Analysis of Continuous Longitudinal Data with ARMA(1, 1) and Antedependence Correlation Structures

Longitudinal or repeated measure data are common in biomedical and clinical trials. These data are often collected on individuals at scheduled times resulting in dependent responses. Inference methods for studying the behavior of responses over time as well as methods to study the association with certain risk factors or covariates taking into account the dependencies are of great importance. In this research we focus our study on the analysis of continuous longitudinal data. To model the dependencies of the responses over time, we consider appropriate correlation structures generated by the stationary and non-stationary time-series models. We develop new estimation procedures depending on the correlation structures considered and compare those procedures with the existing methods. The first part of this dissertation focuses on the robust correlation structure generated by the first-order autoregressive-moving average (ARMA(1, 1)) stationary time-series model. ARMA(1, 1) correlation structure is characterized by two correlation parameters and this correlation structure reduces to the AR(1), MA(1) and CS structures in special cases. Although standard efficient procedures are preferable to estimate the correlation parameters, there are computational challenges in implementing them. To overcome these challenges we employ an alternative estimation procedure based on pairwise likelihoods. A typical advantage of this approach is that the inference procedure does not involve complex computations and it results in a closed form expressions for the estimators of the correlation parameters. We show that the estimates obtained using the pairwise likelihood method for ARMA(1, 1) correlation structure are highly efficient asymptotically when compared to that of maximum likelihood. The second part of the dissertation studies correlation structures generated by non-stationary time-series model known as antedependence models of first order. These correlation structures are capable of modeling the non-constant correlations between the same-lagged observations. Note that while this correlation structure has been extensively studied in the case of heterogeneous variance, we model homogenous variance and use a recent and new method known as quasi-least squares to estimate the correlation parameters. A major advantage of the quasi-least squares method is that it yields closed form expressions for the estimators of correlation parameters unlike the maximum likelihood method. We provide the asymptotic and small-sample properties of these estimators and compare their performance using relative efficiencies

FDA Approval Summary: Nivolumab for the Treatment of Metastatic Non‐Small Cell Lung Cancer With Progression On or After Platinum‐Based Chemotherapy

On October 9, 2015, the U.S. Food and Drug Administration expanded the nivolumab metastatic non-small cell lung cancer (NSCLC) indication to include patients with nonsquamous NSCLC after a 3.25-month review timeline. Approval was based on demonstration of an improvement in overall survival (OS) in an international, multicenter, open-label, randomized trial comparing nivolumab to docetaxel in patients with metastatic nonsquamous NSCLC with progression on or after platinum-based chemotherapy. The CheckMate 057 trial enrolled 582 patients who were randomized (1:1) to receive nivolumab or docetaxel. Nivolumab demonstrated improved OS compared with docetaxel at the prespecified interim analysis with a hazard ratio (HR) of 0.73 (p = .0015), and a median OS of 12.2 months (95% CI: 9.7–15.0 months) in patients treated with nivolumab compared with 9.4 months (95% CI: 8.0–10.7 months) in patients treated with docetaxel. A statistically significant improvement in objective response rate (ORR) was also observed, with an ORR of 19% (95% CI: 15%–24%) in the nivolumab arm and 12% (95% CI: 9%–17%) in the docetaxel arm. The median duration of response was 17 months in the nivolumab arm and 6 months in the docetaxel arm. Progression-free survival was not statistically different between arms. A prespecified retrospective subgroup analysis suggested that patients with programmed cell death ligand 1-negative tumors treated with nivolumab had similar OS to those treated with docetaxel. The toxicity profile of nivolumab was consistent with the known immune-mediated adverse event profile except for 1 case of grade 5 limbic encephalitis, which led to a postmarketing requirement study to better characterize immune-mediated encephalitis. IMPLICATIONS FOR PRACTICE: Based on the results from the CheckMate 057 clinical trial, nivolumab represents a new treatment option for patients requiring second-line treatment for metastatic non-small cell lung cancer. The role of nivolumab in patients with sensitizing epidermal growth factor receptor (EGFR) and anaplastic lymphoma kinase (ALK) alterations is less clear. Until dedicated studies are performed to better characterize the role and sequence of programmed cell death 1 (PD-1) therapy, patients with EGFR or ALK alterations should have progressed on appropriate targeted therapy before initiating PD-1 inhibitor therapy. Some patients whose tumors lack programmed cell death ligand 1 (PD-L1) expression also appear to have durable responses. The U.S. Food and Drug Administration granted approval to Dako’s PD-L1 test, PD-L1 IHC 28-8 pharmDx, which the applicant claimed as a nonessential complementary diagnostic for nivolumab use