By: Paul Shragg, Systems Manager
General Clinical Research Center
UCSD

What is the GCRC?

• Research Resource
• Funded by NCRR of NIH
• 10 Bed Inpatient Unit (Medical Center)
• Outpatient Facility (Campus)
• Specialized Core Lab
• Common and Special Purpose Assays
• Metabolic Kitchen (Research Dietitians)
• Specialized Research Nurses
• Bioinformatics Core
• Biostatistician
• Data Services Lab (Computer Systems Mgr.)
• Scientific Advisory Committee
• Reviews Protocols
• Allocates Resources
• Web Page
• http://gcrc.ucsd.edu
• Program Directors
• Jerold Olefsky, M.D.
• Michael Ziegler, M.D.

Data Services Lab GCRC File Server

• Located at UCSD Medical Center 9 east room 911
• 4 workstations connected to network file servers, printers, and scanners
• Word Processing
• MS Word
• Word Perfect
• Statistical Packages
• SAS
• BMDP
• SPSS
• PC!info
• Power Analysis Software
• nQuery 2.0
• Graphics Software
• Power Point
• Harvard Graphics
• SlideWrite
• Data Reduction/Visualization
• Teleform (Forms oriented data entry)

Statistical Power Analysis (Objectives)

• Overview Statistical Power Analysis
• Provide Detailed Example
• 2 Group Independent Samples t-test
• Demonstrate nQuery 2.0
• Unique Features

Some Terms

• Alpha (α) = Probability of falsely rejecting a true null hypothesis
• Beta (β) = Probability of falsely accepting a false null hypothesis
• Sample size (n) = Size of sample
• Effect Size (ES) = Serves as an index of the degree of departure from the null hypothesis (Cohen; Statistical Power Analysis for SS)

Types of Error

• When hypothesis testing there are two types of statistical error a researcher might make
• Type I
• Falsely rejecting a true null hypothesis
• Alpha (α) = .05, .01
• Considered most important type of statistical error
• Type II
• Falsely accepting a false null hypothesis
• Beta (β) = .20, .10

What is Power?

• The power of a statistical test is the probability that the test will yield statistically significant results (1 - ?)

• the particular alternative hypothesis that is assumed to be true if the null is false
• the value of alpha (α) chosen by the experimenter
• sample size
• the variability of the population under study

Types of Power Analysis

• 4 types of power analysis
• ? as a function of n, power, and effect size
• effect size as a function of ?, n, and power
• n as a function of ?, power, and effect size *
• power as a function of n, ?, and effect size *

? as a function of n, power, and ES

• Least common type of power analysis
• What significance level must I use to detect a given ES with specified power for a fixed given n?

ES as a function of ?, n, and power

• Not very common
• Here, one finds the effect size one can expect to detect for a given ?, n, and with a specified power (detectable ES)
• May be conventionalized for comparisons of research results as in literature surveys

Power as a function of ?, ES, and n

• Very common
• Can be performed on completed studies to determine the power which a given statistical test had
• May be used as part of research planning
• Researcher may decide to change design specifications to increase power (e.g. He/she may decide to increase ES specifications)

Sample size(n) as a function of ES, ?, and power

• Most Common
• Must be at the core of any rational basis for deciding on the sample size to be used in an investigation
• If power is .80, and ? = .05, what sample size is required to reach statistical significance given a specific (specified) ES

Determining appropriate sample size

• Crucial part of study design
• We must choose sample size correctly to allow a study to arrive at valid conclusions
• A study which is too small may produce inconclusive results
• A study which is too large will waste scarce resources

What sample size do I need?

• Requires six steps using nQuery
1. Formulate the study
2. Specify parameters for planned analysis
3. Specify ES for test
4. Compute sample size / power
5. Sensitivity Analysis
6. Choose sample size, write statement

Formulate the study

• Propose study question
• Detail study design
• e.g. 2 group, randomized, double blind.
• Be specific
• Choose outcome measure
• e.g. Mean change, correlation coef., proportion
• Specify the analysis method

Specify parameters for planned analysis

• Will differ depending on proposed statistical methodology and outcome measures

• Often times will include:
1. Significance level of test (?)
2. Whether the procedure is to be one or two sided

Specify ES for a test

• Often the hardest part of study planning
• Will differ depending on type of analysis planned and outcome measure
• Often times a pilot study should be run first
• Often times one may find reasonable ES values in the literature (previous research)
• What might be an important effect of treatment (What’s clinically important?)

Compute sample size or power

• If computing sample size, specify power, in addition to previously entered values of ? and ES
• If computing power, specify sample size, in addition to previously entered values of ? and ES

Sensitivity Analysis

• Allows one to assess variability in required sample size, power, interval width, for a range of plausible parameter values

Choose sample size, write statement

• nQuery will write up the sample size statement for you for any chosen column of an nQuery sample size / power table

Our Example

• Study question
• Does a new drug reduce anemia in elderly women after hip fracture?
• Study design
• A two group, randomized, parallel, double blind study is planned. Patients will be randomly assigned to receive either new drug or placebo 3 times per week. The sample sizes in the two groups will be equal.
• Outcome measure
• The primary outcome measure will be the mean change in hematocrit level from pre-treatment to post treatment.
• Specify the analysis method
• The mean change in hematocrit level will be compared between the two groups of patients using the two-sample, independent groups, t-test (2 sided, ?=.05).