounding and effect modification. Given the large datasets required and access to original data, using these methods may not be feasible for some who would wish to do so.

There is an increased interest in the need for a noninvasive and nonintrusive biometric identification and recognition system such as Automatic Gait Identification (AGI) due to the rise in crime rates in the US, physical assaults, and global terrorism in public places. AGI, a biometric system based on human gait, can recognize people from a distance and current literature shows that AGI has a 95.75% success rate in a closely controlled laboratory environment. Also, this success rate does not take into consideration the effect of covariate factors such as affective state (mood state); and literature shows that there is a lack of understanding of the effect of affective state on gait biometrics. The purpose of this study was to determine the percent success rate of AGI in an uncontrolled outdoor environment with affective state as the main variable. Affective state was measured using the Profile of Mood State (POMS) scales. Other covariate factors such as footwear or clothes were not considered in this study. The theoretical framework that grounded this study was Murray's theory of total walking cycle. This study included the gait signature of 24 participants from a population of 62 individuals, sampled based on simple random sampling. This quantitative research used empirical methods and a Fourier Series Analysis. Results showed that AGI has a 75% percent success rate in an uncontrolled outdoor environment with affective state. This study contributes to social change by enhancing an understanding of the effect of affective state on gait biometrics for positive identification during and after a crime such as bank robbery when the use of facial identification from a surveillance camera is either not clear or not possible. This may also be used in other countries to detect suicide bombers from a distance.

Yes / Gait is a unique non-invasive biometric form that can be utilized to effectively recognize persons, even when they prove to be uncooperative. Computer-aided gait recognition systems usually use image sequences without considering covariates like clothing and possessions of carrier bags whilst on the move. Similarly, in gait recognition, there may exist unknown covariate conditions that may affect the training and testing conditions for a given individual. Consequently, common techniques for gait recognition and measurement require a degree of intervention leading to the introduction of unknown covariate conditions, and hence this significantly limits the practical use of the present gait recognition and analysis systems. To overcome these key issues, we propose a method of gait analysis accounting for both known and unknown covariate conditions. For this purpose, we propose two methods, i.e., a Convolutional Neural Network (CNN) based gait recognition and a discriminative features-based classification method for unknown covariate conditions. The first method can handle known covariate conditions efficiently while the second method focuses on identifying and selecting unique covariate invariant features from the gallery and probe sequences. The feature set utilized here includes Local Binary Patterns (LBP), Histogram of Oriented Gradients (HOG), and Haralick texture features. Furthermore, we utilize the Fisher Linear Discriminant Analysis for dimensionality reduction and selecting the most discriminant features. Three classifiers, namely Random Forest, Support Vector Machine (SVM), and Multilayer Perceptron are used for gait recognition under strict unknown covariate conditions. We evaluated our results using CASIA and OUR-ISIR datasets for both clothing and speed variations. As a result, we report that on average we obtain an accuracy of 90.32% for the CASIA dataset with unknown covariates and similarly performed excellently on the ISIR dataset. Therefore, our proposed method outperforms existing methods for gait recognition under known and unknown covariate conditions. / This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1F1A1060668).

The purpose of this paper is to give a log-linear representation of a generalized Bradley-Terry (BT-) Model for paired comparisons which allows the incorporation of ties, order effects, concomitant variables for the objects and categorical subject specific covariates and interactions between all of them. An advantage of this approach is that standard software for fitting log-linear models, such as GLIM, can be used. The approach is exemplified by analysing data from an experiment concerning the ranking of European universities. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Doctor of Philosophy / Department of Statistics / Haiyan Wang / Statistical tools to detect nonlinear relationship between variables are commonly needed in various practices. The first part of the dissertation presents a test of independence between a response variable, either discrete or continuous, and a continuous covariate after adjusting for heteroscedastic treatment effects. The method first involves augmenting each pair of the data for all treatments with a fixed number of nearest neighbors as pseudo-replicates. A test statistic is then constructed by taking the difference of two quadratic forms. Using such differences eliminate the need to estimate any nonlinear regression function, reducing the computational time. Although using a fixed number of nearest neighbors poses significant difficulty in the inference compared to when the number of nearest neighbors goes to infinity, the parametric standardizing rate is obtained for the asymptotic distribution of the proposed test statistics. Numerical studies show that the new test procedure maintains the intended type I error rate and has robust power to detect nonlinear dependency in the presence of outliers. The second part of the dissertation discusses the theory and numerical studies for testing the nonparametric effects of no covariate-treatment interaction and no main covariate based on the decomposition of the conditional mean of regression function that is potentially nonlinear. A similar test was discussed in Wang and Akritas (2006) for the effects defined through the decomposition of the conditional distribution function, but with the number of pseudo-replicates going to infinity. Consequently, their test statistics have slow convergence rates and computational speeds. Both test limitations are overcome using new model and tests. The last part of the dissertation develops theory and numerical studies to test for no covariate-treatment interaction, no simple covariate and no main covariate effects for cases when the number of factor levels and the number of covariate values are large.

Master of Arts / Department of Statistics / Paul Nelson / There are two important statistical models for multivariate survival analysis, proportional hazards(PH) models and accelerated failure time(AFT) model. PH analysis is most commonly used multivariate approach for analysing survival time data. For example, in clinical investigations where several (known) quantities or covariates, potentially affect patient prognosis, it is often desirable to investigate one factor effect adjust for the impact of others. This report offered a solution to choose appropriate model in testing covariate effects under different situations. In real life, we are very likely to just have limited sample size and censoring rates(people dropping off), which cause difficulty in statistical analysis. In this report, each dataset is randomly repeated 1000 times from three different distributions (Weibull, Lognormal and Loglogistc) with combination of sample sizes and censoring rates. Then both models are evaluated by hypothesis testing of covariate effect using the simulated data using the derived statistics, power, type I error rate and covergence rate for each situation. We would recommend PH method when sample size is small(n<20) and censoring rate is high(p>0.8). In this case, both PH and AFT analyses may not be suitable for hypothesis testing, but PH analysis is more robust and consistent than AFT analysis. And when sample size is 20 or above and censoring rate is 0.8 or below, AFT analysis will have slight higher convergence rate and power than PH, but not much improvement in Type I error rates when sample size is big(n>50) and censoring rate is low(p<0.3). Considering the privilege of not requiring knowledge of distribution for PH analysis, we concluded that PH analysis is robust in hypothesis testing for covariate effects using data generated from an AFT model.

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This Monte Carlo simulation study examined the issue of measurement invariance testing with FMM when there are covariate effects. Specifically, this study investigated the impact of excluding and misspecifying covariate effects on the class enumeration and measurement invariance testing with FMM. Data were generated based on three FMM models where the covariate had impact on the latent class membership only (population model 1), both the latent class membership and the factor (population model 2), and the latent class membership, the factor, and one item (population model 3). The number of latent classes was fixed at two. These two latent classes were distinguished by factor mean difference for conditions where measurement invariance held in the population, and by both factor mean difference and intercept differences across classes when measurement invariance did not hold in the population. For each of the population models, different analysis models that excluded or misspecified covariate effects were fitted to data. Analyses consisted of two parts. First, for each analysis model, class enumeration rates were examined by comparing the fit of seven solutions: 1-class, 2-class configural, metric, and scalar, and 3-class configural, metric, and scalar. Second, assuming the correct solution was selected, the fit of analysis models with the same solution was compared to identify a best-fitting model. Results showed that completely excluding the covariate from the model (i.e., the unconditional model) would lead to under-extraction of latent classes, except when the class separation was large. Therefore, it is recommended to include covariate in FMM when the focus is to identify the number of latent classes and the level of invariance. Specifically, the covariate effect on the latent class membership can be included if there is no priori hypothesis regarding whether measurement invariance might hold or not. Then fit of this model can be compared with other models that included covariate effects in different ways but with the same number of latent classes and the same level of invariance to identify a best-fitting model.

<p>This thesis makes contributions to the statistical research field of causal inference in observational studies. The results obtained are directly applicable in many scientific fields where effects of treatments are investigated and yet controlled experiments are difficult or impossible to implement.</p><p>In the first paper we define a partially specified directed acyclic graph (DAG) describing the independence structure of the variables under study. Using the DAG we show that given that unconfoundedness holds we can use the observed data to select minimal sets of covariates to control for. General covariate selection algorithms are proposed to target the defined minimal subsets.</p><p>The results of the first paper are generalized in Paper II to include the presence of unobserved covariates. Morevoer, the identification assumptions from the first paper are relaxed.</p><p>To implement the covariate selection without parametric assumptions we propose in the third paper the use of a model-free variable selection method from the framework of sufficient dimension reduction. By simulation the performance of the proposed selection methods are investigated. Additionally, we study finite sample properties of treatment effect estimators based on the selected covariate sets.</p><p>In paper IV we investigate misspecifications of parametric models of a scalar summary of the covariates, the propensity score. Motivated by common model specification strategies we describe misspecifications of parametric models for which unbiased estimators of the treatment effect are available. Consequences of the misspecification for the efficiency of treatment effect estimators are also studied.</p>

It is well known that incorporating auxiliary covariates in the analysis of randomized clinical trials (RCTs) can increase efficiency. Questions still remain regarding how to flexibly incorporate baseline covariates while maintaining valid inference. Recent methodological advances that use semiparametric theory to develop covariate-adjusted inference for RCTs have focused on independent outcomes. In biomedical research, however, cluster randomized trials and longitudinal studies, characterized by correlated responses, are commonly used. We develop methods that flexibly incorporate baseline covariates for efficiency improvement in randomized studies with correlated outcomes. In Chapter 1, we show how augmented estimators may be used for cluster randomized trials, in which treatments are assigned to groups of individuals. We demonstrate the potential for imbalance correction and efficiency improvement through consideration of both cluster- and individual-level covariates. To improve small-sample estimation, we consider several variance adjustments. We evaluate this approach for continuous and binary outcomes through simulation and apply it to the Young Citizens study, a cluster randomized trial of a community behavioral intervention for HIV prevention in Tanzania. Chapter 2 builds upon the previous chapter by deriving semiparametric locally efficient estimators of marginal mean treatment effects when outcomes are correlated. Estimating equations are determined by the efficient score under a mean model for marginal effects when data contain baseline covariates and exhibit correlation. Locally efficient estimators are implemented for longitudinal data with continuous outcomes and clustered data with binary outcomes. Methods are illustrated through application to AIDS Clinical Trial Group Study 398, a longitudinal randomized study that compared various protease inhibitors in HIV-positive subjects. In Chapter 3, we empirically evaluate several covariate-adjusted tests of intervention effects when baseline covariates are selected adaptively and the number of randomized units is small. We demonstrate that randomization inference preserves type I error under model selection while tests based on asymptotic theory break down. Additionally, we show that covariate adjustment typically increases power, except at extremely small sample sizes using liberal selection procedures. Properties of covariate-adjusted tests are explored for independent and multivariate outcomes. We revisit Young Citizens to provide further insight into the performance of various methods in small-sample settings.