arXiv subjects

Arvid Sjölander

Publications and source records attributed to Arvid Sjölander.

At least 19 recordsLinked to original sources

arXiv2026

On the limitations of causal inference with current-treatment Cox models

Cox models with time-varying treatments often include only the current treatment level. Translating such a model into causally meaningful intervention-specific survival probabilities relies on the Markov property: that the hazard is independent of treatment history conditional on current treatment. For the Markov property to not be population-specific, it needs to hold also conditional on any unmeasured prognostic heterogeneity (frailty). Using a discrete-time argument, earlier work concluded that the Markov property can hold both conditionally and marginally only in the absence of a treatment effect or an effect of the unmeasured heterogeneity. We broaden this argument by developing a continuous-time framework that encompasses both proposed extensions of the Kaplan-Meier curve and current-treatment marginal structural Cox models, and sharpen it by characterizing precisely the conditions under which the Markov property can hold both conditionally and marginally. Specifically, we show that it requires the absence of treatment-frailty interaction on the additive hazard scale. As frailty is inherently unmeasured, such a no-interaction assumption cannot be verified. Consequently, causal interpretation of a current-treatment marginal structural Cox model rests on a strong and unverifiable structural assumption. Illustrating this point, we construct a setting in which a Cox model is correctly specified conditionally on current treatment only, although the marginal Markov property fails. Transforming the fitted model to the survival scale does not recover the true intervention-specific survival probabilities. Thus, moving from the hazard scale to the survival scale is not in itself sufficient to obtain a causal interpretation in the time-varying treatment setting.

stat.ME↗

arXiv2026

A causal modeling perspective on decision theory

Decision theory provides a formal framework for how agents should make choices under uncertainty, drawing on ideas from philosophy, probability, and causality. Despite significant progress, the field still lacks a unified modeling language, and key concepts - such as the distinction between subjective and objective elements, or what it means for a decision theory to perform well - are often left implicit. This can make it difficult to evaluate and compare competing theories, particularly in controversial cases. In this paper, we address these issues by introducing a formal framework for decision theory based on nonparametric structural equation models (NPSEMs), a well-established tool in causal inference. NPSEMs provide a unified foundation for representing agents, counterfactuals, and causal relationships, allowing for unambiguous definitions of EDT and CDT. Building on this foundation, we propose a novel decision theory - personal decision theory - which instructs agents to maximize a subjective model of their own counterfactual utility. We introduce a formal performance metric based on hypothetical interventions that enforce a given decision theory across a population - such as might be achieved through education or policy -- and show that, under certain assumptions, personal decision theory is optimal with respect to this metric. Throughout, we use the smoking lesion problem as a running example and conclude with a formal analysis of Newcomb's problem. Our aim is to provide decision theory with a clearer modeling language and firmer evaluative ground, thereby enabling more rigorous comparisons and facilitating conceptual progress in the field.

cs.AI↗

arXiv2026

Deriving Complete Constraints in Hidden Variable Models

Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that would otherwise be untestable due to the unobserved variables and can be used to constrain estimation procedures to improve statistical efficiency. Knowing the complete set of observable constraints is thus ideal, but this can be difficult to determine in many settings. In models with categorical observed variables and a joint distribution that is completely characterized by linear relations to the unobservable response function variables, we develop a systematic method for deriving the complete set of observable constraints. We illustrate the method in several new settings, including ones that imply both inequality and equality constraints.

stat.ME↗

arXiv2025

Evaluation of clinical utility in emulated clinical trials

Dynamic treatment regimes have been proposed to personalize treatment decisions by utilizing historical patient data, but they may not always improve on the current standard of care. It is thus meaningful to integrate the standard of care into the evaluation of treatment strategies, and previous works have suggested doing so through the concept of clinical utility. Here we will focus on the comparative component of clinical utility as the average outcome had the full population received treatment based on the proposed dynamic treatment regime in comparison to the full population receiving the ``standard" treatment assignment mechanism, such as a physician's choice. Clinical trials to evaluate clinical utility are rarely conducted, and thus, previous works have proposed an emulated clinical trial framework using observational data. However, only one simple estimator was previously suggested, and the practical details of how one would conduct this emulated trial were not detailed. Here, we illuminate these details and propose several estimators of clinical utility based on estimators proposed in the dynamic treatment regime literature. We illustrate the considerations and the estimators in a real data example investigating treatment rules for rheumatoid arthritis, where we highlight that in addition to the standard of care, the current medical guidelines should also be compared to any estimated ``optimal'' decision rule.

stat.AP↗

arXiv2025

Definition, Identification, and Estimation of the Direct and Indirect Number Needed to Treat

The number needed to treat (NNT) is an efficacy and effect size measure commonly used in epidemiological studies and meta-analyses. The NNT was originally defined as the average number of patients needed to be treated to observe one less adverse effect. In this study, we introduce the novel direct and indirect number needed to treat (DNNT and INNT, respectively). The DNNT and the INNT are efficacy measures defined as the average number of patients that needed to be treated to benefit from the treatment's direct and indirect effects, respectively. We start by formally defining these measures using nested potential outcomes. Next, we formulate the conditions for the identification of the DNNT and INNT, as well as for the direct and indirect number needed to expose (DNNE and INNE, respectively) and the direct and indirect exposure impact number (DEIN and IEIN, respectively) in observational studies. Next, we present an estimation method with two analytical examples. A corresponding simulation study follows the examples. The simulation study illustrates that the estimators of the novel indices are consistent, and their analytical confidence intervals meet the nominal coverage rates.

stat.ME↗

arXiv2025

Nonparametric Bounds for Evaluating the Clinical Utility of Treatment Rules

Evaluating the value of new clinical treatment rules based on patient characteristics is important but often complicated by hidden confounding factors in observational studies. Standard methods for estimating the average patient outcome if a new rule were universally adopted typically rely on strong, untestable assumptions about these hidden factors. This paper tackles this challenge by developing nonparametric bounds - a range of plausible values - for the expected outcome under a new rule, even with unobserved confounders present. We propose and investigate two main strategies for derivation of these bounds. We extend these techniques to incorporate Instrumental Variables (IVs), which can help narrow the bounds, and to directly estimate bounds on the difference in expected outcomes between the new rule and an existing clinical guideline. In simulation studies we compare the performance and width of bounds generated by the reduction and conditioning strategies in different scenarios. The methods are illustrated with a real-data example about prevention of peanut allergy in children. Our bounding frameworks provide robust tools for assessing the potential impact of new clinical treatment rules when unmeasured confounding is a concern.

stat.ME↗

arXiv2025

Propensity weighting plus adjustment in proportional hazards model is not doubly robust

Recently, it has become common for applied works to combine commonly used survival analysis modeling methods, such as the multivariable Cox model and propensity score weighting, with the intention of forming a doubly robust estimator of an exposure effect hazard ratio that is unbiased in large samples when either the Cox model or the propensity score model is correctly specified. This combination does not, in general, produce a doubly robust estimator, even after regression standardization, when there is truly a causal effect. We demonstrate via simulation this lack of double robustness for the semiparametric Cox model, the Weibull proportional hazards model, and a simple proportional hazards flexible parametric model, with both the latter models fit via maximum likelihood. We provide a novel proof that the combination of propensity score weighting and a proportional hazards survival model, fit either via full or partial likelihood, is consistent under the null of no causal effect of the exposure on the outcome under particular censoring mechanisms if either the propensity score or the outcome model is correctly specified and contains all confounders. Given our results suggesting that double robustness only exists under the null, we outline two simple alternative estimators that are doubly robust for the survival difference at a given time point (in the above sense), provided the censoring mechanism can be correctly modeled, and one doubly robust method of estimation for the full survival curve. We provide R code to use these estimators for estimation and inference in the supporting information.

stat.ME↗

arXiv2025

Adding covariates to bounds: What is the question?

Symbolic nonparametric bounds for partial identification of causal effects now have a long history in the causal literature. Sharp bounds, bounds that use all available information to make the range of values as narrow as possible, are often the goal. For this reason, many publications have focused on deriving sharp bounds, but the concept of sharp bounds is nuanced and can be misleading. In settings with ancillary covariates, the situation becomes more complex. We provide clear definitions for pointwise and uniform sharpness of covariate-conditional bounds, that we then use to prove some general and some specific to the IV setting results about the relationship between these two concepts. As we demonstrate, general conditions are much more difficult to determine and thus, we urge authors to be clear when including ancillary covariates in bounds via conditioning about the setting of interest and the assumptions made.

stat.ME↗

arXiv2024

Estimation of the Number Needed to Treat, the Number Needed to be Exposed, and the Exposure Impact Number with Instrumental Variables

The Number needed to treat (NNT) is an efficacy index defined as the average number of patients needed to treat to attain one additional treatment benefit. In observational studies, specifically in epidemiology, the adequacy of the populationwise NNT is questionable since the exposed group characteristics may substantially differ from the unexposed. To address this issue, groupwise efficacy indices were defined: the Exposure Impact Number (EIN) for the exposed group and the Number Needed to be Exposed (NNE) for the unexposed. Each defined index answers a unique research question since it targets a unique sub-population. In observational studies, the group allocation is typically affected by confounders that might be unmeasured. The available estimation methods that rely either on randomization or the sufficiency of the measured covariates for confounding control will result in inconsistent estimators of the true NNT (EIN, NNE) in such settings. Using Rubin's potential outcomes framework, we explicitly define the NNT and its derived indices as causal contrasts. Next, we introduce a novel method that uses instrumental variables to estimate the three aforementioned indices in observational studies. We present two analytical examples and a corresponding simulation study. The simulation study illustrates that the novel estimators are statistically consistent, unlike the previously available methods, and their analytical confidence intervals' empirical coverage rates converge to their nominal values. Finally, a real-world data example of an analysis of the effect of vitamin D deficiency on the mortality rate is presented.

stat.ME↗

arXiv2024

The impact of coarsening an exposure on partial identifiability in instrumental variable settings

In instrumental variable (IV) settings, such as in imperfect randomized trials and observational studies with Mendelian randomization, one may encounter a continuous exposure, the causal effect of which is not of true interest. Instead, scientific interest may lie in a coarsened version of this exposure. Although there is a lengthy literature on the impact of coarsening of an exposure with several works focusing specifically on IV settings, all methods proposed in this literature require parametric assumptions. Instead, just as in the standard IV setting, one can consider partial identification via bounds making no parametric assumptions. This was first pointed out in Alexander Balke's PhD dissertation. We extend and clarify his work and derive novel bounds in several settings, including for a three-level IV, which will most likely be the case in Mendelian randomization. We demonstrate our findings in two real data examples, a randomized trial for peanut allergy in infants and a Mendelian randomization setting investigating the effect of homocysteine on cardiovascular disease.

stat.ME↗

arXiv2023

Inverse probability of treatment weighting with generalized linear outcome models for doubly robust estimation

There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly robust estimator and/or to misuse more complex established doubly robust estimators. A simple alternative, canonical link generalized linear models (GLM) fit via inverse probability of treatment (propensity score) weighted maximum likelihood estimation followed by standardization (the g-formula) for the average causal effect, is a doubly robust estimation method. Our aim is for the reader not just to be able to use this method, which we refer to as IPTW GLM, for doubly robust estimation, but to fully understand why it has the doubly robust property. For this reason, we define clearly, and in multiple ways, all concepts needed to understand the method and why it is doubly robust. In addition, we want to make very clear that the mere combination of propensity score weighting and an adjusted outcome model does not generally result in a doubly robust estimator. Finally, we hope to dispel the misconception that one can adjust for residual confounding remaining after propensity score weighting by adjusting in the outcome model for what remains `unbalanced' even when using doubly robust estimators. We provide R code for our simulations and real open-source data examples that can be followed step-by-step to use and hopefully understand the IPTW GLM method. We also compare to a much better-known but still simple doubly robust estimator.

stat.ME↗

arXiv2023

Sensitivity Analysis of G-estimators to Invalid Instrumental Variables

Instrumental variables regression is a tool that is commonly used in the analysis of observational data. The instrumental variables are used to make causal inference about the effect of a certain exposure in the presence of unmeasured confounders. A valid instrumental variable is a variable that is associated with the exposure, affects the outcome only through the exposure (exclusion criterion), and is not confounded with the outcome (exogeneity). These assumptions are generally untestable and rely on subject-matter knowledge. Therefore, a sensitivity analysis is desirable to assess the impact of assumptions violation on the estimated parameters. In this paper, we propose and demonstrate a new method of sensitivity analysis for G-estimators in causal linear and non-linear models. We introduce two novel aspects of sensitivity analysis in instrumental variables studies. The first is a single sensitivity parameter that captures violations of exclusion and exogeneity assumptions. The second is an application of the method to non-linear models. The introduced framework is theoretically justified and is illustrated via a simulation study. Finally, we illustrate the method by application to real-world data and provide practitioners with guidelines on conducting sensitivity analysis.

stat.ME↗

arXiv2021

Sharp nonparametric bounds for decomposition effects with two binary mediators

In randomized trials, once the total effect of the intervention has been estimated, it is often of interest to explore mechanistic effects through mediators along the causal pathway between the randomized treatment and the outcome. In the setting with two sequential mediators, there are a variety of decompositions of the total risk difference into mediation effects. We derive sharp and valid bounds for a number of mediation effects in the setting of two sequential mediators both with unmeasured confounding with the outcome. We provide five such bounds in the main text corresponding to two different decompositions of the total effect, as well as the controlled direct effect, with an additional thirty novel bounds provided in the supplementary materials corresponding to the terms of twenty-four four-way decompositions. We also show that, although it may seem that one can produce sharp bounds by adding or subtracting the limits of the sharp bounds for terms in a decomposition, this almost always produces valid, but not sharp bounds that can even be completely noninformative. We investigate the properties of the bounds by simulating random probability distributions under our causal model and illustrate how they are interpreted in a real data example.

stat.ME↗

arXiv2021

A General Method for Deriving Tight Symbolic Bounds on Causal Effects

A causal query will commonly not be identifiable from observed data, in which case no estimator of the query can be contrived without further assumptions or measured variables, regardless of the amount or precision of the measurements of observed variables. However, it may still be possible to derive symbolic bounds on the query in terms of the distribution of observed variables. Bounds, numeric or symbolic, can often be more valuable than a statistical estimator derived under implausible assumptions. Symbolic bounds, however, provide a measure of uncertainty and information loss due to the lack of an identifiable estimand even in the absence of data. We develop and describe a general approach for computation of symbolic bounds and characterize a class of settings in which our method is guaranteed to provide tight valid bounds. This expands the known settings in which tight causal bounds are solutions to linear programs. We also prove that our method can provide valid and possibly informative symbolic bounds that are not guaranteed to be tight in a larger class of problems. We illustrate the use and interpretation of our algorithms in three examples in which we derive novel symbolic bounds.

stat.ME↗

arXiv2021

Sharp Lower and Upper Bounds for the Covariance of Bounded Random Variables

In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be viewed as an extension of the Bhatia-Davis Inequality for variances. We also provide a number of different ways to standardize covariance. For a binary pair random variables, one of these standardized measures of covariation agrees with a frequently used measure of dependence between genetic variants.

math.PR↗

arXiv2020

Nonparametric bounds for causal effects in imperfect randomized experiments

Nonignorable missingness and noncompliance can occur even in well-designed randomized experiments making the intervention effect that the experiment was designed to estimate nonidentifiable. Nonparametric causal bounds provide a way to narrow the range of possible values for a nonidentifiable causal effect with minimal assumptions. We derive novel bounds for the causal risk difference for a binary outcome and intervention in randomized experiments with nonignorable missingness caused by a variety of mechanisms and with or without noncompliance. We illustrate the use of the proposed bounds in our motivating data example of peanut consumption on the development of peanut allergies in infants.

math.ST↗

arXiv2020

Causal bounds for outcome-dependent sampling in observational studies

Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally precludes the nonparametric identification of causal effects. Nonparametric bounds can provide a way to narrow the range of possible values for a nonidentifiable causal effect without making additional untestable assumptions. The nonparametric bounds literature has almost exclusively focused on settings with random sampling, and the bounds have often been derived with a particular linear programming method. We derive novel bounds for the causal risk difference, often referred to as the average treatment effect, in six settings with outcome-dependent sampling and unmeasured confounding for a binary outcome and exposure. Our derivations of the bounds illustrate two approaches that may be applicable in other settings where the bounding problem cannot be directly stated as a system of linear constraints. We illustrate our derived bounds in a real data example involving the effect of vitamin D concentration on mortality.

stat.ME↗

arXiv2020

Dealing with multiple testing: To adjust or not to adjust

Multiple testing problems arise naturally in scientific studies because of the need to capture or convey more information with more variables. The literature is enormous, but the emphasis is primarily methodological, providing numerous methods with their mathematical justification and practical implementation. Our aim is to highlight the logical issues involved in the application of multiple testing adjustment.

stat.OT↗