Biostatistics Basics: Part II Leroy R. Thacker, PhD Associate Professor Schools of Nursing and...
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Transcript of Biostatistics Basics: Part II Leroy R. Thacker, PhD Associate Professor Schools of Nursing and...
![Page 1: Biostatistics Basics: Part II Leroy R. Thacker, PhD Associate Professor Schools of Nursing and Medicine.](https://reader035.fdocuments.us/reader035/viewer/2022062301/5697c0131a28abf838ccca02/html5/thumbnails/1.jpg)
Biostatistics Basics: Part IILeroy R. Thacker, PhDAssociate Professor
Schools of Nursing and Medicine
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Outline
• Review of what power is• Components of a power analysis/sample size
calculation• Examples using available software
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Preliminary Thoughts
• First steps of a research study include:– Identifying a measurable/testable hypothesis– Choosing the appropriate study design– Choosing the appropriate set of variables– Conducting a power/sample size study
• Notice that all of these steps would go better/smoother with the assistance of a biostatistician. So consult with your friendly biostatistician early in the study planning process
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Funny Thought/Setting the Tone
“Data! Data! Data! I can’t make bricks without clay” – Sherlock Holmes in The Adventure of the Copper Beeches
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What is Power
Null Hypothesis True State of Nature
Alternative Hypothesis True State of Nature
Fail to reject theNull Hypothesis
Correct Decision(1-α)
True Negative
Type II Error(Denoted by β)
False Negative
Reject theNull Hypothesis
Type I Error(Denoted by α)
(Size of the test)False Positive
Correct Decision(Power = 1 – β)
True Positive
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What is Power?• Statistical power is the 1 – probability(Type II
Error)• What is a Type II error?
– Failing to reject the null hypothesis when it is false
– Assigned probability is β• In simple terms, power is rejecting the null
hypothesis when it is false• Or even more simply, doing what you want to do;
finding a difference/association where there really is one
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Components of a Power Analysis
• Model (test)• Standardized effect size
– Effect size– Variation
• Sample size (n)• Test size (α)• Power (1-β)
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Components of a Power Analysis
• You need to specify a model (test) because the different tests use different formulas and distributions
• How do you select a test?
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Selecting the Proper Test
• With a simple hypothesis, the variable types will determine the test– What is a simple hypothesis?
Linear RegressionCorrelation
t-testANOVA
Logistic Regression Chi-square
Continuous IV Categorical
Continuous
Categorical
DV
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Selecting the Proper Test
• t-test - Two groups, comparing continuous variables between the groups for differences
• ANOVA – Two or more groups, comparing continuous variables between the groups for differences
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Components of a Power Analysis
• The standardized effect size is computed by combining the effect size and the variability
• The effect size is the deviation of the hypothesized value in the alternative hypothesis from that in the null hypothesis
• The variation is actually the standard deviation of the population and comes from previous research or pilot studies; otherwise it needs to be estimated
• Of course you know what sample size, significance level and power are!
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Example #1
• For high risk cardiac patients, daily 50mg eye of newt will produce a reduction in resting systolic BP, measured 7 days post-initiation of treatment, of 20mmHg greater than seen in the placebo group
• What more do we need to do a power analysis/sample size calculation?
• Turning to nQuery
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Example #1
• Pick “New Fixed Term Test”; “Fixed Term”• What is our “Goal”?
– Means, Proportions, Survival, Agreement, Regression
• How many “Groups” do we have?– One, Two or > Two
• For now our Analysis Method is “Test”• What test from the list will we use?
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Example #1
• The investigator wants to have an α = 0.05 size test and a power of 80%
• If the investigator thinks there will be a variability of 100 in the population with regards to SBP; how many patients will he need?
• If the investigator thinks there will be a variability of 400 in the population with regards to SBP; how many patients will he need?
• If the investigator thinks there will be a variability of 10,000 in the population with regards to SBP; how many patients will he need?
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Relationship Among the Components
• As the effect size increases, power….• As the variability increases, power …• As α increases, power…• As n increases, power…
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Example #2
• In pregnant women who exercise, the incidence of back pain is 30%. Using yoga as an alternative form of exercise will reduce the incidence of back pain to 20%.
• The null hypothesis is….• The alternative hypothesis is…• Turning to nQuery
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Example #2
• Pick “New Fixed Term Test”; “Fixed Term”• What is our “Goal”?
– Means, Proportions, Survival, Agreement, Regression
• How many “Groups” do we have?– One, Two or > Two
• For now our Analysis Method is “Test”• What test from the list will we use?
![Page 18: Biostatistics Basics: Part II Leroy R. Thacker, PhD Associate Professor Schools of Nursing and Medicine.](https://reader035.fdocuments.us/reader035/viewer/2022062301/5697c0131a28abf838ccca02/html5/thumbnails/18.jpg)
Example #2
• This problem is set up exactly like Example 6.2 in your text
• But the text gets 313 while we just got (or should have gotten) 294
• Why do you think there is a difference?
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Example #3
• It is know that patients treated with 50mg of daily Eye of Newt have a mean DBP of 86 mmHg. Preliminary studies show that daily 100mg of Toe of Frog will have a mean of DBP of 84mmHg while daily 5mg of Wool of Bat will result in a mean DBP of 82mmHg. If it is assumed that there is a common standard deviation of 10 in the population, how many subjects will be needed to conduct a study at the α = 0.10 level of significance?
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Example #3• Turning to nQuery• Pick “New Fixed Term Test”; “Fixed Term”• What is our “Goal”?
– Means, Proportions, Survival, Agreement, Regression
• How many “Groups” do we have?– One, Two or > Two
• For now our Analysis Method is “Test”• What test from the list will we use?
![Page 21: Biostatistics Basics: Part II Leroy R. Thacker, PhD Associate Professor Schools of Nursing and Medicine.](https://reader035.fdocuments.us/reader035/viewer/2022062301/5697c0131a28abf838ccca02/html5/thumbnails/21.jpg)
Activities
• Scenario 1: An investigator is interested in comparing the impact of several treatments on lymphocyte % The current treatment results in a mean value of 0.80. Preliminary data suggest that Treatment A will result in a mean of 0.82, Treatment B will result in a mean value of 0.83 and Treatment C will result in a mean value of 0.86. It is assumed that the common standard deviation will be 0.1. The investigator wants to conduct this study an α = 0.05 level of significance. How many subject will be needed to conduct the study?
• Scenario 2: An investigator is interested in comparing the impact of different treatment modalities on quality of life in patients undergoing treatment for knee pain. The current treatment results in 80% of subjects reporting an increased quality of life. Preliminary data suggest that Treatment A will result in 82% of patients reporting an increased QOL, Treatment B will also result 83% of subject reporting an increased QOL and Treatment C will result 86% of subjects reporting an increase in QOL. The investigator wants to conduct this study at an α = 0.05 level of significance. How many subject will be needed to conduct the study?
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Activities
• Scenario 3: Discuss among your tablemates your various study ideas for a research project. Decide on one of the studies and perform a sample size calculation.
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Summary• To do a power analysis/sample size calculation
you need to have a testable hypothesis• How you arrive at sample size or power
calculation depends on the type of data, the test used, your effect size, your significance level, your power/your sample size– So do your homework BEFORE you get to
this point• Oh yeah, talk to a biostatistician early!
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Questions?