There has been a growing interest in using propensity scores in the analysis of observational studies. The propensity score is a balancing mechanism that works to create groups of subjects which have a similar distribution on background covariates. Matching, stratification, inverse propensity treatment weighting and regression adjustment are all strategies that can be used with the propensity score to create balance between groups of subjects. The aim of this paper is to introduce propensity scores and the different techniques which make use of them. We use data obtained from the Women's Health Initiative to demonstrate each of the different methods for propensity score analysis. In the example analysis we examined the association between dog ownership and CVD. The results of our analysis were quite consistent, and demonstrate the propensity score analysis can be used effectively to balance treated and untreated groups within an observational study.

Propensity score methods (PSM) that have been widely used to reduce selection bias in observational studies are restricted to a binary treatment. Imai and van Dyk extended PSM to estimate non-binary treatment effect using stratification with P-Function, and generalized inverse treatment probability weighting (GIPTW). However, propensity score (PS) matching methods on multiple treatments received little attention, and existing generalized PSMs merely focused on estimates of main treatment effects but omitted potential interaction effects that are of essential interest in many studies. In this dissertation, I extend Rubin’s PS matching theory to general treatment regimens under the P-Function framework. From theory to practice, I propose an innovative distance measure that can summarize similarities among subjects in multiple treatment groups. Based on this distance measure I propose four generalized propensity score matching methodologies. The first two methods are extensions of nearest neighbor matching. I implemented Monte Carlo simulation studies to compare them with GIPTW and stratification on P-Function methods. The next two methods are extensions of the nearest neighbor caliper width matching and variable matching. I define the caliper width as the product of a weighted standard deviation of all possible pairwise distances between two treatment groups. I conduct a series of simulation studies to determine an optimal caliper width by searching the lowest mean square error of average causal interaction effect. I further compare the ones with optimal caliper width with other methods using simulations. Finally, I apply these methods to the National Medical Expenditure Survey data to examine the average causal main effect of duration and frequency of smoking as well as their interaction effect on annual medical expenditures. Using proposed methods, researchers can apply regression models with specified interaction terms to the matched data and simultaneously obtain both main and interaction effects estimate with improved statistical properties.

The first chapter uses the propensity score matching method to measure the average impact of insurance on health service utilization in terms of office-based physician visits, total number of reported visits to hospital outpatient departments, and emergency room visits. Four matching algorithms are employed to match propensity scores. The results show that insurance significantly increases office-based physician visits, and its impacts on reported visits to hospital outpatient departments and emergency room visits are positive, but not significant. This implies that physician offices will receive a substantial increase in demand if universal insurance is imposed. Government will need to allocate more resources to physician offices relative to outpatient or emergency room services in the case of universal insurance in order to accommodate the increased demand. The second chapter studies the sensitivity of propensity score matching methods to different estimation methods. Traditionally, parametric models, such as logit and probit, are used to estimate propensity score. Current technology allows us to use computationally intensive methods, either semiparametric or nonparametric, to estimate it. We use the Monte Carlo experimental method to investigate the sensitivity of the treatment effect to different propensity score estimation models under the unconfoundedness assumption. The results show that the average treatment effect on the treated (ATT) estimates are insensitive to the estimation methods when index function for treatment is linear, but logit and probit model do better jobs when the index function is nonlinear. The third chapter proposes a Cross-Sectionally Varying (CVC) Coefficient method to approximate individual treatment effects with nonexperimental data, the distribution of treatment effects, the average treatment effect on the treated and the average treatment effect. The CVC method reparameterizes the outcome of no treatment and the treatment effect in terms of observable variables, and uses these observables together with a Bayesian estimator of their coefficients to approximate individual treatment effects. Monte Carlo simulations demonstrate the efficacy and applicability of the proposed estimator. This method is applied to two datasets: data from the U.S. Job Training Partnership ACT (JTPA) program and a dataset that contains firms’ seasoned equity offerings and operating performances.

abstract: Random Forests is a statistical learning method which has been proposed for propensity score estimation models that involve complex interactions, nonlinear relationships, or both of the covariates. In this dissertation I conducted a simulation study to examine the effects of three Random Forests model specifications in propensity score analysis. The results suggested that, depending on the nature of data, optimal specification of (1) decision rules to select the covariate and its split value in a Classification Tree, (2) the number of covariates randomly sampled for selection, and (3) methods of estimating Random Forests propensity scores could potentially produce an unbiased average treatment effect estimate after propensity scores weighting by the odds adjustment. Compared to the logistic regression estimation model using the true propensity score model, Random Forests had an additional advantage in producing unbiased estimated standard error and correct statistical inference of the average treatment effect. The relationship between the balance on the covariates' means and the bias of average treatment effect estimate was examined both within and between conditions of the simulation. Within conditions, across repeated samples there was no noticeable correlation between the covariates' mean differences and the magnitude of bias of average treatment effect estimate for the covariates that were imbalanced before adjustment. Between conditions, small mean differences of covariates after propensity score adjustment were not sensitive enough to identify the optimal Random Forests model specification for propensity score analysis. / Dissertation/Thesis / Ph.D. Psychology 2013

Covariate quality has been primarily theory driven in propensity score matching with a general adversity to the interpretation of group prediction. However, effect sizes are well supported in the literature and may help to inform the method. Specifically, I index can be used as a measure of effect size in logistic regression to evaluate group prediction. As such, simulation was used to create 35 conditions of I, initial bias and sample size to examine statistical differences in (a) post-matching bias reduction and (b) treatment effect sensitivity. The results of this study suggest these conditions do not explain statistical differences in percent bias reduction of treatment likelihood after matching. However, I and sample size do explain statistical differences in treatment effect sensitivity. Treatment effect sensitivity was lower when sample sizes and I increased. However, this relationship was mitigated within smaller sample sizes as I increased above I = .50.

Indiana University-Purdue University Indianapolis (IUPUI) / Observational studies offer unique advantages over randomized clinical trials (RCTs) in many situations where RCTs are not feasible or suffer from major limitations such as insufficient sample sizes and narrowly focused populations. Because observational data are relatively easy and inexpensive to access, and contain rich and comprehensive demographic and medical information on large and representative populations, they have played a major role in the assessment of the effectiveness and safety of medical interventions. However, observational data also have the challenges of higher rates of missing data and the confounding effect. My proposal is on the development of three statistical methods to address these challenges. The first method is on the refinement and extension of a multiply robust (MR) estimation procedure that simultaneously accounts for the confounding effect and missing covariate process, where we derived the asymptotic variance estimator and extended the method to the scenario where the missing covariate is continuous. The second method focuses on the improvement of estimation precision in an RCT by a historical control cohort. This was achieved through augmenting the conventional effect estimator with an extra mean zero (approximately) term correlated with the conventional effect estimator. In the third method, we calibrated the hidden database bias of an electronic medical records database and utilized an empirical Bayes method to improve the accuracy of the estimation of the risk of acute myocardial infarction associated with a drug by borrowing information from other drugs.

O objetivo geral desta pesquisa foi avaliar o impacto da restrição ao crédito rural sobre a produtividade da terra e a produtividade do trabalho para os agricultores familiares do Brasil. Para estimar esse impacto, foram utilizados os dados do Censo Agropecuário de 2006 por município. Para diferenciar os diferentes agricultores familiares, foi utilizado o índice de mercantilização, separando a população em quartis. As estimativas do impacto da restrição ao crédito sobre a produtividade da terra e a produtividade do trabalho foram calculadas a partir da comparação entre o grupo que recebeu crédito e o que não recebeu crédito, obtido através do escore de propensão (propensity score matching). As estimativas do efeito médio de tratamento sobre os tratados, quando apresentaram resultados estatisticamente significativos, evidenciaram os diferentes grupos formados dentro da agricultura familiar. Por exemplo, na região Centro-oeste municípios com crédito tiveram maior produtividade da terra e do trabalho quando pertencentes ao quarto quartil. Os resultados obtidos no modelo estimado mostram que os efeitos da restrição ao crédito rural são diferentes para municípios mais ou menos mercantilizados e, portanto, requerem políticas distintas. / The overall objective of this research is to evaluate the impact of the restriction of rural credit on land and labor productivity for family farmers in Brazil. In order to estimate this impact, we have used data from Brazil\'s 2006 Agricultural Census at the municipal level. To differentiate among family farmers, a trade index was used, separating the population into quartiles. Estimates of the impact of credit restriction on the productivity of land and the productivity of labor were calculated through propensity score matching. Estimates of the average treatment effect on the treated, when presenting statistically significant results, highlight the differences among groups formed within the family farm. For example, in the Midwest of Brazil, municipalities with credit and belonging to the fourth quartile presented higher land and labor productivity. The results of the estimated model confirm that the effects of rural credit restriction are different for municipalities with smaller or larger trade indices, requiring therefore specific policies for each group.

A presente dissertação visa avaliar, a partir do uso dos dados da Pesquisa de Atividade Econômica Paulista - PAEP - do ano de 1996, da RAIS - Relação Anual de Informações Sociais de 1992, 1993, 1997 e 1998 e da SECEX - Secretaria do Comércio Exterior - dos anos de 1992 e 1993, a relação entre a atividade de inovação tecnológica e os potenciais impactos produzidos sobre o nível de emprego e sobre o nível de renda na indústria paulista entre os anos de 1997 e 1998. Como a inovação não é um evento aleatório, há o viés de seleção da amostra, de tal sorte que uma comparação direta entre os efeitos da inovação sobre certas variáveis daquelas firmas que inovaram com aquelas que não inovaram, na situação de ter havido inovação, produziria vieses. Tal problema é resolvido neste trabalho por meio do Propensity Score Matching, que visa o pareamento de unidades tratamento - controle para a obtenção dos resultados intentados, a saber, a variação na renda e no nível de emprego. Ademais, de modo a inibir a presença de efeitos não observáveis, recorre-se ao método de Diferenças em Diferenças (DID). Os resultados obtidos atestam para um aumento, na média, do nível de emprego para quase todos os tipos de atividade inovativa empreendidas. Em contrapartida, os achados se revelaram estatisticamente insignificantes para a variação de renda, também em quase todos os tipos de inovação. / This work intends to analyze, by the usage of three different data sources, PAEP (1996), RAIS - Relação Anual de Informações Sociais (1992, 1993, 1997, and 1998) and SECEX - Secretaria do Comércio Exterior (from 1992, and 1993) the relationship, if that exists, between innovation and its potential impacts over employment level as well as salaries during the 1997 - 1998 period. Once innovation activity cannot be considered as a random event, we incur in the well known selection bias problem. Consequently, a direct comparison of the innovation impacts between those firms which effectively innovated with those which did not innovate would be misleading. Such a problem may be corrected with the Propensity Score Matching, which consists in the establishment of treatment - control pairs in order to obtain the results previously searched. Moreover, in an attempt to control for the unobserved effects, it is applied the Differences in Differences Methodology (DID). Results obtained show that, on the one hand, for almost all the innovation activities considered, there was an increment in the level of employment. On the other hand, for most of the cases, there were not statistically significant results for an impact of innovation activities on the level of salaries.

Neste trabalho analisou-se o impacto das remessas financeiras sobre os patrimônios dos ativos nos domicílios, no país de origem. Utilizamos dados da Encuesta Permanente de Hogares de 2008, os quais foram fornecidos pelo órgão Dirección General de Estadística, Encuestas y Censos do Paraguai. Com estes dados realizamos uma comparação entre os domicílios com e sem remessas, independente de terem ou não emigrantes. A metodologia utilizada para realizar a comparação foi o Propensity Score Matching (PSM) com dois algoritmos, Vizinhos Próximos e Kernel. Os patrimônios dos ativos são carros, aluguéis e combinados. Os resultados em todos os casos foram estatisticamente significativos, porém, negativos. Com amesma metodologia e os mesmos dados, comparamos apenas os domicílios com emigrantes, e os resultados continuaram negativos, porém, com nível de significância menor. / In this study we analyzed the impact of remittances on financial assets in the wealth of households in the country of origin. We use data from the Encuesta Permanente Hogares 2008, which were provided by the agency Dirección General de Estadística, Encuestas y Censos of Paraguay. With these data we performed a comparison between households with and without remittances, regardless of whether or not immigrants. The methodology for conducting the comparison was the Propensity Score Matching (PSM) with two algorithms, Kernel and Nearest Neighbors. The stockholders\' assets are cars, rentals and combined. The results in all cases were statistically significant, but negative. With the same methodology and same data, comparing only households with migrants, the results remained negative, but with lower significance level.

O objetivo geral desta pesquisa foi avaliar o impacto da restrição ao crédito rural sobre a produtividade da terra e a produtividade do trabalho para os agricultores familiares do Brasil. Para estimar esse impacto, foram utilizados os dados do Censo Agropecuário de 2006 por município. Para diferenciar os diferentes agricultores familiares, foi utilizado o índice de mercantilização, separando a população em quartis. As estimativas do impacto da restrição ao crédito sobre a produtividade da terra e a produtividade do trabalho foram calculadas a partir da comparação entre o grupo que recebeu crédito e o que não recebeu crédito, obtido através do escore de propensão (propensity score matching). As estimativas do efeito médio de tratamento sobre os tratados, quando apresentaram resultados estatisticamente significativos, evidenciaram os diferentes grupos formados dentro da agricultura familiar. Por exemplo, na região Centro-oeste municípios com crédito tiveram maior produtividade da terra e do trabalho quando pertencentes ao quarto quartil. Os resultados obtidos no modelo estimado mostram que os efeitos da restrição ao crédito rural são diferentes para municípios mais ou menos mercantilizados e, portanto, requerem políticas distintas. / The overall objective of this research is to evaluate the impact of the restriction of rural credit on land and labor productivity for family farmers in Brazil. In order to estimate this impact, we have used data from Brazil\'s 2006 Agricultural Census at the municipal level. To differentiate among family farmers, a trade index was used, separating the population into quartiles. Estimates of the impact of credit restriction on the productivity of land and the productivity of labor were calculated through propensity score matching. Estimates of the average treatment effect on the treated, when presenting statistically significant results, highlight the differences among groups formed within the family farm. For example, in the Midwest of Brazil, municipalities with credit and belonging to the fourth quartile presented higher land and labor productivity. The results of the estimated model confirm that the effects of rural credit restriction are different for municipalities with smaller or larger trade indices, requiring therefore specific policies for each group.