Ensuring valid inference for Cox hazard ratios after variable selection

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference. A major drawback of routine procedures is that there is no finite sample size at which they are guaranteed to deliver exposure effect estimators and associated confidence intervals with adequate performance. In this work, we will consider this problem when inferring conditional causal hazard ratios from observational studies under the assumption of no unmeasured confounding. The major complication that we face with survival data is that the key confounding variables may not be those that explain the censoring mechanism. In this paper, we overcome this problem using a novel and simple procedure that can be implemented using off-the-shelf software for penalized Cox regression. In particular, we will propose tests of the null hypothesis that the exposure has no effect on the considered survival endpoint, which are uniformly valid under standard sparsity conditions. Simulation results show that the proposed methods yield valid inferences even when covariates are high-dimensional.

Efficient, doubly robust estimation of the effect of dose switching for switchers in a randomized clinical trial

Motivated by a clinical trial conducted by Janssen Pharmaceutica in which a flexible dosing regimen is compared to placebo, we evaluate how switchers in the treatment arm (i.e., patients who were switched to the higher dose) would have fared had they been kept on the low dose. This is done in order to understand whether flexible dosing is potentially beneficial for them. Simply comparing these patients' responses with those of patients who stayed on the low dose does not likely entail a satisfactory evaluation because the latter patients are usually in a better health condition. Because the available information in the considered trial is too limited to enable a reliable adjustment, we will instead transport data from a fixed dosing trial that has been conducted concurrently on the same target, albeit not in an identical patient population. In particular, we propose an estimator that relies on an outcome model, a model for switching, and a propensity score model for the association between study and patient characteristics. The proposed estimator is asymptotically unbiased if either the outcome or the propensity score model is correctly specified, and efficient (under the semiparametric model where the randomization probabilities are known and independent of baseline covariates) when all models are correctly specified. The proposed method for transporting information from an external study is more broadly applicable in studies where a classical confounding adjustment is not possible due to near positivity violation (e.g., studies where switching takes place in a (near) deterministic manner). Monte Carlo simulations and application to the motivating study demonstrate adequate performance.

Principled selection of baseline covariates to account for censoring in randomized trials with a survival endpoint

The analysis of randomized trials with time-to-event endpoints is nearly always plagued by the problem of censoring. In practice, such analyses typically invoke the assumption of noninformative censoring. While this assumption usually becomes more plausible as more baseline covariates are being adjusted for, such adjustment also raises concerns. Prespecification of which covariates will be adjusted for (and how) is difficult, thus prompting the use of data-driven variable selection procedures, which may impede valid inferences to be drawn. The adjustment for covariates moreover adds concerns about model misspecification, and the fact that each change in adjustment set also changes the censoring assumption and the treatment effect estimand. In this article, we discuss these concerns and propose a simple variable selection strategy designed to produce a valid test of the null in large samples. The proposal can be implemented using off-the-shelf software for (penalized) Cox regression, and is empirically found to work well in simulation studies and real data analyses.

Clinical Trials Impacted by the COVID-19 Pandemic: Adaptive Designs to the Rescue?

Very recently the new pathogen severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was identified and the coronavirus disease 2019 (COVID-19) declared a pandemic by the World Health Organization. The pandemic has a number of consequences for ongoing clinical trials in non-COVID-19 conditions. Motivated by four current clinical trials in a variety of disease areas we illustrate the challenges faced by the pandemic and sketch out possible solutions including adaptive designs. Guidance is provided on (i) where blinded adaptations can help; (ii) how to achieve Type I error rate control, if required; (iii) how to deal with potential treatment effect heterogeneity; (iv) how to use early read-outs; and (v) how to use Bayesian techniques. In more detail approaches to resizing a trial affected by the pandemic are developed including considerations to stop a trial early, the use of group-sequential designs or sample size adjustment. All methods considered are implemented in a freely available R shiny app. Furthermore, regulatory and operational issues including the role of data monitoring committees are discussed.

Improving interim decisions in randomized trials by exploiting information on short-term endpoints and prognostic baseline covariates

Conditional power calculations are frequently used to guide the decision whether or not to stop a trial for futility or to modify planned sample size. These ignore the information in short-term endpoints and baseline covariates, and thereby do not make fully efficient use of the information in the data. We therefore propose an interim decision procedure based on the conditional power approach which exploits the information contained in baseline covariates and short-term endpoints. We will realize this by considering the estimation of the treatment effect at the interim analysis as a missing data problem. This problem is addressed by employing specific prediction models for the long-term endpoint which enable the incorporation of baseline covariates and multiple short-term endpoints. We show that the proposed procedure leads to an efficiency gain and a reduced sample size, without compromising the Type I error rate of the procedure, even when the adopted prediction models are misspecified. In particular, implementing our proposal in the conditional power approach enables earlier decisions relative to standard approaches, whilst controlling the probability of an incorrect decision. This time gain results in a lower expected number of recruited patients in case of stopping for futility, such that fewer patients receive the futile regimen. We explain how these methods can be used in adaptive designs with unblinded sample size re-assessment based on the inverse normal P-value combination method to control Type I error. We support the proposal by Monte Carlo simulations based on data from a real clinical trial.

Evaluating futility of a binary clinical endpoint using early read-outs

Interim analyses are routinely used to monitor accumulating data in clinical trials. When the objective of the interim analysis is to stop the trial if the trial is deemed futile, it must ideally be conducted as early as possible. In trials where the clinical endpoint of interest is only observed after a long follow-up, many enrolled patients may therefore have no information on the primary endpoint available at the time of the interim analysis. To facilitate earlier decision-making, one may incorporate early response data that are predictive for the primary endpoint (eg, an assessment of the primary endpoint at an earlier time) in the interim analysis. Most attention so far has been given to the development of interim test statistics that include such short-term endpoints, but not to decision procedures. Existing tests moreover perform poorly when the information is scarce, eg, due to rare events, when the cohort of patients with observed primary endpoint data is small, or when the short-term endpoint is a strong but imperfect predictor. In view of this, we develop an interim decision procedure based on the conditional power approach that utilizes the short-term and long-term binary endpoints in a framework that is expected to provide reliable inferences, even when the primary endpoint is only available for a few patients, and has the added advantage that it allows the use of historical information. The operational characteristics of the proposed procedure are evaluated for the phase III clinical trial that motivated this approach, using simulation studies.