Graphical Presentation of Patient-Treatment Interaction Elucidated by Continuous Biomarkers. Current Practice and Scope for Improvement

Visualizing the (Causal) Effect of a Continuous Variable on a Time-To-Event Outcome

Visualization is a key aspect of communicating the results of any study aiming to estimate causal effects. In studies with time-to-event outcomes, the most popular visualization approach is depicting survival curves stratified by the variable of interest. This approach cannot be used when the variable of interest is continuous. Simple workarounds, such as categorizing the continuous covariate and plotting survival curves for each category, can result in misleading depictions of the main effects. Instead, we propose a new graphic, the survival area plot, to directly depict the survival probability over time and as a function of a continuous covariate simultaneously. This plot utilizes g-computation based on a suitable time-to-event model to obtain the relevant estimates. Through the use of g-computation, those estimates can be adjusted for confounding without additional effort, allowing a causal interpretation under the standard causal identifiability assumptions. If those assumptions are not met, the proposed plot may still be used to depict noncausal associations. We illustrate and compare the proposed graphics to simpler alternatives using data from a large German observational study investigating the effect of the Ankle-Brachial Index on survival. To facilitate the usage of these plots, we additionally developed the contsurvplot R-package, which includes all methods discussed in this paper.

Confidence interval estimation for the changepoint of treatment stratification in the presence of a qualitative covariate-treatment interaction

The goal in stratified medicine is to administer the "best" treatment to a patient. Not all patients might benefit from the same treatment; the choice of best treatment can depend on certain patient characteristics. In this article, it is assumed that a time-to-event outcome is considered as a patient-relevant outcome and a qualitative interaction between a continuous covariate and treatment exists, ie, that patients with different values of one specific covariate should be treated differently. We suggest and investigate different methods for confidence interval estimation for the covariate value, where the treatment recommendation should be changed based on data collected in a randomized clinical trial. An adaptation of Fieller's theorem, the delta method, and different bootstrap approaches (normal, percentile-based, wild bootstrap) are investigated and compared in a simulation study. Extensions to multivariable problems are presented and evaluated. We observed appropriate confidence interval coverage following Fieller's theorem irrespective of sample size but at the cost of very wide or even infinite confidence intervals. The delta method and the wild bootstrap approach provided the smallest intervals but inadequate coverage for small to moderate event numbers, also depending on the location of the true changepoint. For the percentile-based bootstrap, wide intervals were observed, and it was slightly conservative regarding coverage, whereas the normal bootstrap did not provide acceptable results for many scenarios. The described methods were also applied to data from a randomized clinical trial comparing two treatments for patients with symptomatic, severe carotid artery stenosis, considering patient's age as predictive marker.

Constructing treatment selection rules based on an estimated treatment effect function: different approaches to take stochastic uncertainty into account have a substantial effect on performance

BACKGROUND

Today we are often interested in the predictive value of a continuous marker with respect to the expected difference in outcome between a new treatment and a standard treatment. We can investigate this in a randomized control trial, allowing us to assess interactions between treatment and marker and to construct a treatment selection rule. A first step is often to estimate the treatment effect as a function of the marker value. A variety of approaches have been suggested for the second step to define explicitly the rule to select the treatment, varying in the way to take uncertainty into account. Little is known about the merits of the different approaches.

METHODS

Four construction principles for the second step are compared. They are based on the root of the estimated function, on confidence intervals for the root, or on pointwise or simultaneous confidence bands. All of them have been used implicitly or explicitly in the literature. As performance characteristics we consider the probability to select at least some patients, the probability to classify patients with and without a benefit correctly, and the gain in expected outcome at the population level. These characteristics are investigated in a simulation study.

RESULTS

As to be expected confidence interval/band based approaches reduce the risk to select patients who do not benefit from the new treatment, but they tend to overlook patients who can benefit. Simply using positivity of the estimated treatment effect function for selection implies often a larger gain in expected outcome.

CONCLUSIONS

The use of 95% confidence intervals/bands in constructing treatment selection rules is a rather conservative approach. There is a need for better construction principles for treatment selection rules aiming to maximize the gain in expected outcome at the population level. Choosing a confidence level of 80% may be a first step in this direction.