In randomized clinical trials with right-censored time-to-event outcomes, the popular log-rank test without adjusting for baseline covariates is asymptotically valid for treatment effect under simple randomization of treatments but is too conservative under covariate-adaptive randomization. The stratified log-rank test, which adjusts baseline covariates in the test procedure by stratification, is asymptotically valid regardless of what treatment randomization is applied. In the literature, however, under simple randomization there is no affirmative conclusion about whether the stratified log-rank test is asymptotically more powerful than the unstratified log-rank test. In this article we show when the stratified and unstratified log-rank tests aim for the same null hypothesis and that, under simple randomization, the stratified log-rank test is asymptotically more powerful than the unstratified log-rank test in the region of alternative hypothesis that is specified by a Cox proportional hazards model. We also provide some discussion about why we do not have an affirmative conclusion in general.

In the paper, the autoregressive moving average model for matrix time series (MARMA) is investigated. The properties of the MARMA model are investigated by using the conditional least square estimation, the conditional maximum likelihood estimation, the projection theorem in Hilbert space and the decomposition technique of time series, which include necessary and sufficient conditions for stationarity and invertibility, model parameter estimation, model testing and model forecasting.

ABSTRACT Missing data is unavoidable in longitudinal clinical trials, and outcomes are not always normally distributed. In the presence of outliers or heavy-tailed distributions, the conventional multiple imputation with the mixed model with repeated measures analysis of the average treatment effect (ATE) based on the multivariate normal assumption may produce bias and power loss. Control-based imputation (CBI) is an approach for evaluating the treatment effect under the assumption that participants in both the test and control groups with missing outcome data have a similar outcome profile as those with an identical history in the control group. We develop a robust framework to handle non-normal outcomes under CBI without imposing any parametric modeling assumptions. Under the proposed framework, sequential weighted robust regressions are applied to protect the constructed imputation model against non-normality in the covariates and the response variables. Accompanied by the subsequent mean imputation and robust model analysis, the resulting ATE estimator has good theoretical properties in terms of consistency and asymptotic normality. Moreover, our proposed method guarantees the analysis model robustness of the ATE estimation in the sense that its asymptotic results remain intact even when the analysis model is misspecified. The superiority of the proposed robust method is demonstrated by comprehensive simulation studies and an AIDS clinical trial data application.

Sample compression schemes were first proposed by Littlestone and Warmuth in 1986. Undirected graphical model is a powerful tool for classification in statistical learning. In this paper, we consider labelled compression schemes for concept classes induced by discrete undirected graphical models. For the undirected graph of two vertices with no edge, where one vertex takes two values and the other vertex can take any finite number of values, we propose an algorithm to establish a labelled compression scheme of size VC dimension of associated concept class. Further, we extend the result to other two types of undirected graphical models and show the existence of labelled compression schemes of size VC dimension for induced concept classes. The work of this paper makes a step forward in solving sample compression problem for concept class induced by a general discrete undirected graphical model.

In two-level fractional factorial designs, conditional main effects can provide insights by which to analyze factorial effects and facilitate the de-aliasing of fully aliased two-factor interactions. Conditional main effects are of particular interest in situations where some factors are nested within others. Most of the relevant literature has focussed on the development of data analysis tools that use conditional main effects, while the issue of optimal factorial design for a given linear model involving conditional main effects has been largely overlooked. Mukerjee, Wu and Chang [Statist. Sinica 27 (2017) 997–1016] established a framework by which to optimize designs under a conditional effect model. Although theoretically sound, their results were limited to a single pair of conditional and conditioning factors. In this paper, we extend the applicability of their framework to double pairs of conditional and conditioning factors by providing the corresponding parameterization and effect hierarchy. We propose a minimum contamination-based criterion by which to evaluate designs and develop a complementary set theory to facilitate the search of minimum contamination designs. The catalogues of 16- and 32-run minimum contamination designs are provided. For five to twelve factors, we show that all 16-run minimum contamination designs under the conditional effect model are also minimum aberration according to Fries and Hunter [Technometrics 22 (1980) 601–608].

It’s the basic premise of promoting the healthy development of rural finance and strengthening macro-prudential supervision to measure the systemic risk of rural finance accurately. We establish the dynamic factor CAPM and make an all-round and multi-angle quantitative study on the systemic risk of rural finance in China by constructing Macro–micro index system and using machine learning to reduce the dimension of high-dimensional data. Our results show that the dynamic factor CAPM of using Macro–micro big data can evaluate systemic risk of rural finance more comprehensively and systematically, and machine learning performs well in processing high-dimensional data. In addition, China's rural financial systemic risk is stable compared with the Shanghai and Shenzhen main markets, but it is also susceptible to macro and micro influenced factors. Finally, it is pointed out that the early warning system of rural financial systemic risk could be constructed at macro and micro level, respectively.

Phase II clinical trials are commonly conducted as pilot studies to evaluate the efficacy and safety of the investigational drug in the targeted patient population with the disease or condition to be treated or prevented. When designing such a trial considering efficacy conclusions, people naturally think as follows: if efficacy evidence is very strong, a go decision should be made; if efficacy evidence is very weak, a no-go decision should be made; if the efficacy evidence is neither strong nor weak, no decision can be made (inconclusive). The designs presented in this paper match this natural thinking process with go/no-go/inconclusive outcomes. Both two-/three-stage designs are developed with three outcomes. Additionally, a general approach based on conditional error function is implemented such that new decision boundaries can be calculated to handle mid-course sample size change which results in either ‘over-running’ or ‘under-running’ and ensure the control of overall type I error. A free open-source R package tsdf that calculates the proposed two-/three-stage designs is available on CRAN.

This paper deals with the Monte Carlo Simulation in a Bayesian framework. It shows the importance of the use of Monte Carlo experiments through refined descriptive sampling within the autoregressive model , where and the errors are independent random variables following an exponential distribution of parameter θ. To achieve this, a Bayesian Autoregressive Adaptive Refined Descriptive Sampling (B2ARDS) algorithm is proposed to estimate the parameters ρ and θ of such a model by a Bayesian method. We have used the same prior as the one already used by some authors, and computed their properties when the Normality error assumption is released to an exponential distribution. The results show that B2ARDS algorithm provides accurate and efficient point estimates.

This paper introduces a new family of distributions defined in terms of quantile function. The quantile function introduced here is the sum of quantile functions of life time distributions called Burr III and Weibull. Different distributional characteristics and reliability properties are included in the study. Method of Least Square and Method of L-moments are applied to estimate the parameters of the model. Two real life data sets are used to illustrate the performance of the model.

In this paper, we investigate the COVID-19 pandemic in Canada and evaluate the Canadian government policies on controlling COVID-19 outbreaks. The first case of COVID-19 was reported in Ontario on 25 January 2020. Since then, there have been over million cases by now. During this time period, the federal, provincial and local governments have implemented regulations and policies in order to control the pandemic. To evaluate these government policies, which may be done by analysing the infection rate, infection period and reproductive number of COVID-19, we approach the problem by introducing an extended susceptible-exposed-infectious-removed (SEIR) model and conduct the model inference by using the iterated filter ensemble adjustment Kalman filter (IF-EAKF) algorithm. We first divide the time period into phases according to the policy intensities in each province by segmenting the time period from 4 March 2020 to 31 October 2020 into three time phases: the exploding phase, the strict policy implementation phase, and the provincial reopening phase. We then use IF-EAKF algorithm to obtain the estimates of the model parameters. We show that the infection rate in the second phase is lower than that in both first and third phases. We also discuss the number of new COVID-19 cases under different policy intensities and different policy durations in the third wave of the pandemic.