Biostatistics Basics: Part IILeroy R. Thacker, PhDAssociate Professor

Schools of Nursing and Medicine

Outline

• Review of what power is• Components of a power analysis/sample size

calculation• Examples using available software

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

Funny Thought/Setting the Tone

“Data! Data! Data! I can’t make bricks without clay” – Sherlock Holmes in The Adventure of the Copper Beeches

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

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

Components of a Power Analysis

• Model (test)• Standardized effect size

– Effect size– Variation

• Sample size (n)• Test size (α)• Power (1-β)

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?

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

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

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!

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

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?

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?

Relationship Among the Components

• As the effect size increases, power….• As the variability increases, power …• As α increases, power…• As n increases, power…

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

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?

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?

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?

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?

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?

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.

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!

Questions?