Sampling and sample size in epidemiology
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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
Sampling and Sample Size in Epidemiology

Dr. Papia Sultana

Associate Professor

Department of Statistics

University of Rajshahi

Dr. Papia Sultana


Sampling
Sampling

The sample

The population

Dr. Papia Sultana


Representative sample
Representative sample

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

Dr. Papia Sultana


Not representative sample
Not representative sample

Dr. Papia Sultana


Selection bias
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


The sample must be a small picture of the entire population
The sample must be a small picture of the entire population

The sample

The population

Dr. Papia Sultana


Selection biased should be avoided
Selection biased should be avoided

Population

Sample

Dr. Papia Sultana


Internal and external validity
Internal and external validity

Reference population

External validity

Study population

New treatment

Current treatment

Internal validity

Dr. Papia Sultana


Internal external validity
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
External validity

  • Place of the study??

  • Subjects of the study??

Dr. Papia Sultana


Sampling in epidemiology
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
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 study1
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


Zinc supplementation in children with cholera in bangladesh randomized controlled trial
Zinc supplementation in children with cholera in Bangladesh: randomized controlled trial

  • Table 1  Baseline characteristics of study children.

  • Values are mean (SD) unless stated otherwise

Dr. Papia Sultana


Randomization in experimental study2
Randomization in Experimental study randomized controlled trial

  • 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
Sample size randomized controlled trial

  • 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
Calculation of sample size randomized controlled trial

  • 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 size1
Calculation of sample size randomized controlled trial

  • 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 size2
Calculation of sample size randomized controlled trial

  • 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 size3
Calculation of sample size randomized controlled trial

  • 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 size4
Calculation of sample size randomized controlled trial

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 size5
Calculation of sample size randomized controlled trial

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 size6
Calculation of sample size randomized controlled trial

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 size7
Calculation of sample size randomized controlled trial

  • 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 size8
Calculation of sample size randomized controlled trial

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

Dr. Papia Sultana


Calculation of sample size9
Calculation of sample size randomized controlled trial

  • 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 size10
Calculation of sample size randomized controlled trial

  • 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 size11
Calculation of sample size randomized controlled trial

Difference between two proportions:

  • Comparison between two treatments

  • To observe the effect of an intervention

Dr. Papia Sultana


Calculation of sample size12
Calculation of sample size randomized controlled trial

  • = 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 size13
Calculation of sample size randomized controlled trial

Dr. Papia Sultana


Calculation of sample size14
Calculation of sample size randomized controlled trial

  • the variable is continuous

  • Information about mean and sd are available

Dr. Papia Sultana


Calculation of sample size15
Calculation of sample size randomized controlled trial

  • 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 size16
Calculation of sample size randomized controlled trial

  • Equality of two mean test

Dr. Papia Sultana


Calculation of sample size17
Calculation of sample size randomized controlled trial

Dr. Papia Sultana


Calculation of sample size18
Calculation of sample size randomized controlled trial

  • Only population size is known

Dr. Papia Sultana


Calculation of sample size19
Calculation of sample size randomized controlled trial

  • Odd Ratio

  • Chi-square

  • Linear model

  • Logistic model

  • Factorial model

Not in handy

Dr. Papia Sultana


Calculation of sample size20
Calculation of sample size randomized controlled trial

  • Computer Software:

    • PASS

    • EpiCalc 2000

  • Online supports are also available

Dr. Papia Sultana


Using pass z test example
Using PASS: Z-test example randomized controlled trial

  • 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 randomized controlled trial


Dr. Papia Sultana randomized controlled trial


Dr. Papia Sultana randomized controlled trial


Dr. Papia Sultana randomized controlled trial


Example: One-way ANOVA randomized controlled trial

  • 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 randomized controlled trial


Dr. Papia Sultana randomized controlled trial


Dr. Papia Sultana randomized controlled trial


Example: Linear Multiple Regression randomized controlled trial

  • 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


Dr. Papia Sultana randomized controlled trial


Dr. Papia Sultana randomized controlled trial


Other types of hypothesis tests
Other Types of Hypothesis Tests randomized controlled trial

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

Dr. Papia Sultana


Cox regression survival analysis
Cox Regression (Survival analysis) randomized controlled trial

Dr. Papia Sultana


Logistic regression
Logistic Regression randomized controlled trial

Dr. Papia Sultana


Repeated measures
Repeated measures randomized controlled trial

Dr. Papia Sultana


Simple designs may not require complex calculations
Simple designs may not require complex calculations randomized controlled trial

  • 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


Important to remember
Important to remember randomized controlled trial

  • 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


Some situations i have encountered
Some situations I have encountered randomized controlled trial

  • 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


Some situations i have encountered1
Some situations I have encountered randomized controlled trial

  • 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


Some situations i have encountered2
Some situations I have encountered randomized controlled trial

  • 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


Summary
Summary randomized controlled trial

  • 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


Key references
Key references randomized controlled trial

  • 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 randomized controlled trial

Dr. Papia Sultana


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