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Sampling and Sample Size in Epidemiology

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Dr. Papia Sultana

Associate Professor

Department of Statistics

University of Rajshahi

Dr. Papia Sultana

The sample

The population

Dr. Papia Sultana

Every person in the population has the equal possibility to be chosen to be in the sample

Dr. Papia Sultana

Dr. Papia Sultana

- 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

The sample

The population

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Population

Sample

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Reference population

External validity

Study population

New treatment

Current treatment

Internal validity

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- 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

- Place of the study??
- Subjects of the study??

Dr. Papia Sultana

- 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.

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- Controlled trial – trials with control groups
- Randomized controlled trials
- Quasi randomized trials
- Non randomized trials
- Phase III trial
Treatment 1 Treatment 2

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- 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

- Table 1 Baseline characteristics of study children.
- Values are mean (SD) unless stated otherwise

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- Quasi-randomized controlled trials – allocation using schemes such as every alternate person, or according to date of birth (odd or even) etc

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- 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

- 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

- 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

- 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

- Prob (type I error) = Prob (reject H0 when H0 is true) =

Dr. Papia Sultana

- 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

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

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

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

- 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

=Z value at power (at power 80% this value is 0.84)

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- 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

- 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

Difference between two proportions:

- Comparison between two treatments
- To observe the effect of an intervention

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- = 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

Dr. Papia Sultana

- the variable is continuous
- Information about mean and sd are available

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- 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

- Equality of two mean test

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Dr. Papia Sultana

- Only population size is known

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- Odd Ratio
- Chi-square
- Linear model
- Logistic model
- Factorial model

Not in handy

Dr. Papia Sultana

- Computer Software:
- PASS
- EpiCalc 2000

- Online supports are also available

Dr. Papia Sultana

- 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

Dr. Papia Sultana

Dr. Papia Sultana

Dr. Papia Sultana

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

Dr. Papia Sultana

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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?

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Dr. Papia Sultana

Dr. Papia Sultana

- Different methods of data analysis require different input for sample size calculations

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- Read chapter 2 of Statistical Rules of Thumb, by Gerald van Belle (2002, John Wiley and Sons)
- Using specialized software is useful if many calculations will be performed

Dr. Papia Sultana

- Pilot studies do not need sample size calculation!!!
- There is no point in doing power analysis after the study is done
- Sample size is an educated guess, and it works only if:
- The study samples comes from the same or similar populations to the pilot study populations
- The population of interest is not changing over time
- The difference or association being studied exists

Dr. Papia Sultana

- Question: “How many more people do I need to enroll in the study (already in progress) to show statistical significance”?
- Answer: It depends… If the two populations have the same mean, increasing the sample size will not help!
- Since when is the objective of a study to find a statistically significant result??

Dr. Papia Sultana

- Researcher is interested in outcome A, which differs very little for two treatments
- Sample size needed is around 3000!!
- Researchers changes the outcome to B, where sample size is smaller
- B does not answer the researcher’s question and he needs to accept that his new treatment is not really different (clinically speaking) from the already existent treatment

Dr. Papia Sultana

- Researcher is interested in comparing two groups regarding prediction of outcome A by using a regression analysis (using several variables)
- He uses the only available formula from his statistical book (for a t-test)
- Wrong! He should find a software that can calculate the sample size appropriately

Dr. Papia Sultana

- Define research question well
- Consider study design, type of response variable, and type of data analysis
- Decide on the type of difference or change you want to detect (make sure it answers your research question)
- Choose and
- Use appropriate equation sample size calculation

Dr. Papia Sultana

- Chow S-C, Jones B, Liu J-P & Peace KE (2008). Sample Size Calculations in Clinical Research. Second edition. Chapman & Hall.
- Gerald VB, Lloyd DF, Patrick JH & Thomas SL (2004). A methodology for the health sciences. Second Edition. John Wiley & sons.
- Stephen CN (2001). Biostatistical Methods in Epidemiology. John Wiley & sons.
- Gerald VB (2002) Statistical Rules of Thumb, John Wiley and Sons.

Dr. Papia Sultana

Thanks for your attention

Dr. Papia Sultana