ABSTRACT
The word ‘‘analgesic’’ originates from Greek meaning without-pain. An important application of analgesic trials is to help develop pain killers, which influence the peripheral and central nervous systems, such as the nonsteroidal anti-inflammatory
drugs (NSAIDs). Therefore, pain treatment and research have attracted many clinical specialists and pharmaceutical companies. The related analgesic trials have been conducted in many disease categories, toward improving the understanding of the pain mechanisms or providing more efficient interventions for pain control. Sheiner et al. [50] list some typical clinical designs for new analgesic drugs: a pain-inducing procedure is undertaken for medical indications, usually a surgical procedure; when anesthesia has worn off, the patient asks an analgesic; the patient receives a randomly assigned treatment with either placebo or drug; at prespecified times after drug administration, the patient’s pain status is recorded after questioning the patient. An introduction to the history, design, and analysis of analgesic trials can be found in [39]. Depending on the aims of such trials, there can be different types of data and time-to-event data are commonly collected in analgesic trials. In this chapter, we explore the statistical methods to analyze paired time-to-event
data from analgesic trials. In Section 11.2, we discuss the issues in designing clinical trials with time-to-event endpoints and matched pairs design for both situations with complete and censored data. In Section 11.3.1, we review some statistical methods for testing the equality of mean time-to-event endpoints of two treatments based on complete paired data. These methods include parametric methods based on normality distributional assumption, conditional Weibull distributional assumption, and gamma frailty models as well as nonparametric methods. Note that these methods are also applicable to data which are not time-to-event endpoints, for example, they are useful for comparing mean self-reported pain scores in matched paired studies. For censored time-to-event data, nonparametric rank-based tests are discussed in Section 11.3.2. Then, in Section 11.3.3, we focus on the estimation of the dependence by using copula models. In Section 11.4, examples are used to illustrate the methodologies present in the previous sections. Some concluding remarks are given in Section 11.5.
