ABSTRACT
Safety analysis in randomized controlled trials (RCTs) involves estimation of the treatment effect on the numerous adverse events (AEs) that are collected in the study. RCTs are typically designed and powered for efficacy rather than safety. Even when assessment of AEs is a major objective of study, the trial size is generally not increased to improve likelihood of detecting AEs [1]. As a result, power is an important concern in the analysis of the effect of treatment on AEs in RCTs [2]. Typically in an RCT, crude incidences of each AE are reported at some fixed end
point such as the end of study [3-5]. These crude estimates often ignore missing observations that frequently occur in RCTs due to early patient withdrawals [6]. A review of published RCTs in major medical journals found that the censored data are often inadequately accounted for in their statistical analyses [7]. A crude estimator that ignores censoring can be highly biased when the proportion of dropouts differs between treatment groups (see Ref. [3] for examples). The crude incidence is an important consideration in the evaluation of safety for
very rare, severe, or unexpected AEs. Such AEs require clinical evaluation for each case and are not the focus of this chapter. Instead, we focus on those AEs that are routinely collected in RCTs and most often are not associated with a prespecified hypothesis. These AEs are typically reported as an observed rate with a confidence interval or p-value. Patient reporting of AEs occurrence usually occurs at many intervals throughout the
study often collected at follow-up interviews rather than only at a single fixed end point. As such, time-to-event methods that exploit these data structures may provide further insight into the safety profile of the drug. The importance of considering estimators of AE rates that account for time due to differential lengths of exposure and follow-up is discussed in Ref. [8]. Furthermore, in most RCTs in oncology, most if not all patients suffer from some AEs [9] and thus investigators may be interested in the probability of the occurrence of a given AE by a certain time rather than simply the incidence. Time-to-event analysis techniques may be more sensitive than crude estimates in that they readily handle missing observations that frequently occur in RCT due to early patient withdrawals. For example, in Ref. [10] AEs from the Beta-Blocker Heart Attack Trial were analyzed by comparing distributions of the time to the first AE in the two treatment arms. The results of this analysis were contrasted to the cross-sectional crude percentage analysis and were found to be more sensitive in detecting a difference by taking into account the withdrawals. A vast amount of literature exists for time-to-event analysis but these methods are often not applied to the analysis of AEs in RCTs. A general review of survival analysis methods in RCTs (without a particular focus on AEs) is provided in Ref. [11]. In this chapter, we focus on the estimation of treatment-specific survival at a fixed
end point for right-censored survival outcomes using targeted maximum likelihood estimation [12]. Survival is estimated based on a hazard fit and thus the timedependent nature of the data are exploited. There are two main goals of the methodology presented in this chapter over unadjusted crude proportions and
Kaplan-Meier estimators. The first is to provide an estimator that exploits covariates to improve efficiency in the estimation of treatment-specific survival at fixed end points. The second is to provide a consistent estimator in the presence of informative censoring.
