Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Estimating and comparing survival curvesSurvival characteristics can be described by a survival function, S(t), as describedabove. Two methods are available to estimate the survival function:• the parametric method• the nonparametric methodThese vary, depending on whether the underlying survival distribution of thepopulation is known.In the parametric approach, a particular survival distribution is assumed(exponential, Weibull, etc). If we know the population distribution that the samplewas taken from, we can estimate the survival function, S(t), by determining itsparameters through a maximum likelihood approach. For example, if the survivaldata of the pancreatic cancer trial follow an exponential survival distribution thenwe only need to estimate the parameter λ, whose maximum likelihood estimate^(λ) is simply the ratio between the number of deaths and the number of total^months. If λ = 0.017 deaths per month (ie, the overall rate), the estimated survival^function will therefore be S(t) = e –0.017t .In actual applications, however, we rarely know the population survival distribution,and instead use a nonparametric approach to describe the data – the nonparametricapproach does not require any presumption of a survival distribution.The Kaplan–Meier methodThe most common nonparametric method is the Kaplan–Meier (KM) approach.This estimates the proportion of individuals surviving (ie, who have not died orhad an event) at any given time in the study [1,2]. When there is no censoring inthe survival data, the KM estimator is simple and intuitive. S(t) is the probabilitythat an event time is greater than t. Therefore, when no censoring occurs, the^KM estimator, S(t), is the proportion of observations in the sample with eventtimes greater than t. For example, if 50% of observations have times >10, we have^S(10) = 0.50.Censored observations in the dataset can complicate matters. If this is the casethen the KM estimator can be determined by following this procedure:Step 1:Rank the event times in ascending order. Suppose there are k distinctevent times, t 1< t 2< …< t k. Note that more than one event can occurat each time t j.239