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Register a new userSeparable Effects for Causal Inference in the Presence of Competing Events
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Mats Julius Stensrud
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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In time-to-event settings, the presence of competing events complicates the definition of causal effects. Here we propose the new separable effects to study the causal effect of a treatment on an event of interest. The separable direct effect is the treatment effect on the event of interest not mediated by its effect on the competing event. The separable indirect effect is the treatment effect on the event of interest only through its effect on the competing event. Similar to Robins and Richardsons extended graphical approach for mediation analysis, the separable effects can only be identified under the assumption that the treatment can be decomposed into two distinct components that exert their effects through distinct causal pathways. Unlike existing definitions of causal effects in the presence of competing events, our estimands do not require cross-world contrasts or hypothetical interventions to prevent death. As an illustration, we apply our approach to a randomized clinical trial on estrogen therapy in individuals with prostate cancer.
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When interested in a time-to-event outcome, competing events that prevent the occurrence of the event of interest may be present. In the presence of competing events, various statistical estimands have been suggested for defining the causal effect of treatment on the event of interest. Depending on the estimand, the competing events are either accommodated or eliminated, resulting in causal effects with different interpretation. The former approach captures the total effect of treatment on the event of interest while the latter approach captures the direct effect of treatment on the event of interest that is not mediated by the competing event. Separable effects have also been defined for settings where the treatment effect can be partitioned into its effect on the event of interest and its effect on the competing event through different causal pathways. We outline various causal effects that may be of interest in the presence of competing events, including total, direct and separable effects, and describe how to obtain estimates using regression standardisation with the Stata command standsurv. Regression standardisation is applied by obtaining the average of individual estimates across all individuals in a study population after fitting a survival model. With standsurv several contrasts of interest can be calculated including differences, ratios and other user-defined functions. Confidence intervals can also be obtained using the delta method. Throughout we use an example analysing a publicly available dataset on prostate cancer to allow the reader to replicate the analysis and further explore the different effects of interest.
Analyses of environmental phenomena often are concerned with understanding unlikely events such as floods, heatwaves, droughts or high concentrations of pollutants. Yet the majority of the causal inference literature has focused on modelling means, rather than (possibly high) quantiles. We define a general estimator of the population quantile treatment (or exposure) effects (QTE) -- the weighted QTE (WQTE) -- of which the population QTE is a special case, along with a general class of balancing weights incorporating the propensity score. Asymptotic properties of the proposed WQTE estimators are derived. We further propose and compare propensity score regression and two weighted methods based on these balancing weights to understand the causal effect of an exposure on quantiles, allowing for the exposure to be binary, discrete or continuous. Finite sample behavior of the three estimators is studied in simulation. The proposed methods are applied to data taken from the Bavarian Danube catchment area to estimate the 95% QTE of phosphorus on copper concentration in the river.
In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects (Stensrud et al, 2019) to define direct and indirect effects of the treatment on the event of interest. This definition presupposes a treatment decomposition into two components acting along two separate causal pathways, one exclusively outside of the competing event and the other exclusively through it. Unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in a study where separate interventions on the treatment components are available. Here we extend and generalize the notion of the separable effects in several ways, allowing for interpretation, identification and estimation under considerably weaker assumptions. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted, even when they cannot be regarded as direct and indirect effects. We further derive weaker conditions for identification of separable effects in observational studies where decomposed treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. For these general settings, we propose semi-parametric weighted estimators that are straightforward to implement. As an illustration, we apply the estimators to study the separable effects of intensive blood pressure therapy on acute kidney injury, using data from a randomized clinical trial.
The notion of exchangeability has been recognized in the causal inference literature in various guises, but only rarely in the original Bayesian meaning as a symmetry property between individual units in statistical inference. Since the latter is a standard ingredient in Bayesian inference, we argue that in Bayesian causal inference it is natural to link the causal model, including the notion of confounding and definition of causal contrasts of interest, to the concept of exchangeability. Here we relate the Bayesian notion of exchangeability to alternative conditions for unconfounded inferences, commonly stated using potential outcomes, and define causal contrasts in the presence of exchangeability in terms of limits of posterior predictive expectations for further exchangeable units. While our main focus is in a point treatment setting, we also investigate how this reasoning carries over to longitudinal settings.
Propensity score methods have been shown to be powerful in obtaining efficient estimators of average treatment effect (ATE) from observational data, especially under the existence of confounding factors. When estimating, deciding which type of covariates need to be included in the propensity score function is important, since incorporating some unnecessary covariates may amplify both bias and variance of estimators of ATE. In this paper, we show that including additional instrumental variables that satisfy the exclusion restriction for outcome will do harm to the statistical efficiency. Also, we prove that, controlling for covariates that appear as outcome predictors, i.e. predict the outcomes and are irrelevant to the exposures, can help reduce the asymptotic variance of ATE estimation. We also note that, efficiently estimating the ATE by non-parametric or semi-parametric methods require the estimated propensity score function, as described in Hirano et al. (2003)cite{Hirano2003}. Such estimation procedure usually asks for many regularity conditions, Rothe (2016)cite{Rothe2016} also illustrated this point and proposed a known propensity score (KPS) estimator that requires mild regularity conditions and is still fully efficient. In addition, we introduce a linearly modified (LM) estimator that is nearly efficient in most general settings and need not estimation of the propensity score function, hence convenient to calculate. The construction of this estimator borrows idea from the interaction estimator of Lin (2013)cite{Lin2013}, in which regression adjustment with interaction terms are applied to deal with data arising from a completely randomized experiment. As its name suggests, the LM estimator can be viewed as a linear modification on the IPW estimator using known propensity scores. We will also investigate its statistical properties both analytically and numerically.
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