arXiv subjects

Dylan S. Small

Publications and source records attributed to Dylan S. Small.

At least 55 records · Page 3Linked to original sources

arXiv2020

A Test for Differential Ascertainment in Case-Control Studies with Application to Child Maltreatment

We propose a method to test for the presence of differential ascertainment in case-control studies, when data are collected by multiple sources. We show that, when differential ascertainment is present, the use of only the observed cases leads to severe bias in the computation of the odds ratio. We can alleviate the effect of such bias using the estimates that our method of testing for differential ascertainment naturally provides. We apply it to a dataset obtained from the National Violent Death Reporting System, with the goal of checking for the presence of differential ascertainment by race in the count of deaths caused by child maltreatment.

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arXiv2020

A Nonparametric Likelihood Approach for Inference in Instrumental Variable Models

Instrumental variable methods allow for inference about the treatment effect by controlling for unmeasured confounding in randomized experiments with noncompliance. However, many studies do not consider the observed compliance behavior in the testing procedure, which can lead to a loss of power. In this paper, we propose a novel nonparametric likelihood approach, referred to as the binomial likelihood (BL) method, that incorporates information on compliance behavior while overcoming several limitations of previous techniques and utilizing the advantages of likelihood methods. Our proposed method produces proper estimates of the counterfactual distribution functions by maximizing the binomial likelihood over the space of distribution functions. Using this we propose two versions of a binomial likelihood ratio test for the null hypothesis of no treatment effect. We show that both versions are more powerful to detect any distributional change than existing methods in finite sample cases, and are asymptotically equivalent to the two-sample Anderson-Darling test. We also develop an efficient algorithm for computing our estimates, and apply the binomial likelihood method to a study of the effect of Medicaid coverage on mental health using the Oregon Health Insurance Experiment.

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arXiv2020

Two Robust Tools for Inference about Causal Effects with Invalid Instruments

Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents two tools to conduct valid inference and tests in the presence of invalid instruments. First, we propose a simple and general approach to construct confidence intervals based on taking unions of well-known confidence intervals. Second, we propose a novel test for the null causal effect based on a collider bias. Our two proposals, especially when fused together, outperform traditional instrumental variable confidence intervals when invalid instruments are present, and can also be used as a sensitivity analysis when there is concern that instrumental variables assumptions are violated. The new approach is applied to a Mendelian randomization study on the causal effect of low-density lipoprotein on the incidence of cardiovascular diseases.

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arXiv2020

Protocol for a Study of the Effect of Surface Mining in Central Appalachia on Adverse Birth Outcomes

Surface mining has become a major method of coal mining in Central Appalachia alongside the traditional underground mining. Concerns have been raised about the health effects of this surface mining, particularly mountaintop removal mining where coal is mined upon steep mountaintops by removing the mountaintop through clearcutting forests and explosives. We have designed a matched observational study to assess the effects of surface mining in Central Appalachia on adverse birth outcomes. This protocol describes for the study the background and motivation, the sample selection and the analysis plan.

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arXiv2020

Protocol for an Observational Study on the Effects of Early-Life Participation in Contact Sports on Later-Life Cognition in a Sample of Monozygotic and Dizygotic Swedish Twins Reared Together and Twins Reared Apart

A large body of work links traumatic brain injury (TBI) in adulthood to the onset of Alzheimer's disease (AD). AD is the chief cause of dementia, leading to reduced cognitive capacity and autonomy and increased mortality risk. More recently, researchers have sought to investigate whether TBI experienced in early-life may influence trajectories of cognitive dysfunction in adulthood. It has been speculated that early-life participation in collision sports may lead to poor cognitive and mental health outcomes. However, to date, the few studies to investigate this relationship have produced mixed results. We propose to extend this literature by conducting a prospective study on the effects of early-life participation in collision sports on later-life cognitive health using the Swedish Adoption/Twin Study on Aging (SATSA). The SATSA is unique in its sampling of monozygotic and dizygotic twins reared together (respectively MZT, DZT) and twins reared apart (respectively MZA, DZA). The proposed analysis is a prospective study of 660 individuals comprised of 270 twin pairs and 120 singletons. Seventy-eight (11.8% individuals reported participation in collision sports. Our primary outcome will be an indicator of cognitive impairment determined by scores on the Mini-Mental State Examination (MMSE). We will also consider several secondary cognitive outcomes including verbal and spatial ability, memory, and processing speed. Our sample will be restricted to individuals with at least one MMSE score out of seven repeated assessments spaced approximately three years apart. We will adjust for age, sex, and education in each of our models.

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arXiv2020

Protocol for an Observational Study on the Effects of Social Distancing on Influenza-Like Illness and COVID-19

The novel coronavirus disease (COVID-19) is a highly contagious respiratory disease that was first detected in Wuhan, China in December 2019, and has since spread around the globe, claiming more than 69,000 lives by the time this protocol is written. It has been widely acknowledged that the most effective public policy to mitigate the pandemic is \emph{social and physical distancing}: keeping at least six feet away from people, working from home, closing non-essential businesses, etc. There have been a lot of anecdotal evidences suggesting that social distancing has a causal effect on disease mitigation; however, few studies have investigated the effect of social distancing on disease mitigation in a transparent and statistically-sound manner. We propose to perform an optimal non-bipartite matching to pair counties with similar observed covariates but vastly different average social distancing scores during the first week (March 16th through Match 22nd) of President's \emph{15 Days to Slow the Spread} campaign. We have produced a total of $302$ pairs of two U.S. counties with good covariate balance on a total of $16$ important variables. Our primary outcome will be the average observed illness collected by Kinsa Inc. two weeks after the intervention period. Although the observed illness does not directly measure COVID-19, it reflects a real-time aspect of the pandemic, and unlike confirmed cases, it is much less confounded by counties' testing capabilities. We also consider observed illness three weeks after the intervention period as a secondary outcome. We will test a proportional treatment effect using a randomization-based test with covariance adjustment and conduct a sensitivity analysis.

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arXiv2019

Regression to the Mean's Impact on the Synthetic Control Method: Bias and Sensitivity Analysis

To make informed policy recommendations from observational data, we must be able to discern true treatment effects from random noise and effects due to confounding. Difference-in-Difference techniques which match treated units to control units based on pre-treatment outcomes, such as the synthetic control approach have been presented as principled methods to account for confounding. However, we show that use of synthetic controls or other matching procedures can introduce regression to the mean (RTM) bias into estimates of the average treatment effect on the treated. Through simulations, we show RTM bias can lead to inflated type I error rates as well as decreased power in typical policy evaluation settings. Further, we provide a novel correction for RTM bias which can reduce bias and attain appropriate type I error rates. This correction can be used to perform a sensitivity analysis which determines how results may be affected by RTM. We use our proposed correction and sensitivity analysis to reanalyze data concerning the effects of California's Proposition 99, a large-scale tobacco control program, on statewide smoking rates.

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arXiv2019

Estimating Malaria Vaccine Efficacy in the Absence of a Gold Standard Case Definition: Mendelian Factorial Design

Accurate estimates of malaria vaccine efficacy require a reliable definition of a malaria case. However, the symptoms of clinical malaria are unspecific, overlapping with other childhood illnesses. Additionally, children in endemic areas tolerate varying levels of parasitemia without symptoms. Together, this makes finding a gold-standard case definition challenging. We present a method to identify and estimate malaria vaccine efficacy that does not require an observable gold-standard case definition. Instead, we leverage genetic traits that are protective against malaria but not against other illnesses, e.g., the sickle cell trait, to identify vaccine efficacy in a randomized trial. Inspired by Mendelian randomization, we introduce Mendelian factorial design, a method that augments a randomized trial with genetic variation to produce a natural factorial experiment, which identifies vaccine efficacy under realistic assumptions. A robust, covariance adjusted estimation procedure is developed for estimating vaccine efficacy on the risk ratio and incidence ratio scales. Simulations suggest that our estimator has good performance whereas standard methods are systematically biased. We demonstrate that a combined estimator using both our proposed estimator and the standard approach yields significant improvements when the Mendelian factor is only weakly protective.

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arXiv2019

Bracketing in the Comparative Interrupted Time-Series Design to Address Concerns about History Interacting with Group: Evaluating Missouri Handgun Purchaser Law

In the comparative interrupted time series design (also called the method of difference-in-differences), the change in outcome in a group exposed to treatment in the periods before and after the exposure is compared to the change in outcome in a control group not exposed to treatment in either period. The standard difference-in-difference estimator for a comparative interrupted time series design will be biased for estimating the causal effect of the treatment if there is an interaction between history in the after period and the groups; for example, there is a historical event besides the start of the treatment in the after period that benefits the treated group more than the control group. We present a bracketing method for bounding the effect of an interaction between history and the groups that arises from a time-invariant unmeasured confounder having a different effect in the after period than the before period. The method is applied to a study of the effect of the repeal of Missouri's permit-to-purchase handgun law on its firearm homicide rate. We estimate that the effect of the permit-to-purchase repeal on Missouri's firearm homicide rate is bracketed between 0.9 and 1.3 homicides per 100,000 people, corresponding to a percentage increase of 17% to 27% (95% confidence interval: [0.6,1.7] or [11%,35%]). A placebo study provides additional support for the hypothesis that the repeal has a causal effect of increasing the rate of state-wide firearm homicides.

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arXiv2019

Causal Inference with Two Versions of Treatment

Causal effects are commonly defined as comparisons of the potential outcomes under treatment and control, but this definition is threatened by the possibility that the treatment or control condition is not well-defined, existing instead in more than one version. A simple, widely applicable analysis is proposed to address the possibility that the treatment or control condition exists in two versions with two different treatment effects. This analysis loses no power in the main comparison of treatment and control, provides additional information about version effects, and controls the family-wise error rate in several comparisons. The method is motivated and illustrated using an on-going study of the possibility that repeated head trauma in high school football causes an increase in risk of early on-set dementia.

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arXiv2019

New multivariate tests for assessing covariate balance in matched observational studies

We propose new tests for assessing whether covariates in a treatment group and matched control group are balanced in observational studies. The tests exhibit high power under a wide range of multivariate alternatives, some of which existing tests have little power for. The asymptotic permutation null distributions of the proposed tests are studied and the p-values calculated through the asymptotic results work well in finite samples, facilitating the application of the test to large data sets. The tests are illustrated in a study of the effect of smoking on blood lead levels. The proposed tests are implemented in an R package BalanceCheck.

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arXiv2019

Protocol for an Observational Study of the Association of High School Football Participation on Health in Late Adulthood

American football is the most popular high school sport and is among the leading cause of injury among adolescents. While there has been considerable recent attention on the link between football and cognitive decline, there is also evidence of higher than expected rates of pain, obesity, and lower quality of life among former professional players, either as a result of repetitive head injury or through different mechanisms. Previously hidden downstream effects of playing football may have far-reaching public health implications for participants in youth and high school football programs. Our proposed study is a retrospective observational study that compares 1,153 high school males who played varsity football with 2,751 male students who did not. 1,951 of the control subjects did not play any sport and the remaining 800 controls played a non-contact sport. Our primary outcome is self-rated health measured at age 65. To control for potential confounders, we adjust for pre-exposure covariates with matching and model-based covariance adjustment. We will conduct an ordered testing procedure designed to use the full pool of 2,751 controls while also controlling for possible unmeasured differences between students who played sports and those who did not. We will quantitatively assess the sensitivity of the results to potential unmeasured confounding. The study will also assess secondary outcomes of pain, difficulty with activities of daily living, and obesity, as these are both important to individual well-being and have public health relevance.

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arXiv2019

Patterns of Effects and Sensitivity Analysis for Differences-in-Differences

Applied analysts often use the differences-in-differences (DID) method to estimate the causal effect of policy interventions with observational data. The method is widely used, as the required before and after comparison of a treated and control group is commonly encountered in practice. DID removes bias from unobserved time-invariant confounders. While DID removes bias from time-invariant confounders, bias from time-varying confounders may be present. Hence, like any observational comparison, DID studies remain susceptible to bias from hidden confounders. Here, we develop a method of sensitivity analysis that allows investigators to quantify the amount of bias necessary to change a study's conclusions. Our method operates within a matched design that removes bias from observed baseline covariates. We develop methods for both binary and continuous outcomes. We then apply our methods to two different empirical examples from the social sciences. In the first application, we study the effect of changes to disability payments in Germany. In the second, we re-examine whether election day registration increased turnout in Wisconsin.

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arXiv2019

Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score

Mendelian randomization (MR) is a method of exploiting genetic variation to unbiasedly estimate a causal effect in presence of unmeasured confounding. MR is being widely used in epidemiology and other related areas of population science. In this paper, we study statistical inference in the increasingly popular two-sample summary-data MR design. We show a linear model for the observed associations approximately holds in a wide variety of settings when all the genetic variants satisfy the exclusion restriction assumption, or in genetic terms, when there is no pleiotropy. In this scenario, we derive a maximum profile likelihood estimator with provable consistency and asymptotic normality. However, through analyzing real datasets, we find strong evidence of both systematic and idiosyncratic pleiotropy in MR, echoing the omnigenic model of complex traits that is recently proposed in genetics. We model the systematic pleiotropy by a random effects model, where no genetic variant satisfies the exclusion restriction condition exactly. In this case we propose a consistent and asymptotically normal estimator by adjusting the profile score. We then tackle the idiosyncratic pleiotropy by robustifying the adjusted profile score. We demonstrate the robustness and efficiency of the proposed methods using several simulated and real datasets.

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arXiv2018

Powerful genome-wide design and robust statistical inference in two-sample summary-data Mendelian randomization

Two-sample summary-data Mendelian randomization (MR) has become a popular research design to estimate the causal effect of risk exposures. With the sample size of GWAS continuing to increase, it is now possible to utilize genetic instruments that are only weakly associated with the exposure. To maximize the statistical power of MR, we propose a genome-wide design where more than a thousand genetic instruments are used. For the statistical analysis, we use an empirical partially Bayes approach where instruments are weighted according to their strength, thus weak instruments bring less variation to the estimator. The estimator is highly efficient with many weak genetic instruments and is robust to balanced and/or sparse pleiotropy. We apply our method to estimate the causal effect of body mass index (BMI) and major blood lipids on cardiovascular disease outcomes and obtain substantially shorter confidence intervals. Some new and statistically significant findings are: the estimated causal odds ratio of BMI on ischemic stroke is 1.19 (95% CI: 1.07--1.32, p-value < 0.001); the estimated causal odds ratio of high-density lipoprotein cholesterol (HDL-C) on coronary artery disease (CAD) is 0.78 (95% CI 0.73--0.84, p-value < 0.001). However, the estimated effect of HDL-C becomes substantially smaller and statistically non-significant when we only use the strong instruments. By employing a genome-wide design and robust statistical methods, the statistical power of MR studies can be greatly improved. Our empirical results suggest that, even though the relationship between HDL-C and CAD appears to be highly heterogeneous, it may be too soon to completely dismiss the HDL hypothesis.

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arXiv2018

Protocol for an observational study on the effects of playing football in adolescence on mental health in early adulthood

More than 1 million students play high school American football annually, but many health professionals have recently questioned its safety or called for its ban. These concerns have been partially driven by reports of chronic traumatic encephalopathy (CTE), increased risks of neurodegenerative disease, and associations between concussion history and later-life cognitive impairment and depression among retired professional football players. A recent observational study of a cohort of men who graduated from a Wisconsin high school in 1957 found no statistically significant harmful effects of playing high school football on a range of cognitive, psychological, and socio-economic outcomes measured at ages 35, 54, 65, and 72. Unfortunately, these findings may not generalize to younger populations, thanks to changes and improvements in football helmet technology and training techniques. In particular, these changes may have led to increased perceptions of safety but ultimately more dangerous styles of play, characterized by the frequent sub-concussive impacts thought to be associated with later-life neurological decline. In this work, we replicate the methodology of that earlier matched observational study using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health). These include adolescent and family co-morbidities, academic experience, self-reported levels of general health and physical activity, and the score on the Add Health Picture Vocabulary Test. Our primary outcome is the CES-D score measured in 2008 when subjects were aged 24 -- 34 and settling into early adulthood. We also examine several secondary outcomes related to physical and psychological health, including suicidality. Our results can provide insight into the natural history of potential football-related decline and dysfunction.

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arXiv2018

Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the "missing at random" and "no unmeasured confounder" assumptions. However, these assumptions are unverifiable using empirical data and pose serious threats to the validity of the qualitative conclusions of the statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. In this paper we consider a marginal sensitivity model which is a natural extension of Rosenbaum's sensitivity model that is widely used for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that asymptotically the intervals have at least nominal coverage of the estimand whenever the data generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax/maximin inequality to transform this intractable problem to a linear fractional programming problem, which can be solved very efficiently. We illustrate our method using a real dataset to estimate the causal effect of fish consumption on blood mercury level.

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arXiv2018

Two-sample instrumental variable analyses using heterogeneous samples

Instrumental variable analysis is a widely used method to estimate causal effects in the presence of unmeasured confounding. When the instruments, exposure and outcome are not measured in the same sample, Angrist and Krueger (1992) suggested to use two-sample instrumental variable (TSIV) estimators that use sample moments from an instrument-exposure sample and an instrument-outcome sample. However, this method is biased if the two samples are from heterogeneous populations so that the distributions of the instruments are different. In linear structural equation models, we derive a new class of TSIV estimators that are robust to heterogeneous samples under the key assumption that the structural relations in the two samples are the same. The widely used two-sample two-stage least squares estimator belongs to this class. It is generally not asymptotically efficient, although we find that it performs similarly to the optimal TSIV estimator in most practical situations. We then attempt to relax the linearity assumption. We find that, unlike one-sample analyses, the TSIV estimator is not robust to misspecified exposure model. Additionally, to nonparametrically identify the magnitude of the causal effect, the noise in the exposure must have the same distributions in the two samples. However, this assumption is in general untestable because the exposure is not observed in one sample. Nonetheless, we may still identify the sign of the causal effect in the absence of homogeneity of the noise.

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