published_or_final_version / abstract / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

No description available.

No description available.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

No description available.

The central theme of this dissertation is the development of a new approach to conceptualize and quantify dependence structures of capture-recapture data for closed populations, with specific emphasis on epidemiological applications. We introduce a measure of source dependence: the Coefficient of Incremental Dependence (CID). Properties of this and the related Coefficient of Source Dependence (CSD) of Vandal, Walker, and Pearson (2005) are presented, in particular their relationships to the conditional independence structures that can be modelled by hierarchical joint log-linear models (HJLLM). From these measures, we develop a new class of marginal log-linear models (MLLM), which we compare and contrast to HJLLMs. / We demonstrate that MLLMs serve to extend the universe of dependence structures of capture-recapture data that can be modelled and easily interpreted. Furthermore, the CIDs and CSDs enable us to meaningfully interpret the parameters of joint log-linear models previously excluded from the analysis of capture-recapture data for reasons of non-interpretability of model parameters. / In order to explore the challenges and features of MLLMs, we show how to produce inference from them under both a maximum likelihood and a Bayesian paradigm. The proposed modelling approach performs well and provides new insight into the fundamental nature of epidemiological capture-recapture data.

Capture-recapture methods are used to estimate population size from overlapping, incomplete sources of information. With three or more sources, dependence between sources may be modelled using log-linear models. We propose a Coefficient of Incremental Dependence Criterion (CIDC) for selecting an estimate of population size among all possible estimates that result from hierarchical log-linear models. A penalty for the number of parameters in the model was selected via simulation for the three-source and four-source settings. The performance of the proposed criterion was compared to the Akaike Information Criterion (AIC) through simulation. The CIDC was found to modestly outperform the AIC for data generated from a population size of approximately 100, with AIC performing consistently better for larger population sizes. Modifications to the criterion such as incorporating the estimated population size and the type of source interaction present should be investigated, along with the mathematical properties of the CIDC.

No description available.

Recent discussion in the epidemiologic methods and teaching literatures centers around the importance of clearly stating study goals, disentangling the goal of causation from prediction (or description), and clarifying the statistical tools that can address each goal. This discussion illuminates different ways in which mismatches can occur between study goals, methods, and interpretations, which this dissertation synthesizes into the concept of “misalignment”; misalignment occurs when the study methods and/or interpretations are inappropriate for (i.e., do not match) the study’s goal. While misalignments can occur and may cause problems, their pervasiveness and consequences have not been examined in the epidemiologic literature. Thus, the overall purpose of this dissertation was to document and examine the effects of misalignment problems seen in epidemiologic practice. First, a review was conducted to document misalignment in a random sample of epidemiologic studies and explore how the framing of study goals contributes to its occurrence. Among the reviewed articles, full alignment between study goals, methods, and interpretations was infrequently observed, although “clearly causal” studies (those that framed causal goals using causal language) were more often fully aligned (5/13, 38%) than “seemingly causal” ones (those that framed causal goals using associational language; 3/71, 4%). Next, two simulation studies were performed to examine the potential consequences of different types of misalignment problems seen in epidemiologic practice. They are based on the observation that, often, studies that are causally motivated perform analyses that appear disconnected from, or “misaligned” with, their causal goal. A primary aim of the first simulation study was to examine goal--methods misalignment in terms of inappropriate variable selection for exposure effect estimation (a causal goal). The main difference between predictive and causal models is the conceptualization and treatment of “covariates”. Therefore, exposure coefficients were compared from regression models built using different variable selection approaches that were either aligned (appropriate for causation) or misaligned (appropriate for prediction) with the causal goal of the simulated analysis. The regression models were characterized by different combinations of variable pools and inclusion criteria to select variables from the pools into the models. Overall, for valid exposure effect estimation in a causal analysis, the creation of the variable pool mattered more than the specific inclusion criteria, and the most important criterion when creating the variable pool was to exclude mediators. The second simulation study concretized the misalignment problem by examining the consequences of goal--method misalignment in the application of the structured life course approach, a statistical method for distinguishing among different causal life course models of disease (e.g., critical period, accumulation of risk). Although exchangeability must be satisfied for valid results using this approach, in its empirical applications, confounding is often ignored. These applications are misaligned because they use methods for description (crude associations) for a causal goal (identifying causal processes). Simulations were used to mimic this misaligned approach and examined its consequences. On average, when life course data was generated under a “no confounding” scenario - an unlikely real-world scenario - the structured life course approach was quite accurate in identifying the life course model that generated the data. However, in the presence of confounding, the wrong underlying life course model was often identified. Five life course confounding structures were examined; as the complexity of examined confounding scenarios increased, particularly when this confounding was strong, incorrect model selection using the structured life course approach was common. The misalignment problem is recognized but underappreciated in the epidemiologic literature. This dissertation contributes to the literature by documenting, simulating, and concretizing problems of misalignment in epidemiologic practice.