Indiana University-Purdue University Indianapolis (IUPUI) / In this dissertation, I develop a regression-based approach to the specification and estimation of the effect of a presumed causal variable on a count-valued outcome of interest. Statistics for relevant causal inference are also derived. As an illustration and as a basis for comparing alternative parametric specifications with respect to ease of implementation, computational efficiency and statistical performance, the proposed models and estimation methods are used to analyze household fertility decisions. I estimate the effect of a counterfactually imposed additional year of wife’s education on actual family size (AFS) and desired family size (DFS) [count-valued variables]. In order to ensure the causal interpretability of the effect parameter as I define it, the underlying regression model is cast in a potential outcomes (PO) framework. The specification of the relevant data generating process (DGP) is also derived. The regression-based approach developed in the dissertation, in addition to taking explicit account of the fact that the outcome of interest is count-valued, is designed to account for potential sample selection bias due to a particular data deficiency in the count data context and to accommodate the possibility that some structural aspects of the model may vary with the value of a binary switching variable. Moreover, my approach loosens the equi-dispersion constraint [conditional mean (CM) equals conditional variance (CV)] that plagues conventional (poisson) count-outcome regression models. This is a particularly important feature of my model and method because in most contexts in empirical economics the data are either over-dispersed (CM < CV) or under-dispersed (CM > CV) – fertility models are usually characterized by the latter. Alternative count data models were discussed and compared using simulated and real data. The simulation results and estimation results using real data suggest that the estimated effects from my proposed models (models that loosen the equi-dispersion constraint, account for the sample selection, and accommodate variability in structural aspect of the models due to a switching variable) substantively differ from estimates from a conventional linear and count regression specifications.

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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24727号 / 情博第815号 / 新制||情||137(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 鹿島 久嗣, 教授 阿久津 達也, 教授 下平 英寿 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Causal inference methods have been applied in various fields where researchers want to establish causal effects between different phenomena. The goal of causal inference is to estimate treatment effects by comparing outcomes had units received treatment versus outcomes had units not received treatment. We focus on estimating treatment effects in three different projects. We first proposed linear unbiased estimators (LUEs) for general causal effects under the assumption that treatment effects are additive. Under the assumption of additivity, the set of estimands considered grows as contrasts in exposures are now equivalent. Furthermore, we identified a subset of LUEs that forms an affine basis for LUEs, and we characterized LUEs with minimum integrated variance through defining conditions on the support of the estimator. We also estimated the effect of drug-induced homicide (DIH) prosecutions reported by the media on unintentional drug overdose deaths, which have never been empirically assessed, using various models. Using a difference-in-differences-like logistic generalized additive model (GAM) with smoothed time effects where we assumed a constant treatment effect, we found that DIH prosecutions reported by the media were associated with a potential harmful effect (risk ratio: 1.064; 95% CI: (1.012, 1.118)) on drug overdose deaths. Upon further research, however, there are potential issues using a constant treatment effect model in a setting where treatment is staggered and treatment effects are heterogeneous. Therefore, we also used a GAM with a linear link function where we assumed that treatment effects may depend on the treatment duration. With this second model, we estimated a risk ratio for having any DIH prosecutions reported by the media of 0.956 (95% CI: (0.824, 1.110)) and a risk ratio of 0.986 (95% CI: (0.973, 0.999)) for the effect of being exposed to DIH prosecutions reported by the media for each additional six months. Despite being statistically significant, the effects were not practically significant. However, the results call for further research on the effect of DIH prosecutions on drug overdose deaths. Lastly, we shift our focus to Structural Nested Mean Models (SNMMs). We extended SNMMs to a new class of estimators which estimate treatment effects of different treatment regimes in the risk ratio scale---the Structural Nested Risk Ratio Model (SNRRM). We further generalized previous work on SNMMs by estimating treatment effects by modeling a function of treatment, which we choose to be any function that can be modeled by generalized linear models, as opposed to just a model for treatment initiation. We applied SNRRMs to estimate the effect of DIH prosecutions reported by the media on drug overdose deaths.

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Prognostic scores, and more specifically comorbidity scores, are important and widely used measures in the health care field and in health services research. A comorbidity is an existing disease an individual has in addition to a primary condition of interest, such as cancer. A comorbidity score is a summary score that can be created from these individual comorbidities for prognostic purposes, as well as for confounding adjustment. Despite their widespread use, the properties of and conditions under which comorbidity scores are valid dimension reduction tools in statistical models is largely unknown. This dissertation explores the use of summary comorbidity measures in statistical models. Three particular aspects are examined. First, it is shown that, under standard conditions, the predictive ability of these summary comorbidity measures remains as accurate as the individual comorbidities in regression models, which can include factors such as treatment variables and additional covariates. However, these results are only true when no interaction exists between the individual comorbidities and any additional covariate. The use of summary comorbidity measures in the presence of such interactions leads to biased results. Second, it is shown that these measures are also valid in the causal inference framework through confounding adjustment in estimating treatment effects. Lastly, we introduce a time dependent extension of summary comorbidity scores. This time dependent score can account for changes in patients' health over time and is shown to be a more accurate predictor of patient outcomes. A data example using breast cancer data from the SEER Medicare Database is used throughout this dissertation to illustrate the application of these results to the health care field. / Statistics

Doctor of Philosophy / Department of Statistics / Gary L. Gadbury / Studies commonly focus on estimating a mean treatment effect in a population. However, in some applications the variability of treatment effects across individual units may help to characterize the overall effect of a treatment across the population. Consider a set of treatments, {T,C}, where T denotes some treatment that might be applied to an experimental unit and C denotes a control. For each of N experimental units, the duplet {r[subscript]i, r[subscript]Ci}, i=1,2,…,N, represents the potential response of the i[superscript]th experimental unit if treatment were applied and the response of the experimental unit if control were applied, respectively. The causal effect of T compared to C is the difference between the two potential responses, r[subscript]Ti- r[subscript]Ci. Much work has been done to elucidate the statistical properties of a causal effect, given a set of particular assumptions. Gadbury and others have reported on this for some simple designs and primarily focused on finite population randomization based inference. When designs become more complicated, the randomization based approach becomes increasingly difficult. Since linear mixed effects models are particularly useful for modeling data from complex designs, their role in modeling treatment heterogeneity is investigated. It is shown that an individual treatment effect can be conceptualized as a linear combination of fixed treatment effects and random effects. The random effects are assumed to have variance components specified in a mixed effects “potential outcomes” model when both potential outcomes, r[subscript]T,r[subscript]C, are variables in the model. The variance of the individual causal effect is used to quantify treatment heterogeneity. Post treatment assignment, however, only one of the two potential outcomes is observable for a unit. It is then shown that the variance component for treatment heterogeneity becomes non-estimable in an analysis of observed data. Furthermore, estimable variance components in the observed data model are demonstrated to arise from linear combinations of the non-estimable variance components in the potential outcomes model. Mixed effects models are considered in context of a particular design in an effort to illuminate the loss of information incurred when moving from a potential outcomes framework to an observed data analysis.