Sampling and Sample Size in Epidemiology. Dr. Papia Sultana Associate Professor Department of Statistics University of Rajshahi. Sampling. The sample. The population. Representative sample. Every person in the population has the equal possibility to be chosen to be in the sample.

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Sampling and Sample Size in Epidemiology

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Selection bias • Selection bias occurs then patients included in the study are not representative of the population to which the results will be applied • Example • Patients who agree to participate in a study may differ from those who do not agree to participate Dr. Papia Sultana

Internal and external validity Reference population External validity Study population New treatment Current treatment Internal validity Dr. Papia Sultana

Internal & external validity • Internal validity - refers specifically to whether an experimental treatment/condition makes a difference or not, and whether there is sufficient evidence to support the claim • External validity – refers to whether you can generalize the findings to the population of interest Dr. Papia Sultana

External validity • Place of the study?? • Subjects of the study?? Dr. Papia Sultana

Sampling in Epidemiology • Any proper sampling method is used -Simple Random Sampling (SRS) - Cluster Sampling - Systematic Sampling - Stratified Sampling - PPS Sampling - Multistage Sampling • Sometimes combination of more than one sampling scheme. Dr. Papia Sultana

Randomization in Experimental study • Controlled trial – trials with control groups • Randomized controlled trials • Quasi randomized trials • Non randomized trials • Phase III trial Treatment 1 Treatment 2 Dr. Papia Sultana

Randomization in Experimental study • Randomized controlled trials – interventions allocated randomly • Coin tossing is not proper way • Throwing a dice can be used: if the outcome is 1,2 &3 the subject will be allocated to treatment 1 group, otherwise in treatment 2 group. • In RCT, people are randomly allocated to treatment groups and therefore all characteristics such as confounders and other variables should be evenly distributed in the different treatment groups Dr. Papia Sultana

Randomization in Experimental study • Quasi-randomized controlled trials – allocation using schemes such as every alternate person, or according to date of birth (odd or even) etc Dr. Papia Sultana

Sample size • Duringthe planning stage of a study, the following questions are of particular interest to the investigators: (i) how many subjects are needed in order to have a desired power for detecting a meaningful difference (e.g., an 80% chance of correctly detecting a meaningful difference), and (ii) what’s the trade-off between costeffectivenessand power if only a small number of subjects are available for the study due to limited budget and/or some medical considerations. • Sample size calculation plays an important role for assuring validity, accuracy, reliability, and integrity of the intended study. • Ethical issues may come in front, too. Dr. Papia Sultana

Calculation of sample size • What is the study objectives (outcome variable)? • What type of variable it is? • What study design is involved? • Is there any information related to that published in anywhere (historical information)? • Do you need to conduct a pilot study? Dr. Papia Sultana

Calculation of sample size • Basically, sample size calculation can be classified into sample size estimation/ determination (SRS), sample size justification (Lab trial & clinical trial), sample size adjustment (cluster sampling), and sample size re-estimation (in the mid stage of the study). • Level of significance and power play very important role in calculation of sample size. Dr. Papia Sultana

Calculation of sample size • Researcher fixes probabilities of type I and II errors • Prob (type I error) = Prob (reject H0 when H0 is true) = • Smaller error greater precision need more information need larger sample size • Prob (type II error) = Prob (don’t reject H0 when H0 is false) = • Power =1- • More power smaller error need larger sample size Dr. Papia Sultana

Calculation of sample size • Single Proportion n = required sample sizeZ= Standard Normal value at confidence level at 100(1- )% (ideal value is1.96 at 95%)p = referred prevalence for the study d = margin of error (ideal value is 0.05) Dr. Papia Sultana

Calculation of sample size Example: In the Al Haouz project in Morocco, it has been estimated that roughly 30% (0.3) of the children in the project area suffer from chronic malnutrition. This figure has been taken from national statistics on malnutrition in rural areas. Use of the standard values listed above provides the following calculation. n=1.96² x .3(1-.3) .05² = 322.72 ~ 323 Dr. Papia Sultana

Calculation of sample size Design effect: • The anthropometric survey is designed as a cluster sample (a representative selection of villages), not a simple random sample. To correct for the difference in design, the sample size is multiplied by the design effect (D). • The design effect is generally assumed to be 2 for nutrition surveys using cluster-sampling methodology. • n x D = 323 x 2 = 646 Dr. Papia Sultana

Calculation of sample size Contingency: • The sample is further increased by 5% to account for contingencies such as non-response or recording error (provide proper logic). • n + 5% = 646 x 1.05 = 678.3 ˜ 678 Dr. Papia Sultana

Calculation of sample size • In clinical Trial or for the rare diseases we need to analyze power. • I have 2 years to finish my research, of which one year is for data collection. I think I can get data on 50 people in that year. Is 50 a sufficient sample size to test my hypothesis with the significance level I want? Dr. Papia Sultana

Calculation of sample size • Example: Assuming 30% prevalence of the study area with margin of error 0.05 and 95% confidence a sample size 659 is required to achieve 80% power. Dr. Papia Sultana

Calculation of sample size • Example: Assuming 30% prevalence of the study area with margin of error 0.05 a sample size 60 can achieve a power 80%. Dr. Papia Sultana

Calculation of sample size Difference between two proportions: • Comparison between two treatments • To observe the effect of an intervention Dr. Papia Sultana

Calculation of sample size • = prevalence of group 1 • = prevalence of group 2 • = difference between the two groups Equal sample size will be taken in both groups [ total 2n] Dr. Papia Sultana

Calculation of sample size • the variable is continuous • Information about mean and sd are available Dr. Papia Sultana

Calculation of sample size • Single mean test n = required sample sizeZ= Standard Normal value at confidence level at 100(1- )% (ideal value is1.96 at 95%) = referred sd for the variable d = margin of error (ideal value is 0.05) Dr. Papia Sultana

Calculation of sample size • Odd Ratio • Chi-square • Linear model • Logistic model • Factorial model Not in handy Dr. Papia Sultana

Calculation of sample size • Computer Software: • PASS • EpiCalc 2000 • Online supports are also available Dr. Papia Sultana

Using PASS: Z-test example • Question: does exercise help to decrease body weight? • Study design: participants will be randomized into two groups (exercise and control) • Outcome: change in weight • Want to detect: a change of at least 15 pounds • Known: from past studies, the standard deviation varies between 10 and 15 pounds. Dr. Papia Sultana

Example: One-way ANOVA • Number of Groups: 4 • Hypothesized means: 35, 20, 25, 18 (possibly from a pilot study) • Sample size pattern: same number in each group • SD of subjects: 18 (from a previous study) • = 0.01 and 0.05 • Find power for sample sizes from 5 to 30 per group (increments of 5) Dr. Papia Sultana

Example: Linear Multiple Regression • Research Question: is depression score an important factor in explaining pain ratings, after adjusting for age and sex? • Statistical question: does adding depression score increase the explained variation of pain ratings, in a linear regression model that already has age and sex in it and has R2 =.2? • Suppose I may have sample sizes of 20, 30, 50, 70, and 100. What is the minimum R2 change I can detect with power .8? Dr. Papia Sultana