Quantifying the totality of treatment effect with multiple event-time observations in the presence of a terminal event from a comparative clinical study

Causal inference with recurrent and competing events

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.

Nonparametric inference of general while-alive estimands for recurrent events

Measuring the treatment effect on recurrent events like hospitalization in the presence of death has long challenged statisticians and clinicians alike. Traditional inference on the cumulative frequency unjustly penalizes survivorship as longer survivors also tend to experience more adverse events. Expanding a recently suggested idea of the "while-alive" event rate, we consider a general class of such estimands that adjust for the length of survival without losing causal interpretation. Given a user-specified loss function that allows for arbitrary weighting, we define as estimand the average loss experienced per unit time alive within a target period and use the ratio of this loss rate to measure the effect size. Scaling the loss rate by the width of the corresponding time window gives us an alternative, and sometimes more photogenic, way of showing the data. To make inferences, we construct a nonparametric estimator for the loss rate through the cumulative loss and the restricted mean survival time and derive its influence function in closed form for variance estimation and testing. As simulations and analysis of real data from a heart failure trial both show, the while-alive approach corrects for the false attenuation of treatment effect due to patients living longer under treatment, with increased statistical power as a result. The proposed methods are implemented in the R-package WA, which is publicly available from the Comprehensive R Archive Network (CRAN).

Quantifying Treatment Effects in Trials with Multiple Event-Time Outcomes

BACKGROUND

Data on the occurrence times of multiple outcomes, reflecting the temporal profile of disease burden/progression, have been used to estimate treatment effects in various recent randomized trials. Most procedures for analyzing these data require specific model assumptions. When the assumptions are not met, the results may be misleading. Robust, model-free procedures for study design and analysis that enable clinically meaningful interpretations are warranted.

METHODS

For each treatment group, we constructed and summarized the estimated mean cumulative count of events over time by the area under the curve (AUC), which can be interpreted as the mean total event-free time lost from multiple undesirable outcomes. A higher curve, and resulting larger AUC, implies a worse treatment. The treatment effect is quantified by the ratio and/or difference of AUCs. The timing and occurrence of recurrent heart failure hospitalizations (HFHs) and cardiovascular (CV) death from Prospective Comparison of ARNI with ARB Global Outcomes in HF with Preserved Ejection Fraction (PARAGON-HF), comparing sacubitril/valsartan with valsartan, are presented for illustration. We also discuss the design of future studies on the basis of the proposed method.

RESULTS

With 48 months of follow-up, estimated AUCs, representing the total event-free time lost to HFHs and CV death, were 11.3 and 13.1 event-months for sacubitril/valsartan and valsartan, respectively. The ratio of these AUCs was 0.86 (95% confidence interval, 0.75 to 1.00; P=0.049), a 14% reduction of disease burden favoring combination therapy. A future study, similar to PARAGON-HF, designed using the new proposal would require fewer patients would than a conventional time-to-first-event analysis.

CONCLUSIONS

The proposed method is robust and model-free and provides a clinically interpretable, time-scale summary of the treatment effect. (Funded by National Institutes of Health.).

Statistical models for composite endpoints of death and non-fatal events: a review

The proper analysis of composite endpoints consisting of both death and non-fatal events is an intriguing and sometimes contentious topic. The current practice of analyzing time to the first event often draws criticisms for ignoring the unequal importance between component events and for leaving recurrent-event data unused. Novel methods that address these limitations have recently been proposed. To compare the novel versus traditional approaches, we review three typical models for composite endpoints based on time to the first event, composite event process, and pairwise hierarchical comparisons. The pros and cons of these models are discussed with reference to the relevant regulatory guidelines, such as the recently released ICH-E9(R1) Addendum "Estimands and Sensitivity Analysis in Clinical Trials". We also discuss the impact of censoring when the model assumptions are violated and explore sensitivity analysis strategies. Simulation studies are conducted to assess the performance of the reviewed methods under different settings. As demonstration, we use publicly available R-packages to analyze real data from a major cardiovascular trial.

Effects of initial invasive vs. initial conservative treatment strategies on recurrent and total cardiovascular events in the ISCHEMIA trial

AIMS

The International Study of Comparative Health Effectiveness with Medical and Invasive Approaches (ISCHEMIA) trial prespecified an analysis to determine whether accounting for recurrent cardiovascular events in addition to first events modified understanding of the treatment effects.

METHODS AND RESULTS

Patients with stable coronary artery disease (CAD) and moderate or severe ischaemia on stress testing were randomized to either initial invasive (INV) or initial conservative (CON) management. The primary outcome was a composite of cardiovascular death, myocardial infarction (MI), and hospitalization for unstable angina, heart failure, or cardiac arrest. The Ghosh-Lin method was used to estimate mean cumulative incidence of total events with death as a competing risk. The 5179 ISCHEMIA patients experienced 670 index events (318 INV, 352 CON) and 203 recurrent events (102 INV, 101 CON). A single primary event was observed in 9.8% of INV and 10.8% of CON patients while ≥2 primary events were observed in 2.5% and 2.8%, respectively. Patients with recurrent events were older; had more frequent hypertension, diabetes, prior MI, or cerebrovascular disease; and had more multivessel CAD. The average number of primary endpoint events per 100 patients over 4 years was 18.2 in INV [95% confidence interval (CI) 15.8-20.9] and 19.7 in CON (95% CI 17.5-22.2), difference -1.5 (95% CI -5.0 to 2.0, P = 0.398). Comparable results were obtained when all-cause death was substituted for cardiovascular death and when stroke was added as an event.

CONCLUSIONS

In stable CAD patients with moderate or severe myocardial ischaemia enrolled in ISCHEMIA, an initial INV treatment strategy did not prevent either net recurrent events or net total events more effectively than an initial CON strategy.

CLINICAL TRIAL REGISTRATION

ISCHEMIA ClinicalTrials.gov number, NCT01471522, https://clinicaltrials.gov/ct2/show/NCT01471522.

Estimation on conditional restricted mean survival time with counting process

In a comparative longitudinal clinical study, multiple clinical events of interest are typically collected in timing and occurrence during the follow-up period. These clinical events are often indicative of disease burden over the study period and provide overall evidence of benefit/risk of one treatment relative to another. While these clinical events are usually used to form a composite endpoint, only the first occurrence of the composite endpoint event is considered in primary efficacy analysis. This type of analysis is commonly performed but it may not be ideal. Most of the existing methods for analyzing multiple event-time data were developed, relying on certain model assumptions. However, the assumptions may greatly affect the inferences for treatment effect. In this paper, we propose a simple, non-parametric estimator of conditional mean survival time for multiple events to quantify treatment effect which has clinically meaningful interpretation. We use simulation studies to evaluate the performance of the new method. Further, we apply this method to analyze the data from a cardiovascular clinical trial as an illustration.