Transcript Sample Size Calculation - Animal Ethies Committee

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
– Observational or Experimental Study
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
n
4 PQ
L
2
• P = Estimated prevalence (percentage)
• Q =1-P
• L = Allowable Error
Definition
• P = Estimated prevalence (percentage)
– From pilot study, published papers, experience
• Q =1-P
• L = Allowable Error
– เปอร์เซ็นต์ที่ยอมให้คลาดเคลื่อนได้จากค่าจริง (ผูว้ ิ จยั
ระบุเอง; ไม่น่าจะเกิน 1 ใน 5 ของค่า P)
– L and Q and P are in the same unit
L; Allowable Error
• Suppose, the survey wants 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
-L
+L
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)
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
n
4 PQ
L
2
Note: No population size involves in the formula
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
n
4S
L
•
•
•
•
2
2
-L
+L
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
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)
Example
• The required sample size is
n = 4 x (455)2 / (80)2 = 129.39
• Thus approximately 130 rats would be
needed.
n
4S
L
2
2
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
nC
( Pc Q c )  ( Pe Q e )
(d )
•
•
•
•
2

2
2
d
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 Percentages
nC
( Pc Q c )  ( Pe Q e )
(d )
2

2
2
d
• 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
alpha
0.05
0.01
C
7.85
11.68
• When power is 80%
• Power = Ability to find significance when the two
groups are really different (the formula is for two
sided difference)
Example
• สมมุติว่าต้องการทดสอบว่ากลุ่มควบคุมต่างกับ
กลุ่มให้ยาหรือไม่ ในการรักษาโรคชนิดหนึ่ ง สิ่งที่วดั
ในการทดลองคืออัตราการรอด (survival rate) ใน
แต่ละกลุ่ม
• Pc = 0.25, Pe = 0.65, then d = 0.4 and choose
alpha = 0.05
nC
( Pc Q c )  ( Pe Q e )
(d )
2

2
d
2
Example
nC
( Pc Q c )  ( Pe Q e )
(d )
n  7 . 85
2

( 0 . 25  0 . 75 )  ( 0 . 65  0 . 35 )
( 0 .4 )
2
2
2
d

2
2
0 .4
= 27.36 = use 28 animals in each group
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 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 2
• Pe = 0.3, Pc = 0.2
nC
( Pc Q c )  ( Pe Q e )
(d )
n  7 . 85
2
( 0 .3  0 .7 )  ( 0 .2  0 .8 )
( 0 . 1)
2

2
2
d

2
2
0 .1
= 312.45 = use 313 persons in each group
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
 s 
n  1  2C  
d 
2
• S = Standard Deviation of the variable
• d = Difference between the 2 groups
• C = Constant (from previous table)
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
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)
•
Example
• S=1
• d = 10% of 2 litre = 0.2 litre
 1 
n  1  2  7 . 85 

 0 .2 
2
 s 
n  1  2C  
d 
n = 393.5 : Then use 394 patients in each group
2
5. Paired Study
•
•
•
•
Pre-test/Post-test
Before/After treatment
Paired t-test analysis
More powerful than unpaired study
 s 
n  2  C 
d 
2
Example
• From pilot study, Before and After treatment of
the average of blood pressures are estimated
to be 120 and 80, respectively
• S = 38
 38 
n  2  7 . 58 

 40 
2
 s 
n  2  C 
d 
n = 8.84 : Then use 9 patients in each group
2
What affect sample size
• Wants small n ?
• 1. Prevalence study
n
L
– Large L
– Maximized at P = 50%
• 2. Mean study
– Small standard deviation
– Large L
4 PQ
n
4S
L
2
2
2
What affect sample size
• 3. Comparing percentages
– Large d
nC
( Pc Q c )  ( Pe Q e )
(d )
2

2
2
d
• 4. Comparing means (paired and unpaired)
– Small standard deviation
– Large d
– Paired study uses less samples
 s 
n  1  2C  
d 
 s 
n  2  C 
d 
2
2