Sample size calculation
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1. Sample size calculation is an important part of ethical scientific research to avoid underpowered studies. 2. There are different approaches to sample size calculation depending on the study design and endpoints, such as comparing proportions, estimating confidence intervals, or analyzing time to event outcomes. 3. Key steps include defining the research hypothesis, primary and secondary endpoints, how and in whom the endpoints will be measured, and determining what difference is clinically meaningful to detect between study groups.
Sample size calculation
- 1. Sample Size Calculation Dr Santam Chakraborty Assistant Professor, Radiation Oncology Tata Memorial Hospital
- 2. Relax !! No Formulae No Mathematical Jargon No complicated concepts
- 3. Sample Subset of a defined population Defined selection procedure Has sampling points / units / observations Allows inference without a “census”
- 5. Random Sample Derived from a defined population Each individual has the same chance of being included in the sample Sampling can be done with minimum knowledge about the population Allows externally valid conclusions
- 6. Sampling Frame 1. Source material from which the sample is drawn 2. List all who can be sampled from a population 3. Example: Census 4. Must be representative of the population 5. No elements from outside the population of interest are present in the frame Q: Can telephone directory be used as a sampling frame to represent adult population of Mumbai? Q: Can a sample drawn randomly from this be called a random sample?
- 7. Why Does it Matter? 1. Avoids resource wastage 2. Ensures aims are clear 3. Reduces harm 4. Discourages much needed future research 5. Needed for publication and grants Avoids an unethical underpowered study
- 8. Why are underpowered studies unethical? 1. Often yield optimistic differences 2. Confidence intervals around these differences are wider 3. Small reductions of CI (w.r.t no trials) is not justified when risks to patients is considered 4. Combined meta-analyses more susceptible to variability in study design and execution 5. Impairs informed consent - do we inform patient of the limited benefit from an underpowered study ? - a form of deception 6. Serendipitous results are rare - publication bias makes them seem more
- 9. J. P. A. Ioannidis, Why most published research findings are false. PLoS Med. 2, e124 (2005).
- 10. Ellis, P.D. (2010), “Effect Size FAQs,”: https://effectsizefaq.com/
- 12. μ0 μ1 d Basic Theory Probability of rejecting the null hypothesis when it is really true (Type I Error)
- 13. μ0 μ1 d Basic Theory Probability of rejecting the null hypothesis when it is really true (Type I Error) Probability of rejecting the alternate hypothesis when it is true (Type II error)
- 14. μ0 μ1 d Basic Theory Probability of accepting the null hypothesis as true when it is really false (Type I Error) Power of the test
- 18. μ0 μ1 d Non Directional Hypothesis Probability of accepting the null hypothesis as true when it is really false (Type I Error) Power of the test
- 19. How to calculate : Software 1. G*Power 2. PASS 3. SPSS 4. R
- 20. Basic Principles 1. Define a research hypothesis 2. Define the primary and the secondary endpoints 3. Define the measurement: a. What to measure b. In whom to measure c. Where to measure d. When to measure e. Why to measure - most important
- 21. Sample Size Calculation Example Scenarios 1. Cataract surgery in mobile eye surgical unit: Safe and viable alternative 1. Topical sodium cromoglycate in management of chronic non-infectious conjunctivitis: A Double blind controlled clinical trial
- 22. Sample size for comparing proportions 1. Endpoint : Cumulative infection rate at 72 hours. Measure : percent or ratio 2. Single sample design 3. “Hopefully” random 4. We approach in two ways: a. Compare against a “known” rate b. Estimate the precision of the estimate we generate
- 25. Sample Size for Confidence Interval Estimates ● Most commonly used for single sample situations ● Confidence intervals basically indicate the range of plausible values of the population estimate that is desired. ● Essentially implies if the same experiment is repeated, the estimated value will lie within the range of the confidence intervals x% of the time (only if the sample mean is centered though) ● Easier to do as historical precedent need not be present.
- 26. Sample Size for Confidence Interval Estimates Endpoint is the precision of estimate of the mean here. Let us assume that you would be satisfied with a rate of 5% and do not want the estimate to go beyond 8% (士 5%). You want the confidence level to be 95%
- 28. Sample Size Calculation Example Scenarios 1. Cataract surgery in mobile eye surgical unit: Safe and viable alternative 1. Topical sodium cromoglycate in management of chronic non-infectious conjunctivitis: A Double blind controlled clinical trial
- 29. Primary Endpoint 1. What are we measuring : Patient's subjective report of improvement in symptoms 2. Whom are we measuring it in : Patients with B/L chronic non infective conjunctivitis 3. Where are we measuring it : In a hospital where the study is being conducted* 4. When are we measuring it : At 4 weeks 5. Why are we measuring it : Is the drug better than a placebo for this condition.
- 30. Sample Size : Mean Score Endpoint is an estimate of the mean score in the questionnaire at 4 weeks We want to know if the mean score of the patients in the control group is different from the score in the test group Assume a random sample
- 33. Time to Event Endpoint Endpoint is an estimate of median time taken for the symptom score to normalize Here the comparing the median times by a T test approach will fail What we need is a sample size estimation for a time to event outcome
- 34. Hazard rates and ratio Usual survival curves follow an exponential distribution. The probability of Surviving for a specific time period is given as P = e-ht Here h = the instantaneous hazard rate h = ln (1/Median Survival Time) h= - ln (S(T))/T .. where T is time and S is proportion surviving upto time T
- 35. Sample Size : Time to Symptomatic Change Assume that 40% of the patients receiving placebo in the control group at 4 weeks. We consider a clinically meaningful difference exists if the proportion of patients differs by 20% ● 20% or less improve with drug at 4 weeks - significantly worse ● 60% or more improve with drug at 4 weeks - significantly better We assume that the rate of improvement over the 4 weeks is constant implying uniform hazard rate.
- 36. Sample Size : Time to Symptomatic Change % improving in 4 weeks in placebo arm : 40% % not improving in 4 weeks in placebo arm : 60% Hazard rate of not improving : - ln (0.4/4) or -ln(1-0.6)/4 = 2.3 % improving in 4 weeks with drug : 60% Hazard rate of not improving : - ln (0.4/4) = 1.9 Hazard ratio = 1.9 / 2.3 = 0.82
- 38. Summary 1. Sample size calculation integral part of valid and ethical scientific research 2. Lots of tools available 3. Important to define the hypothesis and end point clearly for proper sample size
- 39. Thank You
Editor's Notes
- #5: An unbiased (representative) sample is a set of objects chosen from a complete sample using a selection process that does not depend on the properties of the objects. There are several types of non random sample but the most well known and most abused is convenience sample.
- #18: Increasing the acceptable Type I error rejection threshold can improve the power and vice versa.
- #35: An exponential distribution is produced when events occur CONTINUOUSLY and INDEPENDENTLY at a constant average rate.