Estimation of Multiple Response Rates in Phase II Clinical Trials with Missing Observations

Abstract

Responses are often correlated in clinical trials. A patient who is not evaluable for a response may still provide some information to the response through his or her status on other responses. Under the assumption of missing at random, we propose the utilization of a self-consistent estimator. We show that the proposed estimators are more efficient than the conventional estimators by asymptotic relative efficiency and simulation study. An example from a Phase II clinical trial on children with chronic myelogenous leukemia is provided.

Key Words:

• Asymptotic relative efficiency
• EM procedure
• Maximum likelihood estimator
• Mean squared error
• Missing at random
• Self-consistent estimator

Notes

^a Results were obtained by simulation of 10,000 random samples with P _EE  = 0.50, P _EI  = P _IE  = 0.25, the specified p _ij , and the specified sample size.

^b Estimated bias of the proposed estimator for R ₁ = p ₁₁ + p ₁₂.

^c Estimated coverage probability of 90% confidence intervals for R ₁ = p ₁₁ + p ₁₂.

^d The hypothesis test was performed for the null hypothesis H ₀: R ₁ ≤ p ₁₁ + p ₁₂ vs. the alternative hypothesis H ₁: R ₁ > p ₁₁ + p ₁₂. The significance level was computed under the specified p _ij . The power was computed with p ₁₁ increased by , p ₁₂ and p ₂₁ unchanged, and p ₂₂ decreased by .

^e The relative efficiency is defined as the ratio of the MSE of the conventional estimator over that of the proposed estimator for R ₁ = p ₁₁ + p ₁₂. When the sample size is specified as ∞, the relative efficiency is the asymptotic relative efficiency.