Jenny Zheng, Michael Amantea
Pfizer Inc, San Diego, CA
Objectives: The ER relationship for oncology drug is often examined using the Cox model under an assumed linear relationship between log hazard and drug exposure. When data from control (C) and experimental (E) arms are used and patient’s exposure is assigned a 0 in C, a false ER relationship driven by the efficacy difference between E and C may be developed even the true ER relationship is flat. The simulations evaluated 1) the rate of a false ER relationship, 2) how to identify a false ER relationship, 3) two sensitivity analyses, and 4) the bias on effect estimates.
Methods: Simulations assumed an exponential distribution for event time and a log-normal distribution for exposures. Two scenarios were simulated: 1) a treatment effect is present but ER relationship is flat, or 2) the treatment effect is a linear function of drug exposure. The simulated event times and the status under various sample sizes and treatment effects were fitted using a Cox model. An ER relationship was considered significant if the p value for the coefficient of exposure was < 0.05 and the estimated HR was less than 1.
Results: In scenario 1, N=80, the rate of obtaining a false ER relationship was 18.9%, 45.1%, 74.4%, and 92.0%, when hazard ratios (HR) were 0.8, 0.7, 0.6, and 0.5, respectively. The rate of a false ER relationship was reduced to < 5% by the sensitivity analyses. An upward trend between martingale residual and exposure was observed when an ER relationship was false. A larger sample size resulted in a higher rate of a false ER relationship. In scenario 2, N=80, the power of deriving an ER relationship was 49.9%, 92.8%, 99.8%, and 100%, respectively, when HRs at the median concentration of E to C (HRMC) were 0.76, 0.56, 0.44, and 0.33; sensitivity analyses reduced the power of deriving an ER relationship to 15.1%, 35.1%, 61.5%, and 79.3%, respectively. When N=250, applying the sensitivity analyses, the power of deriving an ER relationship was 26.2%, 77.5%, 96.0%, and 99.4%, respectively, when HRMC were 0.76, 0.56, 0.44, and 0.33. The corresponding bias was 9.5%, 2.8%, 0.6%, and 1.0%.
Conclusions: The power of characterizing an ER relationship is reasonable when a hazard ratio was < 0.56. However, the rate of having a false ER relationship was high. Sensitivity analyses can effectively reduce the rate of a false ER relationship but also the power of charactering an ER relationship. In addition to p values, diagnostic plot and sensitivity analyses are needed for model assessment in ER analysis.
Reference: PAGE 24 (2015) Abstr 3646 [www.page-meeting.org/?abstract=3646]
Poster: Methodology - Model Evaluation