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MPH Fall 09
Sample Size Calculation
nQuery Advisor
Judith L. Jacobsen, MSc. PhD.
www.statcon.dk Choose MPHepi
[email protected]
Agenda
• Sample size calculation program
• Two worked examples
– Epidemiology
– Continuous data
– Binary data
– Proportions
– Survival
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Programs
SPSS cannot do sample size!
• Many specific programs
– nQuery
– Pass
– Power and precision
• I will show nQuery Advisor®
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nQuery Advisor®
Means
• Tests
Confidence Intervals
Equivalence Tests
Proportions
• Tests
Confidence Intervals
Equivalence Tests For paired
proportions
For two independent
proportions
• Regression
• Tests and Confidence Intervals
Logistic regression (one or
multiple covariates)
Linear regression
Multiple regression
Multiple regression (with
partialling)
Tests and confidence intervals
for regression slopes in one
and two sample designs
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• Nonparametric
• Tests
Wilcoxon/Mann-Whitney ranksum test (continuous outcome
or ordered scale)
• Survival
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How to Use
• Formulate the study design, outcome,
analysis.
Use the nQuery Advisor Study Goal and
Design box to select the right table
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Opening Screen
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• Use nQuery Advisor's spreadsheet-style tables
to specify analysis parameters and expected
differences.
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Go Ahead
• Enter sample size to have nQuery Advisor
compute power (or interval width) or
specify power to compute sample size
•
• Additional columns with alternative values
for effect size can be entered for sensitivity
analysis.
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Screen
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Evaluate
• A range of scenarios with nQuery Advisor's
tables and plots
Choose the sample size which best satisfies
your goals and plausible parameter values
• nQuery Advisor then writes up the sample size
decision
• making it easy to report the sample size decision
in the correct language and format
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Evaluate Plot
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Justification
• All ready for the protocol
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Epidemiology Example
Sample Size for confidence interval for odds ratio
• Sample size required for an experiment to
estimate an odds ratio with a confidence interval
of specified width
• Study plan: to evaluate an educational program
for expectant mothers.
– The educational program attempts to reduce the risk
of preterm birth among expectant mothers who are
seen in county prenatal clinics.
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Plan
• Initial plan:
– randomly assign 300 pregnant women to the control
group and 300 to the educational intervention group.
• Question:
– Will the 95% two-sided confidence interval for the
odds ratio be likely to be narrow enough to
demonstrate the effectiveness of the educational
intervention?
• nQuery Advisor® can provide sample size and
interval width calculations for the odds ratio in a
two-sample design.
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Step 1
• Select File ... New, and in the Study Goal
and Design Box
• Select Proportions, Two Groups, and
Confidence Interval and select
Confidence interval for log odds ratio
• In the table, fill in the desired confidence
level
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Information
• Previous studies found preterm birth rates of 7-9%.
– enter an expected proportion of pre-term births of 8%
for the control group
• Specify either the expected proportion for the
intervention group, or the odds ratio, or the ln odds ratio.
– The intervention would be of interest if it reduced the
rate of preterm births enough to produce an odds
ratio of 0.5.
• Specify the planned sample size for each group and
solve for the interval width or specify the desired interval
width and solve for the required sample size per group.
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• We enter a sample size of 300 per group and
request the sample size statement to see what
the expected confidence limits on the odds ratio
will be.
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Step 2
• A sample of 300 women per group would be
expected to result in a confidence interval which
includes 1.0
• In the second column we request the sample
size which will shorten the distance to the limit
for the ln odds ratio to 0.55
– the answer 491 suggests that we study 500 women
per group which would result in expected 95% limits
of 0.29 and 0.86 on an observed odds ratio of 0.5
• In additional columns you can assess the
expected confidence interval width for other
possible preterm rates for the control group
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Step 2 Graph
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Justification Statement
• Sample Size for confidence interval for odds ratio
• nQuery Advisor® provides tables, plots, and
standardized sample size justification statements which
can be printed directly or copied into your protocol
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Survival Example
• Sample size required
– 90% power for a comparison of two year survival after
surgery for a brain tumour
– patients treated with a new combination of
chemotherapy and radiation versus those treated with
standard methods
• The study design calls for randomization to one
of two parallel groups
– primary outcome is time to death due to any cause.
– Accrual occurs uniformly over the two year study, with
no losses to follow up expected.
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Survival Analysis
• log-rank test is planned
– two-sided 5% significance level.
In previous studies with the standard
method about 2/3 of patients survived six
months and 20% survived one year following
surgery.
The new therapy would be considered markedly
better if it increased six months survival by about
15%
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Step 1
• Select File ... New, and in the Study Goal and
Design Box, select Survival, Two Groups, and
Test.
• Select Log-rank test, user specified survival
rates, accrual, dropouts simulation.
• Fill in the desired significance level and the
number of periods for which survival, accrual,
and dropout parameters will be specified
• Select Compute effect size from the
Assistants menu or click on the button marked
/δ\ .
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Step 1 Graph
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Step 2
• Enter end of period times, accrual
percentages, hazard rates or proportion
expected to survive to the end of the
period, and exponential dropout rates for
each period.
• Use Edit Row Names to label the rows
and click on Plot.
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Step 2 Graph
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Step 3
• Select Plot survival vs time to obtain a
plot of the expected survival curves.
• You may edit either the plot or the sidetable to obtain the desired survival curves.
• When the side table is completed and
saved, return to the main table, specify the
number of simulated experiments, a
random seed for the simulation, and a
preliminary choice of sample size.
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Step 3 Graph
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Summary
Sample size calculations
• Canot be done in SPSS
• SAS and nQuery + a multitude of other
programs
• Java Applets for power & sample size
• http://www.math.uiowa.edu/~rlenth/Power/
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