Estimation of treatment effects in observational studies by recovering the assignment probabilities and the population model

In observational studies the assignment of units to treatments is with unknown probabilities. Consequently, estimation and comparison of treatment effects based on the empirical distributions of the response under the various treatments can be biased since units exposed to one treatment could differ in important but unknown characteristics from units exposed to other treatments. In this article we study the plausibility of analyzing observational data by deriving the parametric distribution of the observed response under a given treatment as a function of the distribution that would be obtained under a strongly ignorable assignment, and the assignment process, which is modeled as a function of the observed data (the response and covariate values). The use of this approach is founded by showing that the sample distribution of the observed responses is identifiable under some general conditions. The goodness of fit of this distribution can be tested by using standard test statistics since it refers to the observed data, but we also develop a new test. The proposed approach allows also testing the assumptions underlying the use of methods that employ instrumental variables, or methods that use propensity scores with a given set of covariates.We assess the performance of the proposed approach and compare it to existing approaches using data collected in the year 2000 by OECD for the Programme for International Student Assessment (PISA). In the present application we compare students’ scores in mathematics between public and private schools in Ireland and conclude, somewhat surprisingly, that the public schools perform better than the private schools. This finding is supported by one of the existing methods as well

Estimation of Population Mean Using Exponential Type Imputation Technique for Missing Observations

Some imputation techniques are suggested for estimating the population mean when the data values are missing completely at random under a simple random sample without replacement scheme. Two classes of point estimators are proposed. The bias and mean squared error expressions of the proposed point estimators are derived up to first order of approximation. It has been shown that the proposed point estimators are more efficient than some existing point estimators due to Lee, Rancourt, and Sarndal (1994) and Singh and Horn (2000). Theoretical findings are supported by an empirical study based on five populations to show the superiority of the constructed estimators and methods of imputation over others

Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration (RC), arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to RC, and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next we describe the closely related maximum likelihood and multiple imputation approaches, and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of RC and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey

Measuring overeducation with earnings frontiers and multiply imputed censored income data

"In this paper, we remove one serious drawback of the IAB employment sample impeding its applicability to the estimation of earnings frontiers: the censoring of the income data, by multiple imputation. Then, we estimate individual potential income with stochastic earnings frontiers, and we measure overeducation as the ratio between actual income and potential income. It is shown that the measurement of overeducation by this income ratio is a valuable addition to the overeducation literature because the well-established objective or subjective overeducation measures focus on some ordinal matching aspects and ignore the metric income and efficiency aspects of overeducation." (Author's abstract, IAB-Doku) ((en))Überqualifikation - Messung, Einkommen, Einkommenshöhe, IAB-Beschäftigtenstichprobe, Stichprobenfehler, Datenaufbereitung, Datenanalyse, Schätzung, Imputationsverfahren

Multiple imputation for estimating hazard ratios and predictive abilities in case-cohort surveys

<p>Abstract</p> <p>Background</p> <p>The weighted estimators generally used for analyzing case-cohort studies are not fully efficient and naive estimates of the predictive ability of a model from case-cohort data depend on the subcohort size. However, case-cohort studies represent a special type of incomplete data, and methods for analyzing incomplete data should be appropriate, in particular multiple imputation (MI).</p> <p>Methods</p> <p>We performed simulations to validate the MI approach for estimating hazard ratios and the predictive ability of a model or of an additional variable in case-cohort surveys. As an illustration, we analyzed a case-cohort survey from the Three-City study to estimate the predictive ability of D-dimer plasma concentration on coronary heart disease (CHD) and on vascular dementia (VaD) risks.</p> <p>Results</p> <p>When the imputation model of the phase-2 variable was correctly specified, MI estimates of hazard ratios and predictive abilities were similar to those obtained with full data. When the imputation model was misspecified, MI could provide biased estimates of hazard ratios and predictive abilities. In the Three-City case-cohort study, elevated D-dimer levels increased the risk of VaD (hazard ratio for two consecutive tertiles = 1.69, 95%CI: 1.63-1.74). However, D-dimer levels did not improve the predictive ability of the model.</p> <p>Conclusions</p> <p>MI is a simple approach for analyzing case-cohort data and provides an easy evaluation of the predictive ability of a model or of an additional variable.</p