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Sample Size Calculation. ผศ.ดร. ขวัญเกศ กนิษฐานนท์ คณะสัตวแพทยศาสตร์ มหาวิทยาลัยขอนแก่น. Why. To complete research proposal Reduce unnecessary expense (time, labor, money, materials) Avoid useless research. Type of Experiment. 1. Survey Observational Study 2. Test a Hypothesis

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sample size calculation

Sample Size Calculation

ผศ.ดร. ขวัญเกศ กนิษฐานนท์

คณะสัตวแพทยศาสตร์

มหาวิทยาลัยขอนแก่น

slide2
Why
  • To complete research proposal
  • Reduce unnecessary expense (time, labor, money, materials)
  • Avoid useless research
type of experiment
Type of Experiment
  • 1. Survey
    • Observational Study
  • 2. Test a Hypothesis
    • Observational or Experimental Study
1 sample size for prevalence survey
1. Sample Size for Prevalence Survey
  • For dichotomous data (only 2 outcomes; sick/not sick, male/female, dead/alive)
  • The study describe results in percentage
  • For example, disease prevalence survey
sample size for prevalence survey
Sample Size for Prevalence Survey
  • P = Estimated prevalence (percentage)
  • Q =1-P
  • L = Allowable Error
definition
Definition
  • P = Estimated prevalence (percentage)
    • From pilot study, published papers, experience
  • Q =1-P
  • L = Allowable Error
    • เปอร์เซ็นต์ที่ยอมให้คลาดเคลื่อนได้จากค่าจริง (ผู้วิจัยระบุเอง; ไม่น่าจะเกิน 1 ใน 5 ของค่า P)
    • L and Q and P are in the same unit
l allowable error

- L

+L

L; Allowable Error
  • Suppose, the surveywants to estimate the true prevalence of a disease in population
  • The estimate we get from the survey will be within +/- L% of the true prevalence
example
Example
  • A survey is to estimate prevalence of influenza virus infection in school kids
  • Suppose the available evidence suggests that approximately 20% (P=20) of the children will have antibodies to the virus
  • Assume the investigator wants to estimate the prevalence within 6% of the true value (6% is called allowable error; L)
example9
Example
  • The required sample size is
  • n = (4 x 20 x 80) / (6 x 6) = 177.78
  • Thus approximately 180 kids would be needed for the survey

Note: No population size involves in the formula

2 sample size for estimation of the mean
2. Sample Size for Estimation of the Mean
  • A Survey to find an average of a parameter (birth weight, antibody titre, blood pressure)
  • The study reports average of parameters
  • The parameter must be quantitative
sample size for estimation of the mean

- L

+L

Sample Size for Estimation of the Mean
  • S = Standard Deviation of the parameter
  • L = Allowable Error
  • S and L are in the same unit
  • The average we find in the survey will be within +/- L of the true population mean
example12
Example
  • Suppose an investigator has some evidence suggests that the standard deviation of rat weight is about 455 g
  • He wishes to provide an estimate within 80 g of the true average (80 g is the allowable error; L)
example13
Example
  • The required sample size is

n = 4 x (455)2 / (80)2 = 129.39

  • Thus approximately 130 rats would be needed.
3 sample size to compare percentages
3. Sample Size to Compare Percentages
  • A study to compare percentages of outcomes from different groups (incidence, conversion rate, cure rate, mortality rate, survival rate)
  • For chi-square analysis or logistic regression (one predictor)
sample size to compare percentages
Sample Size to Compare Percentages
  • Pc = percentage from control group
  • Qc = 1- Pc
  • Pe = Percentage from the experimental group
  • Qe = 1- Pe

Pick 2 groups that you think will be most different

sample size to compare percentages16
Sample Size to Compare Percentages
  • d = Difference between the two groups (must be positive)
  • C = Constant (See table next page)

Pc and Pe are from pilot study or published papers

c constant
C : Constant
  • When power is 80%
  • Power = Ability to find significance when the two groups are really different (the formula is for two sided difference)
example18
Example
  • สมมุติว่าต้องการทดสอบว่ากลุ่มควบคุมต่างกับกลุ่มให้ยาหรือไม่ในการรักษาโรคชนิดหนึ่ง สิ่งที่วัดในการทดลองคืออัตราการรอด (survival rate) ในแต่ละกลุ่ม
  • Pc = 0.25, Pe = 0.65, then d = 0.4 and choose alpha = 0.05
example19
Example

= 27.36 = use 28 animals in each group

example 2
Example 2
  • The research question is whether smokers have a greater incidence of skin cancer than nonsmokers
  • A review of previous literature suggests that the incidence of skin cancer is about 0.2 in nonsmokers
  • At alpha=0.05, and power=80%, how many smokers and nonsmokers will need to be studied to determine whether skin cancer incidence is at least 0.3 in smokers?
example 221
Example 2
  • Null Hypothesis : The incidence of skin cancer does not differ in smokers and nonsmokers
  • Alternative Hypothesis : The incidence of skin cancer is different between smokers than nonsmokers
    • (Note that this is a two-tailed hypothesis)
example 222
Example 2
  • Pe = 0.3, Pc = 0.2

= 312.45 = use 313 persons in each group

4 sample size to compare means
4. Sample Size to Compare Means
  • Hypothesis: Compare means of different groups
  • The parameters are quantitative (birth weight, blood pressure)
  • Select 2 groups that you think they will be most different (such as; a control and a treatment group)
  • For t-test, ANOVA
sample size to compare means
Sample Size to Compare Means
  • S = Standard Deviation of the variable
  • d = Difference between the 2 groups
  • C = Constant (from previous table)
example25
Example
  • The research question is to compare the efficacy of metaproterenol and theophylline in the treatment of asthma
  • The outcome variable is FEV1 (forced expiratory in 1 second) 1 hour after treatment
  • A previous study has reported that the mean FEV1 in persons with treated asthma was 2.0 litres, with a standard deviation of 1.0 litre
  • The investigator would like to be able to detect a difference of 10% or more in mean FEV1 between the two treatment groups
example26
Example
  • Null Hypothesis : Mean FEV1 is the same in asthmatics treated with theophylline as in those treated with metaproterenol
  • Alternative Hypothesis : Mean FEV1 is different between asthmatic patients treated with theophylline and those treated with metaproterenol
  • (This is a two-tailed hypothesis)
example27
Example
  • S = 1
  • d = 10% of 2 litre = 0.2 litre

n = 393.5 : Then use 394 patients in each group

5 paired study
5. Paired Study
  • Pre-test/Post-test
  • Before/After treatment
  • Paired t-test analysis
  • More powerful than unpaired study
example29
Example
  • From pilotstudy, Before and After treatment of the average of blood pressures are estimated to be 120 and 80, respectively
  • S = 38

n = 8.84 : Then use 9 patients in each group

what affect sample size
What affect sample size
  • Wants small n ?
  • 1. Prevalence study
    • Large L
    • Maximized at P = 50%
  • 2. Mean study
    • Small standard deviation
    • Large L
what affect sample size31
What affect sample size
  • 3. Comparing percentages
    • Large d
  • 4. Comparing means (paired and unpaired)
    • Small standard deviation
    • Large d
    • Paired study uses less samples