Bios 6648: Design & conduct of clinical research

Transcription

1 Bios 6648: Design & conduct of clinical research Section 2 - Formulating the scientific and statistical design designs 2.5(b) Binary (a) Time-to-event (revisited) (b) Binary (revisited) (c) Skewed (d) Change-from-baseline Bios pg designs (b) Binary (revisited) have listed 3 ways to parameterize in trials with binary data: parameterization: = 0 Risk with comparison treatment = Risk with active treatment = : V = ( )+ ( ) 2.5(b) Binary have not yet illustrated relative risk and odds ratio parameterizations Bios pg 2

2 designs (b) Binary (revisited) 3 approaches to parameterize with binary data: parameterization: = 0 Risk with comparison treatment = Risk with active treatment = V = ( ) + ( ) 2.5(b) Binary parameterization: = = 0 Odds with comparison treatment 0 Odds with active treatment = Odds Ratio V = 0 ( 0 ) + ( ) Bios pg 3 Binary (revisited) (sepsis example) Under the alternative hypothesis ( apple 0.07) Variance: * 0.30, 0.23 * V = = Potential inference (N = 850): * cv =.96 p 0.387/850 = * 95% C: ( , 0.00) N = (3.92/0.07) = 24 2 N = (3.24/0.07) = (b) Binary Bios pg 4

3 Binary (revisited) (sepsis example) Under the alternative hypothesis: apple = Variance: * 0.30, 0.23 * V = = 5.68 Potential inference (N = 850): log(cv) =.96 p 5.68/850 = log(95%c) = ( , 0.00) cv = e 0.6 = % C = (e 0.32, e 0.0 )=(0.726,.00) 2.5(b) Binary N = (3.92/log(0.767)) = N = (3.24/log(0.767)) = Bios pg 5 Binary (revisited) (sepsis example) Under the alternative hypothesis: apple 0.23/ /0.70 = Variance: * , 0.23 * V = = 0.04 Potential inference (N = 850): log(cv) =.96 p 0.04/850 = 0.27 log(95% C) = ( 0.434, 0.00) cv = e 0.27 = % C = (e 0.434, e 0.0 )=(0.648,.00) N = (3.92/log(0.697)) = N = (3.24/log(0.697)) = (b) Binary Bios pg 6

4 Binary (revisited) : Properties of the three parameterizations Each of the 3 parameterizations has a different mean/variance relationship : = V = ( )+ ( ) 2.5(b) Binary : Odds Ratio: k = k ( k ) log( ) = log( ) log( ) V = ( ) + ( ) log( ) = log( ) log( ) V = 0 ( 0 ) + ( ) Bios pg 7 Binary (revisited) Mean-variance relationship: risk difference parameterization Mean ( ) increases linearly with risk ( ) Variance (var(ˆ )) is largest when = 0.5 Risk functional: = Variance = ( ) = ( ) (b) Binary Bios pg 8

5 Binary (revisited) Mean-variance relationship: relative risk parameterization Mean (log( )) decreases (in magnitude) exponentially with increasing risk ( ) Variance (var[log(ˆ )]) decreases with Log(risk) functional: = log() Variance = ( ) 2.5(b) Binary = log() var(^) =( ) Bios pg 9 Binary (revisited) Mean-variance relationship: odds ratio parameterization Mean ( ) increases linearly with risk ( ) Variance (var(ˆ )) is smallest when = 0.5 Log(odds) functional: = log( ( ) Variance = ( ) = log( ( )) var(^) = ( ) (b) Binary Bios pg 0