Fast approximation of small p-values in permutation tests by partitioning the permutations.

Researchers in genetics and other life sciences commonly use permutation tests to evaluate differences between groups. Permutation tests have desirable properties, including exactness if data are exchangeable, and are applicable even when the distribution of the test statistic is analytically intractable. However, permutation tests can be computationally intensive. We propose both an asymptotic approximation and a resampling algorithm for quickly estimating small permutation p-values (e.g., <10-6) for the difference and ratio of means in two-sample tests. Our methods are based on the distribution of test statistics within and across partitions of the permutations, which we define. In this article, we present our methods and demonstrate their use through simulations and an application to cancer genomic data. Through simulations, we find that our resampling algorithm is more computationally efficient than another leading alternative, particularly for extremely small p-values (e.g., <10-30). Through application to cancer genomic data, we find that our methods can successfully identify up- and down-regulated genes. While we focus on the difference and ratio of means, we speculate that our approaches may work in other settings.

Augmenting control arms with real-world data for cancer trials: Hybrid control arm methods and considerations.

Background: Hybrid controlled trials with real-world data (RWD), where the control arm is composed of both trial and real-world patients, could facilitate research when the feasibility of randomized controlled trials (RCTs) is challenging and single-arm trials would provide insufficient information. Methods: We propose a frequentist two-step borrowing method to construct hybrid control arms. We use parameters informed by a completed randomized trial in metastatic triple-negative breast cancer to simulate the operating characteristics of dynamic and static borrowing methods, highlighting key trade-offs and analytic decisions in the design of hybrid studies. Results: Simulated data were generated under varying residual-bias assumptions (no bias: HRRWD = 1) and experimental treatment effects (target trial scenario: HRExp = 0.78). Under the target scenario with no residual bias, all borrowing methods achieved the desired 88% power, an improvement over the reference model (74% power) that does not borrow information externally. The effective number of external events tended to decrease with higher bias between RWD and RCT (i.e. HRRWD away from 1), and with weaker experimental treatment effects (i.e. HRExp closer to 1). All dynamic borrowing methods illustrated (but not the static power prior) cap the maximum Type 1 error over the residual-bias range considered. Our two-step model achieved comparable results for power, type 1 error, and effective number of external events borrowed compared to other borrowing methodologies. Conclusion: By pairing high-quality external data with rigorous simulations, researchers have the potential to design hybrid controlled trials that better meet the needs of patients and drug development.

Stability and Change in Health Behavior Profiles of U.S. Adults.

OBJECTIVES: While understanding of complex within-person clustering of health behaviors into meaningful profiles of risk is growing, we still know little about whether and how U.S. adults transition from one profile to another as they age. This study assesses patterns of stability and change in profiles of tobacco and alcohol use and body mass index (BMI). METHOD: A nationally representative cohort of U.S. adults 25 years and older was interviewed up to 5 times between 1986 and 2011. Latent transition analysis (LTA) models characterized the most common profiles, patterning of transitions across profiles over follow-up, and assessed whether some were associated with higher mortality risk. RESULTS: We identified 5 profiles: "health promoting" with normal BMI and moderate alcohol consumption; "overweight"; "current smokers"; "obese"; and "nondrinkers". Profile membership was largely stable, with the most common transitions to death or weight gain. "Obese" was the most stable profile, while "smokers" were most likely to transition to another profile. Mortality was most frequent in the "obese" and "nondrinker" profiles. DISCUSSION: Stability was more common than transition, suggesting that adults sort into health behavior profiles relatively early. Women and men were differently distributed across profiles at baseline, but showed broad similarity in transitions.

Tests of Matrix Structure for Construct Validation.

Psychologists and other behavioral scientists are frequently interested in whether a questionnaire measures a latent construct. Attempts to address this issue are referred to as construct validation. We describe and extend nonparametric hypothesis testing procedures to assess matrix structures, which can be used for construct validation. These methods are based on a quadratic assignment framework and can be used either by themselves or to check the robustness of other methods. We investigate the performance of these matrix structure tests through simulations and demonstrate their use by analyzing a big five personality traits questionnaire administered as part of the Health and Retirement Study. We also derive rates of convergence for our overall test to better understand its behavior.