Network Meta-Analysis for Decision-Making

10*Network Meta-Analysis of Survival Outcomes

10.1 Introduction

We are often interested in relative effectiveness of competing treatments on the time from treatment initiation to the occurrence of a particular event (time to event). For example, in oncology, nearly all studies report time-to-event data on overall survival (OS), where the event is death from any cause, and on progression-free survival (PFS), where the event is death from any cause or disease progression, whichever occurred first. Time-to-event outcomes have particular features that require different analytical techniques than those for other continuous outcomes. Firstly, the distribution of times to event tends to be skewed, so the normal likelihood is not usually appropriate. Secondly, it is usually the case that not every patient will have experienced the event (e.g. progression or death) during the follow-up period of the study, or they may have become lost to follow-up. Such patients provide censored observations. Censored observations need to be incorporated in the analysis because they provide information regarding the lowest possible value of the time to event for the individual. Statistical procedures for analysis of continuous outcomes that do not account for censoring will provide biased estimates (Collett, 2003).

The hazard and survival functions are central to the analysis of time-to-event data. Let U be a non-negative continuous variable reflecting the time to an event, with probability density ...