Exploratory subgroup identification in the heterogeneous Cox model: A relatively simple procedure.

For survival analysis applications we propose a novel procedure for identifying subgroups with large treatment effects, with focus on subgroups where treatment is potentially detrimental. The approach, termed forest search, is relatively simple and flexible. All-possible subgroups are screened and selected based on hazard ratio thresholds indicative of harm with assessment according to the standard Cox model. By reversing the role of treatment one can seek to identify substantial benefit. We apply a splitting consistency criteria to identify a subgroup considered "maximally consistent with harm." The type-1 error and power for subgroup identification can be quickly approximated by numerical integration. To aid inference we describe a bootstrap bias-corrected Cox model estimator with variance estimated by a Jacknife approximation. We provide a detailed evaluation of operating characteristics in simulations and compare to virtual twins and generalized random forests where we find the proposal to have favorable performance. In particular, in our simulation setting, we find the proposed approach favorably controls the type-1 error for falsely identifying heterogeneity with higher power and classification accuracy for substantial heterogeneous effects. Two real data applications are provided for publicly available datasets from a clinical trial in oncology, and HIV.

Log-Rank Test vs MaxCombo and Difference in Restricted Mean Survival Time Tests for Comparing Survival Under Nonproportional Hazards in Immuno-oncology Trials: A Systematic Review and Meta-analysis.

Importance: The log-rank test is considered the criterion standard for comparing 2 survival curves in pivotal registrational trials. However, with novel immunotherapies that often violate the proportional hazards assumptions over time, log-rank can lose power and may fail to detect treatment benefit. The MaxCombo test, a combination of weighted log-rank tests, retains power under different types of nonproportional hazards. The difference in restricted mean survival time (dRMST) test is frequently proposed as an alternative to the log-rank under nonproportional hazard scenarios. Objective: To compare the log-rank with the MaxCombo and dRMST in immuno-oncology trials to evaluate their performance in practice. Data Sources: Comprehensive literature review using Google Scholar, PubMed, and other sources for randomized clinical trials published in peer-reviewed journals or presented at major clinical conferences before December 2019 assessing efficacy of anti-programmed cell death protein-1 or anti-programmed death/ligand 1 monoclonal antibodies. Study Selection: Pivotal studies with overall survival or progression-free survival as the primary or key secondary end point with a planned statistical comparison in the protocol. Sixty-three studies on anti-programmed cell death protein-1 or anti-programmed death/ligand 1 monoclonal antibodies used as monotherapy or in combination with other agents in 35 902 patients across multiple solid tumor types were identified. Data Extraction and Synthesis: Statistical comparisons (n = 150) were made between the 3 tests using the analysis populations as defined in the original protocol of each trial. Main Outcomes and Measures: Nominal significance based on a 2-sided .05-level test was used to evaluate concordance. Case studies featuring different types of nonproportional hazards were used to discuss more robust ways of characterizing treatment benefit instead of sole reliance on hazard ratios. Results: In this systematic review and meta-analysis of 63 studies including 35 902 patients, between the log-rank and MaxCombo, 135 of 150 comparisons (90%) were concordant; MaxCombo achieved nominal significance in 15 of 15 discordant cases, while log-rank did not. Several cases appeared to have clinically meaningful benefits that would not have been detected using log-rank. Between the log-rank and dRMST tests, 137 of 150 comparisons (91%) were concordant; log-rank was nominally significant in 5 of 13 cases, while dRMST was significant in 8 of 13. Among all 3 tests, 127 comparisons (85%) were concordant. Conclusions and Relevance: The findings of this review show that MaxCombo may provide a pragmatic alternative to log-rank when departure from proportional hazards is anticipated. Both tests resulted in the same statistical decision in most comparisons. Discordant studies had modest to meaningful improvements in treatment effect. The dRMST test provided no added sensitivity for detecting treatment differences over log-rank.

A unified framework for weighted parametric group sequential design.

Group sequential design (GSD) is widely used in clinical trials in which correlated tests of multiple hypotheses are used. Multiple primary objectives resulting in tests with known correlations include evaluating (1) multiple experimental treatment arms, (2) multiple populations, (3) the combination of multiple arms and multiple populations, or (4) any asymptotically multivariate normal tests. In this paper, we focus on the first three of these and extend the framework of the weighted parametric multiple test procedure from fixed designs with a single analysis per objective to a GSD setting where different objectives may be assessed at the same or different times, each in a group sequential fashion. Pragmatic methods for design and analysis of weighted parametric group sequential design under closed testing procedures are proposed to maintain the strong control of the family-wise Type I error rate when correlations between tests are incorporated. This results in the ability to relax testing bounds compared to designs not fully adjusting for known correlations, increasing power, or allowing decreased sample size. We illustrate the proposed methods using clinical trial examples and conduct a simulation study to evaluate the operating characteristics.

Multiplicity for a group sequential trial with biomarker subpopulations.

Biomarker subpopulations have become increasingly important for drug development in targeted therapies. The use of biomarkers has the potential to facilitate more effective outcomes by guiding patient selection appropriately, thus enhancing the benefit-risk profile and improving trial power. Studying a broad population simultaneously with a more targeted one allows the trial to determine the population for which a treatment is effective and allows a goal of making approved regulatory labeling as inclusive as is appropriate. We examine new methods accounting for the complete correlation structure in group sequential designs with hypotheses in nested subgroups. The designs provide full control of family-wise Type I error rate. This extension of previous methods accounting for either group sequential design or correlation between subgroups improves efficiency (power or sample size) over a typical Bonferroni approach for testing nested populations.

On the empirical choice of the time window for restricted mean survival time.

The t-year mean survival or restricted mean survival time (RMST) has been used as an appealing summary of the survival distribution within a time window [0, t]. RMST is the patient's life expectancy until time t and can be estimated nonparametrically by the area under the Kaplan-Meier curve up to t. In a comparative study, the difference or ratio of two RMSTs has been utilized to quantify the between-group-difference as a clinically interpretable alternative summary to the hazard ratio. The choice of the time window [0, t] may be prespecified at the design stage of the study based on clinical considerations. On the other hand, after the survival data have been collected, the choice of time point t could be data-dependent. The standard inferential procedures for the corresponding RMST, which is also data-dependent, ignore this subtle yet important issue. In this paper, we clarify how to make inference about a random "parameter." Moreover, we demonstrate that under a rather mild condition on the censoring distribution, one can make inference about the RMST up to t, where t is less than or even equal to the largest follow-up time (either observed or censored) in the study. This finding reduces the subjectivity of the choice of t empirically. The proposal is illustrated with the survival data from a primary biliary cirrhosis study, and its finite sample properties are investigated via an extensive simulation study.

Pembrolizumab Exposure-Response Assessments Challenged by Association of Cancer Cachexia and Catabolic Clearance.

PURPOSE: To investigate the relationship of pembrolizumab pharmacokinetics (PK) and overall survival (OS) in patients with advanced melanoma and non-small cell lung cancer (NSCLC). PATIENTS AND METHODS: PK dependencies in OS were evaluated across three pembrolizumab studies of either 200 mg or 2 to 10 mg/kg every 3 weeks (Q3W). Kaplan-Meier plots of OS, stratified by dose, exposure, and baseline clearance (CL0), were assessed per indication and study. A Cox proportional hazards model was implemented to explore imbalances of typical prognostic factors in high/low NSCLC CL0 subgroups. RESULTS: A total of 1,453 subjects were included: 340 with pembrolizumab-treated melanoma, 804 with pembrolizumab-treated NSCLC, and 309 with docetaxel-treated NSCLC. OS was dose independent from 2 to 10 mg/kg for pembrolizumab-treated melanoma [HR = 0.98; 95% confidence interval (CI), 0.94-1.02] and NSCLC (HR = 0.98; 95% CI, 0.95-1.01); however, a strong CL0-OS association was identified for both cancer types (unadjusted melanoma HR = 2.56; 95% CI, 1.72-3.80 and NSCLC HR = 2.64; 95% CI, 1.94-3.57). Decreased OS in subjects with higher pembrolizumab CL0 paralleled disease severity markers associated with end-stage cancer anorexia-cachexia syndrome. Correction for baseline prognostic factors did not fully attenuate the CL0-OS association (multivariate-adjusted CL0 HR = 1.64; 95% CI, 1.06-2.52 for melanoma and HR = 1.88; 95% CI, 1.22-2.89 for NSCLC). CONCLUSIONS: These data support the lack of dose or exposure dependency in pembrolizumab OS for melanoma and NSCLC between 2 and 10 mg/kg. An association of pembrolizumab CL0 with OS potentially reflects catabolic activity as a marker of disease severity versus a direct PK-related impact of pembrolizumab on efficacy. Similar data from other trials suggest such patterns of exposure-response confounding may be a broader phenomenon generalizable to antineoplastic mAbs.See related commentary by Coss et al., p. 5787.

Baseline Tumor Size Is an Independent Prognostic Factor for Overall Survival in Patients with Melanoma Treated with Pembrolizumab.

Purpose: The purpose of this study was to assess the association of baseline tumor size (BTS) with other baseline clinical factors and outcomes in pembrolizumab-treated patients with advanced melanoma in KEYNOTE-001 (NCT01295827).Experimental Design: BTS was quantified by adding the sum of the longest dimensions of all measurable baseline target lesions. BTS as a dichotomous and continuous variable was evaluated with other baseline factors using logistic regression for objective response rate (ORR) and Cox regression for overall survival (OS). Nominal P values with no multiplicity adjustment describe the strength of observed associations.Results: Per central review by RECIST v1.1, 583 of 655 patients had baseline measurable disease and were included in this post hoc analysis. Median BTS was 10.2 cm (range, 1-89.5). Larger median BTS was associated with Eastern Cooperative Oncology Group performance status 1, elevated lactate dehydrogenase (LDH), stage M1c disease, and liver metastases (with or without any other sites; all P ≤ 0.001). In univariate analyses, BTS below the median was associated with higher ORR (44% vs. 23%; P < 0.001) and improved OS (HR, 0.38; P < 0.001). In multivariate analyses, BTS below the median remained an independent prognostic marker of OS (P < 0.001) but not ORR. In 459 patients with available tumor programmed death ligand 1 (PD-L1) expression, BTS below the median and PD-L1-positive tumors were independently associated with higher ORR and longer OS.Conclusions: BTS is associated with many other baseline clinical factors but is also independently prognostic of survival in pembrolizumab-treated patients with advanced melanoma. Clin Cancer Res; 24(20); 4960-7. ©2018 AACR See related commentary by Warner and Postow, p. 4915.

Stepwise two-stage sample size adaptation.

Several adaptive design methods have been proposed to reestimate sample size using the observed treatment effect after an initial stage of a clinical trial while preserving the overall type I error at the time of the final analysis. One unfortunate property of the algorithms used in some methods is that they can be inverted to reveal the exact treatment effect at the interim analysis. We propose using a step function with an inverted U-shape of observed treatment difference for sample size reestimation to lessen the information on treatment effect revealed. This will be referred to as stepwise two-stage sample size adaptation. This method applies calculation methods used for group sequential designs. We minimize expected sample size among a class of these designs and compare efficiency with the fully optimized two-stage design, optimal two-stage group sequential design, and designs based on promising conditional power. The trade-off between efficiency versus the improved blinding of the interim treatment effect will be discussed.

On efficient two-stage adaptive designs for clinical trials with sample size adjustment.

Group sequential designs are rarely used for clinical trials with substantial over running due to fast enrollment or long duration of treatment and follow-up. Traditionally, such trials rely on fixed sample size designs. Recently, various two-stage adaptive designs have been introduced to allow sample size adjustment to increase statistical power or avoid unnecessarily large trials. However, these adaptive designs can be seriously inefficient. To address this infamous problem, we propose a likelihood-based two-stage adaptive design where sample size adjustment is derived from a pseudo group sequential design using cumulative conditional power. We show through numerical examples that this design cannot be improved by group sequential designs. In addition, the approach may uniformly improve any existing two-stage adaptive designs with sample size adjustment. For statistical inference, we provide methods for sequential p-values and confidence intervals, as well as median unbiased and minimum variance unbiased estimates. We show that the claim of inefficiency of adaptive designs by Tsiatis and Mehta ( 2003 ) is logically flawed, and thereby provide a strong defense of Cui et al. ( 1999 ).

The BATTLE trial: a bold step toward improving the efficiency of biomarker-based drug development.

Successful completion of the Biomarker-integrated Approaches of Targeted Therapy for Lung Cancer Elimination (BATTLE) trial, reported in this issue of Cancer Discovery, is an important advance in the effort to improve clinical trial approaches to the simultaneous development of new therapeutics with matching diagnostic tests so that patients most likely to benefit from these therapies can be identified.

Finding the right dose for cancer therapeutics--can we do better?

Unlike other diseases, dose-selection for cancer therapeutics is often based on the maximum-tolerated dose in phase 1 studies involving relatively few patients. In this issue of Clinical Cancer Research, Jain and colleagues provide evidence that lower doses may be as effective as maximum-tolerated doses in the treatment of cancer patients.

Fitting spending functions.

Group sequential monitoring is used to provide guidance on stopping a clinical trial in progress based on interim evaluation of its efficacy objectives. A trial could stop because an experimental regimen (1) is efficacious, (2) lacks any sign of efficacy, or (3) is specifically less efficacious than a control. Group sequential methods using alpha- and beta-spending functions (Biometrika 1983; 70:659-663) are often used to create stopping boundaries for test statistics for efficacy hypotheses computed at interim analyses. This paper explores fitting alpha- and beta-spending functions that have specific values at specific interim analyses. Commonly used one-parameter families may not provide an adequate fit to more than one desired critical value. We define new one- and two-parameter families to provide additional flexibility along with examples to demonstrate their usefulness. The logistic family is one of these two-parameter families, which has been applied in several trials.

Detection bias due to the effect of finasteride on prostate volume: a modeling approach for analysis of the Prostate Cancer Prevention Trial.

BACKGROUND: The Prostate Cancer Prevention Trial (PCPT) demonstrated a 24.8% reduction in the 7-year prevalence of prostate cancer among patients treated with finasteride (5 mg daily) compared with that among patients treated with placebo; however, a 25.5% increase in the prevalence of high-Gleason grade tumors was observed, the clinical significance of which is unknown. One hypothesized explanation for this increase is that finasteride reduced prostate volume, leading to detection of more high-grade tumors due to increased sampling density. This possibility was investigated in an observational reanalysis of the PCPT data, with adjustment for sampling density. METHODS: A logistic model for the association of high-grade (Gleason score 7-10) prostate cancer with baseline covariates and/or baseline covariates plus prostate volume and number of cores obtained at biopsy was developed using the placebo group (n = 4775) of the PCPT. This model was then applied to the finasteride group (n = 5123) to compare the predicted and observed numbers of high-grade tumors in that group. In a second approach, odds ratios (ORs) for prostate cancer in the finasteride versus placebo groups calculated from binary and polytomous logistic regression models that contained or excluded covariates for gland volume and number of needle cores were compared. RESULTS: Median prostate volume was 25% lower in the finasteride group (median = 25.1 cm3) than in the placebo group (median = 33.5 cm3). The logistic model developed in the placebo group showed that the likelihood of detection of high-grade prostate cancer decreased as volume increased (for each 10 cm3 increase in prostate volume, OR = 0.81, 95% confidence interval [CI] = 0.74 to 0.90). Based on this model, 239 high-grade prostate cancers were predicted in the finasteride group, whereas 243 were observed, a non-statistically significant difference. Among all participants, the odds ratios for high-grade cancer in the finasteride versus placebo groups decreased from 1.27 (95% CI = 1.05 to 1.54) with adjustment for baseline covariates to 1.03 (95% CI = 0.84 to 1.26) following additional adjustment for gland volume and number of biopsy cores in binary outcome models and from 1.14 (95% CI = 0.94 to 1.38) to 0.88 (95% CI = 0.72 to 1.09) following these adjustments in the polytomous models. CONCLUSIONS: Although analyses using postrandomization data require cautious interpretation, these results suggest that sampling density bias alone could explain the excess of high-grade cancers among the finasteride-assigned participants in the PCPT.

Optimal spending functions for asymmetric group sequential designs.

We present optimized group sequential designs where testing of a single parameter theta is of interest. We require specification of a loss function and of a prior distribution for theta. For the examples presented, we pre-specify Type I and II error rates and minimize the expected sample size over the prior distribution for theta. Minimizing the square of sample size rather than the sample size is found to produce designs with slightly less aggressive interim stopping rules and smaller maximum sample sizes with essentially identical expected sample size. We compare optimal designs using Hwang-Shih-DeCani and Kim-DeMets spending functions to fully optimized designs not restricted by a spending function family. In the examples selected, we also examine when there might be substantial benefit gained by adding an interim analysis. Finally, we provide specific optimal asymmetric spending function designs that should be generally useful and simply applied when a design with minimal expected sample size is desired.