3. Fixed-sample Clinical Trial Design

Transcription

1 3. Fixed-sample Clinical Trial Design 3. Fixed-sample clinical trial design 3.1 On choosing the sample size 3.2 Frequentist evaluation of a fixed-sample trial 3.3 Bayesian evaluation of a fixed-sample trial 3.4 Case study 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 1

2 Examples (introduced) Pre-specified information (sample size): Inference at the boundary Examples (revisited) Selecting the information (sample size): Hypotheses discriminated (decision-theoretic approach) Statistical power Examples (revisited) 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 2

3 Examples (introduced) Example: Phase II Iloprost Background: A previous phase II chemoprevention trial of 13-cis retinoic acid (vitamin A) did not show effect on lung histology. There was good biological rationale (and lab data) to suggest that iloprost might be effective. A phase II trial was designed to evaluate effects on histology. Study Population: Former or current smokers with > 20 pack years, and sputum atypia. Scientific Hypotheses: Iloprost treatment will result in improved histology relative to placebo. 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 3

4 Examples (introduced) Example: Phase II Iloprost Outcome Parameterization: Outcome (Yik ): Average histology (also maximum histology and dysplasia index) Probability model: Non-parametric: Y i0 F 0 (y); Y i1 F 1 (y) Functional: Mean: E(Yi0 ) = θ 0, E(Y i1 ) = θ 1 Contrast: Difference: θ = θ1 θ Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 4

5 Examples (introduced) Example: Sepsis trial Background: Critically ill patients often get overwhelming bacterial infection (sepsis), after which mortality is high. Gram negative sepsis is often characterized by production of endotoxin which is thought to be the cause of many of the ill effects of gram negative sepsis. Hypothesize that administering an antibody to the endotoxin may decrease morbidity and mortality. Two previous randomized clinical trials showed slight benefit with suggestion of difference in benefit within subgroups. There are no safety concerns (based on previous studies). 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 5

6 Examples (introduced) Example: Sepsis trial Design: Double-blind, placebo controlled RCT. Study Population: Patients entering ICU with newly proven gram-negative sepsis. Scientific Hypotheses: Antibody to the endotoxin will improve survival Outcome Parameterization: Outcome (Y ik ): 28-day mortality Probability model: Bernoulli: Yi0 B(1, p 0 ); Y i1 B(1, p 1 ) Functional: Mean: E(Yi0 ) = p 0 = θ 0, E(Y i1 ) = p 1 = θ 1 Contrast: Difference: θ = θ1 θ Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 6

7 Examples (introduced) Example: Daptomycin Trial Background: Standard therapy for S. aureus bacteremia and endocarditis is not fully successful. Daptomycin is another antibiotic that might also be effective for this condition. Clinical Question: Is daptomycin as successful as standard care in treating S. aureus bacteremia? Study Population: Patients with S. aureus bacteremia Outcome Parameterization: Outcome (Yik ): Success at 42-days after the end of treatment Probability model: Bernoulli: Y i0 B(1, p 0 ); Y i1 B(1, p 1 ) Functional: Mean: E(Y i0 ) = p 0 = θ 0, E(Y i1 ) = p 1 = θ 1 Contrast: Difference: θ = θ1 θ Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 7

8 Examples (introduced) Example: Prostate cancer screening (PLCO) Background: PSA screening for prostate cancer is common, but the tradeoff between risks and benefits is not known. Public Health Question: Should screening for prostate cancer be part of routine practice? Study Population: Men age Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 8

9 Examples (introduced) Example: Prostate cancer screening (PLCO) Outcome Parameterization: Outcome Y ik = (T ik, δ ik ): Time to death from prostate cancer: T ik = time from study entry to end of follow-up δ ik = 1 if died from prostate cancer; 0 otherwise. Probability model: Incidence rate follows Poisson distribution: ˆθ k = and ˆθ N N k T ik P(λ k T ik ). i=1 i=1 N δ ik i=1 N T ik i=1 Functional: Mean rate: θ 0 = λ 0, θ 1 = λ 1 Contrast: Ratio: θ = θ 1 /θ Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21

10 Pre-specified information (sample size): Suppose that the sample size is pre-determined. How should we evaluate the information? 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 10

11 Pre-specified information (sample size): Recall inference upon trial completion: Point estimate Interval estimate P-value Decision Can we examine the potential inference upon trial completion prior to starting the trial? 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 11

12 Pre-specified information (sample size): Inference at the boundary: Critical value: Threshold for declaring that the treatment works. Hypotheses discriminated (interval estimate): What hypothesis will be rejected if the results are significant? What hypothesis will be rejected if the results are not significant? P-value at the boundary? 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 12

13 Example: Phase II Iloprost Sample Size: N = 76 per group Variance: From 13 cis-retinoic acid trial: Observation Retinoic Acid Non-smokers Smokers Non-smokers Smokers Avg. Histol (0.59) 0.19 (0.73) (0.84) (1.22) Worst Histol (1.22) (1.38) (1.32) (1.63) Dysp. Index 0.05 (0.25) 0.08 (0.25) (0.21) (0.27) (Notice: Potential mean-variance relationship.) 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 13

14 Example: Phase II Iloprost Variance: Preliminary variance estimate: S pooled = 1 4 ( ) SE = S pooled + 1 N 0 N 1 2 = = Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 14

15 Example: Phase II Iloprost Potential Inference: Critical value: cv = 1.96 SE = Interval estimate at cv: (0, 0.572) Possible conclusions: If ˆθ cv then reject θ If ˆθ > cv then reject θ 0 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 15

16 Example: Sepsis Trial Sample Size: N = 850 per group Variance: Assume that placebo mortality rate is p 0 = 0.3. S = p(1 p) = SE = S + 1 N 0 N 1 2 = = Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21

17 Example: Sepsis Trial Potential Inference: Critical value: cv = SE = Interval estimate at cv: ( 0.087, 0) Possible conclusions: If ˆθ cv then reject θ If ˆθ < cv then reject θ 0 3. Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 17

18 Example: Daptomycin Trial Sample Size: N = 90 per group Variance: Assume that placebo success rate is p 0 = S = p(1 p) = SE = S + 1 N 0 N 1 2 = = Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21

19 Example: Daptomycin Trial Potential Inference (superiority): Critical value: cv = SE = Interval estimate at cv: (0, 279) Possible conclusions: If ˆθ cv then reject θ If ˆθ > cv then reject θ 0 Potential Inference (non-inferiority): Critical value: cv = 0 Interval estimate at cv: ( 0.139, 0.139) Possible conclusions: If ˆθ cv then reject θ If ˆθ < cv then reject θ Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 19

20 Example: Prostate cancer screening (PLCO) Sample Size: N 38, 350 per group; person-years 250, 000 per group Variance: Assuming prostate cancer death rate 2/10,000 py. Assuming that there will be about 50 deaths per group. ( SE log( θ ) 1 ) θ 0 1 = + 1 θ 0 P 1 θ 0 P 0 1 = = Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 20

21 Example: Prostate cancer screening (PLCO) Potential Inference: Critical value: cv = e = Interval estimate at cv: (e 0.784, e 0 ) = (0.457, 1.0) Possible conclusions: If ˆθ cv then reject θ If ˆθ < cv then reject θ Fixed-Sample Design 3.2 Frequentist evaluation 27 Feb / 21 21