A Simple Approach For Incorporating Multiple Toxicity Thresholds In Phase I Trials

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1 A Simple Approach For Incorporating Multiple Toxicity Thresholds In Phase I Trials Jieling Miao and Shing M. Lee Columbia University, Department of Biostatistics May 20, 2015 Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

Lee Columbia University, Department of Biostatistics May 20,

2 Phase I trials Phase I clinical trials Toxicity Typically small studies Evaluate safety and identify a dose for further study Grades (from 0 to 5) for severity of adverse events (AE) provided by National Cancer Institute Common Terology Criteria for Adverse Events (NCI CTCAE) Dose-limiting Toxicity (DLT) Usually summarize toxicity into a binary DLT outcome In most phase I cancer clinical trials, a DLT is defined as a grade 3 or higher toxicity according to the NCI CTCAE Maximum Tolerated Dose (MTD) The dose associated with a pre-specified probability (θ) of DLT MTD is defined as the dose level whose toxicity probability is closest to θ. Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

outcome In most phase I cancer clinical trials, a DLT is defined as a grade 3 or higher toxicity according to the NCI CTCAE Maximum Tolerated Dose (MTD) The dose associated with

3 Multiple toxicity gradations Multiple toxicity gradations DLT does not take into account toxicity gradations However, sometimes interested in various gradations of toxicity Consider an example: Phase I trial in lymphoma patients treated with bortezomib plus the standard CHOP-Rituximab regimen. Grade 3 neuropathy is symptomatic toxicity interfering with activities of daily life, resolved by treatment VS. Grade 4 neuropathy is life threatening or disabling and hence irreversible. Wish to specify different thresholds θ 3 is the target toxicity probability for Y 3 θ 4 is the target toxicity probability for Y 4 Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

Grade 3 neuropathy is symptomatic toxicity interfering with activities of daily life, resolved by treatment VS.

4 CRM Continual Reassessment Method (CRM) for binary outcome Model-based method for dose finding Start with an assumed dose toxicity curve and a chosen target toxicity rate After observing a patient s toxicity outcome, dose toxicity curve re-fit and model parameter(s) re-estimated, using Bayesian or maximum likelihood methods Next person assigned dose with estimated toxicity probability closest to the target rate Repeat until a specific sample size is met Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

parameter(s) re-estimated, using Bayesian or maximum likelihood methods Next person assigned dose with estimated toxicity

5 CRM Design parameters to be specified for CRM target DLT probability θ for Y 3 number of doses/dose levels prior MTD sample size dose toxicity model F (, β) prior distribution for model parameters β skeleton - initial guess of toxicity probabilities for each dose, which provides rescaled dose levels by backward substitution Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

parameters β skeleton - initial guess of toxicity probabilities for each dose, which provides

6 Existing methods Method1: Bayesian CRM with multiple toxicity constraints Lee SM, Cheng B, Cheung YK Biostatistics 2010 paper Method2: Likelihood CRM with multiple toxicity constraints Cheng B, Lee SM Journal of Statistical Planning and Inference 2015 paper Other methods: Model as an Ordinal Outcome (0-5) using, for example, a Proportional Odds Model 2 stage design with lower grades Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

Statistical Planning and Inference 2015 paper Other methods: Model as an Ordinal Outcome (0-5) using, for

7 Proposed methods Approach Two chosen target toxicity rates (θ 3, θ 4 ) After getting the toxicity data, create two binary outcomes based on the two thresholds (Y 3, Y 4). Use two CRMs independently to find the recommended dose levels based on each threshold. That is x 3 = arg F 3 (x, ˆβ 3 ) θ 3 x x 4 = arg F 4 (x, ˆβ 4 ) θ 4 x where x is the dose level and F 3 (, ˆβ 3 ) and F 4 (, ˆβ 4 ) are models for the two toxicity outcomes MIN: assign dose of {x 3, x 4 } to the next patients Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

That is x 3 = arg F 3 (x, ˆβ 3 ) θ 3 x x 4 = arg F 4 (x, ˆβ 4 ) θ 4 x where x is the dose level and F 3 (, ˆβ 3 ) and F 4 (, ˆβ 4 ) are

8 Design parameters for simulation study Applied to the bortezomib lymphoma trial Target toxicity probability θ 3 = 0.25, θ 4 = 0.10 Dose levels K = 5 Prior MTD = 3 Sample size = 18 Dose toxicity models: F 3 (d, β 3 ) = d exp(β 3), F 4 (d, β 4 ) = d exp(β 4) Skeleton: optimal pair (δ 3, δ 4 ) = (0.08, 0.05), using similar approach by Lee and Cheung (2009) to get the optimal δ. Grid search for optimal (δ 3, δ 4 ) pair Proportion of correct selection (PCS) δ 3= δ 4 Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

optimal pair (δ 3, δ 4 ) = (0.08, 0.05), using similar approach by Lee and Cheung (2009) to get the optimal δ.

9 Results Comparison of proposed method (MIN) to CRM, MCB, MCL Dose P(Y 3) P(Y 4) MTD3 and MTD4 match at dose 3 Dose P(Y 3) P(Y 4) MTD3 and MTD4 match at dose Proportion of Recommendation Proportion of Recommendation Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

04 3 0.25 0.10 3 0.08 0.02 2 0.05 0.01 2 0.05 0.01 1 0.05 0.01 1 0.05 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.

10 Results Comparison of proposed method (MIN) to CRM, MCB, MCL Dose P(Y 3) P(Y 4) MTD3 at dose 3; MTD4 at dose 4 Dose P(Y 3) P(Y 4) MTD3 at dose 3; MTD4 at dose Proportion of Recommendation Proportion of Recommendation Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

45 0.35 3 0.25 0.05 3 0.25 0.23 2 0.05 0.01 2 0.16 0.10 1 0.05 0.00 1 0.05 0.01 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Proportion of Recommendation 0.

11 Conclusions When MTD3 > MTD4, CRM fails to choose the right dose, since it does not take into account the secondary constraint. MIN, MCB, and MCL perform equally well except when the target dose is the highest level. MIN is simple and can be easily implemented, using existing df R package Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

MIN, MCB, and MCL perform equally well except when the target dose is the highest level.

12 References O Quigley J, Pepe M, Fisher L. Continual reassessment method: a practical design for phase 1 clinical trials in cancer. Biometrics Mar; 46(1): Lee SM, Cheung YK. Model calibration in the continual reassessment method. Clin Trials Jun;6(3): Lee SM, Cheng B, Cheung YK. Continual reassessment method with multiple toxicity constraints. Biostatistics Apr;12(2): Cheng B, Lee SM. On the consistency of the continual reassessment method with multiple toxicity. Journal of Statistical Planning and Inference. Available online 14 March Cheung YK. df: Dose-finding by the continual reassessment method. R package version Cheung YK. Dose finding by the continual reassessment method. Chapman and Hall/CRC Biostatistics Series Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

2011 Apr;12(2):386-98. Cheng B, Lee SM. On the consistency of the continual reassessment method with multiple toxicity. Journal of Statistical Planning and Inference. Available online 14 March 2015.

13 Acknowledgments Shing M Lee Jimmy K Duong Bin Cheng Ken YK Cheung Dose finding working group at Columbia University, Department of Biostatistics Jieling Miao (Columbia University) Simple CRM-MC May 20, / 13

University, Department of Biostatistics Jieling Miao

Specification of the Bayesian CRM: Model and Sample Size. Ken Cheung Department of Biostatistics, Columbia University

Specification of the Bayesian CRM: Model and Sample Size Ken Cheung Department of Biostatistics, Columbia University Phase I Dose Finding Consider a set of K doses with labels d 1, d 2,, d K Study objective: