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## PowerPoint Slideshow about ' Sample Size and Power' - kuper

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### Supplementary slides

The Secret of Long Life

- Resveratrol
- In the skin of red grapes
- Makes mice
- Run faster
- Live longer

What I want to show

- Consuming reservatrol prolongs healthy life

Sample Size Ingredients

- Testable hypothesis
- Type of study
- Statistical test
- Type of variables
- Effect size (and its variance)
- Power and alpha

My research question

- I need to plan the study
- My question is

Does consuming reservatrol

lead to a long and healthy life?

What’s wrong with the question?

- I need to plan the study
- My question is

Does consuming reservatrol

lead to a long and healthy life?

What’s wrong with the question?

Does consuming reservatrol

lead to a long and healthy life?

- Vague
- Must be measurable

Consuming resveratrol

- Most rigorous design: randomized placebo-controlled trial
- Comparing red wine to placebo would be difficult
- Resveratrol supplements available and widely used

Measurable (specific)

- Consuming resevertrol = taking resveratrol supplements vs. taking placebo
- Prolong healthy life = reduces all-cause mortality

Do people randomized to get a resveratrol supplement have a lower mortality rate than those who get a placebo?

In whom?

Do people randomized to get a resveratrol supplement have a lower mortality rate than those who get a placebo?

- Must study a sample from the larger ‘target population’
- What is the target population?

In whom?

- Elderly men and women (≥70 years)

The research hypothesisThe ‘alternative’ hypothesis

Men and women > age 70 years randomized to get a resveratrol supplement have a lower mortality rate than those who get a placebo.

- Cannot be tested statistically
- Statistical tests can only reject null hypothesis - that there is no effect

The Null Hypothesis

Men and women > age 70 years randomized to receive a resveratrol supplement do not have lower mortality rate than those who receive placebo.

- Can be rejected by statistical tests

Ingredients for Sample Size

Testable hypothesis

- Type of study
- Statistical test
- Type of variables
- Effect size (and its variance)
- Power and alpha

Type of study

- Descriptive
- Only one variable / measurements
- What proportion of centenarians take resveratrol supplements?
- Confidence interval for proportions
- What is the mean red wine intake of centenarians?
- Confidence interval for the mean

Sample size for a descriptive study

- “What proportion of centenarians take resveratrol supplements?”
- How much precision do you want?
- Sample size is based on the width of the confidence interval (Table 6D and 6E)
- For example, assume that 20% of centenarians take resveratrol
- I want to be confident that the truth is within ±10%

Type of study

- Analytical: comparison
- Cross-sectional
- Mean red wine intake in centenarians vs. 60-80 years old
- Randomized trial
- Elders who get resveratrol have lower mortality than those who get placebo

Ingredients for Sample Size

Testable hypothesis

Type of study: analytical (RCT)

- Statistical test
- Type of variables
- Effect size (and its variance)
- Power and alpha

Types of variables?

- Dichotomous
- Treatment or placebo
- Continuous
- Walking speed

The types of variables?

Men and women > age 70 years randomized to receive a resveratrol supplement do not have lower mortality rate than those who receive placebo

- Dichotomous: reseveratrol or placebo
- Dichotomous: mortality rate
- 3-4% per year*; 3 year study: 10%
- Statistical test: Chi-squaree (Tables 6B)

* ~ mean annual male @ 78 yrs

Ingredients for Sample Size

Testable hypothesis

Type of study: analytical (RCT)

Statistical test

Type of variables

- Effect size (and its variance)
- Power and alpha

Effect sizethe hardest part

Considerations

- What is likely, based on other data?
- Pilot study
- Estimates from biomarkers
- What difference is important to detect?
- “We don’t want to miss a ____ difference”
- What can we afford to find?

The effect of resveratrol on mortality rate?

- What is likely, based on other data?
- Pilot study
- Estimates from biomarkers
- What difference is important to detect?
- “We don’t want to miss a _1%_ difference”
- What can we afford?
- 1%: too expensive; 5%: cheap

* ~ mean annual male @ 78 yrs

The effect of resveratrol on mortality rate?

- Finding a smaller effect is important to health
- Power to find a larger effect is important for your budget
- Too small! vs. too large!

The Science of Effect SizesToo large! Too small!Just right.

- Smaller effect is important to health
- Larger effect is important for your budget

Effect size

Men and women > age 70 years randomized to receive a resveratrol supplement do not have lower mortality rate than those who receive placebo

- Placebo rate: 10%
- Resveratrol rate: 8%
- Chi-squared (Table 6B.2)

* ~ mean annual male @ 78 yrs

Ingredients for Sample Size

Testable hypothesis

Type of study: analytical (RCT)

Statistical test

Type of variables

Effect size (and its variance)

- Power and alpha

I will need to convince people

- The result must be statistically significant

Customarily, P<0.05

AKA

- Probability of a type I error (oops, we lied)
- (alpha) = 0.05

I will need to convince skeptics

- Very small chance that we are fooling you

(alpha) = 0.01

P<0.01

- Smaller means larger sample size

Two-sided vs. one-sided

- Use 2-sided if the result could go the opposite way you want
- 1-sided reduces sample size somewhat
- You may believe that your effect could only go one way!
- Resveratrol could not increase mortality!
- Be humble.
- The history of research is filled with results that contradicted expectations
- A 1-sided test is almost never the best choice

If it’s true, I don’t want to miss it

- The chance of missing the effect ()

customarily 20%

AKA

- Type II error
- (beta): 0.20
- Power = 1- 0.80

I really don’t want to miss it

- = .10
- Power (1- ) = 0.90
- Greater power means larger sample size

We have all of the ingredients

Testable hypothesis

Type of study: analytical (RCT)

Statistical test: Chi-squared

Effect size 10% vs 8%

Power: 0.90; alpha: 0.20

From Table 6B.2

- Sample size: 4,401
- Per group
- Total: 8,802
- Does not include drop-outs
- 20% drop-out: 11,002 total sample size

Alternatives

- Tweak : one-sided
- Almost never appropriate
- Tweak the power: 0.80
- Modest effect: 3,308 (6,616 total)

Alternatives

- Tweak and
- = 0.20
- 3,308/group; 6,616 total
- Also increase the effect size
- 10% vs. 6%

Alternatives

- Tweak and
- = 0.20
- 3,308/group; 6,616 total
- Also increase the effect size
- 10% vs. 6%
- 930 / group; 1,680 total
- Big difference, still not affordable
- Not believable

Alternatives: a new hypothesis

- Change the outcome measure
- Continuous measurement
- A ‘surrogate’ for mortality rate
- Strongly associated with mortality rate
- Likely to be influenced by resveratrol
- Walking speed

Mice on resveratrol

- Mice fed resveratrol
- Live 25% longer
- Are significantly faster
- Have greater endurance

Increased gait speed (0.1 m/s) in 1 year and survival over 8 years

Faster by ≥0.1 m/s

Slower

~20% decreased

mortality rate

What you need to know about a continuous variable

- Outcome: change in walking speed
- Mean value in the population
- Effect size
- Change in walking speed
- Variability in the change

What you need to know about a continuous variable

- Outcome: change in walking speed
- Mean value in the population = 1.0 m/sec
- Effect size
- Change in walking speed
- 1.0 to 1.1 m/sec
- Variability in the change

Variability

- No variability
- Extremely reproducible
- Relatively small sample size
- Highly variable
- Poor reproducibility
- Relatively large sample size
- Assessed by the Standard Deviation

Variability

- Standard deviation for the measurement
- Cross-sectional: 0.25 m / sec
- However, we are interested in change
- Standard deviation of change in speed?

What if you don’t know the SD?

- Standard deviation of change in speed?
- If you cannot find data from other studies for change over 3 years
- Pilot study?
- Well educated guess

Estimating S.D.the 1/4 rule

- Range of changes
- 0.2 m/sec to -0.6 m/sec
- Range = 0.8 m/sec
- 1/4 of the range = 0.2 m/sec

E/S

- Effect size: 0.1 m/sec difference in change
- Standard deviation: 0.2 m/sec
- E/S = 0.5

The new ingredients

New testable hypothesis

Type of study: analytical (RCT)

Statistical test: t-test

- Continuous variable
- Difference between means

Effect size 1.0 vs. 1.1 m/sec; E/S = 0.5

Power: 0.90; alpha: 0.20

The new ingredients

New testable hypothesis

Type of study: analytical (RCT)

T-test

Effect size 1.0 vs.1.1 m/sec; E/S: 0.5

Power: 0.90; alpha: 0.20

Sample size: 64 per group; 128 total

With 20% drop out: 160 total

Summary

- Estimate sample size early
- Systematically collect the ingredients
- Effect size is the most difficult - and important - judgement
- Alternatives that reduce sample size
- Compromise power
- Increase effect size
- Prefer precise continuous outcomes

The effect of increasing the rate of events in the population while maintaining the same effect size

Supplementary slides

- The effect of increasing the rate of events in the population
- Maintaining the same effect size

Alternatives

- Increase the event rate
- Choose an older population with higher mortality
- Enroll men ≥ 80 years old
- 3-year mortality: 25%
- Effect size: 20% reduction: 25% vs. 20%

Alternatives

- Increase the event rate
- Choose an older population with higher mortality
- Enroll men ≥ 80 years old
- 3-year mortality: 25%
- Effect size: 20% reduction: 25% vs. 20%
- 1,133 per group; 2,266 total

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