Handling Covariates in the Design Rosenberger of Clinical Trials - PowerPoint PPT Presentation

Handling Covariates in Clinical Trials W. F. Handling Covariates in the Design Rosenberger of Clinical Trials I. Introduction Covariates and randomized phase III trials Two approaches for handling William F. Rosenberger covariates II. Two Oleksandr Sverdlov approaches Covariate- adaptive randomization Department of Statistics, George Mason University Model-based approach III. CARA May 31, 2007 Randomiza- tion Logistic regression Survival trials W. F. Rosenberger (GMU) May 31, 2007 1 / 24 Handling Covariates in Clinical Trials

Outline Handling Covariates in Clinical I. Introduction 1 Trials W. F. Covariates and randomized phase III clinical trials Rosenberger Two approaches for handling covariates I. Introduction Covariates and randomized II. Two approaches 2 phase III trials Two approaches Covariate-adaptive randomization for handling covariates The model-based approach II. Two approaches Covariate- III. CARA Randomization (Hu and Rosenberger, 2006, adaptive 3 randomization Model-based Chapter 9 approach Logistic regression III. CARA Randomiza- Survival trials tion Logistic regression Survival trials W. F. Rosenberger (GMU) May 31, 2007 2 / 24 Handling Covariates in Clinical Trials

Randomized phase III clinical trial Handling Covariates Two treatments: A and B in Clinical Trials n patients enter the trial sequentially and must be W. F. Rosenberger randomized immediately to either A or B Randomization sequence: I. Introduction Covariates and randomized phase III trials � 1 , if A ; Two approaches T n = ( T 1 , ..., T n ) ′ , T j = for handling covariates − 1 , if B . II. Two approaches Patients’ covariate vectors: Z 1 , ..., Z M Covariate- adaptive randomization Patients’ responses: Y n = ( Y 1 , ..., Y n ) ′ Model-based approach Statistical model: III. CARA Randomiza- tion Logistic E ( Y n ) = f ( θ | T n , Z 1 , ..., Z M ) regression Survival trials W. F. Rosenberger (GMU) May 31, 2007 3 / 24 Handling Covariates in Clinical Trials

Treatment allocation procedures Handling Complete randomization: Covariates in Clinical φ j +1 = Pr( T j +1 = 1) = 1 / 2 Trials W. F. Rosenberger Restricted randomization: φ j +1 = Pr( T j +1 = 1 | T j ) I. Introduction Covariates and randomized phase III trials Two approaches Permuted block design: B blocks of size m = n / B , where for handling covariates m is even; II. Two φ j +1 = m / 2 − N A | block ( j ) approaches Covariate- m − N block ( j ) adaptive randomization Model-based Efron’s (1971) biased coin design: approach III. CARA  1 / 2 , if N A ( j ) = N B ( j ); Randomiza-  tion φ j +1 = p , if N A ( j ) < N B ( j ); Logistic 1 − p , if N A ( j ) > N B ( j ), regression  Survival trials where p ∈ (1 / 2 , 1]. W. F. Rosenberger (GMU) May 31, 2007 4 / 24 Handling Covariates in Clinical Trials

Philosophies regarding covariates Handling Covariates in Clinical Design based: Use stratified blocks to ensure balance on a Trials few known covariates; use covariate-adaptive W. F. Rosenberger randomization procedures if more than a few: “splitters” (Grizzle). I. Introduction Covariates and randomized Analysis based: Adjust for any covariates that are phase III trials Two approaches imbalanced using regression modeling of post-stratification for handling covariates after the trial: “lumpers” (Grizzle). II. Two approaches Mantel, Whitehead are lumpers; Senn, Crowley, Harrell are Covariate- adaptive splitters. randomization Model-based approach In view of presenter, design should drive analysis; post-hoc III. CARA Randomiza- adjustment should only be done if specified in design tion phase, not based on observed data imbalances. Logistic regression Survival trials W. F. Rosenberger (GMU) May 31, 2007 5 / 24 Handling Covariates in Clinical Trials

Two approaches for handling covariates Handling Covariates Let T n = σ ( T 1 , ..., T n ), Y n = σ ( Y 1 , ..., Y n ), Z n = σ ( Z 1 , ..., Z n ). in Clinical Trials W. F. I. Covariate-adaptive II. Covariate-adjusted Rosenberger randomization response-adaptive I. Introduction (CARA) randomization Covariates and φ n +1 = Pr( T n +1 = 1 |T n , Z n +1 ) φ n +1 = Pr( T n +1 = 1 |T n , Y n , Z n +1 ) randomized phase III trials Two approaches for handling covariates Goal Balance the treatments Target possibly II. Two across covariates unbalanced allocations approaches Covariate- adaptive randomization Why? 1. Increase credibility 1. Allocate more patients Model-based approach of the trial results to the better treatment III. CARA adjusting for covariates Randomiza- tion 2. Balance ⇔ efficiency in 2. Balance � efficiency in Logistic homoscedastic linear models heteroscedastic nonlinear models regression Survival trials W. F. Rosenberger (GMU) May 31, 2007 6 / 24 Handling Covariates in Clinical Trials

Pocock and Simon’s (1975) procedure Handling Z 1 , ..., Z M : discrete covariates, Z i has levels 1 , ..., l i Covariates in Clinical For patient ( n + 1) observe ( z 1 , ..., z M ) Trials W. F. Compute hypothetical imbalances within the levels: Rosenberger D iA ( n ) = ( N iz i A ( n ) + 1) − N iz i B ( n ) , I. Introduction Covariates and D iB ( n ) = N iz i A ( n ) − ( N iz i B ( n ) + 1) . randomized phase III trials Two approaches for handling Compute overall covariate imbalances covariates II. Two M approaches � G k ( n ) = | D ik ( n ) | , k = A , B . Covariate- adaptive randomization i =1 Model-based approach Allocate the patient to treatment A with probability III. CARA Randomiza-  1 / 2 , if G A ( n ) = G B ( n ); tion  Logistic φ n +1 = p , if G A ( n ) < G B ( n ); regression Survival trials 1 − p , if G A ( n ) > G B ( n ).  W. F. Rosenberger (GMU) May 31, 2007 7 / 24 Handling Covariates in Clinical Trials

Handling Taves (1974) was the first to propose a covariate-adaptive Covariates procedure, and Pocock-Simon reduces to Taves when p = 1, in Clinical Trials but the procedure is deterministic. W. F. Rosenberger Taves, now living in a retirement home, still favors his procedure, and does not believe in randomization: I. Introduction Covariates and I hope that the day is not too far distant when we look randomized phase III trials back on the current belief that randomization is essential Two approaches for handling covariates to good clinical trial design and realize that it was... II. Two “credulous idolatry”. (Taves, 2004) approaches Covariate- adaptive randomization Countless simulations have been done on the Pocock-Simon Model-based approach method, but little theoretical work. Most simulations show that III. CARA the method does achieve balance on a large number of Randomiza- covariates. However, the use of covariate-adaptive tion Logistic randomization is not without controversy. The CMPC states regression Survival trials that the procedures should be strongly discouraged. W. F. Rosenberger (GMU) May 31, 2007 8 / 24 Handling Covariates in Clinical Trials

Atkinson’s D − (or D A − ) optimal approach Handling After n allocations one has Covariates in Clinical Trials M n = diag { Z ′ A W A Z A , Z ′ B W B Z B } , W. F. Rosenberger where Z k is n k × p , and W k = diag { p k ( z i ) q k ( z i ) } . I. Introduction Let Z n +1 = z n +1 . Then Covariates and � det M n (1 + z ′ randomized phase III trials n +1 ( Z ′ A W A Z A ) − 1 z n +1 p A q A ) , if A ; Two approaches det M n +1 = for handling n +1 ( Z ′ det M n (1 + z ′ B W B Z B ) − 1 z n +1 p B q B ) , if B . covariates II. Two approaches Choose the treatment with the maximum value of Covariate- adaptive randomization d ( k , θ , z n +1 ) = 1 + z ′ n +1 ( Z ′ k W k Z k ) − 1 z n +1 p k q k Model-based approach III. CARA Randomized version: Randomiza- tion d ( A , z n +1 ) Logistic φ n +1 = regression � B k = A d ( k , z n +1 ) Survival trials W. F. Rosenberger (GMU) May 31, 2007 9 / 24 Handling Covariates in Clinical Trials