Upload
priyanka-divekar
View
224
Download
0
Embed Size (px)
Citation preview
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 1/22
Sample Size Determination
The Fundamentals of Biostatistics inClinical Research Workshop
India, March 2007
Mario Chen
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 2/22
Framework
Objectives
Type of Inference: Estimation orEstimation orHypothesis TestingHypothesis Testing
Study Design: Type of Study andSample SizeSample Size
Data Collection
Data Management Data AnalysisData Analysis
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 3/22
Selection of summary measure
ObjectiveObjective
EndpointEndpoint
Summary measure*Summary measure*
Parameter Parameter
PopulationPopulation
IndividualIndividual
SampleSample
PopulationPopulation
* Depends of primary analysis method
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 4/22
Sample Size for Estimation
Necessary Components:
1. Indicator or summary measure of interest(proportions or means)
2. Desired Confidence Level (1-α)
3. Desired Precision Level (d)
4. Expected Variability in the study population:
For means (σ) For proportions (P)
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 5/22
Sample Size for Estimation
(Proportions)Example:
1. Summary measure: Prevalence of VibrioCholerae
2. Confidence Level: 95%
3. Precision Level:d = 3 percent points, i.e. 0.03
4. Variability: Estimate of P = 15% (from
previous studies)Recommendation: If there is not a good estimatefor P, use P closest to 50% to be conservativeRecommendation: If there is not a good estimateRecommendation: If there is not a good estimatefor P, use P closest to 50% to be conservativefor P, use P closest to 50% to be conservative
n = 523
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 6/22
Sample Size for Estimation
(Means)Example:
1. Summary measure: Mean hydrocele sizeamong filariasis infected patients
2. Confidence Level: 95%
3. Precision Level: d = 1.5 mm.
4. Variability: Estimate for σ = 5.7 mm.
To estimate σ we can use previous studies,expert advice, or a pilot studyTo estimateTo estimate σσ we can use previous studies,we can use previous studies,expert advice, or a pilot studyexpert advice, or a pilot study
n = 58
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 7/22
Sample Size for Hypothesis
Testing
Necessary Components:
1. Summary measure of interest (proportionsor means)
2. Statistical Hypotheses
3. Significance Level (α)
4. Desired Power (1-β)
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 8/22
Sample Size for Hypothesis
TestingNecessary Components (cont’d):
5. Effect Size: Smallest difference worthdetecting (clinically)
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 9/22
What is a clinically important
difference to detect?
Standard drug has 75% Cure rate
And New treatment . . .
76%?. . . 77%? . . . 78%? . . . 79%?
87%? . . . 88%? . . . 89% . . . 90%?
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 10/22
Cured rate for the New Treatment?
“Ridiculous notion” . . .
“How would I know this – I’m doing the studyto estimate the effect.”
“I have no data on which to base an estimate.”
--------------------True, but----------------------
You do not estimate the cure rate for the newtreatment!
You determine the cure rate reflecting theclinically important difference to detect, whichmay have no relation to the actual cure rate
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 11/22
Example
Standard drug
Cost of $30.00 for 28 days
2 oral doses per day
Minimal side effects
New treatment
Cost of $500.00 for 28 days
A single oral dose per day Neutropenia, blurred vision, and proteinuria
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 12/22
What is a clinically important
difference to detect?
Standard drug has 75% Cure rate
And New treatment . . .
76%?. . . 77%? . . . 78%? . . . 79%?
87%? . . . 88%? . . . 89% . . . 90%? We believe 15 % represents a clinically
important difference to detect If the difference is greater then changes will occur If the difference is smaller, groups are considered
“equivalent” (status quo preserved)
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 13/22
Sample Size for Hypothesis
TestingNecessary Components (cont’d):
6. Variability expected in the population For means (σ1, σ2)
For proportions (P1, P2)
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 14/22
Sample Size for Hypothesis
Testing
Example for proportions:
1. Summary measure: Proportion Cured
2. Statistical Hypotheses:
H0: Proportion cured is the same with both thenew treatment and the standard treatment
H1: Proportion cured is higher with the new
treatment than with the standard treatment
One sided vs. two sided Alternative
Hypothesis.
One sided vs. two sided AlternativeOne sided vs. two sided Alternative
Hypothesis.Hypothesis.
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 15/22
Recommendation:
a) Define level for P for the “baseline” groupb) Use effect size to obtain level of P for the “study”
group
Recommendation:Recommendation:
a) Define level for P for thea) Define level for P for the ““baselinebaseline”” groupgroup
b) Use effect size to obtain level of P for theb) Use effect size to obtain level of P for the ““studystudy””
groupgroup
n = 109
Sample Size for Hypothesis Testing(cont-d)
3. Significance Level: α = 5%
4. Power: 1-β = 90%(never lower than 80%)
5. Effect size: P2
– P1
= 15%
6. Variability:Estimate for P1 = 75%Estimate for P
2= 90%
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 16/22
Main Determinant of Study SizeRecommendations when budget is not enough:1. (Estimation) Lower desired precision.
2. (Hypothesis Testing) Lower desired power or increaseminimum detectable effect size.
3. It is not recommended to change confidence levels,significance levels, or variance estimates.
4. If after all these changes, budget is still insufficient,one has to decide between:• Not conducting the study until enough budget has
been obtained, or • go ahead with the study knowing that the resultsare likely to be inconclusive (pilot study or exploratory).
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 17/22
Adjustments to Sample Size Non-Response (and attrition):
n2 = n1/(1-NR)n2 = final size, n1 = effective size
NR = Non-response (and attrition) rate
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 18/22
Other Considerations Data dependencies (e.g., Matching, Repeated
Measures).
Multivariate methods (e.g., control for
confounding).
Multiplicity issues (e.g., Multiple testing,
endpoints, treatments, interim analyses).
Other variables of interest (e.g., time to
event).
Other hypotheses (e.g., equivalence).
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 19/22
Software PASS
(www.ncss.com/pass.html) nQUERY
(www.statsolusa.com/nquery/nquery.htm)
EPI-INFO(www.cdc.gov/epiinfo)
EPIDAT(www.paho.org/English/SHA/epidat.htm)
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 20/22
What should be included in the
protocol?
Justification in terms of power or precision for
the primary endpoint Method used to calculate the sample size
should be consistent with the primary method for
data analysis and appropriate for the study design Historical data to support the assumptions
Justification in terms of feasibility
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 21/22
Questions?
8/6/2019 Sample Size Determination India 2007
http://slidepdf.com/reader/full/sample-size-determination-india-2007 22/22