arXiv subjects

Dylan S. Small

Publications and source records attributed to Dylan S. Small.

At least 19 recordsLinked to original sources

arXiv2026

Powerful Multivariate Sensitivity Analysis via Sample Splitting in an Observational Study of the Effects of Poverty on Cardiovascular Disease Risk Factors

When assessing the causal effect of an exposure on two or more outcomes in an observational study, a linear combination of outcomes may lessen the sensitivity of a test of the global null hypothesis to potential unmeasured biases. While all linear combinations of scored outcomes can be considered using Scheffe projections or constrained variants thereof, finding the combination that minimizes sensitivity to unmeasured biases requires corrections for multiple testing, which can erode power, especially when many outcomes are of interest. To mitigate this issue, we propose splitting the sample into a planning sample to identify an optimal linear combination and an analysis sample to conduct inference. We provide a novel characterization of the set of linear combinations for which this approach is guaranteed to achieve the same asymptotic power as full-sample alternatives and conduct extensive simulation studies that demonstrate enhanced power in finite samples. Finally, we apply our method to investigate the effects of poverty on the emergence of cardiovascular disease risk factors in children and adolescents. We discover adverse consequences on outcomes related to body composition, physical activity, and tobacco exposure. Although the impact of poverty on elevated tobacco exposure shows some robustness to unmeasured confounding, the other findings remain sensitive to potential biases.

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arXiv2026

The Role of Measured Covariates in Assessing Sensitivity to Unmeasured Confounding

Sensitivity analysis is widely used to assess the robustness of causal conclusions in observational studies, yet its interaction with the structure of measured covariates is often overlooked. When latent confounders cannot be directly adjusted for and are instead controlled using proxy variables, strong associations between exposure and measured proxies can amplify sensitivity to residual confounding. We formalize this phenomenon in linear regression settings by showing that a simple ratio involving the exposure model coefficient and residual exposure variance provides an observable measure of this increased sensitivity. Applying our framework to smoking and lung cancer, we document how growing socioeconomic stratification in smoking behavior over time leads to heightened sensitivity to unmeasured confounding in more recent data. These results highlight the importance of multicollinearity when interpreting sensitivity analyses based on proxy adjustment.

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arXiv2026

Optimal Sample Splitting for Observational Studies

In observational studies of treatment effects, estimates may be biased by unmeasured confounders, which can potentially affect the validity of the results. Understanding sensitivity to such biases helps assess how unmeasured confounding impacts credibility. The design of an observational study strongly influences its sensitivity to bias. Previous work has shown that the sensitivity to bias can be reduced by dividing a dataset into a planning sample and a larger analysis sample, where the planning sample guides design decisions. But the choice of what fraction of the data to put in the planning sample vs. the analysis sample was ad hoc. Here, we develop an approach to find the optimal fraction using plasmode datasets. We show that our method works well in high-dimensional outcome spaces. We apply our method to study the effects of exposure to second-hand smoke in children. The OptimalSampling R package implementing our method is available at GitHub.

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arXiv2025

Beyond the ACE Score: Replicable Combinations of Adverse Childhood Experiences That Worsen Depression Risk

Adverse childhood experiences (ACEs) are categories of childhood abuse, neglect, and household dysfunction. Screening by a single additive ACE score (e.g., a $\ge 4$ cutoff) has poor individual-level discrimination. We instead identify replicable combinations of ACEs that elevate adult depression risk. Our data turnover framework enables a single research team to explore, confirm, and replicate within one observational dataset while controlling the family-wise error rate. We integrate isotonic subgroup selection (ISS) to estimate a higher-risk subgroup under a monotonicity assumption -- additional ACE exposure or higher intensity cannot reduce depression risk. We pre-specify a risk threshold $\tau$ corresponding to roughly a two-fold increase in the odds of depression relative to the no-ACE baseline. Within data turnover, the prespecified component improves power while maintaining FWER control, as demonstrated in simulations. Guided by EDA, we adopt frequency coding for ACE items, retaining intensity information that reduces false positives relative to binary or score codings. The result is a replicable, pattern-based higher-risk subgroup. On held-out BRFSS 2022, we show that, at the same level of specificity (0.95), using our replicable subgroup as the screening rule increases sensitivity by 26\% compared with an ACE-score cutoff, yielding concrete triggers that are straightforward to implement and help target scarce clinical screening resources toward truly higher-risk profiles.

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arXiv2025

Randomization inference for stepped-wedge designs with noncompliance with application to a palliative care pragmatic trial

While palliative care is increasingly commonly delivered to hospitalized patients with serious illnesses, few studies have estimated its causal effects. Courtright et al. (2016) adopted a stepped-wedge cluster-randomized design to assess the effect of palliative care on a patient-centered outcome. The randomized intervention was a nudge to administer palliative care but did not guarantee receipt of palliative care, resulting in noncompliance. A subsequent analysis using methods suited for standard trial designs produced statistically anomalous results, as an intention-to-treat analysis found no effect while an instrumental variable analysis did (Courtright et al. 2024). This highlights the need for a more principled approach to address noncompliance in stepped-wedge designs. We provide a formal causal inference framework for the stepped-wedge design with noncompliance by introducing a relevant causal estimand and corresponding estimators and inferential procedures. Through numerical studies, we compare an array of estimators and provide practical guidance in choosing an analysis method. Finally, we apply our recommended methods to reanalyze the palliative care pragmatic trial, producing point estimates suggesting a larger effect than the original analysis, but intervals that did not reach statistical significance.

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arXiv2025

Exploration, Confirmation, and Replication in the Same Observational Study: A Two Team Cross-Screening Approach to Studying the Effect of Unwanted Pregnancy on Mothers' Later Life Outcomes

The long term consequences of unwanted pregnancies carried to term on mothers have not been much explored. We use data from the Wisconsin Longitudinal Study (WLS) and propose a novel approach, namely two team cross-screening, to study the possible effects of unwanted pregnancies carried to term on various aspects of mothers' later-life mental health, physical health, economic well-being and life satisfaction. Our method, unlike existing approaches to observational studies, enables the investigators to perform exploratory data analysis, confirmatory data analysis and replication in the same study. This is a valuable property when there is only a single data set available with unique strengths to perform exploratory, confirmatory and replication analysis. In two team cross-screening, the investigators split themselves into two teams and the data is split as well according to a meaningful covariate. Each team then performs exploratory data analysis on its part of the data to design an analysis plan for the other part of the data. The complete freedom of the teams in designing the analysis has the potential to generate new unanticipated hypotheses in addition to a prefixed set of hypotheses. Moreover, only the hypotheses that looked promising in the data each team explored are forwarded for analysis (thus alleviating the multiple testing problem). These advantages are demonstrated in our study of the effects of unwanted pregnancies on mothers' later life outcomes.

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arXiv2025

Probabilistic Record Linkage of Two Gun Violence Data Sets

Objective: Gun violence is a serious public health problem in the United States. The Gun Violence Archive (GVA) provides detailed geographic information, while the National Violent Death Reporting System (NVDRS) offers demographic, socioeconomic, and narrative data on gun homicides. We developed and tested a method for merging datasets to inform analysis and strategies to reduce gun violence rates in the United States. Methods: After preprocessing the data, we used a probabilistic record linkage program to link records from the GVA (n = 36,245) with records from the NVDRS (n = 30,592). We evaluated sensitivity (the false match rate) by using a manual approach. Results: The linkage returned 27,420 matches of gun violence incidents from the GVA and NVDRS datasets. Because of restricted details accessible from GVA online records, only 942 of these matched records could be manually evaluated. Our framework achieved a 90.12% (849 of 942 accuracy rate in linking GVA incidents with corresponding NVDRS records. Practice Implications: Electronic linkage of gun violence data from 2 sources is feasible and can be used to increase the utility of the datasets.

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arXiv2025

Protocol For An Observational Study On The Effects Of Combinations Of Adverse Childhood Experiences On Adult Depression

Adverse childhood experiences (ACEs) have been linked to a wide range of negative health outcomes in adulthood. However, few studies have investigated what specific combinations of ACEs most substantially impact mental health. In this article, we provide the protocol for our observational study of the effects of combinations of ACEs on adult depression. We use data from the 2023 Behavioral Risk Factor Surveillance System (BRFSS) to assess these effects. We will evaluate the replicability of our findings by splitting the sample into two discrete subpopulations of individuals. We employ data turnover for this analysis, enabling a single team of statisticians and domain experts to collaboratively evaluate the strength of evidence, and also integrating both qualitative and quantitative insights from exploratory data analysis. We outline our analysis plan using this method and conclude with a brief discussion of several specifics for our study.

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arXiv2024

Protocol for an Observational Study on the Effects of Paternal Alcohol Use Disorder on Children's Later Life Outcomes

The harmful effects of growing up with a parent with an alcohol use disorder have been closely examined in children and adolescents, and are reported to include mental and physical health problems, interpersonal difficulties, and a worsened risk of future substance use disorders. However, few studies have investigated how these impacts evolve into later life adulthood, leaving the ensuing long-term effects of interest. In this article, we provide the protocol for our observational study of the long-term consequences of growing up with a father who had an alcohol use disorder. We will use data from the Wisconsin Longitudinal Study to examine impacts on long-term economic success, interpersonal relationships, physical, and mental health. To reinforce our findings, we will conduct this investigation on two discrete subpopulations of individuals in our study, allowing us to analyze the replicability of our conclusions. We introduce a novel statistical design, called data turnover, to carry out this analysis. Data turnover allows a single group of statisticians and domain experts to work together to assess the strength of evidence gathered across multiple data splits, while incorporating both qualitative and quantitative findings from data exploration. We delineate our analysis plan using this new method and conclude with a brief discussion of some additional considerations for our study.

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arXiv2024

A subgroup-aware scoring approach to the study of effect modification in observational studies

Effect modification means the size of a treatment effect varies with an observed covariate. Generally speaking, a larger treatment effect with more stable error terms is less sensitive to bias. Thus, we might be able to conclude that a study is less sensitive to unmeasured bias by using these subgroups experiencing larger treatment effects. Lee et al. (2018) proposed the submax method that leverages the joint distribution of test statistics from subgroups to draw a firmer conclusion if effect modification occurs. However, one version of the submax method uses M-statistics as the test statistics and is implemented in the R package submax (Rosenbaum, 2017). The scaling factor in the M-statistics is computed using all observations combined across subgroups. We show that this combining can confuse effect modification with outliers. We propose a novel group M-statistic that scores the matched pairs in each subgroup to tackle the issue. We examine our novel scoring strategy in extensive settings to show the superior performance. The proposed method is applied to an observational study of the effect of a malaria prevention treatment in West Africa.

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arXiv2024

Planning for gold: Hypothesis screening with split samples for valid powerful testing in matched observational studies

Observational studies are valuable tools for inferring causal effects in the absence of controlled experiments. However, these studies may be biased due to the presence of some relevant, unmeasured set of covariates. One approach to mitigate this concern is to identify hypotheses likely to be more resilient to hidden biases by splitting the data into a planning sample for designing the study and an analysis sample for making inferences. We devise a powerful and flexible method for selecting hypotheses in the planning sample when an unknown number of outcomes are affected by the treatment, allowing researchers to gain the benefits of exploratory analysis and still conduct powerful inference under concerns of unmeasured confounding. We investigate the theoretical properties of our method and conduct extensive simulations that demonstrate pronounced benefits, especially at higher levels of allowance for unmeasured confounding. Finally, we demonstrate our method in an observational study of the multi-dimensional impacts of a devastating flood in Bangladesh.

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arXiv2024

Sensitivity Analysis for Attributable Effects in Case$^2$ Studies

The case$^2$ study, also referred to as the case-case study design, is a valuable approach for conducting inference for treatment effects. Unlike traditional case-control studies, the case$^2$ design compares treatment in two types of cases with the same disease. A key quantity of interest is the attributable effect, which is the number of cases of disease among treated units which are caused by the treatment. Two key assumptions that are usually made for making inferences about the attributable effect in case$^2$ studies are 1.) treatment does not cause the second type of case, and 2.) the treatment does not alter an individual's case type. However, these assumptions are not realistic in many real-data applications. In this article, we present a sensitivity analysis framework to scrutinize the impact of deviations from these assumptions on obtained results. We also include sensitivity analyses related to the assumption of unmeasured confounding, recognizing the potential bias introduced by unobserved covariates. The proposed methodology is exemplified through an investigation into whether having violent behavior in the last year of life increases suicide risk via 1993 National Mortality Followback Survey dataset.

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arXiv2024

Protocols for Observational Studies: Methods and Open Problems

For learning about the causal effect of a treatment, a randomized controlled trial (RCT) is considered the gold standard. However, randomizing treatment is sometimes unethical or infeasible, and instead an observational study may be conducted. While some aspects of a well designed RCT cannot be replicated in an observational study, one aspect that can is to have a protocol with prespecified hypotheses about prespecified outcomes and a prespecified analysis. We illustrate the value of protocols for observational studies in three applications -- the effect of playing high school football on later life mental functioning, the effect of police seizing a gun when arresting a domestic violence suspect on future domestic violence and the effect of mountaintop mining on health. We then discuss methodologies for observational study protocols. We discuss considerations for protocols that are similar between observational studies and RCTs, and considerations that are different. The considerations that are different include (i) whether the protocol should be specified before treatment assignment is known or after; (ii) how multiple outcomes should be incorporated into the planned analysis and (iii) how subgroups should be incorporated into the planned analysis. We conclude with discussion of a few open problems in the methodology of observational study protocols.

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arXiv2023

A Differential Effect Approach to Partial Identification of Treatment Effects

We consider identification and inference for the average treatment effect and heterogeneous treatment effect conditional on observable covariates in the presence of unmeasured confounding. Since point identification of these treatment effects is not achievable without strong assumptions, we obtain bounds on these treatment effects by leveraging differential effects, a tool that allows for using a second treatment to learn the effect of the first treatment. The differential effect is the effect of using one treatment in lieu of the other. We provide conditions under which differential treatment effects can be used to point identify or partially identify treatment effects. Under these conditions, we develop a flexible and easy-to-implement semi-parametric framework to estimate bounds and leverage a two-stage approach to conduct statistical inference on effects of interest. The proposed method is examined through a simulation study and a case study that investigates the effect of smoking on the blood level of cadmium using the National Health and Nutrition Examination Survey.

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arXiv2023

RobustIV and controlfunctionIV: Causal Inference for Linear and Nonlinear Models with Invalid Instrumental Variables

We present R software packages RobustIV and controlfunctionIV for causal inference with possibly invalid instrumental variables. RobustIV focuses on the linear outcome model. It implements the two-stage hard thresholding method to select valid instrumental variables from a set of candidate instrumental variables and make inferences for the causal effect in both low- and high-dimensional settings. Furthermore, RobustIV implements the high-dimensional endogeneity test and the searching and sampling method, a uniformly valid inference method robust to errors in instrumental variable selection. controlfunctionIV considers the nonlinear outcome model and makes inferences about the causal effect based on the control function method. Our packages are demonstrated using two publicly available economic data sets together with applications to the Framingham Heart Study.

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arXiv2022

Model-robust and efficient covariate adjustment for cluster-randomized experiments

Cluster-randomized experiments are increasingly used to evaluate interventions in routine practice conditions, and researchers often adopt model-based methods with covariate adjustment in the statistical analyses. However, the validity of model-based covariate adjustment is unclear when the working models are misspecified, leading to ambiguity of estimands and risk of bias. In this article, we first adapt two conventional model-based methods, generalized estimating equations and linear mixed models, with weighted g-computation to achieve robust inference for cluster-average and individual-average treatment effects. To further overcome the limitations of model-based covariate adjustment methods, we propose an efficient estimator for each estimand that allows for flexible covariate adjustment and additionally addresses cluster size variation dependent on treatment assignment and other cluster characteristics. Such cluster size variations often occur post-randomization and, if ignored, can lead to bias of model-based estimators. For our proposed efficient covariate-adjusted estimator, we prove that when the nuisance functions are consistently estimated by machine learning algorithms, the estimator is consistent, asymptotically normal, and efficient. When the nuisance functions are estimated via parametric working models, the estimator is triply-robust. Simulation studies and analyses of three real-world cluster-randomized experiments demonstrate that the proposed methods are superior to existing alternatives.

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arXiv2022

Protocol for an Observational Study on the Effects of Giving Births from Unintended Pregnancies on Later Life Physical and Mental Health

There has been increasing interest in studying the effect of giving births to unintended pregnancies on later life physical and mental health. In this article, we provide the protocol for our planned observational study on the long-term mental and physical health consequences for mothers who bear children resulting from unintended pregnancies. We aim to use the data from the Wisconsin Longitudinal Study (WLS) and examine the effect of births from unintended pregnancies on a broad range of outcomes, including mental depression, psychological well-being, physical health, alcohol usage, and economic well-being. To strengthen our causal findings, we plan to address our research questions on two subgroups, Catholics and non-Catholics, and discover the "replicable" outcomes for which the effect of unintended pregnancy is negative (or, positive) in both subgroups. Following the idea of non-random cross-screening, the data will be split according to whether the woman is Catholic or not, and then one part of the data will be used to select the hypotheses and design the corresponding tests for the second part of the data. In past use of cross-screening (automatic cross-screening) there was only one team of investigators that dealt with both parts of the data so that the investigators would need to decide on an analysis plan before looking at the data. In this protocol, we describe plans to carry out a novel flexible cross-screening in which there will be two teams of investigators with access only to one part of data and each team will use their part of the data to decide how to plan the analysis for the second team's data. In addition to the above replicability analysis, we also discuss the plan to test the global null hypothesis that is intended to identify the outcomes which are affected by unintended pregnancy for at least one of the two subgroups of Catholics and non-Catholics.

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arXiv2022

Randomization-based Test for Censored Outcomes: A New Look at the Logrank Test

Two-sample tests with censored outcomes are a classical topic in statistics with wide use even in cutting edge applications. There are at least two modes of inference used to justify two-sample tests. One is usual superpopulation inference assuming that units are independent and identically distributed (i.i.d.) samples from some superpopulation; the other is finite population inference that relies on the random assignments of units into different groups. When randomization is actually implemented, the latter has the advantage of avoiding distributional assumptions on the outcomes. In this paper, we focus on finite population inference for censored outcomes, which has been less explored in the literature. Moreover, we allow the censoring time to depend on treatment assignment, under which exact permutation inference is unachievable. We find that, surprisingly, the usual logrank test can also be justified by randomization. Specifically, under a Bernoulli randomized experiment with non-informative i.i.d. censoring, the logrank test is asymptotically valid for testing Fisher's null hypothesis of no treatment effect on any unit. The asymptotic validity of the logrank test does not require any distributional assumption on the potential event times. We further extend the theory to the stratified logrank test, which is useful for randomized block designs and when censoring mechanisms vary across strata. In sum, the developed theory for the logrank test from finite population inference supplements its classical theory from usual superpopulation inference, and helps provide a broader justification for the logrank test.

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