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Table 6 Mathematical Notation

From: Sequential interim analyses of survival data in DNA microarray experiments

1. Patient Data

 

   N

samples

   

anticipated length of the recruitment part of the study

   a = (a1, ..., a N )

arrival times

 

where a i ~ U(0, l1), i = 1, ..., N

   l1 = max(a)

length of the recruitment part

   l2

length of the follow-up part

   L = l1 + l2

study length

   M1

number of analyses within l1

   M2

number of analyses within l2

   M = M1 + M2

number of analyses

   t = (t1, ..., t N )

analysis times

   λ

mean survival time

   s = (s1, ..., s N )

survival times

 

where s i ~ Exp(λ), i = 1, ..., N

   

censor variable

 

where

2. Gene Expression Data

 

   d

genes

   d0

genes not associated with survival

   d1

genes associated with survival

   R

number of positive test decisions

   FN

false negative test decisions

   TN

true negative test decisions

   FP

false positive test decisions

   TP

true positive test decisions

   τ

fraction of differentially expressed genes

   

gene expression data

   ϑ

tuning parameter within the estimation of the proportion of true null hypotheses

   αBH

the level for the type I error that is adjusted according to the BH- procedure