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Research Curriculum Session III – Estimating Sample Size and Power

Research Curriculum Session III – Estimating Sample Size and Power. Jim Quinn MD MS Research Director , Division of Emergency Medicine Stanford University. Overview. Funding Issues ACEP.org - 2004-2005 Research Grant Program Overview Kaiser - Mid December Sample Size Calculations

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Research Curriculum Session III – Estimating Sample Size and Power

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  1. Research CurriculumSession III – Estimating Sample Size and Power Jim Quinn MD MS Research Director , Division of Emergency Medicine Stanford University

  2. Overview Funding Issues • ACEP.org - 2004-2005 Research Grant Program Overview • Kaiser - Mid December Sample Size Calculations • Basic statistical testing • Variables • Assumptions • Strategies for minimizing sample size

  3. Estimating Sample Size • Clearly stated simple question • One predictor and one outcome measure • Ensure that our sample is representative of the population we are basing our hypothesis on.

  4. Hypothesis Testing • Null Hypothesis • There is no difference between the predictor and outcome variables in the population • Assuming there is no association, statistical tests estimate the probability that the association is due to chance • Alternate Hypothesis • The proposition that there is an association between the predictor and outcome variable • We do not test this directly but accept it by default if the statistical test rejects the null hypothesis

  5. Hypothesis testingStatistical Principles • Always use two sided tests • Level of statistical significance • Type I and II errors • Effect Size • Variability of the population/sample

  6. Level of Significance • Set at 0.05 for alpha and 0.20 for beta “If there is less than a 1/20 chance that difference between two group is due to chance alone we reject the Null hypothesis and accept the Alternate hypothesis that they are different” • For two sided tests that is 0.025 in each tail

  7. Type I and II Errors • Many types of errors, not just statistical • False negative and false positive can occur because of errors due to bias • Type I (statistical false positive)- reject the null hypothesis but in fact it is true. (or you think there is a difference but there really isn’t one) • Type II (statistical false negative) – accept the null hypothesis but in fact there is a difference

  8. Type I and II Errors • Type I and II errors are usually avoidable by having adequate sample size or manipulating the design of the study and measure of outcomes. • 0.05 and 0.20 are arbitrary and many believe beta should be 0.10

  9. Effect Size “What is a meaningful difference between the groups” • It is truly an estimate and often the most challenging aspect of sample size planning • Large difference – small sample size • Small differences – large sample size • Find data from other studies • Survey people • Cost/benefit

  10. Variability • The greater the variability in the outcome measure the more likely the groups will overlap • Less precise measures and measurement error increase the variability • Variability is decreased by increasing the sample size • For sample size calculations of continuous variables the variability needs to be estimated - Can get from other studies or small pilot study

  11. Sample Size CalculationComparative Studies • State the Null Hypothesis • Determine appropriate statistical test (For simplicity use T-test for continuous of chi square for dichotomous) • Predict effect size and variability • Set α and ß • Use the appropriate formula or table

  12. Sample Size Calculation for Descriptive Studies • Continuous • Estimate std deviation • Specify precision (width of CI) • Select the confidence level for the interval • Dichotomous • Estimate the expected proportion of the variable of interest (if > 50% calculate based on proportion not expected to have the characteristic) • Select the CI width • Select the confidence for the interval

  13. Other Considerations • Account for dropouts • Ordinal variables especially if 5-6 groups can be treated as continuous • Survival analysis • Matching • Equivalence studies

  14. Strategies for Minimizing Sample Size • Use continuous variables • Paired measurements (consider measuring the change) • Use more precise variables • Use unequal group sizes N = [(c+1)/2c] x n (c = controls per cases) • Use more common outcome

  15. Errors to Avoid • Dichotomous outcomes can appear continuous when expressed as a percentage • Sample size is for those who complete the study not those enrolled • Tables assume equal numbers in both groups (if in doubt use formulae) • For continuous variables use the standard deviation best associated with the outcome • Do the calculation before you start your study and use it to plan • Cluster data is confusing and needs a statistical consultation

  16. Questions and Answers

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