arXiv subjects

Tyler J. VanderWeele

Publications and source records attributed to Tyler J. VanderWeele.

At least 19 recordsLinked to original sources

arXiv2024

Generalizing and transporting causal inferences from randomized trials in the presence of trial engagement effects

Trial engagement effects are effects of trial participation on the outcome that are not mediated by treatment assignment. Most work on extending (generalizing or transporting) causal inferences from a randomized trial to a target population has, explicitly or implicitly, assumed that trial engagement effects are absent, allowing evidence about the effects of the treatments examined in trials to be applied to non-experimental settings. Here, we define novel causal estimands and present identification results for generalizability and transportability analyses in the presence of trial engagement effects. Our approach allows for trial engagement effects under assumptions of no causal interaction between trial participation and treatment assignment on the absolute or relative scales. We show that under these assumptions, even in the presence of trial engagement effects, the trial data can be combined with covariate data from the target population to identify average treatment effects in the context of usual care as implemented in the target population (i.e., outside the experimental setting). The identifying observed data functionals under these no-interaction assumptions are the same as those obtained under the stronger identifiability conditions that have been invoked in prior work. Therefore, our results suggest a new interpretation for previously proposed generalizability and transportability estimators; this interpretation may be useful in analyses under causal structures where background knowledge suggests that trial engagement effects are present but interactions between trial participation and treatment are negligible.

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arXiv2022

On the dimensional indeterminacy of one-wave factor analysis under causal effects

It is shown, with two sets of indicators that separately load on two distinct factors, independent of one another conditional on the past, that if it is the case that at least one of the factors causally affects the other, then, in many settings, the process will converge to a factor model in which a single factor will suffice to capture the covariance structure among the indicators. Factor analysis with one wave of data can then not distinguish between factor models with a single factor versus those with two factors that are causally related. Therefore, unless causal relations between factors can be ruled out a priori, alleged empirical evidence from one-wave factor analysis for a single factor still leaves open the possibilities of a single factor or of two factors that causally affect one another. The implications for interpreting the factor structure of psychological scales, such as self-report scales for anxiety and depression, or for happiness and purpose, are discussed. The results are further illustrated through simulations to gain insight into the practical implications of the results in more realistic settings prior to the convergence of the processes. Some further generalizations to an arbitrary number of underlying factors are noted.

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arXiv2022

A statistical test to reject the structural interpretation of a latent factor model

Factor analysis is often used to assess whether a single univariate latent variable is sufficient to explain most of the covariance among a set of indicators for some underlying construct. When evidence suggests that a single factor is adequate, research often proceeds by using a univariate summary of the indicators in subsequent research. Implicit in such practices is the assumption that it is the underlying latent, rather than the indicators, that is causally efficacious. The assumption that the indicators do not have effects on anything subsequent, and that they are themselves only affected by antecedents through the underlying latent is a strong assumption, effectively imposing a structural interpretation on the latent factor model. In this paper, we show that this structural assumption has empirically testable implications, even though the latent variable itself is unobserved. We develop a statistical test to potentially reject the structural interpretation of a latent factor model. We apply this test to data concerning associations between the Satisfaction-with-Life-Scale and subsequent all-cause mortality, which provides strong evidence against a structural interpretation for a univariate latent underlying the scale. Discussion is given to the implications of this result for the development, evaluation, and use of measures and for the use of factor analysis itself.

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arXiv2021

Longitudinal Mediation Analysis with Latent Growth Curves

The paper considers mediation analysis with longitudinal data under latent growth curve models within a counterfactual framework. Estimators and their standard errors are derived for natural direct and indirect effects when the mediator, the outcome, and possibly also the exposure can be modeled by an underlying latent variable giving rise to a growth curve. Settings are also considered in which the exposure is instead fixed at a single point in time.

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arXiv2021

Bias and sensitivity analysis for unmeasured confounders in linear structural equation models

In this paper, we consider the extent of the biases that may arise when an unmeasured confounder is omitted from a structural equation model (SEM) and we propose sensitivity analysis techniques to correct for such biases. We give an analysis of which effects in an SEM are, and are not, biased by an unmeasured confounder. It is shown that a single unmeasured confounder will bias not just one, but numerous, effects in an SEM. We present sensitivity analysis techniques to correct for biases in total, direct, and indirect effects when using SEM analyses, and illustrate these techniques with a study of aging and cognitive function.

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arXiv2021

Constructed measures and causal inference: towards a new model of measurement for psychosocial constructs

Psychosocial constructs can only be assessed indirectly, and measures are typically formed by a combination of indicators that are thought to relate to the construct. Reflective and formative measurement models offer different conceptualizations of the relation between the indicators and what is sometimes conceived of as a univariate latent variable supposed to correspond in some way to the construct. It is argued that the empirical implications of reflective and formative models will often be violated by data since the causally relevant constituents will generally be multivariate, not univariate. These empirical implications can be formally tested but factor analysis is not adequate to do so. It is argued that formative models misconstrue the relationship between the constructed measures and the underlying reality by which causal processes operate, but that reflective models misconstrue the nature of the underlying reality itself by typically presuming that the constituents of it that are causally efficacious are unidimensional. The ensuing problems arising from these misconstruals are discussed. A causal interpretation is proposed of associations between constructed measures and various outcomes that is applicable to both reflective and formative models and is applicable even if the usual assumptions of these models are violated. An outline for a new model of the process of measure construction is put forward. Discussion is given to the practical implications of these observations and proposals for the provision of definitions, the selection of items, item-by-item analyses, the construction of measures, and the interpretation of the associations of these measures with subsequent outcomes.

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arXiv2020

On the identification of individual principal stratum direct, natural direct and pleiotropic effects without cross world independence assumptions

The analysis of natural direct and principal stratum direct effects has a controversial history in statistics and causal inference as these effects are commonly identified with either untestable cross world independence or graphical assumptions. This paper demonstrates that the presence of individual level natural direct and principal stratum direct effects can be identified without cross world independence assumptions. We also define a new type of causal effect, called pleiotropy, that is of interest in genomics, and provide empirical conditions to detect such an effect as well. Our results are applicable for all types of distributions concerning the mediator and outcome.

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arXiv2020

Multiple-bias sensitivity analysis using bounds

Unmeasured confounding, selection bias, and measurement error are well-known sources of bias in epidemiologic research. Methods for assessing these biases have their own limitations. Many quantitative sensitivity analysis approaches consider each type of bias individually, while more complex approaches are harder to implement or require numerous assumptions. By failing to consider multiple biases at once, researchers can underestimate -- or overestimate -- their joint impact. We show that it is possible to bound the total composite bias due to these three sources, and to use that bound to assess the sensitivity of a risk ratio to any combination of these biases. We derive bounds for the total composite bias under a variety of scenarios, providing researchers with tools to assess their total potential impact. We apply this technique to a study where unmeasured confounding and selection bias are both concerns, and to another study in which possible differential exposure misclassification and unmeasured confounding are concerns. We also show that a "multi-bias E-value" can describe the minimal strength of joint bias-parameter association necessary for an observed risk ratio to be compatible with a null causal effect (or with other pre-specified effect sizes). This may provide intuition about the relative impacts of each type of bias. The approach we describe is easy to implement with minimal assumptions, and we provide R functions to do so.

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arXiv2020

Quantifying and Detecting Individual Level `Always Survivor' Causal Effects Under `Truncation by Death' and Censoring Through Time

The analysis of causal effects when the outcome of interest is possibly truncated by death has a long history in statistics and causal inference. The survivor average causal effect is commonly identified with more assumptions than those guaranteed by the design of a randomized clinical trial or using sensitivity analysis. This paper demonstrates that individual level causal effects in the `always survivor' principal stratum can be identified with no stronger identification assumptions than randomization. We illustrate the practical utility of our methods using data from a clinical trial on patients with prostate cancer. Our methodology is the first and, as of yet, only proposed procedure that enables detecting causal effects in the presence of truncation by death using only the assumptions that are guaranteed by design of the clinical trial. This methodology is applicable to all types of outcomes.

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arXiv2019

Simple Sensitivity Analysis for Differential Measurement Error

Simple sensitivity analysis results are given for differential measurement error of either the exposure or the outcome. In the case of differential measurement error of the outcome it is shown that the true effect of the exposure on the outcome on the risk ratio scale must be at least as large as the observed association between the exposure and the mis-measured outcome divided by the maximum strength of differential measurement error, assessed as the risk ratio of the controlled direct effect of the exposure on mis-measured outcome not through the true outcome. In the case of differential measurement error of the exposure it is shown that the true effect on the risk ratio scale of the exposure on the outcome must be at least as large as the observed association between the mis-measured exposure measurement and the outcome divided by the maximum strength of differential measurement error, assessed as the risk ratio of the effect of the outcome on mis-measured exposure measurement conditional on the true exposure. The results can also be immediately used to indicate the minimum strength of differential measurement error that would be needed to explain away an observed association between an exposure measurement and an outcome measurement.

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arXiv2019

Bounding bias due to selection

When epidemiologic studies are conducted in a subset of the population, selection bias can threaten the validity of causal inference. This bias can occur whether or not that selected population is the target population, and can occur even in the absence of exposure-outcome confounding. However, it is often difficult to quantify the extent of selection bias, and sensitivity analysis can be challenging to undertake and to understand. In this article we demonstrate that the magnitude of the bias due to selection can be bounded by simple expressions defined by parameters characterizing the relationships between unmeasured factor(s) responsible for the bias and the measured variables. No functional form assumptions are necessary about those unmeasured factors. Using knowledge about the selection mechanism, researchers can account for the possible extent of selection bias by specifying the size of the parameters in the bounds. We also show that the bounds, which differ depending on the target population, result in summary measures that can be used to calculate the minimum magnitude of the parameters required to shift a risk ratio to the null. The summary measure can be used to determine the overall strength of selection that would be necessary to explain away a result. We then show that the bounds and summary measures can be simplified in certain contexts or with certain assumptions. Using examples with varying selection mechanisms, we also demonstrate how researchers can implement these simple sensitivity analyses.

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arXiv2018

Outcome-wide longitudinal designs for causal inference: a new template for empirical studies

In this paper we propose a new template for empirical studies intended to assess causal effects: the outcome-wide longitudinal design. The approach is an extension of what is often done to assess the causal effects of a treatment or exposure using confounding control, but now, over numerous outcomes. We discuss the temporal and confounding control principles for such outcome-wide studies, metrics to evaluate robustness or sensitivity to potential unmeasured confounding for each outcome, and approaches to handle multiple testing. We argue that the outcome-wide longitudinal design has numerous advantages over more traditional studies of single exposure-outcome relationships including results that are less subject to investigator bias, greater potential to report null effects, greater capacity to compare effect sizes, a tremendous gain in the efficiency for the research community, a greater policy relevance, and a more rapid advancement of knowledge. We discuss both the practical and theoretical justification for the outcome-wide longitudinal design and also the pragmatic details of its implementation.

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arXiv2018

Selecting optimal subgroups for treatment using many covariates

We consider the problem of selecting the optimal subgroup to treat when data on covariates is available from a randomized trial or observational study. We distinguish between four different settings including (i) treatment selection when resources are constrained, (ii) treatment selection when resources are not constrained, (iii) treatment selection in the presence of side effects and costs, and (iv) treatment selection to maximize effect heterogeneity. We show that, in each of these cases, the optimal treatment selection rule involves treating those for whom the predicted mean difference in outcomes comparing those with versus without treatment, conditional on covariates, exceeds a certain threshold. The threshold varies across these four scenarios but the form of the optimal treatment selection rule does not. The results suggest a move away from traditional subgroup analysis for personalized medicine. New randomized trial designs are proposed so as to implement and make use of optimal treatment selection rules in health care practice.

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arXiv2017

Sensitivity Analysis for Unmeasured Confounding in Meta-Analyses

Random-effects meta-analyses of observational studies can produce biased estimates if the synthesized studies are subject to unmeasured confounding. We propose sensitivity analyses quantifying the extent to which unmeasured confounding of specified magnitude could reduce to below a certain threshold the proportion of true effect sizes that are scientifically meaningful. We also develop converse methods to estimate the strength of confounding capable of reducing the proportion of scientifically meaningful true effects to below a chosen threshold. These methods apply when a "bias factor" is assumed to be normally distributed across studies or is assessed across a range of fixed values. Our estimators are derived using recently proposed sharp bounds on confounding bias within a single study that do not make assumptions regarding the unmeasured confounders themselves or the functional form of their relationships to the exposure and outcome of interest. We provide an R package, ConfoundedMeta, and a freely available online graphical user interface that compute point estimates and inference and produce plots for conducting such sensitivity analyses. These methods facilitate principled use of random-effects meta-analyses of observational studies to assess the strength of causal evidence for a hypothesis.

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arXiv2017

Decomposition analysis to identify intervention targets for reducing disparities

There has been considerable interest in using decomposition methods in epidemiology (mediation analysis) and economics (Oaxaca-Blinder decomposition) to understand how health disparities arise and how they might change upon intervention. It has not been clear when estimates from the Oaxaca-Blinder decomposition can be interpreted causally because its implementation does not explicitly address potential confounding of target variables. While mediation analysis does explicitly adjust for confounders of target variables, it does so in a way that entails equalizing confounders across racial groups, which may not reflect the intended intervention. Revisiting prior analyses in the National Longitudinal Survey of Youth on disparities in wages, unemployment, incarceration, and overall health with test scores, taken as a proxy for educational attainment, as a target intervention, we propose and demonstrate a novel decomposition that controls for confounders of test scores (measures of childhood SES) while leaving their association with race intact. We compare this decomposition with others that use standardization (to equalize childhood SES alone), mediation analysis (to equalize test scores within levels of childhood SES), and one that equalizes both childhood SES and test scores. We also show how these decompositions, including our novel proposals, are equivalent to causal implementations of the Oaxaca-Blinder decomposition.

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arXiv2016

Sharp sensitivity bounds for mediation under unmeasured mediator-outcome confounding

It is often of interest to decompose a total effect of an exposure into the component that acts on the outcome through some mediator and the component that acts independently through other pathways. Said another way, we are interested in the direct and indirect effects of the exposure on the outcome. Even if the exposure is randomly assigned, it is often infeasible to randomize the mediator, leaving the mediator-outcome confounding not fully controlled. We develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured mediator-outcome confounding.

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arXiv2015

The Differential Geometry of Homogeneity Spaces Across Effect Scales

If an effect measure is more homogeneous than others, then its value is more likely to be stable across different subgroups or subpopulations. Therefore, it is of great importance to find a more homogeneous effect measure that allows for transportability of research results. For a binary outcome, applied researchers often claim that the risk difference is more heterogeneous than the risk ratio or odds ratio, because they find, based on evidence from surveys of meta-analyses, that the null hypotheses of homogeneity are rejected more often for the risk difference than for the risk ratio and odds ratio. However, the evidence for these claims are far from satisfactory, because of different statistical powers of the homogeneity tests under different effect scales. For binary treatment, covariate and outcome, we theoretically quantify the homogeneity of different effect scales. Because when homogeneity holds the four outcome probabilities lie in a three dimensional sub-space of the four dimensional space, we can use results from differential geometry to compute the volumes of these three dimensional spaces to compare the relative homogeneity of the risk difference, risk ratio, and odds ratio. We demonstrate that the homogeneity space for the risk difference has the smallest volume, and the homogeneity space for the odds ratio has the largest volume, providing some further evidence for the previous claim that the risk difference is more heterogeneous than the risk ratio and odds ratio.

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arXiv2015

Causal Diagrams for Interference

The term "interference" has been used to describe any setting in which one subject's exposure may affect another subject's outcome. We use causal diagrams to distinguish among three causal mechanisms that give rise to interference. The first causal mechanism by which interference can operate is a direct causal effect of one individual's treatment on another individual's outcome; we call this direct interference. Interference by contagion is present when one individual's outcome may affect the outcomes of other individuals with whom he comes into contact. Then giving treatment to the first individual could have an indirect effect on others through the treated individual's outcome. The third pathway by which interference may operate is allocational interference. Treatment in this case allocates individuals to groups; through interactions within a group, individuals may affect one another's outcomes in any number of ways. In many settings, more than one type of interference will be present simultaneously. The causal effects of interest differ according to which types of interference are present, as do the conditions under which causal effects are identifiable. Using causal diagrams for interference, we describe these differences, give criteria for the identification of important causal effects, and discuss applications to infectious diseases.

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