LECTURE 16 2011 - How many patients do I need for my study...

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How many patients do I need for my study?
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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 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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Useful References Lachin JM, Cont Clin Trials , 2:93-113, 1981 (a general overview) Shih J, Cont Clin Trials, 16:395-407, 1995 (time to event studies with dropouts, dropins, and lag issues) – see size program on biostatistics network Farrington CP and Manning G, Stat Med, 9:1447- 1454, 1990 (sample size for equivalence trials) Whitehead J, Stat Med , 12:2257-2271, 1993 (sample size for ordinal outcomes) Donner A, Amer J Epid , 114:906-914, 1981 (sample size for cluster randomized trials)
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Key Points Sample size should be specified in advance Sample size estimation requires collaboration Often sample size is based on uncertain assumptions, therefore estimates should consider a range of values for key parameters (i.e., investigate the impact on power in case sample size and treatment effect is not achieved) Parameters on which sample size is based should be evaluated as part of interim monitoring It pays to be conservative; however, ultimate size and duration of a study involves compromises, e.g., power, costs, timeliness.
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Steps in Planning a Study 1) Specify the research question 2) Define target population 3) Assess feasibility of studying question (compute sample size) 4) Decide how to recruit study participants, e.g., single center, multi-center, and make sure you have back-up plans
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Beginning: A Protocol Stating Null and Alternative Hypotheses Along with Significance Level and Power Null hypothesis (H O ) Hypothesis of no difference or no association Alternative hypothesis (H A ) Hypothesis that there is a specified difference ( ) Δ No direction specified (2-tailed) A direction specified (1-tailed) Significance Level ( α ): Type I Error The probability of rejecting H 0 given that H 0 is true Power = (1 - β ): ( β = Type II Error ) The probability of rejecting H 0 given that H 0 is not true
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2-Sided Versus 1-Sided Comment sided - 2 are studies Most .025 use tests sided - 1 as designed are that trials many so , difference SE 1.96 least at on insist would Most sided) - (1 . as same the is sided) - (2 . : Note : sided - 1 For : sided - 2 For = = = α α α α α 025 05 Z Z Z Z
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End: Test of Significance According to Protocol Statistically Significant? Yes No Reject H O Do not reject H O Sampling variation is an unlikely explanation for the discrepancy Sampling variation is a likely explanation for the discrepancy
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Normal Distribution If Z is large (lies in yellow area), we assume difference in means is too large to have come from a distribution with mean zero.
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Continuous Outcome Example Observations: Many people have stage 1 (mild) hypertension (SBP
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