Estimation of Regression Coefficients When Some Regressors Are Not Always Observed

Robins, James M.; Rotnitzky, Andrea; Zhao, Lue Ping

doi:10.2307/2290910

Cited by 591 publications

(741 citation statements)

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“…The main idea of our method is inverse probability weighting, that is, we weight the completely observed cases inversely proportionally to the probability of being observed. The proposed methodology and theory extend those for the inverse probability weighted conditional mean regression models (e.g., [4]). We investigate the asymptotic normality of the weighted estimator and reveal an interesting phenomenon that using estimated weights often leads to asymptotically more efficient estimator than using the true weights, which echoes the same finding for weighted estimation in linear mean regression model [4].…”

Section: Introductionmentioning

confidence: 84%

Weighted quantile regression for analyzing health care cost data with missing covariates

Sherwood

Wang

Zhou

2013

Statistics in Medicine

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Analysis of health care cost data is often complicated by a high level of skewness, heteroscedastic variances and the presence of missing data. Most of the existing literature on cost data analysis have been focused on modeling the conditional mean. In this paper, we study a weighted quantile regression approach for estimating the conditional quantiles health care cost data with missing covariates. The weighted quantile regression estimator is consistent, unlike the naive estimator, and asymptotically normal. Furthermore, we propose a modified BIC for variable selection in quantile regression when the covariates are missing at random. The quantile regression framework allows us to obtain a more complete picture of the effects of the covariates on the health care cost and is naturally adapted to the skewness and heterogeneity of the cost data. The method is semiparametric in the sense that it does not require to specify the likelihood function for the random error or the covariates. We investigate the weighted quantile regression procedure and the modified BIC via extensive simulations. We illustrate the application by analyzing a real data set from a health care cost study.

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Section: Introductionmentioning

confidence: 84%

Weighted quantile regression for analyzing health care cost data with missing covariates

Sherwood

Wang

Zhou

2013

Statistics in Medicine

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“…To address potential bias resulting from loss to followup, we repeated the linear and logistic regressions using inverse probability weighting (IPW [12,21]), a technique that places greater weight on the age 7 observations of participants who were similar to those lost to follow-up. We first estimated the probability that a subject was observed at the age 7 visit, conditioned upon values of the covariates that were empirically associated with the probability of retention at age 7, case status, and the outcomes (continuous and dichotomous).…”

Section: Discussionmentioning

confidence: 99%

Sex differences in the neurodevelopment of school-age children with and without single-suture craniosynostosis

et al. 2015

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“…Robins et al [19] and Robins [18] established that in a model for data O D .Y; A; X/ in which k D P .A D kjX/ is known, any regular and asymptotically linear estimator forˇcan be found as the solution to P i i aug .Y; A; XI N K / D 0 for a specific choice of N K .X /. Zhang et al [17] demonstrated the use of this theory in RCTs with univariate outcomes.…”

Section: The Simple Augmented Generalized Estimating Equationmentioning

confidence: 99%

“…N K / T aug . N K / < 1, the optimal estimator within this class for a fixed .Y; AIˇ/ is obtained by setting k opt .X i / D Ef i .Y; AIˇ/jA i D k; X i g [17][18][19]. When only two treatment arms are considered, the augmentation term…”

Section: The Simple Augmented Generalized Estimating Equationmentioning

confidence: 99%

Augmented generalized estimating equations for improving efficiency and validity of estimation in cluster randomized trials by leveraging cluster‐level and individual‐level covariates

Stephens

Tchetgen

Gruttola

2012

Statistics in Medicine

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Recent methodological advances in covariate adjustment in RCTs have used semiparametric theory to improve efficiency of inferences by incorporating baseline covariates; these methods have focused on independent outcomes. We modify one of these approaches, augmentation of standard estimators, for use within cluster randomized trials in which treatments are assigned to groups of individuals, thereby inducing correlation. We demonstrate the potential for imbalance correction and efficiency improvement through consideration of both cluster- and individual-level covariates. To improve small-sample estimation, we consider several variance adjustments. We evaluate this approach for continuous and binary outcomes through simulation, and apply it to data from a cluster randomized trial of a community behavioral intervention related to HIV prevention in Tanzania.

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Estimation of Regression Coefficients When Some Regressors Are Not Always Observed

Cited by 591 publications

References 0 publications

Weighted quantile regression for analyzing health care cost data with missing covariates

Weighted quantile regression for analyzing health care cost data with missing covariates

Sex differences in the neurodevelopment of school-age children with and without single-suture craniosynostosis

Augmented generalized estimating equations for improving efficiency and validity of estimation in cluster randomized trials by leveraging cluster‐level and individual‐level covariates

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