ABSTRACT

The methods discussed for survival analyses so far are based on the number

of patients at each stage, instead of number of events. The reason for this

is that the methods are based on the assumption of independent stagewise

statistics. Therefore, the first N1 patients enrolled will be used for the first

interim analysis regardless of whether they have the event or not. Strictly

speaking, for the commonly used log-rank test statistics based on number of

events, the test statistics at different stages,

T ( Dˆk

) =

√ Dˆk 2

ln λˆ1

λˆ2 ∼ N

(√ Dk 2

ln λ1 λ2 , 1

) , (6.1)

are not independent, where Dk is the number of events at the k th stage.

However, Breslow and Haug (1977) and Canner (1997) showed that the in-

dependent normal approximation works well for small Dk. The relationship

between the number of deaths and number of patients is simple under expo-

nential survival models. Whether based on the number of events or patients,

the results are very similar (Chang, 2007c, and 2014, Chapter 4). Other meth-

ods for adaptive design with a survival endpoint can be found from work by

Li, Shih, and Wang (2005), and Jenkins, Stone, and Jennison (2011). Practi-

cally, the accrual has to continue in most cases when collecting the data and

performing the interim analysis; it is often the case that at the time when

interim analysis is done, most or all patients are enrolled. What is the point

to have the interim analysis? The answer is that a positive interim analysis

would allow the drug to be on the market earlier.