Adverse events in single-arm clinical trials with non-fatal time-to-event efficacy endpoint: from clinical questions to methods for statistical analysis

Abstract

Background: In any single-arm trial on novel treatments, assessment of toxicity plays an important role as occurrence of adverse events (AEs) is relevant for application in clinical practice. In the presence of a non-fatal time-to-event(s) efficacy endpoint, the analysis should be broadened to consider AEs occurrence in time. The AEs analysis could be tackled with two approaches, depending on the clinical question of interest. Approach 1 focuses on the occurrence of AE as first event. Treatment ability to protect from the efficacy endpoint event(s) has an impact on the chance of observing AEs due to competing risks action. Approach 2 considers how treatment affects the occurrence of AEs in the potential framework where the efficacy endpoint event(s) could not occur.

Methods: In the first part of the work we review the strategy of analysis for these two approaches. We identify theoretical quantities and estimators consistent with the following features: (a) estimators should address for the presence of right censoring; (b) theoretical quantities and estimators should be functions of time. In the second part of the work we propose the use of alternative methods (regression models, stratified Kaplan-Meier curves, inverse probability of censoring weighting) to relax the assumption of independence between the potential times to AE and to event(s) in the efficacy endpoint for addressing Approach 2.

Results: We show through simulations that the proposed methods overcome the bias due to the dependence between the two potential times and related to the use of standard estimators.

Conclusions: We demonstrated through simulations that one can handle patients selection in the risk sets due to the competing event, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates that induce dependence.

Keywords: Adverse events; Competing risks; Dependent censoring; IPCW; Survival analysis.

Fig. 1

a Scatterplot of the potential times $T_{\mathit{AE}}$ and $T_{\mathit{RL}}$ according to the four groups identified by the binary covariates $X_1$ and $X_2$; b Zoom of the scatterplot in panel a) selecting potential times $T_{\mathit{AE}}$ and $T_{\mathit{RL}}$ lower than 1; c histogram of the distribution of the failure times calculated as the minimum value between $T_{\mathit{AE}}$ and $T_{\mathit{RL}}$, in the simulated data of $N=300$ subjects

Fig. 2

a $C{I}_{\mathit{AE}}(t)$ estimated through the AJ formula; b $A{N}_{\mathit{AE}}(t)$ and $K{M}_{\mathit{AE}}(t)$ step curves of the cumulative $CS{H}_{\mathit{AE}}(t)$ and of the cumulative incidence of AE, respectively

Fig. 3

a ${\widehat{\mathit{AN}}}_{\mathit{AE}}(t)$ calculated for different sample sizes; b ${\widehat{\mathit{KM}}}_{\mathit{AE}}(t)$ calculated for different sample sizes

Fig. 4

a) $C{I}_{\mathit{ON}}(t)$ estimated through the AJ formula; b) $A{N}_{\mathit{ON}}(t)$ and $K{M}_{\mathit{ON}}(t)$ step curves of the cumulative $CS{H}_{\mathit{ON}}(t)$ and of the cumulative incidence of ON, respectively

Fig. 5

Incidence probability estimates obtained with the naïve KM estimator, the weighted KM estimator stratifying only for 1 covariate (risk group) or for 2 covariates (risk group and age at diagnosis) and the weighted Cox model including only risk group or both risk group and age at diagnosis as covariates

Fig. 6

Simulation results in the four scenarios at times $t=0.2$ and $t=0.3$. The grey horizontal line is the reference null bias

Fig. 7

Simulation results for scenario 3 of the IPCW estimator accounting for the presence of an interaction between $X_1$ and $X_2$ in the estimate of the weights. The grey horizontal line is the reference null bias

Fig. 8

Simulation results for the variation of scenario 4 when $P(X_1=1)=P(X_2=1)=0.5$ (Case A) or $P(X_1=1)=0.3$ and $P(X_2=1)=0.1$ (Case B). The grey horizontal line is the reference null bias

Fig. 9

Simulation results for the variation of scenario 4 when fixed $X_1=0$ (or $X_1=1$), if $X_2$ changes, the hazard of relapse increases of 2 times (Case A) or of 1.5 times (Case B). The grey horizontal line is the reference null bias