SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptx
- 1. SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS Dr Aswathi T
- 2. Sample Size Estimation • Scientific research - requires carefully designed methods to produce valid and relevant results • Scientifically proven sample size estimation needed for this • Most crucial methodological part of a research study • Key questions health researchers are likely to ask is, how much of a population is needed for valid and reliable study?
- 3. • Exhaustive survey • Researchers may choose to study all those within a target population • Possible when the entire population of interest is small and there are resources to study them • Sample size calculation may not be required or may not be applicable even when estimated • Not feasible to study the entire subjects or respondents in a population of interest
- 4. Sample • Sub-set of the study population • Representatives of the study population • Make an inference from the sample and apply it to the whole population • Study the characters of the population by measuring them from a smaller number of subjects
- 5. If sample is too large Good precision Close to the truth provided BUT × Administrative, economical, ethical & some scientific issue × Wastage of time, money and resources × More sample – more work – more expenditure × A small difference in the test parameter value may become statistically significant ,but it may not have any clinical significance
- 6. If sample is too small ×Inaccurate results ×Study fails to give meaningful information ×Might have been obtained by chance only ×Power of the study comes down ×Waste of resources on an inaccurate study ×Ethical issues about recruiting patients into a meaningless study ×A substantial difference in the estimates between the groups may become statistically insignificant, but may have some clinical significance
- 7. Incorrect sample size will lead to • Wrong conclusion • Poor quality of research • Loss of money • Ethical problems • Delay in completion Neither too small nor too big
- 8. Factors affecting the Sample size 1. Rough estimate of the magnitude of the study variable – existing literature/pilot study 2. Minimum clinically relevant effect size To detect small effect size, large sample size is required vice versa
- 9. Factors affecting the Sample size… 3. Standard Error ( SE ): ( Standard Deviation ) / √n Larger the sample size - lesser the SE 4. Precision : Reliability or the Consistency of the estimate in repeated sampling precision = √n / S.E. Larger the sample size, smaller will be the SE and Larger will be the precision
- 10. Factors affecting the Sample size… 5. Accuracy • The extent to which the sample estimate is closer to the True value • When there is no bias or it is negligible, the sample estimate will be closer to the True value and the estimate will be more accurate
- 12. Factors affecting the Sample size… 6. Type I and II Errors Type I : false positive Reject null hypothesis when it is true (probability of making this error is α) Type II : false negative Accept hypothesis when it is false (probability of making this error is β) 1- α is the confidence of a study 1-β is the power of a study
- 13. Factors affecting the Sample size… Confidence & power • A minimum of 95 % confidence ( 5% Type-I error) – 95% probability that true population parameter will be within the calculated interval • A minimum of 80% power (20% Type-II error) should be fixed for any type of study – chance of detecting an effect / association if it exists • Small alpha error means more sample • Small beta error/high power means more sample size
- 14. Study Truth Truth (Reality) in the population Null Hypothesis False Null Hypothesis True Study results from sample Null Rejected Correct decision (power) Alpha Error Null not Rejected Beta Error Correct decision
- 15. Factors affecting the Sample size… 7. Other factors: • Type of design - CS/CC/C/CT • Comparative design generally require a larger sample size than descriptive designs • One tailed tests will require 30% less sample size than two tailed test • Dropout rate, lost to follow up, missed data, non compliance to treatment – all will increase sample size
- 17. Types Of Variable Based on what we are measuring Qualitative 1. Calculating the proportion 2. Calculating the difference of proportions Quantitative 1. Calculating the mean 2. Calculating the difference in means
- 18. Qualitative • Qualitative are those which can be answered as YES or NO, Male or Female, etc • We can only measure their numbers, eg: Number of males, Number of MDR-TB cases among TB patients, etc. • A set of qualitative data can be expressed as proportions. Eg: Prevalence, success rate • In general sample size is higher for qualitative variable
- 19. Quantitative • Quantitative are those which can be measured in numbers, like Blood pressure, Age, Height, Weight, etc • A set of quantitative date can be expressed in mean and its standard deviation • Mean is the average of all variables in the data • Standard deviation is a measure of the distribution of variables around the mean • In general, sample size is low for quantitative variables
- 20. Estimation of Sample Size for Cross-sectional or Descriptive Research Studies • Done to estimate a population parameter like prevalence of some disease in a community or finding the average value of some quantitative variable in a population • Sample size formula for qualitative variable and quantities variable are different.
- 21. Cross Sectional Studies… • For qualitative variable
- 22. Cross Sectional Studies… • Example -1 • A researcher wants to carry out a descriptive study to understand the prevalence or proportion of diabetes mellitus among adults in a city. A previous study stated that diabetes in the adult population was 40%. At 95% CI and 5% margin of error, calculate the sample required to conduct other new research? • p=0.4, q=0.6, d=0.05 • 369 • 10% dropout406
- 23. Cross Sectional Studies… • For quantitative variable
- 24. Cross Sectional Studies… • Example -2 • A researcher wants to know the average hemoglobin level among adults in the city at 95% CI and the margin of error is 2 g/dl. From a previous study, the SD of hemoglobin level among adults was found to be 4.5 g/dl. How many study subjects will be required to conduct a new study? • 𝜎 = SD=4.5, d=2 • 19 • 10% dropout21
- 25. Sample Estimation for Case–control Studies • Retrospective • In case control studies cases (the group with disease/condition under consideration) are compared with controls (the group without disease/condition under consideration) regarding exposure to the risk factor under question
- 27. Case–control Studies… • Example - 3 • If a researcher wants to conduct a case–control design to identify the link between deep vein thrombosis and pulmonary embolism. He decides to work at 95% CI and 80% power of the study. He assumes expected proportion in case is 40% and control group is 30% and decides to have a same number of cases in both groups. Find out the optimum sample size for each group in study. • P=0.35, P1=0.4, P2=0.3, r=1 • 357 • 10% dropout393 in cases & control group
- 29. Case–control Studies… • Example – 4 • Suppose a researcher wants to conduct a study to identify the association between the amount or quantity of alcohol consumption and liver cirrhosis. From the previous study, he finds that the mean difference in alcohol consumption between the case and control groups was 10 ml/day and SD was 18 ml/day. He decides to conduct the study at 95% CI and fix power of the study at 80%. Find the sample size to have a equal number in case and control group for study.
- 30. Case–control Studies… • Example – 4 • 𝜎 = 18, d=10, r=1 • 51 • 10% drop out56 in cases & control group
- 31. Same Size Estimation for Cohort Studies • Prospective • Healthy subjects with or without exposure to some risk factor are observed over a time period to see the event rate in both groups
- 32. Cohort Studies…
- 33. Sample size estimation for comparative studies • Various types of observational study that compare population proportions (P1 and P2 ) and means (µ1 and µ2 ) • Formerly known as ‘comparative study’ • There is no form of intervention or experimentation
- 34. Comparative Studies… • compare population proportions (P1 and P2 ) and means (µ1 and µ2 )
- 36. Sample Size Estimation for Experimental Studies or Randomized Controlled Trials • In this investigator provides intervention and study its effect and compare in experiential and control group • Superiority trial: The aim of this type of trial is to view that a novice drug/treatment/intervention is superior to a control treatment. • Equivalence trial: The aim of this type of trial is to view that novice treatment/intervention is equally effective to control treatment. • Non-inferiority trial: The aim of this type trial is to view that novice treatment/intervention is effective but must not superior than the control treatment. Equality trial - hypothesise that there is no clinical difference or effect between the mean of the new treatment/intervention (µT) and the mean of the comparator
- 37. Randomized Controlled Trials… • The trials can also be one-sided (one-tail) hypothesis Direction of the difference or the effect is stated (more/greater or less/lower than) • Many researchers prefer to adopt two-sided (two-tail) hypothesis which usually do not state the direction of the differences or effects expected This states that there is no difference between the effect of the treatment/intervention and the comparator (standard/usual/placebo) • Design variants of the trials such as the parallel, cross-over and cluster RCTs also have effects on the sample size
- 40. Sample size formula for animal studies • E = Total number of animals – Total number of groups • The value if E should lies within 10 to 20 for optimum sample size.
- 41. Electronic Resources for Sample Size Calculation StatCalc WinPepi OpenEpi Stata PASS nMaster nQuery Adviser