Bias Mechanisms in Intention-to-Treat Analysis With Data Subject to Treatment Noncompliance and Missing Outcomes
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An analytical approach was employed to compare sensitivity of causal effect estimates with different assumptions on treatment noncompliance and non-response behaviors. The core of this approach is to fully clarify bias mechanisms of considered models and to connect these models based on common parameters. Focusing on intention-to-treat analysis, systematic model comparisons are performed on the basis of explicit bias mechanisms and connectivity between models. The method is applied to the Johns Hopkins school intervention trial, where assessment of the intention-to-treat effect on school children's mental health is likely to be affected by assumptions about intervention noncompliance and nonresponse at follow-up assessments. The example calls attention to the importance of focusing on each case in investigating relative sensitivity of causal effect estimates with different identifying assumptions, instead of pursuing a general conclusion that applies to every occasion.Keywords:
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Sensitivity analysis is popular in dealing with missing data problems particularly for non-ignorable missingness, where full-likelihood method cannot be adopted. It analyses how sensitively the conclusions (output) may depend on assumptions or parameters (input) about missing data, i.e. missing data mechanism. We call models with the problem of uncertainty sensitivity models. To make conventional sensitivity analysis more useful in practice we need to define some simple and interpretable statistical quantities to assess the sensitivity models and make evidence based analysis. We propose a novel approach in this paper on attempting to investigate the possibility of each missing data mechanism model assumption, by comparing the simulated datasets from various MNAR models with the observed data non-parametrically, using the K-nearest-neighbour distances. Some asymptotic theory has also been provided. A key step of this method is to plug in a plausibility evaluation system towards each sensitivity parameter, to select plausible values and reject unlikely values, instead of considering all proposed values of sensitivity parameters as in the conventional sensitivity analysis method. The method is generic and has been applied successfully to several specific models in this paper including meta-analysis model with publication bias, analysis of incomplete longitudinal data and mean estimation with non-ignorable missing data.
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Abstract With the growing amount of methodology to analyze incomplete data, the awareness has grown that the results of such an analysis may be very sensitive to the modeling assumptions made, many of which are not, strictly speaking, verifiable from the data. Therefore, a lot of the later work is devoted to the exploration of such sensitivities. For both categorical as well as continuous outcomes, we provide a broad definition for such sensitivity analyses, give an overview of methods, and provide some detail about a number of strategies that have become available.
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In this paper, stochastic production frontier models are estimated with IAB establishment data from waves 2002 and 2003 to analyze productivity and inefficiency. The data suffer from nonresponse in the most important variables (output, capital and labor) leading to the loss of 25% of the observations and possibly imprecise estimates and invalid test statistics. Therefore the missing values are multiply imputed. The analysis of the estimation results shows that, particularly in the inefficiency submodel, working with multiply imputed data reveals some interesting and plausible results which are not available when missing observations are ignored.
Frontier
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This paper develops methods for assessing the sensitivity of empirical conclusions regarding conditional distributions to departures from the missing at random (MAR) assumption. We index the degree of non-ignorable selection governing the missingness process by the maximal Kolmogorov-Smirnov (KS) distance between the distributions of missing and observed outcomes across all values of the covariates. Sharp bounds on minimum mean square approximations to conditional quantiles are derived as a function of the nominal level of selection considered in the sensitivity analysis and a weighted bootstrap procedure is developed for conducting inference. Using these techniques, we conduct an empirical assessment of the sensitivity of observed earnings patterns in U.S. Census data to deviations from the MAR assumption. We find that the well-documented increase in the returns to schooling between 1980 and 1990 is relatively robust to deviations from the missing at random assumption except at the lowest quantiles of the distribution, but that conclusions regarding heterogeneity in returns and changes in the returns function between 1990 and 2000 are very sensitive to departures from ignorability.
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The effects of slight changes in the parameters on the characteristic roots of a model (sensitivity analysis) has great potential in econometrics.The author, after suggesting a criterion for giving empirical contents to the notion of slight, shows how the application of sensitivity analysis to a continuous time econometric model of the Italian economy gives important insoghts into the effects of a possible complete liberalization of capital movements.
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Abstract With the growing amount of methodology to analyze incomplete data, the awareness has grown that the results of such an analysis may be very sensitive to the modeling assumptions made, many of which are not, strictly speaking, verifiable from the data. Therefore, a lot of the later work is devoted to the exploration of such sensitivities. For both categorical as well as continuous outcomes, we provide a broad definition for such sensitivity analyses, give an overview of methods, and provide some detail about a number of strategies that have become available.
Categorical variable
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Causal inference in observational studies is frequently challenged by the occurrence of missing data, in addition to confounding. Motivated by the Consortium on Safe Labor, a large observational study of obstetric labor practice and birth outcomes, this article focuses on the problem of missing exposure information in a causal analysis of observational data. This problem can be approached from different angles (i.e. missing covariates and causal inference), and useful methods can be obtained by drawing upon the available techniques and insights in both areas. In this article, we describe and compare a collection of methods based on different modeling assumptions, under standard assumptions for missing data (i.e. missing-at-random and positivity) and for causal inference with complete data (i.e. no unmeasured confounding and another positivity assumption). These methods involve three models: one for treatment assignment, one for the dependence of outcome on treatment and covariates, and one for the missing data mechanism. In general, consistent estimation of causal quantities requires correct specification of at least two of the three models, although there may be some flexibility as to which two models need to be correct. Such flexibility is afforded by doubly robust estimators adapted from the missing covariates literature and the literature on causal inference with complete data, and by a newly developed triply robust estimator that is consistent if any two of the three models are correct. The methods are applied to the Consortium on Safe Labor data and compared in a simulation study mimicking the Consortium on Safe Labor.
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We present a method to analyze sensitivity of frequentist inferences to potential nonignorability of the missingness mechanism. Rather than starting from the selection model, as is typical in such analyses, we assume that the missingness arises through unmeasured confounding. Our model permits the development of measures of sensitivity that are analogous to those for unmeasured confounding in observational studies. We define an index of sensitivity, denoted MinNI, to be the minimum degree of nonignorability needed to change the mean value of the estimate of interest by a designated amount. We apply our model to sensitivity analysis for a proportion, but the idea readily generalizes to more complex situations.
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Quantile regression
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