Double Robust Estimators Research Articles

Inference for big data assisted by small area methods: an application on sustainable development goals sensitivity of enterprises in Italy

Abstract In this study, we proposed a new method for estimating the sensitivity of enterprises in Italy to the United Nation’s sustainable development goals at the provincial level using web-scraping data (a nonprobability sample) because this value is not surveyed by the Italian National Institute of Statistics. The proposed method used a probability sample to reduce the selection bias of estimates obtained from the nonprobability sample in the context of small area estimation and integrated nonprobability and probability samples using a double robust estimator that combined (i) propensity weighting to improve the representativeness of the nonprobability sample and (ii) a statistical model to predict the units that were not in the nonprobability sample. A bootstrap procedure for estimating variance was also proposed. To validate the proposed method, a Monte Carlo simulation was performed. Results showed that the proposed method allowed the correction of bias from the nonprobability sample while maintaining a good level of estimate reliability.

Consumption responses to sweetened beverage taxes by household income in four U.S. cities.

Taxes on sweetened beverages have become an important policy response to growing obesity rates and the prevalence of type 2 diabetes in the U.S. and other nations. Since 2015, eight U.S. cities have implemented these taxes, but so far direct evidence of their impacts on household purchasing behavior is scarce. Of particular interest to many researchers and policy makers is the response of lower-income consumers to these taxes, both because they have higher sweetened beverage consumption on average and because of concerns that sweetened beverage taxes are regressive. This project investigates the income-stratified household response to SSB taxes using a data set containing the purchasing behavior of approximately 400 households in the cities of Seattle, San Francisco, Oakland, and Philadelphia, all of which have recently introduced beverage taxes. Using doubly-robust estimation of dynamic and heterogeneous treatment effects relative to a propensity-matched set of households in three comparison cities, we find that households in taxed cities experience increased prices and reduce their purchases of those beverages, with no evidence of cross-border shopping. We further find differential tax impacts by income level, with lower-income households (households with income <200% of the federal poverty line for their size) reducing their purchases of taxed beverages by nearly 50% - more than double the 18% reduction found in higher-income households (households with income >400% of the federal poverty line for their size). Our finding that lower-income households decrease their consumption more than twice as much as higher-income households suggests that these taxes may reduce health disparities and promote population health.

Association of Dementia with Adverse Outcomes in Older Patients with Acute Myocardial Infarction in the ICU.

Dementia limits timely revascularization in individuals with acute myocardial infarction (AMI). However, it remains unclear whether dementia affects prognosis negatively in older individuals with AMI in the intensive care unit (ICU). This research aimed to evaluate the dementia effect on the outcomes in individuals with AMI in ICU.Data from 3,582 patients aged ≥ 65 years with AMI in ICU from the Medical Information Mart for Intensive Care IV (MIMIC IV) database were evaluated. The independent variable was dementia at baseline, and the primary finding was death from any cause during follow-up. A 1:1 propensity score matching (PSM) showed 208 participants with and without dementia. The correlation between dementia and poor prognosis of AMI was verified using a double-robust estimation method.In the PSM cohort, the 30-day all-cause mortality was 37.50% and 33.17% in the dementia and non-dementia groups (P = 0.356), respectively, and the 1-year all-cause mortality was 61.06% and 51.44%, respectively (P = 0.048). Cox regression analysis showed no association between dementia and elevated 30-day (hazard ratio [HR] 1.15, 95% confidence interval [CI] 0.84, 1.60) and 1-year (HR 1.28, 95% CI 0.99, 1.66) all-cause mortality after AMI. Similarly, dementia was not connected with in-hospital mortality, bleeding, or stroke after AMI. Interaction analysis showed that 1-year all-cause mortality was 48.00% higher in individuals with dementia and diabetic complications than in those without diabetic complications.Dementia is not an independent risk factor for adverse outcomes in AMI. Thus, it may be inappropriate to include dementia as a contraindication for invasive AMI therapy.

Calibrating doubly-robust estimators with unbalanced treatment assignment

Machine learning methods, particularly the double machine learning (DML) estimator (Chernozhukov et al., 2018), are increasingly popular for the estimation of the average treatment effect (ATE). However, datasets often exhibit unbalanced treatment assignments where only a few observations are treated, leading to unstable propensity score estimations. We propose a simple extension of the DML estimator which undersamples data for propensity score modeling and calibrates scores to match the original distribution. The paper provides theoretical results showing that the estimator retains the DML estimator’s asymptotic properties. A simulation study illustrates the finite sample performance of the estimator.

Intravenous fluid therapy in hospitalized adult dengue patients without shock: Impact on subsequent severe dengue and potential adverse effects.

There is a lack of evidence on the optimal administration of intravenous (IV) fluids in hospitalized adult dengue patients without compensated and hypotensive shock. This study utilized a well-established cohort of dengue patients to compare risks of progressing to severe dengue (SD) over time for patients who were administered IV fluid versus others who were not. We included adult patients (n = 4781) who were hospitalized for dengue infection from 2005 to 2008. Cases were patients who developed SD (n = 689) and controls were patients who did not up until discharge (n = 4092). We estimated the hazardratios (HRs) and risk of SD over time between groups administered different volumes of IV fluids versus the no IV fluid comparison group using Cox models with time-dependent covariates. The doubly-robust estimation approach was used to control for the propensity of fluid administration given clinical characteristics of patients. Subgroup analyses by age, sex, and dengue warning signs before IV fluid administration were conducted. High (>2000 mL/day) IV fluids volume was associated with a higher risk of development of SD for those who had warning signs (HR: 1.77 [1.05-2.97], p: 0.0713) and for those below 55 years old (HR: 1.53 [1.04-2.25], p: 0.0713). Low (<1000 mL/day) IV fluids volume was protective against SD for patients without warning signs (HR: 0.757 [0.578-0.990], p: 0.0883), no lethargy (HR: 0.770 [0.600-0.998], p: 0.0847), and females (HR: 0.711 [0.516-0.980], p: 0.0804). Over the course of hospitalization, there were no significant differences in IV fluid administration and SD risk in most subgroups, except in those who experienced lethargy and were administered IV fluid volume or quantity. Administering high volumes of IV fluids may be associated with an increased risk of SD during hospitalization for adult dengue patients without shock. Judicious use of IV fluids as supportive therapy is warranted.

Dynamic borrowing of historical controls adjusting for covariates in vaccine efficacy clinical trials.

Traditional vaccine efficacy trials usually use fixed designs and often require large sample sizes. Recruiting a large number of subjects can make the trial expensive, long, and difficult to conduct. A possible approach to reduce the sample size and speed up the development is to use historical controls. In this paper, we extend the robust mixture prior (RMP) approach (a well established approach for Bayesian dynamic borrowing of historical controls) to adjust for covariates. The adjustment is done using classical methods from causal inference: inverse probability of treatment weighting, G-computation and double-robust estimation. We evaluate these covariate-adjusted RMP approaches using a comprehensive simulation study and demonstrate their use by performing a retrospective analysis of a prophylactic human papillomavirus vaccine efficacy trial. Adjusting for covariates reduces the drift between current and historical controls, with a beneficial effect on bias, control of type I error and power.

Assessing efficacy in non-inferiority trials with non-adherence to interventions: Are intention-to-treat and per-protocol analyses fit for purpose?

Non-inferiority trials comparing different active drugs are often subject to treatment non-adherence. Intention-to-treat (ITT) and per-protocol (PP) analyses have been advocated in such studies but are not guaranteed to be unbiased in the presence of differential non-adherence. The REMoxTB trial evaluated two 4-month experimental regimens compared with a 6-month control regimen for newly diagnosed drug-susceptible TB. The primary endpoint was a composite unfavorable outcome of treatment failure or recurrence within 18 months post-randomization. We conducted a simulation study based on REMoxTB to assess the performance of statistical methods for handling non-adherence in non-inferiority trials, including: ITT and PP analyses, adjustment for observed adherence, multiple imputation (MI) of outcomes, inverse-probability-of-treatment weighting (IPTW), and a doubly-robust (DR) estimator. When non-adherence differed between trial arms, ITT, and PP analyses often resulted in non-trivial bias in the estimated treatment effect, which consequently under- or over-inflated the type I error rate. Adjustment for observed adherence led to similar issues, whereas the MI, IPTW and DR approaches were able to correct bias under most non-adherence scenarios; they could not always eliminate bias entirely in the presence of unobserved confounding. The IPTW and DR methods were generally unbiased and maintained desired type I error rates and statistical power. When non-adherence differs between trial arms, ITT and PP analyses can produce biased estimates of efficacy, potentially leading to the acceptance of inferior treatments or efficacious regimens being missed. IPTW and the DR estimator are relatively straightforward methods to supplement ITT and PP approaches.

The impact of smart input subsidy program on farm productivity: Evidence from Tanzania

Policymakers have a renewed interest in input subsidy programs in sub-Saharan Africa. However, the evidence of the program's impact is mixed. This paper uses the case of Tanzania's National Agricultural Input Voucher Scheme (NAIVS) to examine its effect on farm productivity. To account for the endogeneity problem arising from the non-random targeting of beneficiaries, this study employed a staggered difference-in-differences approach with a double robust estimator method on a three-wave panel survey. This approach is relevant because the treatment variable—NAIVS participation was gradually rolled out to households over multiple periods and groups. The results do not show evidence that the NAIVS program increased farm productivity. However, the group aggregate effects suggest that the group initially treated in 2010 experienced a positive and significant impact on maize production and income. This could indicate that during the early stages of the NAIVS program, extra effort was likely invested to ensure its effectiveness. Furthermore, the heterogeneous effect of farm size reveals that the NAIVS program increased the participation of beneficiary households with large-scale farms rather than small-scale farms. This suggests that the program did not effectively target resource-poor households. Finally, this paper calls for effective targeting and careful implementation of programs to improve farmer productivity.

Enhanced doubly robust estimation with concave link functions for estimands in clinical trials

ABSTRACT For observational studies or clinical trials not fully randomised, the baseline covariates are often not balanced between the treatment and control groups. In this case, the traditional estimates of treatment effects are biased, and causal inference method is needed to get unbiased estimate. The doubly robust estimator (DRE) is a recent popular development in casual inference. However, the unbiasedness of DRE relies on the correct specification of either propensity score or outcome models, which is hardly guaranteed. To overcome this issue, Yuan et al. [(2021), ‘Enhanced Doubly Robust Procedure for Causal Inference’, Statistics in Bioscience, 13(3), 454–478. https://doi.org/10.1007/s12561-021-09300-y.] proposed an enhanced doubly robust estimator which utilises semiparametric models and nonparametric monotone link functions for both propensity score and outcome models. In this article, we further develop an enhanced doubly robust estimator with concave link functions for both propensity score and outcome models. The asymptotic properties of the enhanced doubly robust estimator are studied. Simulation studies are conducted to evaluate the proposed method. A clinical trial data analysis is used to illustrate the method.

Targeted learning in observational studies with multi-valued treatments: An evaluation of antipsychotic drug treatment safety.

We investigate estimation of causal effects of multiple competing (multi-valued) treatments in the absence of randomization. Our work is motivated by an intention-to-treat study of the relative cardiometabolic risk of assignment to one of six commonly prescribed antipsychotic drugs in a cohort of nearly 39000 adults with serious mental illnesses. Doubly-robust estimators, such as targeted minimum loss-based estimation (TMLE), require correct specification of either the treatment model or outcome model to ensure consistent estimation; however, common TMLE implementations estimate treatment probabilities using multiple binomial regressions rather than multinomial regression. We implement a TMLE estimator that uses multinomial treatment assignment and ensemble machine learning to estimate average treatment effects. Our multinomial implementation improves coverage, but does not necessarily reduce bias, relative to the binomial implementation in simulation experiments with varying treatment propensity overlap and event rates. Evaluating the causal effects of the antipsychotics on 3-year diabetes risk or death, we find a safety benefit of moving from a second-generation drug considered among the safest of the second-generation drugs to an infrequently prescribed first-generation drug known for having low cardiometabolic risk.

The impact of racism on subsequent healthcare use and experiences for adult New Zealanders: a prospective cohort study

BackgroundRacism is an important determinant of health and driver of racial/ethnic health inequities. Experience of racism has been linked to negative healthcare use and experiences although most studies have been cross-sectional. This study examines the relationship between reported experience of racism and subsequent use and experience of health services.MethodsThis is a prospective cohort study design. The 2016/2017 adult New Zealand Health Survey (NZHS) provided the sampling frame and baseline data on exposures, health status and confounders. This stand-alone study invited all exposed individuals to participate when sampled based on their reported experience of racism (ever), stratified by broad ethnic groupings (Māori, Pacific, Asian, European/Other). Equal numbers of unexposed participants were selected for invitation using propensity score matching (propensity to experience racism, based on key available predictive factors). Follow-up was one to two years after NZHS interview. Outcome variables (last 12 months) were: unmet healthcare need (overall, for mental health, for a general practitioner); satisfaction with usual medical centre; and experiences with general practitioners (explaining care, involvement in decision-making, treated with respect/dignity, confidence and trust). Logistic regression models examining the association between experience of racism (at baseline) and health service use and experience (at follow-up) used doubly-robust estimation to weight for propensity scores used in the sampling with additional adjustment for confounders.ResultsThe study had 2010 participants. Experience of racism (ever) at baseline was associated with higher overall unmet need at follow-up (adjusted OR (aOR) = 1.71, 95% CI 1.31, 2.23), with similar patterns for other unmet need measures. Experience of racism was associated with higher dissatisfaction with a usual medical centre (aOR = 1.41, 95% CI 1.10, 1.81) and with higher reporting of negative patient experiences.ConclusionIn line with how racism structures oppression, exposure to racism is largely felt by non-European groups in Aotearoa New Zealand. Experiences of racism potentially lead to poorer healthcare and healthcare inequities through higher unmet need, lower satisfaction and more negative experiences of healthcare. The health system has a critical role to play in addressing racism within healthcare and supporting societal efforts to eliminate racism and ethnic inequities.

Outlier-Resistant Estimators for Average Treatment Effect in Causal Inference

The inverse probability (IPW) and doubly robust (DR) estimators are often used to estimate the average causal effect (ATE), but are vulnerable to outliers. The IPW/DR median can be used for outlier-resistant estimation of the ATE, but the outlier resistance of the median is limited and it is not resistant enough for heavy contamination. We propose extensions of the IPW/DR estimators with density power weighting, which can eliminate the influence of outliers almost completely. The outlier resistance of the proposed estimators is evaluated through the unbiasedness of the estimating equations. Unlike the median-based methods, our estimators are resistant to outliers even under heavy contamination. Interestingly, the naive extension of the DR estimator requires bias correction to keep the double robustness even under the most tractable form of contamination. In addition, the proposed estimators are found to be highly resistant to outliers in more difficult settings where the contamination ratio depends on the covariates. The outlier resistance of our estimators from the viewpoint of the influence function is also favorable. Our theoretical results are verified via Monte Carlo simulations and real data analysis. The proposed methods were found to have more outlier resistance than the median-based methods and estimated the potential mean with a smaller error than the median-based methods.

Effect of high-risk versus low-risk pregnancy at the first antenatal care visit on the occurrence of complication during pregnancy and labour or delivery in Kenya: a double-robust estimation

ObjectivesWe evaluated the causal effects of high-risk versus low-risk pregnancy at the first antenatal care (ANC) visit on the occurrence of complications during pregnancy and labour or delivery among women...

Associations between long-term exposure to PM2.5 chemical constituents and allergic diseases: evidence from a large cohort study in China

BackgroundExposure to air pollutants may cause immune responses and further allergic diseases, but existing studies have mostly, if not all, focused on effects of short-term exposure to PM2.5 on allergic diseases. ObjectivesWe estimated associations of long-term exposure to PM2.5 chemical constituents with allergic disease risks and effect modification. MethodsWe used the baseline of a newly established, provincially representative cohort of 51,480 participants in southwest China. The presence of allergic rhinitis, allergic asthma, urticaria, and allergic conjunctivitis was self-reported by following a formed questionnaire in face-to-face interviews. The average concentrations of PM2.5 chemical constituents (NO3−, SO42−, NH4+, organic matter [OM], and black carbon [BC]) over participants' residence were estimated using machine learning models. Logistic regression with double robust estimator and weighted quantile sum regression were used to estimate the effects of PM2.5 chemical constituents on allergic disease risks, as well as relative importance of each PM2.5 chemical constituent. ResultsPer interquartile range increase in the concentration of all PM2.5 chemical constituents was associated with the elevated risks for allergic asthma (OR = 1.79 [1.41–2.26]), allergic conjunctivitis (1.54 [1.19–2.00]), urticaria (1.36 [1.25–1.48]), and allergic rhinitis (1.18 [1.11–1.26]). NO3− contributed more to risks for allergic asthma (weight = 46.05 %), urticaria (72.29 %), and allergic conjunctivitis (47.65 %), while NH4+ contributed more to allergic rhinitis (78.07 %). OM contributed most to the risks for allergic asthma (30.81 %) and allergic conjunctivitis (31.40 %). BC was also associated with allergic rhinitis, urticaria, and allergic conjunctivitis, only with a considerable weight for urticaria (24.59 %). Joint effects of PM2.5 chemical constituents on risks for allergic rhinitis and urticaria were stronger in minorities and farmers than their counterparts. ConclusionLong-term exposure to PM2.5 chemical constituents was associated with the increased allergic disease risks, with NO3− and NH4+ accounting for the largest variance of the associations. Our findings would serve as scientific evidence for developing more explicit strategies of air pollution control.

An efficient doubly-robust imputation framework for longitudinal dropout, with an application to an Alzheimer’s clinical trial

We develop a novel doubly-robust (DR) imputation framework for longitudinal studies with monotone dropout, motivated by the informative dropout that is common in FDA-regulated trials for Alzheimer's disease. In this approach, the missing data are first imputed using a doubly-robust augmented inverse probability weighting (AIPW) estimator, then the imputed completed data are substituted into a full-data estimating equation, and the estimate is obtained using standard software. The imputed completed data may be inspected and compared to the observed data, and standard model diagnostics are available. The same imputed completed data can be used for several different estimands, such as subgroup analyses in a clinical trial, allowing for reduced computation and increased consistency across analyses. We present two specific DR imputation estimators, AIPW-I and AIPW-S, study their theoretical properties, and investigate their performance by simulation. AIPW-S has substantially reduced computational burden compared to many other DR estimators, at the cost of some loss of efficiency and the requirement of stronger assumptions. Simulation studies support the theoretical properties and good performance of the DR imputation framework. Importantly, we demonstrate their ability to address time-varying covariates, such as a time by treatment interaction. We illustrate using data from a large randomized Phase III trial investigating the effect of donepezil in Alzheimer's disease, from the Alzheimer's Disease Cooperative Study (ADCS) group.

Inference for Treatment-Specific Survival Curves Using Machine Learning

ABSTRACT In the absence of data from a randomized trial, researchers may aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves, that is, the survival curves were the population under study to be assigned to receive the treatment or not. Under certain conditions, including that all confounders of the treatment-outcome relationship are observed, the treatment-specific survival curve can be identified with a covariate-adjusted survival curve. In this article, we propose a novel cross-fitted doubly-robust estimator that incorporates data-adaptive (e.g., machine learning) estimators of the conditional survival functions. We establish conditions on the nuisance estimators under which our estimator is consistent and asymptotically linear, both pointwise and uniformly in time. We also propose a novel ensemble learner for combining multiple candidate estimators of the conditional survival estimators. Notably, our methods and results accommodate events occurring in discrete or continuous time, or an arbitrary mix of the two. We investigate the practical performance of our methods using numerical studies and an application to the effect of a surgical treatment to prevent metastases of parotid carcinoma on mortality. Supplementary materials for this article are available online.

Double robust semi-supervised inference for the mean: selection bias under MAR labeling with decaying overlap

Abstract Semi-supervised (SS) inference has received much attention in recent years. Apart from a moderate-sized labeled data, $\mathcal L$, the SS setting is characterized by an additional, much larger sized, unlabeled data, $\mathcal U$. The setting of $|\mathcal U\ |\gg |\mathcal L\ |$, makes SS inference unique and different from the standard missing data problems, owing to natural violation of the so-called ‘positivity’ or ‘overlap’ assumption. However, most of the SS literature implicitly assumes $\mathcal L$ and $\mathcal U$ to be equally distributed, i.e., no selection bias in the labeling. Inferential challenges in missing at random type labeling allowing for selection bias, are inevitably exacerbated by the decaying nature of the propensity score (PS). We address this gap for a prototype problem, the estimation of the response’s mean. We propose a double robust SS mean estimator and give a complete characterization of its asymptotic properties. The proposed estimator is consistent as long as either the outcome or the PS model is correctly specified. When both models are correctly specified, we provide inference results with a non-standard consistency rate that depends on the smaller size $|\mathcal L\ |$. The results are also extended to causal inference with imbalanced treatment groups. Further, we provide several novel choices of models and estimators of the decaying PS, including a novel offset logistic model and a stratified labeling model. We present their properties under both high- and low-dimensional settings. These may be of independent interest. Lastly, we present extensive simulations and also a real data application.

Identifying and estimating effects of sustained interventions under parallel trends assumptions.

Many research questions in public health and medicine concern sustained interventions in populations defined by substantive priorities. Existing methods to answer such questions typically require a measured covariate set sufficient to control confounding, which can be questionable in observational studies. Differences-in-differences rely instead on the parallel trends assumption, allowing for some types of time-invariant unmeasured confounding. However, most existing difference-in-differences implementations are limited to point treatments in restricted subpopulations. We derive identification results for population effects of sustained treatments under parallel trends assumptions. In particular, in settings where all individuals begin follow-up with exposure status consistent with the treatment plan of interest but may deviate at later times, a version of Robins' g-formula identifies the intervention-specific mean under stable unit treatment value assumption, positivity, and parallel trends. We develop consistent asymptotically normal estimators based on inverse-probability weighting, outcome regression, and a double robust estimator based on targeted maximum likelihood. Simulation studies confirm theoretical results and support the use of the proposed estimators at realistic sample sizes. As an example, the methods are used to estimate the effect of a hypothetical federal stay-at-home order on all-cause mortality during the COVID-19 pandemic in spring 2020 in the UnitedStates.

Doubly robust estimation for non‐probability samples with modified intertwined probabilistic factors decoupling

AbstractIn recent years, non‐probability samples, such as web survey samples, have become increasingly popular in many fields, but they may be subject to selection biases, which results in the difficulty for inference from them. Doubly robust (DR) estimation is one of the approaches to making inferences from non‐probability samples. When many covariates are available, variable selection becomes important in DR estimation. In this paper, a new DR estimator for the finite population mean is constructed, where the intertwined probabilistic factors decoupling (IPAD) and modified IPAD are used to select important variables in the propensity score model and the outcome superpopulation model, respectively. Unlike the traditional variable selection approaches, such as adaptive least absolute shrinkage and selection operator and smoothly clipped absolute deviations, IPAD and the modified IPAD not only can select important variables and estimate parameters, but also can control the false discovery rate, which can produce more accurate population estimators. Asymptotic theories and variance estimation of the DR estimator with a modified IPAD are established. Results from simulation studies indicate that our proposed estimator performs well. We apply the proposed method to the analysis of the Pew Research Center data and the Behavioral Risk Factor Surveillance System data.

Doubly Robust Estimation for Correcting Position Bias in Click Feedback for Unbiased Learning to Rank

Clicks on rankings suffer from position bias: generally items on lower ranks are less likely to be examined—and thus clicked—by users, in spite of their actual preferences between items. The prevalent approach to unbiased click-based learning-to-rank (LTR) is based on counterfactual inverse-propensity-scoring (IPS) estimation. In contrast with general reinforcement learning, counterfactual doubly robust (DR) estimation has not been applied to click-based LTR in previous literature. In this article, we introduce a novel DR estimator that is the first DR approach specifically designed for position bias. The difficulty with position bias is that the treatment—user examination—is not directly observable in click data. As a solution, our estimator uses the expected treatment per rank, instead of the actual treatment that existing DR estimators use. Our novel DR estimator has more robust unbiasedness conditions than the existing IPS approach, and in addition, provides enormous decreases in variance: our experimental results indicate it requires several orders of magnitude fewer datapoints to converge at optimal performance. For the unbiased LTR field, our DR estimator contributes both increases in state-of-the-art performance and the most robust theoretical guarantees of all known LTR estimators.