arXiv subjects

Mats Julius Stensrud

Publications and source records attributed to Mats Julius Stensrud.

14 recordsLinked to original sources

arXiv2026

Sample splitting for valid statistical inference in target trial emulations

\noindent Target trial emulation has improved comparative effectiveness research by making the causal question, assumptions, and analysis plan explicit. However, target trial protocols are usually developed iteratively. That is, after examining the data, investigators revise the protocol to reflect which target trials the observational data can realistically support. This iterative procedure is part of normal scientific practice, but it raises concerns about selective choices and invalid statistical inference. A simple procedure based on sample splitting addresses the concerns about valid inference. In the initial split, investigators can explore the data to define a target trial protocol. When these choices are made, the target trial protocol is implemented on the second split. Even though the investigators used the data to select the target trial protocol, the statistical inference has the usual coverage guarantees. The procedure intentionally mirrors how trialists move from pilot studies to a phase 3 trial. First, they use data from pilots and early-phase trials to decide on a final protocol. Then they implement this protocol and analyze a new set of data in a phase 3 trial.

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arXiv2026

On the choice of using raw or demographically-corrected scores

Demographic corrections are routinely performed in many disciplines, including psychology. Yet, there are ongoing debates about whether these corrections are appropriate and improve classification accuracy. Here, we focus on cognitive screening tests, and show that common demographic corrections, like the z-score correction, can be detrimental for classification in some settings. Formally, we present sufficient conditions ensuring that raw scores outperform the demographically-corrected ones, and give a substantive interpretation of this result. We also investigate the claim that using demographically-corrected scores results in more fair decisions compared to using raw scores. We apply our results to the Mini-Mental State Examination in the OASIS-3 dataset.

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arXiv2026

On causal inference with marked point process data

We define dynamic treatment regimes and associated potential outcomes for data described by marked point processes (MPPs). These definitions motivate MPP analogues of the commonly used consistency, exchangeability, and positivity conditions that are sufficient for identifying effects in MPP data structures. The conditions are formulated based on martingale theory, which allows us to derive explicit identifying assumptions for data described by stochastic processes. The definitions and conditions align with well-established discrete-time results in important special cases. Thus, this work bridges the large literatures on survival (event history) analysis with counting processes in continuous time and causal inference with variables in discrete-time. After formulating a set of identification conditions, we derive and characterize marginal g-formulas. The g-formulas are generally different from those studied in related works, though they coincide in important special cases. We relate our findings to previous work on causal inference with (counting) processes, the classical survival literature, and the discrete-time causal inference literature.

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arXiv2025

Add-On Regimes and Their Relevance for Quantifying the Effects of Opioid-Sparing Treatments

Medical researchers and practitioners want to know if supplementing opioid treatments with other analgesics, such as nonsteroidal anti-inflammatory drugs (NSAIDs), can reduce opioid consumption. However, quantifying opioid-sparing effects is challenging; even coming up with a policy-relevant estimand requires care. We propose defining these effects in terms of add-on regimes. An add-on regime assigns NSAIDs over time based on the opioid and NSAID treatments a patient would naturally take without any intervention. The regime uses the physician's decision to administer opioids as a clinically meaningful, and practically feasible, indication for NSAID administration. In contrast, static regimes assign NSAIDs at predefined time points, regardless of clinical context. When opioids are not administered, the add-on regime requires no intervention, thereby preserving the natural level of NSAIDs. This differs from conventional dynamic regimes, which define treatment decisions at every time point during the treatment period. We identify the effect of add-on regimes under assumptions that are easier to assess than those used in existing methods. Finally, we apply the methods to estimate opioid-sparing effects of NSAIDs in a cohort of Norwegian trauma patients using national registry data.

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arXiv2025

Encoding and inference on separable effects for sustained treatments

Sustained treatment strategies are common in many domains, particularly in medicine, where many treatment are delivered repeatedly over time. The effects of adherence to a treatment strategy throughout follow-up are often more relevant to decision-makers than effects of treatment assignment or initiation. Here we consider the separable effect of sustained use of a time-varying treatment. Despite the potential usefulness of this estimand, the theory of separable effects has yet to be extended to settings with sustained treatment strategies. To derive our results, we use an unconventional encoding of time-varying treatment strategies. This allows us to obtain concise formulations of identifying assumptions with better practical properties; for example, they admit frugal graphical representations and formulations of identifying functionals. These functionals are used to motivate doubly robust semiparametrically efficient estimators. The results are applied to the Systolic Blood Pressure Intervention Trial (SPRINT), where we estimate a separable effect of modified blood pressure treatments on the risk of acute kidney injury.

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arXiv2023

Separable effects for adherence

Comparing different medications is complicated when adherence to these medications differs. We can overcome the adherence issue by assessing effectiveness under sustained use, as in the usual causal `per-protocol' estimand. However, when sustained use is challenging to satisfy in practice, the usefulness of this estimand can be limited. Here we propose a different class of estimands: separable effects for adherence. These estimands compare modified medications, holding fixed a component responsible for non-adherence. Under assumptions about treatment components' mechanisms of effect, the separable effects estimand can eliminate differences in adherence. These assumptions are amenable to interrogation by subject-matter experts and can be evaluated using causal graphs. We describe an algorithm for constructing causal graphs for separable effects, illustrate how these graphs can be used to reason about assumptions required for identification, and provide semi-parametric weighted estimators.

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arXiv2020

Estimation of separable direct and indirect effects in continuous time

Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause specific or subdistribution hazards, are fundamentally hard to be interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause specific hazard functions. We describe the asymptotic properties of these estimators, and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we re-analyze the prostate cancer trial from Stensrud et al (2020).

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arXiv2020

Transforming cumulative hazard estimates

Time to event outcomes are often evaluated on the hazard scale, but interpreting hazards may be difficult. Recently, there has been concern in the causal inference literature that hazards actually have a built in selection-effect that prevents simple causal interpretations. This is even a problem in randomized controlled trials, where hazard ratios have become a standard measure of treatment effects. Modeling on the hazard scale is nevertheless convenient, e.g. to adjust for covariates. Using hazards for intermediate calculations may therefore be desirable. Here, we provide a generic method for transforming hazard estimates consistently to other scales at which these built in selection effects are avoided. The method is based on differential equations, and generalize a well known relation between the Nelson-Aalen and Kaplan-Meier estimators. Using the martingale central limit theorem we also find that covariances can be estimated consistently for a large class of estimators, thus allowing for rapid calculations of confidence intervals. Hence, given cumulative hazard estimates based on e.g. Aalen's additive hazard model, we can obtain many other parameters without much more effort. We present several examples and associated estimators. Coverage and convergence speed is explored using simulations, suggesting that reliable estimates can be obtained in real-life scenarios.

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arXiv2019

Effect heterogeneity and variable selection for standardizing causal effects to a target population

The participants in randomized trials and other studies used for causal inference are often not representative of the populations seen by clinical decision-makers. To account for differences between populations, researchers may consider standardizing results to a target population. We discuss several different types of homogeneity conditions that are relevant for standardization: Homogeneity of effect measures, homogeneity of counterfactual outcome state transition parameters, and homogeneity of counterfactual distributions. Each of these conditions can be used to show that a particular standardization procedure will result in unbiased estimates of the effect in the target population, given assumptions about the relevant scientific context. We compare and contrast the homogeneity conditions, in particular their implications for selection of covariates for standardization and their implications for how to compute the standardized causal effect in the target population. While some of the recently developed counterfactual approaches to generalizability rely upon homogeneity conditions that avoid many of the problems associated with traditional approaches, they often require adjustment for a large (and possibly unfeasible) set of covariates.

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arXiv2019

The additive hazard estimator is consistent for continuous-time marginal structural models

Marginal structural models (MSMs) allow for causal analysis of longitudinal data. The MSMs were originally developed as discrete time models. Recently, continuous-time MSMs were presented as a conceptually appealing alternative for survival analysis. In applied analyses, it is often assumed that the theoretical treatment weights are known, but these weights are usually unknown and must be estimated from the data. Here we provide a sufficient condition for a class of continuous-time MSMs to be consistent even when the weights are estimated, and we show how additive hazard models can be used to estimate such weights. Our results suggest that the continuous-time weights perform better than IPTW when the underlying treatment process is continuous. Furthermore, we may wish to transform effect estimates of hazards to other scales that are easier to interpret causally. We show that a general transformation strategy can be used on weighted cumulative hazard estimates to obtain a range of other parameters in survival analysis, and demonstrate how this strategy can be applied on data using our R packages ahw and transform.hazards.

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arXiv2019

On null hypotheses in survival analysis

The conventional nonparametric tests in survival analysis, such as the log-rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. Finally, we use our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomised controlled trial.

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arXiv2018

Interpreting Hazard Ratios: Insights from Frailty Models

Hazard ratios are often used to evaluate time to event outcomes, but they may be hard to interpret. A particular issue arise because hazards are typically estimated conditional on survival, i.e.\ on left truncated samples. Then, hazard ratios from conventional models cannot be interpreted as counterfactual hazard ratios that are immediately relevant to individual patients. This article explores how the hazard ratios from Cox models may differ from hazard ratios with a causal interpretation. Using summary data from twin studies, I suggest an approach to learn about the unmeasured heterogeneity in risk of an outcome, and this information allows us to explore the interpretation and magnitude of hazard ratios. Under explicit parametric assumptions, I present a two-step method to obtain hazard ratios that are more relevant to individual subjects. The strategy relies on untestable assumptions, but may nevertheless be useful for sensitivity analyses that are relatively easy to interpret.

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arXiv2017

The surprising implications of familial association in disease risk

Background: A wide range of diseases show some degree of clustering in families; family history is therefore an important aspect for clinicians when making risk predictions. Familial aggregation is often quantified in terms of a familial relative risk (FRR), and although at first glance this measure may seem simple and intuitive as an average risk prediction, its implications are not straightforward. Methods: We use two statistical models for the distribution of disease risk in a population: a dichotomous risk model that gives an intuitive understanding of the implication of a given FRR, and a continuous risk model that facilitates a more detailed computation of the inequalities in disease risk. Published estimates of FRRs are used to produce Lorenz curves and Gini indices that quantifies the inequalities in risk for a range of diseases. Results: We demonstrate that even a moderate familial association in disease risk implies a very large difference in risk between individuals in the population. We give examples of diseases for which this is likely to be true, and we further demonstrate the relationship between the point estimates of FRRs and the distribution of risk in the population. Conclusions: The variation in risk for several severe diseases may be larger than the variation in income in many countries. The implications of familial risk estimates should be recognized by epidemiologists and clinicians.

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arXiv2017

On the collapsibility of measures of effect in the counterfactual causal framework

A measure of association is said to be collapsible over a set of baseline covariates if the marginal value of the measure of association is equal to a weighted average of the stratum-specific measures of association. In this paper, we consider two subtly different definitions of collapsibility, and show that by considering causal measures of effect based on counterfactual variables it is possible to separate out the component of non-collapsibility which is due to the mathematical properties of the effect measure. We provide weights such that the causal risk difference and the causal risk ratio are collapsible over arbitrary baseline covariates, and demonstrate that such general weights do not exist for the odds ratio.

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