sample size calculations in different types of study..pptx

Sample size calculation is crucial in research to ensure that your study has enough power to detect an effect or difference if one exists.
Sample size calculation is essential for designing a study that can reliably detect the effects or differences being investigated. It involves determining the number of participants needed to achieve a desired level of statistical power while minimizing errors. Key factors include the expected effect size, which represents the magnitude of the impact being studied; the alpha level, typically set at 0.05, which defines the threshold for statistical significance; and the power, commonly set at 80%, which indicates the likelihood of detecting a true effect. Variability in the data also affects sample size, with higher variability requiring a larger sample. Using statistical formulas or software, researchers can calculate the necessary sample size to ensure their study results are both robust and reliable.

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2. Sample size calculations PRESENTED BY: Dr. KAJAL MEHTA PG RESIDENT GUIDED BY: PROF. DR. RABINDRA MAN SHRESTHA ASSO. PROF. DR. JYOTI DHAKAL DR. SUJITA SHRESTHA DR. SUNITA KHANAL (Dept. of Community Dentistry) DEPARTMENT OF ORTHODONTICS, KANTIPUR DENTAL COLLEGE 2

3. In research methodology: -Sample size calculations -Study design -Sampling technique -Preparing the protocols -Collection and presentation of data 3

4. Objectives 4 To understand What is sample and population? Different sampling technique Different type of Study design What is sample size determination? How large a sample do we need? Different method of calculating sample size

5. Sample and population? 5

6. Sampling Is the process or technique of selecting a sample of appropriate & manageable size for study 6

7. Sampling method Non-probability sampling a) Quota Sampling b) Purposive Sampling c) Convenience Sampling Probability Sampling a) Simple random sampling b) Systematic Sampling c) Stratified Sampling 3. Other Sampling method a) Multiphase Sampling b) Multistage Sampling 7

8. Different types of study design Epidemiological study 8 Descriptive Analytical Case report Case series Cross sectional Ecological Observational Interventional Cross sectional Ecological Case control Cohort Quasi- experimental Trial Clinical trial Field trial Community trial

9. What is sample size determination? Is the mathematical estimation of the number of subjects/units to be included in a study. Optimum sample size determination is required for following reason: a) to allow for appropriate analysis b) to provide the desired level of accuracy c) to allow validity of significance test 9

10. How large a sample do we need? If the sample is too small: Even a well conducted study may fail to answer it’s research question may fail to detect important effects or associations can not generalize the result in the affected population 10

11. conversely If the sample size is too large: The study will be difficult & costly Time constraint Loss of accuracy Hence, optimum sample size must be determined before commencement of a study. 11

12. When to Calculate Sample Size? It should be calculated when the protocol for study is being prepared A s it helps in determination if the study is feasible, ethical, and scientifically sound 12

13. terminologies Hypothesis testing starts with the assumption of no difference between groups or no relationship between variables in the population— which is   null hypothesis A lternative hypothesis , is an actual difference between groups or a true relationship between variables. H ypothesis  is an assumption that is made based on some evidence. 13

14. In conducting any kind of research, two types of errors, i.e., Type I and Type II error. Type I Error occurs when null hypothesis is true in reality and a significant result is obtained (null hypothesis is rejected). Type II Error occurs when null hypothesis is false in reality and a non-significant result is found ( null hypothesis is accepted). Probability of conducting Type I error is alpha (α) error , (the level of significance) whereas Probability of making Type II error is beta (β) error . Types of Errors 14

15. is an ability to see the existence of treatment effect in a study. Probability of type II error is beta value of 1 – beta (1 – β) is power of the test. Power is the probability of correctly rejecting a null hypothesis Power 15

16. 16 Higher the power larger the sample size lower are the chances of missing a real effect. Z values for conventional values of beta Beta Z (1- ) 0.20(power 80%) 0.842 0.10(power 90%) 1.28 0.05(power (95%) 1.64 0.01(power(99%) 2.33 Beta 0.20(power 80%) 0.842 0.10(power 90%) 1.28 0.05(power (95%) 1.64 0.01(power(99%) 2.33

17. Confidence level C onfidence level tell how sure we can be that our data is accurate is expressed as a percentage For example, if confidence level is 90%, results will most likely be 90% accurate 17

18. Effect size 18 It is a standardized difference between the mean of a group & the overall mean =  

19. How to estimate effect size 19 Use background information in the form of similar studies to get means and variation, then calculate effect size directly With no prior information, make an estimated guess on the effect size expected

20. I s the degree of accuracy or precision of our estimate R epresents the maximum amount that our estimate can differ from the true population parameter, given a certain level of confidence Margin of error 20 For example, Suppose there is 40% prevalence of anaemia study sample & we set margin of error of as 5%; It means that range of anaemia in population would be between 40+- 5 i.e., 35% & 45%

21. Standard deviation is the measure of the dispersion of a data set from its mean 21 The higher the dispersion or variability the greater the standard deviation the greater the magnitude of the deviation i.e. Dispersion/variance Standard Deviation  

22. 22 Standard deviation can be calculated as: = score for each point in data = mean of the scores n= number of observations or cases  

23. PREREQUISITES OF SAMPLE SIZE CALCULATIONS What is the study design? What kind of primary outcome variable is there? What is the desired level of significance (α) and Confidence Interval 23

24. What kind of primary outcome variable is there? 24

25. What is the desired level of significance (α) and Confidence Interval Level of significance (alpha, α) has to be assumed by the researcher. If researcher is considering 5% level of significance at the time of sample size calculation, we will be able to interpret results with 95% confidence. By fixing 5% level of significance, then we are taking type I error into account, which means that there might be 5% chance of rejecting null hypothesis when in fact it is true 25

26. Sample size calculations 26

27. Procedure for calculating sample size Three procedures: Use of formulae Readymade table Computer software 27

28. Use of formulae 28

29. Cross-sectional study In such studies, data are collected at a particular time to answer questions about the status of population at that particular time Such studies include questionnaires, disease prevalence surveys etc U sually involves estimation of prevalence and estimation of mean 29

30. Statistical formula for Proportion and prevalence n= where z= confidence level at 95% (standard value of 1.96) p= Estimated prevalence or proportions of project area d= Margin of error (has to be decided by researcher.)   in error sample size 30

31. For example A researcher wants to calculate the sample size for a cross-sectional study to know prevalence/proportion of asthma in traffic police in a city, A nd as per the previously published study, the value of prevalence of asthma in traffic police in the city is around 10%, and the researcher wants to calculate sample size with the margin of error of 5% and type-1 error of 5%. Where, Z will be 1.96, p = 0.10 (percentage converted into the proportion) d will be 0.05 31

32. Hence by putting the values in the above-mentioned formula, Sample size= = 276   This sample size can be adjusted for the non-response/dropout rate. If nonresponse rate of 10% is expected then as per the formula, Adjusted sample size (N1) = n/(1-d) Where N1 is adjusted sample size n is required sample size, and d is dropout rate. Corrected sample size = 276/([1– (10/100)] = 307 So, total of 307 traffic police men need to be screened for asthma for this study 32

33. Sample size = Z = is standard normal variate SD = Standard deviation of variable. Value of standard deviation can be taken from previously done study d = absolute error   If the study involves estimation of mean in cross sectional study, then the formula for sample size calculation will be mentioned below Sample size for the mean: 33

34. For example I f the researcher is interested in knowing the average systolic blood pressure in pediatric age group of that city at 5% of type1 error and error of 5 mmHg of either side (more or less than mean systolic BP) and standard deviation, based on previously done studies, is 25 mmHg then formula for sample size calculation will be Sample size =   Thus, the sample size needed for this study will be 96 . It can be adjusted as per the expected dropout rate. 34

35. Clinical Trials is the type of research that studies new tests and treatments evaluates their effects on human health outcome In this type of study, the researcher could be calculating , E ither difference between the proportion of two groups OR D ifference between quantitative endpoint, that is the mean between two groups 35

36. If the clinical trial involves estimation of qualitative end point between two groups, that is the difference between proportions, then, Sample Size =   Where value of Z α is the standard normal variate is 1.96 at 5% error Z β is 0.842 at 80% power ( Table) p 1 –p 2 is the effect size (the expected difference between two groups) P = prevalence calculated by adding prevalence is group 1 and prevalence in group 2 and then dividing the sum by 2 36

37. If in clinical trial, the estimation of the difference of quantitative endpoint between two groups is the objective, then sample size calculation is Sample Size = Where, Z α is the standard normal variate is 1.96 at 5% error Z β is 0.842 at 80% power SD is Standard deviation   37

38. Sample size calculation for case control studies In case control studies cases (the group with disease/condition under consideration) are compared with controls ( the group without disease) regarding exposure to the risk factor.

39. For qualitative variable Sample size=   r= Ratio of control to cases P*= Average proportion exposed = proportion of exposed cases + proportion of control exposed/2 = standard normal variate for power= for 80% power it is 0.84 (from table) Z = standard normal variate for level of significance P 1 -p 2 = Effect size or different in proportion expected based on previous studies. P 1 is proportion in cases & p 2 is proportion in control  

40. For quantitative variable Sample size=   SD=Standard Deviation= researcher can take value from previously published studies d= Expected mean difference between case and control (from previously published studies) r, & Z are already explained in previous study  

41. Sample size calculation of cohort study In Cohort study, healthy subjects with or without exposure to some risk factor are observed over a time period to see the event rate in both groups.

42. Use of table 43

43. Readymade table Can be used at a given population size, a specific margin of error & a desired confidence interval 44

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45. If we have 5000 population. we want to sample a sufficient number with 95% confidence interval that predicted the proportion who would be repeat customers within plus or minus 2.5%, you would need responses from a (random) sample of  1176  of all your customers For example

46. Computer software 47

47. G-power software 48 is a tool to compute statistical power analyses for different types of test. Also used to compute effect sizes and to display graphically the results of power analyses. Three basics step: Select appropriate test Input parameters Determine effect size

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49. summary 50 Three procedures for sample size calculations: Use of formulae Readymade table Computer software

50. S.N. Component What is it? Where to find it? 1. Type-1 error ( error) False + ve result due to probability of falsely detecting the difference when there is no actual difference Usually taken as 0.05 or 0.01 2. Power(1- ) Probability of correctly rejecting the null hypothesis Usually taken above 80% 3. Effect size The smallest clinically relevant difference in the outcome From previous studies, pilot studies or by experience of researcher 4. standard deviation How dispersed or spread out the data values are. From previous studies, pilot studies or by experience of researcher 5. Dropout rate Anticipated percentage of patient that do not complete the study From previous studies, pilot studies or by experience of researcher S.N. Component What is it? Where to find it? 1. False + ve result due to probability of falsely detecting the difference when there is no actual difference Usually taken as 0.05 or 0.01 2. Probability of correctly rejecting the null hypothesis Usually taken above 80% 3. Effect size The smallest clinically relevant difference in the outcome From previous studies, pilot studies or by experience of researcher 4. standard deviation How dispersed or spread out the data values are. From previous studies, pilot studies or by experience of researcher 5. Dropout rate Anticipated percentage of patient that do not complete the study From previous studies, pilot studies or by experience of researcher Different component that effect the sample size

51. conclusion 52 Sample size calculation is always an essential step during the planning of scientific studies. An insufficient sample size may not be able to demonstrate the desired difference, or estimate the frequency of the event of interest with acceptable precision A very large sample may add to the complexity of the study, and its associated costs, rendering it unfeasible.

52. references Das S, Mitra K, Mandal M. Sample size calculation: Basic principles. Indian J Anaesth . 2016 Sep;60(9):652-656. doi : 10.4103/0019-5049.190621. PMID: 27729692; PMCID: PMC5037946. Rodríguez Del Águila M, González-Ramírez A. Sample size calculation. Allergol Immunopathol ( Madr ). 2014 Sep-Oct;42(5):485-92. doi : 10.1016/j.aller.2013.03.008. Epub 2013 Nov 23. PMID: 24280317. The Research Advisors: Research Methodology, Study Design & Statistical Analysis (research-advisors.com) Kang H. Sample size determination and power analysis using the G*Power software. J Educ Eval Health Prof. 2021;18:17. doi : 10.3352/jeehp.2021.18.17. Epub 2021 Jul 30. PMID: 34325496; PMCID: PMC8441096. https://www.researchgate.net/publication/350836701_Sample_Size_Calculation_in_Medical_Research_A_Primer https://www.researchgate.net/publication/343860693_Epidemiological_study_designs-_Examples_of_medical_sciences Hiremath SS. Textbook of preventive and community dentistry. Elsevier India; 2011 Aug 15. 53

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55. Difference Between margin of error and SD 56 Margin of error Standard error - Is a statistical measure that accounts for the degree of error received from the outcome of your research sample - Measures the accuracy of representation of population sample to the mean using SD of the set data. -goal is to estimate how much allowable difference can exist between the research population & sample size -Purpose is to measure the spread of random variables within the data set