Introduction to Sample Size and Power Tamuno Alfred, PhD - - PowerPoint PPT Presentation

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Introduction to Sample Size and Power Tamuno Alfred, PhD - - PowerPoint PPT Presentation

Mar 27, 2024 267 likes •953 views

DataCamp Designing and Analyzing Clinical Trials in R DESIGNING AND ANALYZING CLINICAL TRIALS IN R Introduction to Sample Size and Power Tamuno Alfred, PhD Biostatistician DataCamp Designing and Analyzing Clinical Trials in R Statistical

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DataCamp Designing and Analyzing Clinical Trials in R

Introduction to Sample Size and Power

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

Statistical inference

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DataCamp Designing and Analyzing Clinical Trials in R

Importance of correct sample size

Costs Study completion time Exposure to experimental drug Patients receiving no treatment Ability to reject null hypothesis

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

Trial purpose (compare weight loss between drug and placebo)

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

Trial purpose (compare weight loss between drug and placebo) Primary endpoint (difference in mean % weight loss)

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

Trial purpose (compare weight loss between drug and placebo) Primary endpoint (difference in mean % weight loss) Statistical analysis of primary endpoint (two-sample t-test)

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

Trial purpose (compare weight loss between drug and placebo) Primary endpoint (difference in mean % weight loss) Statistical analysis of primary endpoint (two-sample t-test) Smallest meaningful difference, δ (3)

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

Trial purpose (compare weight loss between drug and placebo) Primary endpoint (difference in mean % weight loss) Statistical analysis of primary endpoint (two-sample t-test) Smallest meaningful difference, δ (3) Variability (standard deviation=10)

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

Trial purpose (compare weight loss between drug and placebo) Primary endpoint (difference in mean % weight loss) Statistical analysis of primary endpoint (two-sample t-test) Smallest meaningful difference, δ (3) Variability (standard deviation=10) Significance level, α (0.05)

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DataCamp Designing and Analyzing Clinical Trials in R

Requirements

Trial purpose (compare weight loss between drug and placebo) Primary endpoint (difference in mean % weight loss) Statistical analysis of primary endpoint (two-sample t-test) Smallest meaningful difference, δ (3) Variability (standard deviation=10) Significance level, α (0.05) Power to detect treatment effect (80%)

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DataCamp Designing and Analyzing Clinical Trials in R

Hypothesis testing

H0: μ1 = μ2, i.e. no treatment difference

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DataCamp Designing and Analyzing Clinical Trials in R

Two-sample t-test

power.t.test(delta=3, sd=10, power=0.8, type = "two.sample", alternative = "two.sided")

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DataCamp Designing and Analyzing Clinical Trials in R

Relationship between power and sample size

power.t.test(delta=3, sd=10, power=0.9, type = "two.sample", alternative = "two.sided")

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DataCamp Designing and Analyzing Clinical Trials in R

Relationship between power and sample size

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DataCamp Designing and Analyzing Clinical Trials in R

Relationship between treatment difference and sample size

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DataCamp Designing and Analyzing Clinical Trials in R

Test of proportions

power.prop.test(p1=0.3, p2=0.15, power=0.8)

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DataCamp Designing and Analyzing Clinical Trials in R

Let's practice!

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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DataCamp Designing and Analyzing Clinical Trials in R

Sample size adjustments

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

One-sided tests

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DataCamp Designing and Analyzing Clinical Trials in R

One-sided tests

power.t.test(delta=3, sd=10, power=0.8, type = "two.sample", alternative = "two.sided")

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DataCamp Designing and Analyzing Clinical Trials in R

One-sided tests

power.t.test(delta=3, sd=10, power=0.8, type = "two.sample", alternative = "one.sided")

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DataCamp Designing and Analyzing Clinical Trials in R

Unequal group sizes

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DataCamp Designing and Analyzing Clinical Trials in R

Unequal group sizes

library(samplesize) n.ttest(power = 0.8, alpha = 0.05, mean.diff = 3, sd1 = 10, sd2 = 10, k = 0.5, design = "unpaired", fraction = "unbalanced")

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DataCamp Designing and Analyzing Clinical Trials in R

Unequal group sizes

library(samplesize) n.ttest(power = 0.8, alpha = 0.05, mean.diff = 3, sd1 = 10, sd2 = 10, k = 0.5, design = "unpaired", fraction = "unbalanced")

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Unequal variances

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DataCamp Designing and Analyzing Clinical Trials in R

Unequal variances

n.ttest(power = 0.8, alpha = 0.05, mean.diff = 3, sd1 = 9.06, sd2 = 9.06, k = 1, design = "unpaired", fraction = "balanced")

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DataCamp Designing and Analyzing Clinical Trials in R

Unequal variances

n.ttest(power = 0.8, alpha = 0.05, mean.diff = 3, sd1 = 9.06, sd2 = 9.06, k = 1, design = "unpaired", fraction = "balanced")

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Loss to follow-up

Q: anticipated dropout rate Multiply original sample size by

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DataCamp Designing and Analyzing Clinical Trials in R

Loss to follow-up

Q: anticipated dropout rate Multiply original sample size by

  • rig.n <- power.t.test(delta=3, sd=10, power=0.8,

type = "two.sample", alternative = "one.sided")$n

  • rig.n

ceiling(orig.n/(1-0.1))

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DataCamp Designing and Analyzing Clinical Trials in R

Let's practice!

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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DataCamp Designing and Analyzing Clinical Trials in R

Interim analyses and stopping rules

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

Motivation

Patients recruited over time

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DataCamp Designing and Analyzing Clinical Trials in R

Motivation

Patients recruited over time Data accumulated gradually

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DataCamp Designing and Analyzing Clinical Trials in R

Motivation

Patients recruited over time Data accumulated gradually Safety and efficacy can be monitored regularly

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DataCamp Designing and Analyzing Clinical Trials in R

Motivation

Patients recruited over time Data accumulated gradually Safety and efficacy can be monitored regularly Investigators must safeguard patients' interests

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When to stop a trial early

Efficacy

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When to stop a trial early

Efficacy Safety

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When to stop a trial early

Efficacy Safety Futility

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When to stop a trial early

Efficacy Safety Futility Other Cost Inability to recruit enough patients Poor trial design

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Stopping rules

Interim analyses often require increased sample size

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Stopping rules

Interim analyses often require increased sample size Multiple testing increases chance of Type I error

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DataCamp Designing and Analyzing Clinical Trials in R

Stopping rules

Interim analyses often require increased sample size Multiple testing increases chance of Type I error

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DataCamp Designing and Analyzing Clinical Trials in R

Stopping rules

Interim analyses often require increased sample size Multiple testing increases chance of a Type I error Stopping rules use p-values or test- statistics

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Pocock (Fixed Nominal) Rule

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Pocock (Fixed Nominal) Rule

library(gsDesign) Pocock <- gsDesign(k=3, test.type=2, sfu="Pocock") 2*(1-pnorm(Pocock$upper$bound))

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Pocock (Fixed Nominal) Rule

library(gsDesign) Pocock<- gsDesign(k=3, test.type=2, sfu="Pocock") 2*(1-pnorm(Pocock$upper$bound))

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Pocock (Fixed Nominal) Rule

library(gsDesign) Pocock<- gsDesign(k=3, test.type=2, sfu="Pocock") 2*(1-pnorm(Pocock$upper$bound)) Pocock.ss <- gsDesign(k=3, test.type=2, sfu="Pocock", n.fix=200, beta=0.1) ceiling(Pocock.ss$n.I)

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Pocock (Fixed Nominal) Rule

library(gsDesign) Pocock<- gsDesign(k=3, test.type=2, sfu="Pocock") 2*(1-pnorm(Pocock$upper$bound)) Pocock.ss<- gsDesign(k=3, test.type=2, sfu="Pocock", n.fix=200, beta=0.1) ceiling(Pocock.ss$n.I)

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O’Brien-Fleming Rule

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O’Brien-Fleming Rule

OF <- gsDesign(k=3, test.type=2, sfu="OF") 2*(1-pnorm(OF$upper$bound))

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O’Brien-Fleming Rule

OF <- gsDesign(k=3, test.type=2, sfu="OF") 2*(1-pnorm(OF$upper$bound)) OF.ss <- gsDesign(k=3, test.type=2, sfu="OF", n.fix=200, beta=0.1) ceiling(OF.ss$n.I)

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DataCamp Designing and Analyzing Clinical Trials in R

Let's practice!

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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DataCamp Designing and Analyzing Clinical Trials in R

Sample size for alternative trial designs

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

Tamuno Alfred, PhD

Biostatistician

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DataCamp Designing and Analyzing Clinical Trials in R

Equivalence trials

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Equivalence trials: binary outcomes

Response rate in existing drug: 70% Delta: 5% Power: 90% Two one-sided tests (TOST) 90% sure that two-sided 90% CI excludes delta +/-5%

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Equivalence trials: binary outcomes

Response rate in existing drug: 70% Delta: 5% Power: 90% Two one-sided tests (TOST) 90% sure that two-sided 90% CI excludes delta +/-5%

library(TOSTER) powerTOSTtwo.prop(alpha = 0.05, statistical_power = 0.9, prop1 = 0.7, prop2 = 0.7, low_eqbound_prop = -0.05, high_eqbound_prop = 0.05)

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DataCamp Designing and Analyzing Clinical Trials in R

Equivalence trials: binary outcomes

Response rate in existing drug: 70% Delta: 5% Power: 90% Two one-sided tests (TOST) 90% sure that two-sided 90% CI excludes delta +/-5%

library(TOSTER) powerTOSTtwo.prop(alpha = 0.05, statistical_power = 0.9, prop1 = 0.7, prop2 = 0.7, low_eqbound_prop = -0.05, high_eqbound_prop = 0.05)

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Equivalence trials: continuous outcomes

Delta: 3 units Pooled standard deviation: 15 Power: 80% Two one-sided tests (TOST) 80% sure that two-sided 90% CI excludes delta +/-3

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Equivalence trials: continuous outcomes

Delta: 3 units Pooled standard deviation: 15 Power: 80% Two one-sided tests (TOST) 80% sure that two-sided 90% CI excludes delta +/-3

library(TOSTER) powerTOSTtwo.raw(alpha=0.05, statistical_power=0.8, sdpooled=15, low_eqbound=-3,high_eqbound=3)

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Cluster randomized trials

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Cluster randomized trials

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Cluster randomized trials

Delta: 1 unit Pooled standard deviation: 2.5 Average cluster size: 25 Intraclass correlation coefficient (ICC): 0.1 Power: 90%

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Cluster randomized trials

Delta: 1 unit Pooled standard deviation: 2.5 Average cluster size: 25 Intraclass correlation coefficient (ICC): 0.1 Power: 90%

libarary(CRTSize) n4means(delta=1, sigma=2.5, m=25, ICC=0.1, alpha=0.05, power=0.90)

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Factorial designs

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Factorial designs

Assume independence Expected rate in placebo: 40% Expected rate in intervention A: 25% Expected rate in intervention B: 23% Power: 90%

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Factorial designs

power.prop.test(p1=0.40, p2=0.25, power=0.9) power.prop.test(p1=0.40, p2=0.23, power=0.9)

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DataCamp Designing and Analyzing Clinical Trials in R

Let's practice!

DESIGNING AND ANALYZING CLINICAL TRIALS IN R

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