LECTURE 17 2011 - Sample Size Estimation 1 Continuous...

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Sample Size Estimation 1. Continuous response variable Parallel group comparisons Comparison of response after a specified period of follow-up Comparison of changes from baseline Crossover study 2. Success/failure response variable (dichotomous response) Impact of non-compliance, lag Realistic estimates of control event rate (Pc) and event rate pattern Use of epidemiological data to obtain realistic estimates of experimental group event rate (Pe) 3. Time to event designs and variable follow-up
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Survey of 71 “Negative” Trials (Freiman et al., NEJM , 299:690-694,1978) Authors stated “no difference” P > 0.10 (2-sided) Success/failure endpoint Expected number of events >5 in control and experimental groups Using the stated Type I error and control group event rate, power was determined corresponding to: 25% difference between groups 50% difference between groups
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0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 0 5 10 15 20 25 Power (1 - ß ) 5.63% 25% Reduction Frequency Distribution of Power Estimates for 71 “Negative” Trials References: Frieman et al, NEJM 1978.
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0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 0 5 10 15 20 25 Power (1 - ß ) 29.58% Frequency Distribution of Power Estimates for 71 “Negative” Trials 50% Reduction References: Frieman et al, NEJM 1978.
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Implications of Review by Frieman et al. Many investigations do not estimate sample size in advance Many studies should never have been initiated; some were stopped too soon “Non-significant” difference does not mean there is not an important difference Design estimates (in Methods) are important to interpret study findings Confidence intervals should be used to summarize treatment differences
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Studies with Power to Detect 25% and 50% Differences 6 6 6 6 l l l l 0 5 10 15 20 25 30 35 40 45 50 Percent of Studies with at Least 80% Power 6 25% Difference l 50% Difference 1975 1980 1985 1990 Moher et al, JAMA , 272:122-124,1994
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Comparison of Sample Size Formulae for Means and Proportions (n per group) n= 1 (P c -P e ) 2 z 1- α /2 2 P (1- P ) + z 1- β P c (1-P c )+P e (1-P e ) [ ] 2 n= 1 (P c -P e ) 2 P c (1-P c )+P e (1-P e ) [ ] z 1- α /2 + z 1- β [ ] 2 P c = Control group event rate P e = Experimental group event rate P = (P c +P e ) 2 ∆ = P c -P e For means: n= 2 σ 2 z 1- α /2 +z 1- β ( 29 2 2 The formula above is sometimes just
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Derivation of Sample Size for Comparing 2 Proportions is Similar to that for Comparing 2 Means β α Z α σ pe – pc Z β σ pe – pc X pc - pe 0 B A If pc-pe > A, reject H o If pc-pe ≤ A, accept H o
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Derivation of Sample Size for Comparing Two Proportions ( 29 2 2 2 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 ) ( 2 ) ( ) ( ) 2 ( ) ( ) 2 ( ) ( ) ( ) 2 ( ) ( Under / 2 2 and , Under c e e e e c c c c e e c c c c c e e e c c c c c e e e c c pe pc A c c pc pe pc pe pc e c o p p Z Z pq n p p q p q p Z q p Z n q p q p Z q p Z p p n n q p n q p Z n q p Z p p n q p n q p , σ H n q p σ σ σ , σ p , p H c - + - + + = + + = - + + = - + = = = = = - - β α β α β α β α
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Example H 0 : Pc = Pe (proportion with event on control arm = proportion with event on experimental arm) H A : Pc = .40, Pe = .30 = .40 - .30 = .10 Assume α = .05 Z α = 1.96 (2-sided) 1 - β = .90 Z β = 1.28 p = (.40 + .30 )/2 = .35
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Example (cont.)
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