Pal Christie Ryalen

Related publications (6)

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Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports injuries in athletes. Competing events, such as death, complicate causal inference in studies of recurrent events because once a competing event occurs, an individual cannot have more recurrent events. Several statistical estimands have been studied in recurrent event settings, with and without competing events. However, the causal interpretations of these estimands, and the conditions that are required to identify these estimands from observed data, have yet to be formalized. Here we use a formal framework for causal inference to formulate several causal estimands in recurrent event settings, with and without competing events. When competing events exist, we clarify when commonly used classical statistical estimands can be interpreted as causal quantities from the causal mediation literature, such as (controlled) direct effects and total effects. Furthermore, we show that recent results on interventionist mediation estimands allow us to define new causal estimands with recurrent and competing events that may be of particular clinical relevance in many subject matter settings. We use causal directed acyclic graphs and single world intervention graphs to illustrate how to reason about identification conditions for the various causal estimands based on subject matter knowledge. Furthermore, using results on counting processes, we show that our causal estimands and their identification conditions, which are articulated in discrete time, converge to classical continuous time counterparts in the limit of fine discretizations of time. We propose estimators and establish their consistency for the various identifying functionals. Finally, we use the proposed estimators to compute the effect of blood pressure lowering treatment on the recurrence of acute kidney injury using data from the Systolic Blood Pressure Intervention Trial.

SPRINGER2023

Causal inference in continuous time: an example on prostate cancer therapy

Pal Christie Ryalen, Mats Julius Stensrud

In marginal structural models (MSMs), time is traditionally treated as a discrete parameter. In survival analysis on the other hand, we study processes that develop in continuous time. Therefore, Røysland (2011. A martingale approach to continuous-time marginal structural models. Bernoulli 17, 895–915) developed the continuous-time MSMs, along with continuous-time weights. The continuous-time weights are conceptually similar to the inverse probability weights that are used in discrete time MSMs. Here, we demonstrate that continuous-time MSMs may be used in practice. First, we briefly describe the causal model assumptions using counting process notation, and we suggest how causal effect estimates can be derived by calculating continuous-time weights. Then, we describe how additive hazard models can be used to find such effect estimates. Finally, we apply this strategy to compare medium to long-term differences between the two prostate cancer treatments radical prostatectomy and radiation therapy, using data from the Norwegian Cancer Registry. In contrast to the results of a naive analysis, we find that the marginal cumulative incidence of treatment failure is similar between the strategies, accounting for the competing risk of other death.

2020

On null hypotheses in survival analysis

Pal Christie Ryalen, Mats Julius Stensrud

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. As an illustration, we apply our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomized controlled trial.

2019

Sufficient Cause Interaction for Time-to-event Outcomes

Pal Christie Ryalen, Mats Julius Stensrud

Methods to assess sufficient cause interactions are well developed for binary outcomes. We extend these methods to handle time-to-event outcomes, which occur frequently in medicine and epidemiology. Based on theory for marginal structural models in continuous time, we show how to assess sufficient cause interaction nonparametrically, allowing for censoring and competing risks. We apply the method to study interaction between intensive blood pressure therapy and statin treatment on all-cause mortality.

2019

Marginal structural models (MSMs) allow for causal analysis of longitudinal data. The standard MSM is based on discrete time models, but the continuous-time MSM is 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 continuous-time MSM 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 continuous-time weights perform better than IPTW when the underlying 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 explain how this strategy can be applied on data using our R packages ahw and transform.hazards.

2019

Transforming cumulative hazard estimates

Pal Christie Ryalen, Mats Julius Stensrud

Time-to-event outcomes are often evaluated on the hazard scale, but interpreting hazards may be difficult. Recently in the causal inference literature concerns have been raised that hazards actually have a built-in selection bias that prevents simple causal interpretations. This is a problem even in randomized controlled trials, where hazard ratios have become a standard measure of treatment effects. Modelling on the hazard scale is nevertheless convenient, for example to adjust for covariates; using hazards for intermediate calculations may therefore be desirable. In this paper we present a generic method for transforming hazard estimates consistently to other scales at which these built-in selection biases are avoided. The method is based on differential equations and generalizes a well-known relation between the Nelson–Aalen and Kaplan–Meier estimators. Using the martingale central limit theorem, we show that covariances can be estimated consistently for a large class of estimators, thus allowing for rapid calculation of confidence intervals. Hence, given cumulative hazard estimates based on, for example, Aalen’s additive hazard model, we can obtain many other parameters without much more effort. We give several examples and the associated estimators. Coverage and convergence speed are explored via simulations, and the results suggest that reliable estimates can be obtained in real-life scenarios.

2018

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SPRINGER2023