Semiparametric Regression for Repeated Outcomes with Nonignorable Nonresponse

Sociodemographic disparities and potential biases in persistent pain estimates: Findings from 5 waves of the Irish Longitudinal Study on Ageing (TILDA)

BACKGROUND

Pain is a prevalent, debilitating condition among older adults. Much evidence on this topic comes from cohort studies, which may be affected by attrition and measurement bias. Little is known about the impact of these biases on pain estimates for European older adults. Additionally, there is a lack of longitudinal research on pain and sociodemographic disparities in Irish older adults.

METHODS

We analysed data from 8171 participants (aged ≥50 at baseline) across five waves of the Irish Longitudinal Study on Ageing. Longitudinal pain severity and sociodemographic disparities in pain were explored visually and using a latent growth curve model. Using multivariate logistic regression, we examined bias due to attrition at later waves associated with reported pain at Wave 1. Measurement biases due to reporting heterogeneity were assessed by investigating associations between sociodemographic factors and pain-related disability for given pain levels.

RESULTS

Wave 1 severe pain was associated with increased odds of attrition due to death by Wave 5 (AOR: 1.63, 95% CI: 1.20, 2.19). Not having private health insurance was associated with increased odds of pain-related disability at Wave 1, controlling for pain severity (AOR: 1.37, 95% CI: 1.15, 1.64). These results suggested mortality bias and reporting heterogeneity measurement bias, respectively. Sex, education level, and private health insurance status disparities in pain were observed longitudinally.

CONCLUSIONS

Mortality bias and reporting heterogeneity measurement bias must be accounted for to improve older adult pain estimates. There is a need for policymakers to address sociodemographic disparities in older adult pain levels.

SIGNIFICANCE

This study highlights a need to address bias in the estimation of pain in observational studies of older adults. Understanding the sources and extent of these biases is important so that health practices and policies to address pain disparities can be guided by accurate estimates. Women, those with lower educational attainment, and those without private health insurance were found to have the highest pain burden longitudinally, suggesting a need for targeted interventions for these groups in Ireland and internationally.

Cross-prediction-powered inference

While reliable data-driven decision-making hinges on high-quality labeled data, the acquisition of quality labels often involves laborious human annotations or slow and expensive scientific measurements. Machine learning is becoming an appealing alternative as sophisticated predictive techniques are being used to quickly and cheaply produce large amounts of predicted labels; e.g., predicted protein structures are used to supplement experimentally derived structures, predictions of socioeconomic indicators from satellite imagery are used to supplement accurate survey data, and so on. Since predictions are imperfect and potentially biased, this practice brings into question the validity of downstream inferences. We introduce cross-prediction: a method for valid inference powered by machine learning. With a small labeled dataset and a large unlabeled dataset, cross-prediction imputes the missing labels via machine learning and applies a form of debiasing to remedy the prediction inaccuracies. The resulting inferences achieve the desired error probability and are more powerful than those that only leverage the labeled data. Closely related is the recent proposal of prediction-powered inference [A. N. Angelopoulos, S. Bates, C. Fannjiang, M. I. Jordan, T. Zrnic, Science 382, 669-674 (2023)], which assumes that a good pretrained model is already available. We show that cross-prediction is consistently more powerful than an adaptation of prediction-powered inference in which a fraction of the labeled data is split off and used to train the model. Finally, we observe that cross-prediction gives more stable conclusions than its competitors; its CIs typically have significantly lower variability.

Relaxed Doubly Robust Estimation in Causal Inference

Causal inference plays a crucial role in biomedical studies and social sciences. Over the years, researchers have devised various methods to facilitate causal inference, particularly in observational studies. Among these methods, the doubly robust estimator distinguishes itself through a remarkable feature: it retains its consistency even when only one of the two components-either the propensity score model or the outcome mean model-is correctly specified, rather than demanding correctness in both simultaneously. In this paper, we focus on scenarios where semiparametric models are employed for both the propensity score and the outcome mean. Semiparametric models offer a valuable blend of interpretability akin to parametric models and the adaptability characteristic of nonparametric models. In this context, achieving correct model specification involves both accurately specifying the unknown function and consistently estimating the unknown parameter. We introduce a novel concept: the relaxed doubly robust estimator. It operates in a manner reminiscent of the traditional doubly robust estimator but with a reduced requirement for double robustness. In essence, it only mandates the consistent estimate of the unknown parameter, without requiring the correct specification of the unknown function. This means that it only necessitates a partially correct model specification. We conduct a thorough analysis to establish the double robustness and semiparametric efficiency of our proposed estimator. Furthermore, we bolster our findings with comprehensive simulation studies to illustrate the practical implications of our approach.

Prior and posterior checking of implicit causal assumptions

Causal inference practitioners have increasingly adopted machine learning techniques with the aim of producing principled uncertainty quantification for causal effects while minimizing the risk of model misspecification. Bayesian nonparametric approaches have attracted attention as well, both for their flexibility and their promise of providing natural uncertainty quantification. Priors on high-dimensional or nonparametric spaces, however, can often unintentionally encode prior information that is at odds with substantive knowledge in causal inference-specifically, the regularization required for high-dimensional Bayesian models to work can indirectly imply that the magnitude of the confounding is negligible. In this paper, we explain this problem and provide tools for (i) verifying that the prior distribution does not encode an inductive bias away from confounded models and (ii) verifying that the posterior distribution contains sufficient information to overcome this issue if it exists. We provide a proof-of-concept on simulated data from a high-dimensional probit-ridge regression model, and illustrate on a Bayesian nonparametric decision tree ensemble applied to a large medical expenditure survey.

Quantifying and correcting bias due to outcome dependent self-reported weights in longitudinal study of weight loss interventions

In response to the escalating global obesity crisis and its associated health and financial burdens, this paper presents a novel methodology for analyzing longitudinal weight loss data and assessing the effectiveness of financial incentives. Drawing from the Keep It Off trial-a three-arm randomized controlled study with 189 participants-we examined the potential impact of financial incentives on weight loss maintenance. Given that some participants choose not to weigh themselves because of small weight change or weight gains, which is a common phenomenon in many weight-loss studies, traditional methods, for example, the Generalized Estimating Equations (GEE) method tends to overestimate the effect size due to the assumption that data are missing completely at random. To address this challenge, we proposed a framework which can identify evidence of missing not at random and conduct bias correction using the estimating equation derived from pairwise composite likelihood. By analyzing the Keep It Off data, we found that the data in this trial are most likely characterized by non-random missingness. Notably, we also found that the enrollment time (i.e., duration time) would be positively associated with the weight loss maintenance after adjusting for the baseline participant characteristics (e.g., age, sex). Moreover, the lottery-based intervention was found to be more effective in weight loss maintenance compared with the direct payment intervention, though the difference was non-statistically significant. This framework's significance extends beyond weight loss research, offering a semi-parametric approach to assess missing data mechanisms and robustly explore associations between exposures (e.g., financial incentives) and key outcomes (e.g., weight loss maintenance). In essence, the proposed methodology provides a powerful toolkit for analyzing real-world longitudinal data, particularly in scenarios with data missing not at random, enriching comprehension of intricate dataset dynamics.

Multiple imputation for non-monotone missing not at random data using the no self-censoring model

Although approaches for handling missing data from longitudinal studies are well-developed when the patterns of missingness are monotone, fewer methods are available for non-monotone missingness. Moreover, the conventional missing at random assumption-a natural benchmark for monotone missingness-does not model realistic beliefs about the non-monotone missingness processes (Robins and Gill, 1997). This has provided the impetus for alternative non-monotone missing not at random mechanisms. The "no self-censoring" model is such a mechanism and assumes the probability an outcome variable is missing is independent of its value when conditioning on all other possibly missing outcome variables and their missingness indicators. As an alternative to "weighting" methods that become computationally demanding with increasing number of outcome variables, we propose a multiple imputation approach under no self-censoring. We focus on the case of binary outcomes and present results of simulation and asymptotic studies to investigate the performance of the proposed imputation approach. We describe a related approach to sensitivity analysis to departure from no self-censoring. We discuss the relationship between missing at random and no self-censoring and prove that one is not a special case of the other. Finally, we discuss extensions to non-binary data settings. The proposed methods are illustrated with application to a substance use disorder clinical trial.

A causal roadmap for generating high-quality real-world evidence

Increasing emphasis on the use of real-world evidence (RWE) to support clinical policy and regulatory decision-making has led to a proliferation of guidance, advice, and frameworks from regulatory agencies, academia, professional societies, and industry. A broad spectrum of studies use real-world data (RWD) to produce RWE, ranging from randomized trials with outcomes assessed using RWD to fully observational studies. Yet, many proposals for generating RWE lack sufficient detail, and many analyses of RWD suffer from implausible assumptions, other methodological flaws, or inappropriate interpretations. The Causal Roadmap is an explicit, itemized, iterative process that guides investigators to prespecify study design and analysis plans; it addresses a wide range of guidance within a single framework. By supporting the transparent evaluation of causal assumptions and facilitating objective comparisons of design and analysis choices based on prespecified criteria, the Roadmap can help investigators to evaluate the quality of evidence that a given study is likely to produce, specify a study to generate high-quality RWE, and communicate effectively with regulatory agencies and other stakeholders. This paper aims to disseminate and extend the Causal Roadmap framework for use by clinical and translational researchers; three companion papers demonstrate applications of the Causal Roadmap for specific use cases.

Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint distribution

We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to non-ignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for n -estimability of the mean functional. This condition naturally strengthens the identifying condition, and it requires the existence of a function as a solution to a representer equation that connects the shadow variable to the mean functional. Solutions to the representer equation may not be unique, which presents substantial challenges for non-parametric estimation, and standard theories for non-parametric sieve estimators are not applicable here. We construct a consistent estimator of the solution set and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator of an appropriately chosen solution. The estimator is asymptotically normal, locally efficient and attains the semi-parametric efficiency bound under certain regularity conditions. We illustrate the proposed approach via simulations and a real data application on home pricing.

Nonparametric inverse-probability-weighted estimators based on the highly adaptive lasso

Inverse-probability-weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an effect of interest by constructing a pseudopopulation in which selection biases are eliminated. Despite their ease of use, these estimators require the correct specification of a model for the weighting mechanism, are known to be inefficient, and suffer from the curse of dimensionality. We propose a class of nonparametric inverse-probability-weighted estimators in which the weighting mechanism is estimated via undersmoothing of the highly adaptive lasso, a nonparametric regression function proven to converge at nearlyn - 1 / 3 $ n^{-1/3}$ -rate to the true weighting mechanism. We demonstrate that our estimators are asymptotically linear with variance converging to the nonparametric efficiency bound. Unlike doubly robust estimators, our procedures require neither derivation of the efficient influence function nor specification of the conditional outcome model. Our theoretical developments have broad implications for the construction of efficient inverse-probability-weighted estimators in large statistical models and a variety of problem settings. We assess the practical performance of our estimators in simulation studies and demonstrate use of our proposed methodology with data from a large-scale epidemiologic study.

Causal inference for longitudinal data based on historical controls

Use of historical data has become a hot topic recently, considered to provide a way to reduce patient burden, lower drug development cost, and make innovative therapies available to patients earlier. In a single-arm study designed to examine the benefit of an experimental treatment, there is often a desire to compare the outcomes of patients receiving the new intervention with those receiving a control treatment, which can be extracted from sources such as historical trials or electronic medical records. Since the treatment is not randomly assigned, there is a need to adjust for the potential imbalance in key patient characteristics between the current study and historical controls. If the outcome of interest is measured longitudinally and subject to random missing, the required adjustment becomes more complicated. In this paper, we propose a doubly robust adjustment procedure specifically designed for longitudinal data analysis with missing data. The proposed method yields valid analysis results, if either the propensity score model or the mixed effects model for repeated measures (MMRM) regression model is correctly specified. An extensive numerical study is conducted to examine the performance of the proposed method. Data from a real clinical trial comparing with historical data are analyzed as an example applying the proposed procedure.

Analysis of local sensitivity to nonignorability with missing outcomes and predictors

The ISNI (index of sensitivity to local nonignorability) method quantifies local sensitivity of parametric inferences to nonignorable missingness in an outcome variable. Here we extend ISNI to the situations where both outcomes and predictors can be missing and where the missingness mechanism can be either parametric or semi-parametric. We define the quantity MinNI (minimum nonignorability) to be an approximation to the norm of the smallest value of the transformed nonignorability that gives a nonnegligible displacement of the estimate of the parameter of interest. We illustrate our method in a complete data set from which we synthetically delete observations according to various patterns. We then apply the method to real-data examples involving the normal linear model and conditional logistic regression.

Adjusting for time of infection or positive test when estimating the risk of a post-infection outcome in an epidemic

When comparing the risk of a post-infection binary outcome, for example, hospitalisation, for two variants of an infectious pathogen, it is important to adjust for calendar time of infection. Typically, the infection time is unknown and positive test time used as a proxy for it. Positive test time may also be used when assessing how risk of the outcome changes over calendar time. We show that if time from infection to positive test is correlated with the outcome, the risk conditional on positive test time is a function of the trajectory of infection incidence. Hence, a risk ratio adjusted for positive test time can be quite different from the risk ratio adjusted for infection time. We propose a simple sensitivity analysis that indicates how risk ratios adjusted for positive test time and infection time may differ. This involves adjusting for a shifted positive test time, shifted to make the difference between it and infection time uncorrelated with the outcome. We illustrate this method by reanalysing published results on the relative risk of hospitalisation following infection with the Alpha versus pre-existing variants of SARS-CoV-2. Results indicate the relative risk adjusted for infection time may be lower than that adjusted for positive test time.

Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging

Geostatistical modeling for continuous point-referenced data has extensively been applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique characterizing the brain's anatomical structure, produces a positive-definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing spatial dependence among p.d. matrices properly is challenging. In this paper, we use the spatial Wishart process, a spatial stochastic process (random field), where each p.d. matrix-variate random variable marginally follows a Wishart distribution, and spatial dependence between random matrices is induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations and is almost-surely continuous, leading to a reasonable way of modeling spatial dependence. Motivated by a DTI data set of cocaine users, we propose a spatial matrix-variate regression model based on the spatial Wishart process. A problematic issue is that the spatial Wishart process has no closed-form density function. Hence, we propose an approximation method to obtain a feasible Cholesky decomposition model, which we show to be asymptotically equivalent to the spatial Wishart process model. A local likelihood approximation method is also applied to achieve fast computation. The simulation studies and real data application demonstrate that the Cholesky decomposition process model produces reliable inference and improved performance, compared to other methods.

Sensitivity analysis for calibrated inverse probability-of-censoring weighted estimators under non-ignorable dropout

Inverse probability of censoring weighting is a popular approach to handling dropout in longitudinal studies. However, inverse probability-of-censoring weighted estimators (IPCWEs) can be inefficient and unstable if the weights are estimated by maximum likelihood. To alleviate these problems, calibrated IPCWEs have been proposed, which use calibrated weights that directly optimize covariate balance in finite samples rather than the weights from maximum likelihood. However, the existing calibrated IPCWEs are all based on the unverifiable assumption of sequential ignorability and sensitivity analysis strategies under non-ignorable dropout are lacking. In this paper, we fill this gap by developing an approach to sensitivity analysis for calibrated IPCWEs under non-ignorable dropout. A simple technique is proposed to speed up the computation of bootstrap and jackknife confidence intervals and thus facilitate sensitivity analyses. We evaluate the finite-sample performance of the proposed methods using simulations and apply our methods to data from an international inception cohort study of systemic lupus erythematosus. An R Markdown tutorial to demonstrate the implementation of the proposed methods is provided.

Handling Missing Values in Information Systems Research: A Review of Methods and Assumptions

Data have never been more essential to the success of decision making. However, data are often messy. A perennial data challenge is missing values, which frequently occur in real-world data, such as unreported data items in public firms’ financial statements and skipped product ratings from consumers. What is the influence of missing values and how should they be handled? Although we are in a big data era, missing values are not ignorable if data are missing for nonrandom reasons. In the case of product ratings, if only people who favor the product provide ratings while others put aside the product and do not respond, then even a simple mean estimation of the product rating would be significantly biased. Such bias challenges the validity of data analysis, and it cannot be eliminated simply by increasing the sample size of the data. To correct the bias arising from nonrandom missing values, it is necessary to examine and model what causes the missing values. We propose and demonstrate the superior performance of a Monte Carlo likelihood approach to correct the bias. Overall, we recommend well-designed data collection processes with documentation of the possible reasons for missing values, cautious adoption of missing value handling methods, and structured missing value reporting practices.

Semiparametric Inference for Nonmonotone Missing-Not-at-Random Data: The No Self-Censoring Model

We study the identification and estimation of statistical functionals of multivariate data missing non-monotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called "no self-censoring" or "itemwise conditionally independent nonresponse," which roughly corresponds to the assumption that no partially-observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously-studied data set of HIV-positive mothers in Botswana.

Sensitivity analysis of unmeasured confounding in causal inference based on exponential tilting and super learner

Causal inference under the potential outcome framework relies on the strongly ignorable treatment assumption. This assumption is usually questionable in observational studies, and the unmeasured confounding is one of the fundamental challenges in causal inference. To this end, we propose a new sensitivity analysis method to evaluate the impact of the unmeasured confounder by leveraging ideas of doubly robust estimators, the exponential tilt method, and the super learner algorithm. Compared to other existing methods of sensitivity analysis that parameterize the unmeasured confounder as a latent variable in the working models, the exponential tilting method does not impose any restrictions on the structure or models of the unmeasured confounders. In addition, in order to reduce the modeling bias of traditional parametric methods, we propose incorporating the super learner machine learning algorithm to perform nonparametric model estimation and the corresponding sensitivity analysis. Furthermore, most existing sensitivity analysis methods require multivariate sensitivity parameters, which make its choice difficult and subjective in practice. In comparison, the new method has a univariate sensitivity parameter with a nice and simple interpretation of log-odds ratios for binary outcomes, which makes its choice and the application of the new sensitivity analysis method very easy for practitioners.

Weighted generalized estimating equations and unified estimation for longitudinal data with nonmonotone missing data patterns

Missing data are a major complication in longitudinal data analysis. Weighted generalized estimating equations (WGEEs, Robins et al, J Am Stat Assoc 1995;90:106-121) were developed to deal with missing response data. They have been extended for data with both missing responses and missing covariates (Chen et al, J Am Stat Assoc 2010;105:336-353). However, it may introduce more variability in dealing with the correlation structure of the responses. We propose new WGEEs for missing at random data where both response and (time-dependent) covariates may have values missing in nonmonotone missing data patterns. We also explain how to improve the estimation efficiency of WGEEs using a unified approach (Zhao and Liu, AStA Adv Stat Anal 2021;105(1):87-101). The proposed unified estimator is consistent and more efficient than the regular WGEE estimator. It is computationally simple and can be directly implemented in standard software. Simulation studies for both continuous response and binary response data are provided to examine the performance of the proposed estimators. A clinical trial example investigating the quality of life of women with early-stage breast cancer and the associated factors is analyzed.

Bayesian sensitivity analyses for longitudinal data with dropouts that are potentially missing not at random: A high dimensional pattern-mixture model

Randomized clinical trials with outcome measured longitudinally are frequently analyzed using either random effect models or generalized estimating equations. Both approaches assume that the dropout mechanism is missing at random (MAR) or missing completely at random (MCAR). We propose a Bayesian pattern-mixture model to incorporate missingness mechanisms that might be missing not at random (MNAR), where the distribution of the outcome measure at the follow-up time t k , conditional on the prior history, differs across the patterns of missing data. We then perform sensitivity analysis on estimates of the parameters of interest. The sensitivity parameters relate the distribution of the outcome of interest between subjects from a missing-data pattern at time t k with that of the observed subjects at time t k . The large number of the sensitivity parameters is reduced by treating them as random with a prior distribution having some pre-specified mean and variance, which are varied to explore the sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the proposed model, allowing a sensitivity analysis of deviations from MAR. The proposed approach is applied to data from the Trial of Preventing Hypertension.

Robust and efficient semi-supervised estimation of average treatment effects with application to electronic health records data

We consider the problem of estimating the average treatment effect (ATE) in a semi-supervised learning setting, where a very small proportion of the entire set of observations are labeled with the true outcome but features predictive of the outcome are available among all observations. This problem arises, for example, when estimating treatment effects in electronic health records (EHR) data because gold-standard outcomes are often not directly observable from the records but are observed for a limited number of patients through small-scale manual chart review. We develop an imputation-based approach for estimating the ATE that is robust to misspecification of the imputation model. This effectively allows information from the predictive features to be safely leveraged to improve efficiency in estimating the ATE. The estimator is additionally doubly-robust in that it is consistent under correct specification of either an initial propensity score model or a baseline outcome model. It is also locally semiparametric efficient under an ideal semi-supervised model where the distribution of the unlabeled data is known. Simulations exhibit the efficiency and robustness of the proposed method compared to existing approaches in finite samples. We illustrate the method by comparing rates of treatment response to two biologic agents for treatment inflammatory bowel disease using EHR data from Partners' Healthcare.

Multiply robust estimation of causal quantile treatment effects

In causal inference, often the interest lies in the estimation of the average causal effect. Other quantities such as the quantile treatment effect may be of interest as well. In this article, we propose a multiply robust method for estimating the marginal quantiles of potential outcomes by achieving mean balance in (a) the propensity score, and (b) the conditional distributions of potential outcomes. An empirical likelihood or entropy measure approach can be utilized for estimation instead of inverse probability weighting, which is known to be sensitive to the misspecification of the propensity score model. Simulation studies are conducted across different scenarios of correctness in both the propensity score models and the outcome models. Both simulation results and theoretical development indicate that our proposed estimator is consistent if any of the models are correctly specified. In the data analysis, we investigate the quantile treatment effect of mothers' smoking status on infants' birthweight.

Robust estimation of models for longitudinal data with dropouts and outliers

Missing data and outliers usually arise in longitudinal studies. Ignoring the effects of missing data and outliers will make the classical generalized estimating equation approach invalid. The longitudinal cohort study of rheumatoid arthritis patients was designed to investigate whether the Health Assessment Questionnaire score was associated with baseline covariates and changed with time. There exist dropouts and outliers in the data. In order to analyze the data, we develop a robust estimating equation approach. To deal with the responses missing at random, we extend a doubly robust method. To achieve robustness against outliers, we utilize an outlier robust method, which corrects the bias induced by outliers through centralizing the covariate matrix in the estimating equation. The doubly robust method for dropouts is easy to combine with the outlier robust method. The proposed method has the property of robustness in the sense that the proposed estimator is not only doubly robust against model misspecification for dropouts when there is no outlier in the data, but also robust against outliers. Consistency and asymptotic normality of the proposed estimator are established under regularity conditions. A comprehensive simulation study and real data analysis demonstrate that the proposed estimator does have the property of robustness.

A Semiparametric Bayesian Approach to Dropout in Longitudinal Studies with Auxiliary Covariates

We develop a semiparametric Bayesian approach to missing outcome data in longitudinal studies in the presence of auxiliary covariates. We consider a joint model for the full data response, missingness and auxiliary covariates. We include auxiliary covariates to "move" the missingness "closer" to missing at random (MAR). In particular, we specify a semiparametric Bayesian model for the observed data via Gaussian process priors and Bayesian additive regression trees. These model specifications allow us to capture non-linear and non-additive effects, in contrast to existing parametric methods. We then separately specify the conditional distribution of the missing data response given the observed data response, missingness and auxiliary covariates (i.e. the extrapolation distribution) using identifying restrictions. We introduce meaningful sensitivity parameters that allow for a simple sensitivity analysis. Informative priors on those sensitivity parameters can be elicited from subject-matter experts. We use Monte Carlo integration to compute the full data estimands. Performance of our approach is assessed using simulated datasets. Our methodology is motivated by, and applied to, data from a clinical trial on treatments for schizophrenia.

Causal Isotonic Regression

In observational studies, potential confounders may distort the causal relationship between an exposure and an outcome. However, under some conditions, a causal dose-response curve can be recovered using the G-computation formula. Most classical methods for estimating such curves when the exposure is continuous rely on restrictive parametric assumptions, which carry significant risk of model misspecification. Nonparametric estimation in this context is challenging because in a nonparametric model these curves cannot be estimated at regular rates. Many available nonparametric estimators are sensitive to the selection of certain tuning parameters, and performing valid inference with such estimators can be difficult. In this work, we propose a nonparametric estimator of a causal dose-response curve known to be monotone. We show that our proposed estimation procedure generalizes the classical least-squares isotonic regression estimator of a monotone regression function. Specifically, it does not involve tuning parameters, and is invariant to strictly monotone transformations of the exposure variable. We describe theoretical properties of our proposed estimator, including its irregular limit distribution and the potential for doubly-robust inference. Furthermore, we illustrate its performance via numerical studies, and use it to assess the relationship between BMI and immune response in HIV vaccine trials.

Robust Q-learning

Q-learning is a regression-based approach that is widely used to formalize the development of an optimal dynamic treatment strategy. Finite dimensional working models are typically used to estimate certain nuisance parameters, and misspecification of these working models can result in residual confounding and/or efficiency loss. We propose a robust Q-learning approach which allows estimating such nuisance parameters using data-adaptive techniques. We study the asymptotic behavior of our estimators and provide simulation studies that highlight the need for and usefulness of the proposed method in practice. We use the data from the "Extending Treatment Effectiveness of Naltrexone" multi-stage randomized trial to illustrate our proposed methods.

Extending inferences from a randomized trial to a new target population

When treatment effect modifiers influence the decision to participate in a randomized trial, the average treatment effect in the population represented by the randomized individuals will differ from the effect in other populations. In this tutorial, we consider methods for extending causal inferences about time-fixed treatments from a trial to a new target population of nonparticipants, using data from a completed randomized trial and baseline covariate data from a sample from the target population. We examine methods based on modeling the expectation of the outcome, the probability of participation, or both (doubly robust). We compare the methods in a simulation study and show how they can be implemented in software. We apply the methods to a randomized trial nested within a cohort of trial-eligible patients to compare coronary artery surgery plus medical therapy versus medical therapy alone for patients with chronic coronary artery disease. We conclude by discussing issues that arise when using the methods in applied analyses.

Sensitivity analysis for non-monotone missing binary data in longitudinal studies: Application to the NIDA collaborative cocaine treatment study

Conventional approaches for handling missingness in substance use disorder trials commonly rely upon a single deterministic "worst value" imputation that posits a perfect relationship between missingness and drug use ("missing value = presumed drug use"); this yields biased estimates of treatment effects and their standard errors. Instead, deterministic imputations should be replaced by probabilistic versions that encode researchers prior beliefs that those with missing data are more likely to be using drugs at those occasions. Motivated by this problem, we present a method for handling non-monotone missing binary data in longitudinal studies. Specifically, we consider a joint model that combines a not missing at random (NMAR) selection model with a generalized linear mixed model for longitudinal binary data. The selection model links the distribution of a missing outcome to the corresponding distribution of the outcome for those observed at that occasion via a fixed and known sensitivity parameter. The mixed model for longitudinal binary data assumes the random effects have bridge distributions; the latter yields regression parameters that have both subject-specific and marginal interpretations. This approach is completely transparent about what is being assumed about missing data and can be used as the basis for sensitivity analysis.

Regression analysis of longitudinal data with outcome-dependent sampling and informative censoring

We consider regression analysis of longitudinal data in the presence of outcome-dependent observation times and informative censoring. Existing approaches commonly require correct specification of the joint distribution of the longitudinal measurements, observation time process and informative censoring time under the joint modeling framework, and can be computationally cumbersome due to the complex form of the likelihood function. In view of these issues, we propose a semi-parametric joint regression model and construct a composite likelihood function based on a conditional order statistics argument. As a major feature of our proposed methods, the aforementioned joint distribution is not required to be specified and the random effect in the proposed joint model is treated as a nuisance parameter. Consequently, the derived composite likelihood bypasses the need to integrate over the random effect and offers the advantage of easy computation. We show that the resulting estimators are consistent and asymptotically normal. We use simulation studies to evaluate the finite-sample performance of the proposed method, and apply it to a study of weight loss data that motivated our investigation.

Bayesian analysis of longitudinal dyadic data with informative missing data using a dyadic shared-parameter model

Analyzing longitudinal dyadic data is a challenging task due to the complicated correlations from repeated measurements and within-dyad interdependence, as well as potentially informative (or non-ignorable) missing data. We propose a dyadic shared-parameter model to analyze longitudinal dyadic data with ordinal outcomes and informative intermittent missing data and dropouts. We model the longitudinal measurement process using a proportional odds model, which accommodates the within-dyad interdependence using the concept of the actor-partner interdependence effects, as well as dyad-specific random effects. We model informative dropouts and intermittent missing data using a transition model, which shares the same set of random effects as the longitudinal measurement model. We evaluate the performance of the proposed method through extensive simulation studies. As our approach relies on some untestable assumptions on the missing data mechanism, we perform sensitivity analyses to evaluate how the analysis results change when the missing data mechanism is misspecified. We demonstrate our method using a longitudinal dyadic study of metastatic breast cancer.

TREE-BASED REINFORCEMENT LEARNING FOR ESTIMATING OPTIMAL DYNAMIC TREATMENT REGIMES

Dynamic treatment regimes (DTRs) are sequences of treatment decision rules, in which treatment may be adapted over time in response to the changing course of an individual. Motivated by the substance use disorder (SUD) study, we propose a tree-based reinforcement learning (T-RL) method to directly estimate optimal DTRs in a multi-stage multi-treatment setting. At each stage, T-RL builds an unsupervised decision tree that directly handles the problem of optimization with multiple treatment comparisons, through a purity measure constructed with augmented inverse probability weighted estimators. For the multiple stages, the algorithm is implemented recursively using backward induction. By combining semiparametric regression with flexible tree-based learning, T-RL is robust, efficient and easy to interpret for the identification of optimal DTRs, as shown in the simulation studies. With the proposed method, we identify dynamic SUD treatment regimes for adolescents.

Bayesian Approaches for Missing Not at Random Outcome Data: The Role of Identifying Restrictions

Missing data is almost always present in real datasets, and introduces several statistical issues. One fundamental issue is that, in the absence of strong uncheckable assumptions, effects of interest are typically not nonparametrically identified. In this article, we review the generic approach of the use of identifying restrictions from a likelihood-based perspective, and provide points of contact for several recently proposed methods. An emphasis of this review is on restrictions for nonmonotone missingness, a subject that has been treated sparingly in the literature. We also present a general, fully-Bayesian, approach which is widely applicable and capable of handling a variety of identifying restrictions in a uniform manner.

Machine Learning-Augmented Propensity Score-Adjusted Multilevel Mixed Effects Panel Analysis of Hands-On Cooking and Nutrition Education versus Traditional Curriculum for Medical Students as Preventive Cardiology: Multisite Cohort Study of 3,248 Trainees over 5 Years

Background

Cardiovascular disease (CVD) annually claims more lives and costs more dollars than any other disease globally amid widening health disparities, despite the known significant reductions in this burden by low cost dietary changes. The world's first medical school-based teaching kitchen therefore launched CHOP-Medical Students as the largest known multisite cohort study of hands-on cooking and nutrition education versus traditional curriculum for medical students.

Methods

This analysis provides a novel integration of artificial intelligence-based machine learning (ML) with causal inference statistics. 43 ML automated algorithms were tested, with the top performer compared to triply robust propensity score-adjusted multilevel mixed effects regression panel analysis of longitudinal data. Inverse-variance weighted fixed effects meta-analysis pooled the individual estimates for competencies.

Results

3,248 unique medical trainees met study criteria from 20 medical schools nationally from August 1, 2012, to June 26, 2017, generating 4,026 completed validated surveys. ML analysis produced similar results to the causal inference statistics based on root mean squared error and accuracy. Hands-on cooking and nutrition education compared to traditional medical school curriculum significantly improved student competencies (OR 2.14, 95% CI 2.00–2.28, p < 0.001) and MedDiet adherence (OR 1.40, 95% CI 1.07–1.84, p = 0.015), while reducing trainees' soft drink consumption (OR 0.56, 95% CI 0.37–0.85, p = 0.007). Overall improved competencies were demonstrated from the initial study site through the scale-up of the intervention to 10 sites nationally (p < 0.001).

Discussion

This study provides the first machine learning-augmented causal inference analysis of a multisite cohort showing hands-on cooking and nutrition education for medical trainees improves their competencies counseling patients on nutrition, while improving students' own diets. This study suggests that the public health and medical sectors can unite population health management and precision medicine for a sustainable model of next-generation health systems providing effective, equitable, accessible care beginning with reversing the CVD epidemic.

Global sensitivity analysis of clinical trials with missing patient-reported outcomes

Randomized trials with patient-reported outcomes are commonly plagued by missing data. The analysis of such trials relies on untestable assumptions about the missing data mechanism. To address this issue, it has been recommended that the sensitivity of the trial results to assumptions should be a mandatory reporting requirement. In this paper, we discuss a recently developed methodology (Scharfstein et al., Biometrics, 2018) for conducting sensitivity analysis of randomized trials in which outcomes are scheduled to be measured at fixed points in time after randomization and some subjects prematurely withdraw from study participation. The methodology is explicated in the context of a placebo-controlled randomized trial designed to evaluate a treatment for bipolar disorder. We present a comprehensive data analysis and a simulation study to evaluate the performance of the method. A software package entitled SAMON (R and SAS versions) that implements our methods is available at www.missingdatamatters.org .

On Inverse Probability Weighting for Nonmonotone Missing at Random Data

The development of coherent missing data models to account for nonmonotone missing at random (MAR) data by inverse probability weighting (IPW) remains to date largely unresolved. As a consequence, IPW has essentially been restricted for use only in monotone missing data settings. We propose a class of models for nonmonotone missing data mechanisms that spans the MAR model, while allowing the underlying full data law to remain unrestricted. For parametric specifications within the proposed class, we introduce an unconstrained maximum likelihood estimator for estimating the missing data probabilities which can be easily implemented using existing software. To circumvent potential convergence issues with this procedure, we also introduce a Bayesian constrained approach to estimate the missing data process which is guaranteed to yield inferences that respect all model restrictions. The efficiency of the standard IPW estimator is improved by incorporating information from incomplete cases through an augmented estimating equation which is optimal within a large class of estimating equations. We investigate the finite-sample properties of the proposed estimators in a simulation study and illustrate the new methodology in an application evaluating key correlates of preterm delivery for infants born to HIV infected mothers in Botswana, Africa.