arXiv subjects

Baoshan Zhang

Publications and source records attributed to Baoshan Zhang.

5 recordsLinked to original sources

arXiv2026

Bridging Balancing Weights and Augmentation in Covariate-adjusted Analyses with Time-to-Event Endpoints: Theory and Practical Recommendations

Covariate adjustment improves the efficiency of treatment-effect analyses in randomized clinical trials, provided the adjustment targets the correct quantity. For time-to-event endpoints, two marginal targets are of primary interest: the log-rank test for the presence of a treatment effect and the marginal hazard ratio for its magnitude. Existing covariate adjustment approaches reach these targets by different ways. Augmentation adjusts the log-rank score by regressing derived outcomes on the baseline covariates within each arm. Weighting instead reweights the two arms to balance the covariates before the survival comparison is formed: inverse probability weighting does so through a fitted propensity model, while calibration weighting solves directly for weights that match covariate means. In this manuscript, we first develop balancing weighting for time-to-event endpoints, covering both calibration weights (stable balancing weights and entropy balancing) and propensity score weights, and prove that any balancing-regular weighting is first-order equivalent to the augmented log-rank score and to the root of the marginal Cox score. All three routes therefore deliver the same estimator to first order, and calibration reaches it without fitting any model. The weighted procedures thereby inherit the validity and guaranteed efficiency gain of the augmentation approach. In addition, we show that the efficiency gain grows with the prognostic strength of the adjustment covariates, while the practical caveat lies in variance estimation, for which we give recommendations to guard against finite-sample Type I error inflation. We further confirm our results through simulation studies and an analysis of the REWIND cardiovascular trial.

stat.ME↗

arXiv2026

The FORSS Framework for Sample Size and Power Calculations With Win Statistics for Hierarchical Endpoints

Win statistics have gained increasing popularity as primary analysis methods for clinical trials with hierarchical endpoints (HEs) as primary endpoints. However, existing sample size and power calculation approaches in trial design still face several limitations and challenges: simulation-based approaches are computationally intensive, while existing formula-based methods often rely on simplifying assumptions such as independence among HEs, or require specification of overall win statistics and tie probability that are difficult to elicit a priori in practice. To address these challenges, we propose the FORSS framework, a FORmula-based Super-Sample approach that allows investigators to specify marginal treatment effects using familiar metrics (e.g., hazard ratios, mean differences, and risk differences) together with a flexible joint working distribution for the HEs. Rather than repeatedly simulating full trials at each candidate sample size, FORSS uses super-samples to estimate the population-level plug-in quantities required by analytical formulas for both power and sample size calculation. We evaluated the performance of the proposed FORSS through extensive simulation studies. The results show that the formula-based FORSS closely matches empirical power across a wide range of scenarios while maintaining Type~I error rates near the nominal 5\% level. An illustration based on the HEART-FID trial further shows that endpoint-dependence specifications can materially affect projected power and required sample size when planning trials with HEs.

stat.ME↗

arXiv2025

Improving Variance and Confidence Interval Estimation in Small-Sample Propensity Score Analyses: Bootstrap vs. Asymptotic Methods

Propensity score (PS) methods are widely used to estimate treatment effects in non-randomized studies. Variance is typically estimated using sandwich or bootstrap methods, which can either treat the PS as estimated or fixed. The latter is thought to be conservative. Comparisons between the sandwich and bootstrap estimators have been compared in moderate to large sample sizes, favoring the bootstrap estimator. With the growing interest in treatments for rare disease and externally controlled clinical trials, very small sample sizes are not uncommon and the asymptotic properties of sandwich estimators may not hold. Bootstrap methods that allow for PS re-estimation can also generate problems with quasi-separation in small samples. It is unclear whether it is safe to prefer sandwich estimators or to assume that treating the PS as fixed is conservative. We conducted a Monte Carlo simulation to compare the performance of bootstrap versus sandwich variance and CI estimators for average treatment effects estimated with PS methods. We systematically evaluated the impact of treating the PS as fixed versus re-estimating it. These methodological comparisons were performed using Inverse Probability of Treatment Weighting (IPTW) and Augmented Inverse Probability of Treatment Weighting (AIPW) estimators. Simulations assessed performance under various conditions, including small sample sizes and different outcome and treatment prevalences. We illustrate the differences in our motivating example, the LIMIT-JIA trial. We show that the sandwich estimators can perform quite poorly in small samples, and fixed PS methods are not necessarily conservative. A stratified bootstrap avoids quasi-separation and performs well. Differences were large enough to alter statistical conclusions in our motivating example, LIMIT-JIA.

stat.ME↗

arXiv2024

Sequential Design with Derived Win Statistics

The Win Ratio has gained significant traction in cardiovascular trials as a novel method for analyzing composite endpoints (Pocock and others, 2012). Compared with conventional approaches based on time to the first event, the Win Ratio accommodates the varying priorities and types of outcomes among components, potentially offering greater statistical power by fully utilizing the information contained within each outcome. However, studies using Win Ratio have largely been confined to fixed design, limiting flexibility for early decisions, such as stopping for futility or efficacy. Our study proposes a sequential design framework incorporating multiple interim analyses based on Win Ratio or Net Benefit statistics. Moreover, we provide rigorous proof of the canonical joint distribution for sequential Win Ratio and Net Benefit statistics, and an algorithm for sample size determination is developed. We also provide results from a finite sample simulation study, which show that our proposed method controls Type I error maintains power level, and has a smaller average sample size than the fixed design. A real study of cardiovascular study is applied to illustrate the proposed method.

stat.ME↗

arXiv2013

Matrix Online Characteristic Number and Its applications in Goldbach Conjecture,Polignac Conjecture,the Twin Prime Conjecture

This article consists of three chapters.In Chapter 1, it is determined by the consecutive odd numbers, and study to the intrinsic properties of a class of matrix sequence. Through the establishment of matrix online number concept, characteristics and the online number column use mathematical induction to prove the some properties of this kind of matrix on the number of online features (Theorem 1). Finally, it is given a trial to prove the Goldbach conjecture (Theorem 6). This is the author in the years to explore prime properties in the process of research and discovery, and believe that this finding is of great significance.In Chapter 2, it is defined the concepts of matrix master characteristic number and the Matrix Master Characteristic Sequence (Definition 1). Firstly, we prove that any even number can be expressed as for the difference of two odd prime numbers at least two groups (Theorem 4). Secondly, we prove that there are infinitely many odd prime numbers separated by four (Theorem 9). Finally, we prove that if there is greater than 1 in the intersection by S(3) and s(2m+3) for any natural number m, so that there are infinitely many odd prime numbers separated by 2m(Theorem11). The results will undoubtedly promote the research for Polignac conjecture.In Chapter 3, mainly as a result of any odd natural number a, the intersection by S(a) and s(a+2) is not empty number set, and there are far more than 1 number in the set, where S(a)={k,If 2k+a be prime as k be natural number},and P is a prime number set, N is natural number set. we prove that there are an infinite number of twin prime, and then solve the problem of the twin primes in number theory.

math.GM↗