Comparing Two Exponential Distributions Using the Exact Likelihood Ratio Test

Designing historical control studies with survival endpoints using exact statistical inference

Historical control trials compare an experimental treatment with a previously conducted control treatment. By assigning all recruited samples to the experimental arm, historical control trials can better identify promising treatments in early phase trials compared with randomized control trials. Existing designs of historical control trials with survival endpoints are based on asymptotic normal distribution. However, it remains unclear whether the asymptotic distribution of the test statistic is close enough to the true distribution given relatively small sample sizes in early phase trials. In this article, we address this question by introducing an exact design approach for exponentially distributed survival endpoints, and compare it with an asymptotic design in both real examples and simulation examples. Simulation results show that the asymptotic test could lead to bias in the sample size estimation. We conclude the proposed exact design should be used in the design of historical control trials.

Randomized phase II trial of fulvestrant alone or in combination with bortezomib in hormone receptor-positive metastatic breast cancer resistant to aromatase inhibitors: a New York Cancer Consortium trial

The proteasome inhibitor bortezomib enhances the effect of the selective estrogen receptor (ER) downregulator (SERD) fulvestrant by causing accumulation of cytoplasmic ER aggregates in preclinical models. The purpose of this trial was to determine whether bortezomib enhanced the effectiveness of fulvestrant. One hundred eighteen postmenopausal women with ER-positive metastatic breast cancer resistant to aromatase inhibitors (AIs) were randomized to fulvestrant alone (Arm A-500 mg intramuscular (i.m.) day -14, 1, 15 in cycle 1, and day 1 of additional cycles) or in combination with bortezomib (Arm B-1.6 mg/m² intravenous (i.v.) on days 1, 8, 15 of each cycle). The study was powered to show an improvement in median progression-free survival (PFS) from 5.4 to 9.0 months and compare PFS rates at 6 and 12 months (α=0.10, β=0.10). Patients with progression on fulvestrant could cross over to the combination (arm C). Although there was no difference in median PFS (2.7 months in both arms), the hazard ratio for PFS in Arm B versus Arm A (referent) was 0.73 (95% confidence interval (CI)=0.49, 1.09, P=0.06, 1-sided log-rank test, significant at the prespecified 1-sided 0.10 α level). At 12 months, the PFS proportion in Arm A and Arm B was 13.6% and 28.1% (P=0.03, 1-sided χ²-test; 95% CI for difference (14.5%)=-0.06, 29.1%). Of 27 patients on arm A who crossed over to the combination (arm C), 5 (18%) were progression-free for at least 24 weeks. Bortezomib likely enhances the effectiveness of fulvestrant in AI-resistant, ER-positive metastatic breast cancer by reducing acquired resistance, supporting additional evaluation of proteasome inhibitors in combination with SERDs.

Testing violations of the exponential assumption in cancer clinical trials with survival endpoints

Personalized cancer therapy requires clinical trials with smaller sample sizes compared to trials involving unselected populations that have not been divided into biomarker subgroups. The use of exponential survival modeling for survival endpoints has the potential of gaining 35% efficiency or saving 28% required sample size (Miller, 1983), making personalized therapy trials more feasible. However, the use of exponential survival has not been fully accepted in cancer research practice due to uncertainty about whether or not the exponential assumption holds. We propose a test for identifying violations of the exponential assumption using a reduced piecewise exponential approach. Compared with an alternative goodness-of-fit test, which suffers from inflation of type I error rate under various censoring mechanisms, the proposed test maintains the correct type I error rate. We conduct power analysis using simulated data based on different types of cancer survival distribution in the SEER registry database, and demonstrate the implementation of this approach in existing cancer clinical trials.

Improved survival modeling in cancer research using a reduced piecewise exponential approach

Statistical models for survival data are typically nonparametric, for example, the Kaplan-Meier curve. Parametric survival modeling, such as exponential modeling, however, can reveal additional insights and be more efficient than nonparametric alternatives. A major constraint of the existing exponential models is the lack of flexibility due to distribution assumptions. A flexible and parsimonious piecewise exponential model is presented to best use the exponential models for arbitrary survival data. This model identifies shifts in the failure rate over time based on an exact likelihood ratio test, a backward elimination procedure, and an optional presumed order restriction on the hazard rate. Such modeling provides a descriptive tool in understanding the patient survival in addition to the Kaplan-Meier curve. This approach is compared with alternative survival models in simulation examples and illustrated in clinical studies.

Comparative effectiveness research in cancer genomics and precision medicine: current landscape and future prospects

A major promise of genomic research is information that can transform health care and public health through earlier diagnosis, more effective prevention and treatment of disease, and avoidance of drug side effects. Although there is interest in the early adoption of emerging genomic applications in cancer prevention and treatment, there are substantial evidence gaps that are further compounded by the difficulties of designing adequately powered studies to generate this evidence, thus limiting the uptake of these tools into clinical practice. Comparative effectiveness research (CER) is intended to generate evidence on the "real-world" effectiveness compared with existing standards of care so informed decisions can be made to improve health care. Capitalizing on funding opportunities from the American Recovery and Reinvestment Act of 2009, the National Cancer Institute funded seven research teams to conduct CER in genomic and precision medicine and sponsored a workshop on CER on May 30, 2012, in Bethesda, Maryland. This report highlights research findings from those research teams, challenges to conducting CER, the barriers to implementation in clinical practice, and research priorities and opportunities in CER in genomic and precision medicine. Workshop participants strongly emphasized the need for conducting CER for promising molecularly targeted therapies, developing and supporting an integrated clinical network for open-access resources, supporting bioinformatics and computer science research, providing training and education programs in CER, and conducting research in economic and decision modeling.