On modelling response propensity for dwelling unit (DU) level non-response adjustment in the Medical Expenditure Panel Survey (MEPS)

Non-response is a common problem in household sample surveys. The Medical Expenditure Panel Survey (MEPS), sponsored by the Agency for Healthcare Research and Quality (AHRQ), is a complex national probability sample survey. The survey is designed to produce annual national and regional estimates of health-care use, expenditures, sources of payment, and insurance coverage for the U.S. civilian non-institutionalized population. The MEPS sample is a sub-sample of respondents to the prior year's National Health Interview Survey (NHIS) conducted by the National Center for Health Statistics (NCHS). The MEPS, like most sample surveys, experiences unit, or total, non-response despite intensive efforts to maximize response rates. This paper summarizes research on comparing alternative approaches for modelling response propensity to compensate for dwelling unit (DU), i.e. household level non-response in the MEPS.Non-response in sample surveys is usually compensated for by some form of weighting adjustment to reduce the bias in survey estimates. To compensate for potential bias in survey estimates in the MEPS, two separate non-response adjustments are carried out. The first is an adjustment for DU level non-response at the round one interview to account for non-response among those households subsampled from NHIS for the MEPS. The second non-response adjustment is a person level adjustment to compensate for attrition across the five rounds of data collection. This paper deals only with the DU level non-response adjustment. Currently, the categorical search tree algorithm method, the chi-squared automatic interaction detector (CHAID), is used to model the response probability at the DU level and to create the non-response adjustment cells. In this study, we investigate an alternative approach, i.e. logistic regression to model the response probability. Main effects models and models with interaction terms are both evaluated. We further examine inclusion of the base weights as a covariate in the logistic models. We compare variability of weights of the two alternative response propensity approaches as well as direct use of propensity scores.The logistic regression approaches produce results similar to CHAID; however, using propensity scores from logistic models with interaction terms to form five classification groups for weight adjustment appears to perform best in terms of limiting variability and bias. Published in 2007 by John Wiley & Sons, Ltd.     

The problem of attrition in a Finnish longitudinal survey on depression

A cohort of all school children aged 16 years in 1983 (n=2194, 96.7%) in Tampere, Finland were studied at 16, 22 and 32 years of age by self-reported questionnaires. The non-response pattern was considered by modelling the individual response probability by panel year and gender. Gender and school performance at age 16 years were the most important predictors of non-response. They explained away the effect of all other variables at 16 and 22 years, except for earlier non-response at age 22. However, the ability of the models to predict non-respondents was very poor. The effect of attrition for the estimation of depression prevalence was evaluated first by longitudinal weighting methods used commonly in survey studies and then by Markov chain Monte Carlo (MCMC) simulation of the missing depression status. Under the missing-at-random assumption (MAR), both applied correction methods gave estimates of roughly the same size and did not significantly differ from the observed prevalence of depression. No indication of informative missingness was found. We therefore conclude that attrition does not seriously bias the estimation of depression prevalence in the data. In general, non-response models, which are needed to correct for informative missingness, are likely to have poor ability to predict non-response. Therefore, the plausibility of the MAR assumption is important in the presence of attrition.     

ANALYSIS OF SEMI-PARAMETRIC REGRESSION MODELS WITH NON-IGNORABLE NON-RESPONSE

In this article we consider the problem of making inferences about the parameter β₀ indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables (outcome or covariates) are missing for some study subjects and the probability of non-response depends upon both observed and unobserved data values, that is, non-response is non-ignorable. We propose a new class of inverse probability of censoring weighted estimators that are consistent and asymptotically normal (CAN) for estimating β₀ when the non-response probabilities can be parametrically modelled and a CAN estimator exists. The proposed estimators do not require full specification of the likelihood and their computation does not require numerical integration. We show that the asymptotic variance of the optimal estimator in our class attains the semi-parametric variance bound for the model. In some models, no CAN estimator of β₀ exists. We provide a general algorithm for determining when CAN estimators of β₀ exist. Our results follow after specializing a general representation described in the article for the efficient score and the influence function of regular, asymptotically linear estimators in an arbitrary semi-parametric model with non-ignorable non-response in which the probability of observing complete data is bounded away from zero and the non-response probabilities can be parametrically modelled. © 1997 by John Wiley & Sons, Ltd.     

An alternative empirical likelihood method in missing response problems and causal inference

Missing responses are common problems in medical, social, and economic studies. When responses are missing at random, a complete case data analysis may result in biases. A popular debias method is inverse probability weighting proposed by Horvitz and Thompson. To improve efficiency, Robins et al. proposed an augmented inverse probability weighting method. The augmented inverse probability weighting estimator has a double‐robustness property and achieves the semiparametric efficiency lower bound when the regression model and propensity score model are both correctly specified. In this paper, we introduce an empirical likelihood‐based estimator as an alternative to Qin and Zhang (2007). Our proposed estimator is also doubly robust and locally efficient. Simulation results show that the proposed estimator has better performance when the propensity score is correctly modeled. Moreover, the proposed method can be applied in the estimation of average treatment effect in observational causal inferences. Finally, we apply our method to an observational study of smoking, using data from the Cardiovascular Outcomes in Renal Atherosclerotic Lesions clinical trial. Copyright © 2016 John Wiley & Sons, Ltd.     

On weighting the rates in non-response weights

A basic estimation strategy in sample surveys is to weight units inversely proportional to the probability of selection and response. Response weights in this method are usually estimated by the inverse of the sample-weighted response rate in an adjustment cell, that is, the ratio of the sum of the sampling weights of respondents in a cell to the sum of the sampling weights for respondents and non-respondents in that cell. We show by simulations that weighting the response rates by the sampling weights to adjust for design variables is either incorrect or unnecessary. It is incorrect, in the sense of yielding biased estimates of population quantities, if the design variables are related to survey non-response; it is unnecessary if the design variables are unrelated to survey non-response. The correct approach is to model non-response as a function of the adjustment cell and design variables, and to estimate the response weight as the inverse of the estimated response probability from this model. This approach can be implemented by creating adjustment cells that include design variables in the cross-classification, if the number of cells created in this way is not too large. Otherwise, response propensity weighting can be applied.     

A marginal structural model for multiple‐outcome survival data:assessing the impact of injection drug use on several causes of death in the Canadian Co‐infection Cohort

It is often the case that interest lies in the effect of an exposure on each of several distinct event types. For example, we are motivated to investigate in the impact of recent injection drug use on deaths due to each of cancer, end‐stage liver disease, and overdose in the Canadian Co‐infection Cohort (CCC). We develop a marginal structural model that permits estimation of cause‐specific hazards in situations where more than one cause of death is of interest. Marginal structural models allow for the causal effect of treatment on outcome to be estimated using inverse‐probability weighting under the assumption of no unmeasured confounding; these models are particularly useful in the presence of time‐varying confounding variables, which may also mediate the effect of exposures. An asymptotic variance estimator is derived, and a cumulative incidence function estimator is given. We compare the performance of the proposed marginal structural model for multiple‐outcome data to that of conventional competing risks models in simulated data and demonstrate the use of the proposed approach in the CCC. Copyright © 2013 John Wiley & Sons, Ltd.     

Partial questionnaire designs, questionnaire non-response, and attributable fraction: applications to adult onset asthma

The attributable fraction (AF) is often used to explore the policy implications of an association between a disease and an exposure. To date, there have been no proposed estimators of AF in the context of partial questionnaire designs (PQD). The PQD, first proposed in a public health context by Wacholder is often used to enhance response rates in questionnaires. It involves eliciting responses from each subject on preassigned subsets of questions, thereby reducing the burden of response. We propose a computationally efficient method of estimating logistic (or more generally, binary) regression parameters from a PQD model where there is non-response to the questionnaire and the rates of non-response differ between sub-populations. Assuming a log-linear model for the distribution of missing covariates, we employ the methods of Wacholder to motivate consistent estimating equations, and weight each subject's contribution to the estimating function by the inverse probability of responding to the questionnaire. We also propose techniques for goodness-of-fit to assist in model selection. We then use the PQD regression estimates to derive an estimate of AF similar to that proposed by Bruzzi. Finally, we demonstrate our methods using data obtained from a study on adult occupational asthma, conducted within a Massachusetts HMO. Although we concentrate on a particular type of missing data mechanism, other missing data techniques can be incorporated into AF estimation in a similar manner.     

Estimating cumulative incidence functions in competing risks data with dependent left-truncation

Both delayed study entry (left-truncation) and competing risks are common phenomena in observational time-to-event studies. For example, in studies conducted by Teratology Information Services (TIS) on adverse drug reactions during pregnancy, the natural time scale is gestational age, but women enter the study after time origin and upon contact with the service. Competing risks are present, because an elective termination may be precluded by a spontaneous abortion. If left-truncation is entirely random, the Aalen-Johansen estimator is the canonical estimator of the cumulative incidence functions of the competing events. If the assumption of random left-truncation is in doubt, we propose a new semiparametric estimator of the cumulative incidence function. The dependence between entry time and time-to-event is modeled using a cause-specific Cox proportional hazards model and the marginal (unconditional) estimates are derived via inverse probability weighting arguments. We apply the new estimator to data about coumarin usage during pregnancy. Here, the concern is that the cause-specific hazard of experiencing an induced abortion may depend on the time when seeking advice by a TIS, which also is the time of left-truncation or study entry. While the aims of counseling by a TIS are to reduce the rate of elective terminations based on irrational overestimation of drug risks and to lead to better and safer medical treatment of maternal disease, it is conceivable that women considering an induced abortion are more likely to seek counseling. The new estimator is also evaluated in extensive simulation studies and found preferable compared to the Aalen-Johansen estimator in non–misspecified scenarios and to at least provide for a sensitivity analysis otherwise.     

Estimation of non-response bias in the Medicare FFS HOS

We examined non-response bias in physical component summary scores (PCS) and mental component summary scores (MCS) in the Medicare fee-for-service (FFS) Health Outcomes Survey (HOS) using two alternative methods, response propensity weighting and imputation for non-respondents. The two approaches gave nearly identical estimates of non-response bias. PCS scores were 0.74 points lower and MCS scores 0.51 points lower after adjustment for non-response through imputation and 0.63 and 0.46 lower after adjustment for propensity weighting. These levels are small for component scores suggesting that survey non-response to the FFS HOS does not adversely affect estimates of average health status for this population.     

True verification probabilities should not be used in estimating the area under receiver operating characteristic curve

In medical research, a two-phase study is often used for the estimation of the area under the receiver operating characteristic curve (AUC) of a diagnostic test. However, such a design introduces verification bias. One of the methods to correct verification bias is inverse probability weighting (IPW). Since the probability a subject is selected into phase 2 of the study for disease verification is known, both true and estimated verification probabilities can be used to form an IPW estimator for AUC. In this article, we derive explicit variance formula for both IPW AUC estimators and show that the IPW AUC estimator using the true values of verification probabilities even when they are known are less efficient than its counterpart using the estimated values. Our simulation results show that the efficiency loss can be substantial especially when the variance of test result in disease population is small relative to its counterpart in nondiseased population.     

Supplementary analysis of probabilities at the termination of a group sequential phase II trial

We consider estimation of various probabilities after termination of a group sequential phase II trial. A motivating example is that the stopping rule of a phase II oncologic trial is determined solely based on response to a drug treatment, and at the end of the trial estimating the rate of toxicity and response is desirable. The conventional maximum likelihood estimator (sample proportion) of a probability is shown to be biased, and two alternative estimators are proposed to correct for bias, a bias-reduced estimator obtained by using Whitehead's bias-adjusted approach, and an unbiased estimator from the Rao-Blackwell method of conditioning. All three estimation procedures are shown to have certain invariance property in bias. Moreover, estimators of a probability and their bias and precision can be evaluated through the observed response rate and the stage at which the trial stops, thus avoiding extensive computation.     

Model misspecification and robustness in causal inference: comparing matching with doubly robust estimation

In this paper, we compare the robustness properties of a matching estimator with a doubly robust estimator. We describe the robustness properties of matching and subclassification estimators by showing how misspecification of the propensity score model can result in the consistent estimation of an average causal effect. The propensity scores are covariate scores, which are a class of functions that removes bias due to all observed covariates. When matching on a parametric model (e.g., a propensity or a prognostic score), the matching estimator is robust to model misspecifications if the misspecified model belongs to the class of covariate scores. The implication is that there are multiple possibilities for the matching estimator in contrast to the doubly robust estimator in which the researcher has two chances to make reliable inference. In simulations, we compare the finite sample properties of the matching estimator with a simple inverse probability weighting estimator and a doubly robust estimator. For the misspecifications in our study, the mean square error of the matching estimator is smaller than the mean square error of both the simple inverse probability weighting estimator and the doubly robust estimators.     

Inference for the median residual life function in sequential multiple assignment randomized trials

In survival analysis, median residual lifetime is often used as a summary measure to assess treatment effectiveness; it is not clear, however, how such a quantity could be estimated for a given dynamic treatment regimen using data from sequential randomized clinical trials. We propose a method to estimate a dynamic treatment regimen‐specific median residual life (MERL) function from sequential multiple assignment randomized trials. We present the MERL estimator, which is based on inverse probability weighting, as well as, two variance estimates for the MERL estimator. One variance estimate follows from Lunceford, Davidian and Tsiatis' 2002 survival function‐based variance estimate and the other uses the sandwich estimator. The MERL estimator is evaluated, and its two variance estimates are compared through simulation studies, showing that the estimator and both variance estimates produce approximately unbiased results in large samples. To demonstrate our methods, the estimator has been applied to data from a sequentially randomized leukemia clinical trial. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimating treatment effects on healthcare costs under exogeneity: is there a ��magic bullet��?

Methods for estimating average treatment effects, under the assumption of no unmeasured confounders, include regression models; propensity score adjustments using stratification, weighting, or matching; and doubly robust estimators (a combination of both). Researchers continue to debate about the best estimator for outcomes such as health care cost data, as they are usually characterized by an asymmetric distribution and heterogeneous treatment effects,. Challenges in finding the right specifications for regression models are well documented in the literature. Propensity score estimators are proposed as alternatives to overcoming these challenges. Using simulations, we find that in moderate size samples (n= 5000), balancing on propensity scores that are estimated from saturated specifications can balance the covariate means across treatment arms but fails to balance higher-order moments and covariances amongst covariates. Therefore, unlike regression model, even if a formal model for outcomes is not required, propensity score estimators can be inefficient at best and biased at worst for health care cost data. Our simulation study, designed to take a 'proof by contradiction' approach, proves that no one estimator can be considered the best under all data generating processes for outcomes such as costs. The inverse-propensity weighted estimator is most likely to be unbiased under alternate data generating processes but is prone to bias under misspecification of the propensity score model and is inefficient compared to an unbiased regression estimator. Our results show that there are no 'magic bullets' when it comes to estimating treatment effects in health care costs. Care should be taken before naively applying any one estimator to estimate average treatment effects in these data. We illustrate the performance of alternative methods in a cost dataset on breast cancer treatment.     

Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis

Propensity score methods are used to reduce the effects of observed confounding when using observational data to estimate the effects of treatments or exposures. A popular method of using the propensity score is inverse probability of treatment weighting (IPTW). When using this method, a weight is calculated for each subject that is equal to the inverse of the probability of receiving the treatment that was actually received. These weights are then incorporated into the analyses to minimize the effects of observed confounding. Previous research has found that these methods result in unbiased estimation when estimating the effect of treatment on survival outcomes. However, conventional methods of variance estimation were shown to result in biased estimates of standard error. In this study, we conducted an extensive set of Monte Carlo simulations to examine different methods of variance estimation when using a weighted Cox proportional hazards model to estimate the effect of treatment. We considered three variance estimation methods: (i) a naïve model‐based variance estimator; (ii) a robust sandwich‐type variance estimator; and (iii) a bootstrap variance estimator. We considered estimation of both the average treatment effect and the average treatment effect in the treated. We found that the use of a bootstrap estimator resulted in approximately correct estimates of standard errors and confidence intervals with the correct coverage rates. The other estimators resulted in biased estimates of standard errors and confidence intervals with incorrect coverage rates. Our simulations were informed by a case study examining the effect of statin prescribing on mortality. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

Identification of the optimal treatment regimen in the presence of missing covariates

Covariates associated with treatment-effect heterogeneity can potentially be used to make personalized treatment recommendations towards best clinical outcomes. Methods for treatment-selection rule development that directly maximize treatment-selection benefits have attracted much interest in recent years, due to the robustness of these methods to outcome modeling. In practice, the task of treatment-selection rule development can be further complicated by missingness in data. Here, we consider the identification of optimal treatment-selection rules for a binary disease outcome when measurements of an important covariate from study participants are partly missing. Under the missing at random assumption, we develop a robust estimator of treatment-selection rules under the direct-optimization paradigm. This estimator targets the maximum selection benefits to the population under correct specification of at least one mechanism from each of the two sets—missing data or conditional covariate distribution, and treatment assignment or disease outcome model. We evaluate and compare performance of the proposed estimator with alternative direct-optimization estimators through extensive simulation studies. We demonstrate the application of the proposed method through a real data example from an Alzheimer's disease study for developing covariate combinations to guide the treatment of Alzheimer's disease.     

Quantile estimation following non-parametric phase I clinical trials with ordinal response

A non-parametric multi-dimensional isotonic regression estimator is developed for use in estimating a set of target quantiles from an ordinal toxicity scale. We compare this estimator to the standard parametric maximum likelihood estimator from a proportional odds model for extremely small data sets. A motivating example is from phase I oncology clinical trials, where various non-parametric designs have been proposed that lead to very small data sets, often with ordinal toxicity response data. Our comparison of estimators is performed in conjunction with three of these non-parametric sequential designs for ordinal response data, two from the literature and a new design based on a random walk rule. We also compare with a non-parametric design for binary response trials, by keeping track of ordinal data for estimation purposes, but dichotomizing the data in the design phase. We find that a multidimensional isotonic regression-based estimator far exceeds the others in terms of accuracy and efficiency. A rule by Simon et al. (J. Natl. Cancer Inst. 1997; 89:1138-1147) yields particularly efficient estimators, more so than the random walk rule, but has higher numbers of dose-limiting toxicity. A small data set from a leukemia clinical trial is analysed using our multidimensional isotonic regression-based estimator.     

Doubly robust generalized estimating equations for longitudinal data

A popular method for analysing repeated‐measures data is generalized estimating equations (GEE). When response data are missing at random (MAR), two modifications of GEE use inverse‐probability weighting and imputation. The weighted GEE (WGEE) method involves weighting observations by their inverse probability of being observed, according to some assumed missingness model. Imputation methods involve filling in missing observations with values predicted by an assumed imputation model. WGEE are consistent when the data are MAR and the dropout model is correctly specified. Imputation methods are consistent when the data are MAR and the imputation model is correctly specified. Recently, doubly robust (DR) methods have been developed. These involve both a model for probability of missingness and an imputation model for the expectation of each missing observation, and are consistent when either is correct. We describe DR GEE, and illustrate their use on simulated data. We also analyse the INITIO randomized clinical trial of HIV therapy allowing for MAR dropout. Copyright © 2009 John Wiley & Sons, Ltd.     

A qualifier Q for the survival function to describe the prevalence of a transient condition

We propose an estimator of the prevalence of a transient condition among surviving patients using right censored data. The prevalence of opportunistic infection among surviving AIDS patients and the probability of being in tumour response following cancer therapy conditional on being alive are two examples of such functions. In essence these functions describe a major aspect of the quality of life for surviving patients and may be useful when viewed in conjunction with the survival curves themselves. The method is illustrated using data from a randomized trial of bone marrow transplant patients where the prevalence of chronic graft-versus-host disease is of interest. The non-parametric estimator which we have proposed is contrasted with estimators derived from Markov and semi-Markov models.