Improved inference for a linear mixed-effects model when the subpopulation effects are clustered

We provide Bayesian methodology to relax the assumption that all subpopulation effects in a linear mixed-effects model have, after adjustment for covariates, a common mean. We expand the model specification by assuming that the m subpopulation effects are allowed to cluster into d groups where the value of d, 1?d?m, and the composition of the d groups are unknown, a priori. Specifically, for each partition of the m effects into d groups we only assume that the subpopulation effects in each group are exchangeable and are independent across the groups. We show that failure to take account of this clustering, as with the customary method, will lead to serious errors in inference about the variances and subpopulation effects, but the proposed, expanded, model leads to appropriate inferences. The efficacy of the proposed method is evaluated by contrasting it with both the customary method and use of a Dirichlet process prior. We use data from small area estimation to illustrate our method.     

An adaptive seamless phase II/III design for oncology trials with subpopulation selection using correlated survival endpoints

Although the statistical methods enabling efficient adaptive seamless designs are increasingly well established, it is important to continue to use the endpoints and specifications that best suit the therapy area and stage of development concerned when conducting such a trial. Approaches exist that allow adaptive designs to continue seamlessly either in a subpopulation of patients or in the whole population on the basis of data obtained from the first stage of a phase II/III design: our proposed design adds extra flexibility by also allowing the trial to continue in all patients but with both the subgroup and the full population as co-primary populations. Further, methodology is presented which controls the Type-I error rate at less than 2.5% when the phase II and III endpoints are different but correlated time-to-event endpoints. The operating characteristics of the design are described along with a discussion of the practical aspects in an oncology setting.     

Bayesian adaptive patient enrollment restriction to identify a sensitive subpopulation using a continuous biomarker in a randomized phase 2 trial

With the development of molecular targeted drugs, predictive biomarkers have played an increasingly important role in identifying patients who are likely to receive clinically meaningful benefits from experimental drugs (i.e., sensitive subpopulation) even in early clinical trials. For continuous biomarkers, such as mRNA levels, it is challenging to determine cutoff value for the sensitive subpopulation, and widely accepted study designs and statistical approaches are not currently available. In this paper, we propose the Bayesian adaptive patient enrollment restriction (BAPER) approach to identify the sensitive subpopulation while restricting enrollment of patients from the insensitive subpopulation based on the results of interim analyses, in a randomized phase 2 trial with time‐to‐endpoint outcome and a single biomarker. Applying a four‐parameter change‐point model to the relationship between the biomarker and hazard ratio, we calculate the posterior distribution of the cutoff value that exhibits the target hazard ratio and use it for the restriction of the enrollment and the identification of the sensitive subpopulation. We also consider interim monitoring rules for termination because of futility or efficacy. Extensive simulations demonstrated that our proposed approach reduced the number of enrolled patients from the insensitive subpopulation, relative to an approach with no enrollment restriction, without reducing the likelihood of a correct decision for next trial (no‐go, go with entire population, or go with sensitive subpopulation) or correct identification of the sensitive subpopulation. Additionally, the four‐parameter change‐point model had a better performance over a wide range of simulation scenarios than a commonly used dichotomization approach. Copyright © 2016 John Wiley & Sons, Ltd.     

试论秦观的个性特征及其演变过程

后人多视秦观为多愁善感、风流柔弱的书生,其实这种认识并不全面。实际上秦观的个性气质既有多面性,也有变化性。青少年时代的秦观聪颖、豪迈、风流、俊逸,这与他出身于一个江南世宦家庭、受到江南城乡文化的影响是有关的。秦观后来变得多愁善感、凄婉伤心,与他所遭受的来自科举考试的失利、党争的攻击与迫害、仕途的坎坷与贬谪等一系列的人生不幸是密切相关的。秦观的个性中虽然存在着有些脆弱、易于波动的弱点,但是直率自然、任情守真则是贯穿他整个生命历程的一种极重要的个性特征和精神品质。     

Estimating the Basic Reproductive Number in the General Epidemic Model with an Unknown Initial Number of Susceptible Individuals

Abstract. In any epidemic, there may exist an unidentified subpopulation which might be naturally immune or isolated and who will not be involved in the transmission of the disease. Estimation of key parameters, for example, the basic reproductive number, without accounting for this possibility would underestimate the severity of the epidemics. Here, we propose a procedure to estimate the basic reproductive number ( R ₀ ) in an epidemic model with an unknown initial number of susceptibles. The infection process is usually not completely observed, but is reconstructed by a kernel‐smoothing method under a counting process framework. Simulation is used to evaluate the performance of the estimators for major epidemics. We illustrate the procedure using the Abakaliki smallpox data.     

Fast Inference for Network Models of Infectious Disease Spread

Models of infectious disease over contact networks offer a versatile means of capturing heterogeneity in populations during an epidemic. Highly connected individuals tend to be infected at a higher rate early during an outbreak than those with fewer connections. A powerful approach based on the probability generating function of the individual degree distribution exists for modelling the mean field dynamics of outbreaks in such a population. We develop the same idea in a stochastic context, by proposing a comprehensive model for 1‐week‐ahead incidence counts. Our focus is inferring contact network (and other epidemic) parameters for some common degree distributions, in the case when the network is non‐homogeneous ‘at random’. Our model is initially set within a susceptible–infectious–removed framework, then extended to the susceptible–infectious–removed–susceptible scenario, and we apply this methodology to influenza A data.     

Maximizing Health Benefits and Minimizing Inequality: Incorporating Local‐Scale Data in the Design and Evaluation of Air Quality Policies

The U.S. Environmental Protection Agency undertook a case study in the Detroit metropolitan area to test the viability of a new multipollutant risk‐based (MP/RB) approach to air quality management, informed by spatially resolved air quality, population, and baseline health data. The case study demonstrated that the MP/RB approach approximately doubled the human health benefits achieved by the traditional approach while increasing cost less than 20%—moving closer to the objective of Executive Order 12866 to maximize net benefits. Less well understood is how the distribution of health benefits from the MP/RB and traditional strategies affect the existing inequalities in air‐pollution‐related risks in Detroit. In this article, we identify Detroit populations that may be both most susceptible to air pollution health impacts (based on local‐scale baseline health data) and most vulnerable to air pollution (based on fine‐scale PM_2.5 air quality modeling and socioeconomic characteristics). Using these susceptible/vulnerable subpopulation profiles, we assess the relative impacts of each control strategy on risk inequality, applying the Atkinson Index (AI) to quantify health risk inequality at baseline and with either risk management approach. We find that the MP/RB approach delivers greater air quality improvements among these subpopulations while also generating substantial benefits among lower‐risk populations. Applying the AI, we confirm that the MP/RB strategy yields less PM_2.5 mortality and asthma hospitalization risk inequality than the traditional approach. We demonstrate the value of this approach to policymakers as they develop cost‐effective air quality management plans that maximize risk reduction while minimizing health inequality.     

A ratio estimator of the total of a subpopulation

If the total of an auxiliary variable is known for an entire population but is unknown for some subpopulation, the usual estimator of the total of the primary variable for the subpopulation is the ratio estimator that uses the auxiliary total for the entire population. This article proposes a ratio estimator that uses an estimator of the auxiliary total over the subpopulation as suggested by Kish (1967, p. 438). Under some conditions, it is shown that the latter estimator is unbiased and has smaller variance than the former estimator in large simple random samples.     

Spatial variation in female fertility related to interactions with flower consumers and pathogens in a forest metapopulation ofPrimula sieboldii

Antagonistic biological interactions with flower consumers and pathogens may influence reproductive success of flowering plants, affecting population dynamics and natural selection for floral traits. However, ecological and evolutionary consequences of the interactions may depend on both spatial and temporal patterns of the interactions. In a forest metapopulation ofPrimula sieboldii E. Morren, an endangered clonal plant species, we measured between-subpopulation patterns of seed sets and interactions with an influential flower consumer, a rove beetle,Eusphalerum bosatsu Watanabe, and a specific smut fungal pathogen,Urocystis tranzschelina (Lavrov) Zundel (Ustilaginales), for three years. Mean female fertility (seed set per flower) for individual subpopulations fluctuated moderately among years but was highly variable within each year among the five subpopulations studied. In two subpopulations, the impact ofEusphalerum beetle, was sufficiently large to result in almost complete failure in seed production over eight years including the three study and five previous preliminary observation years. In the two other subpopulations, seed set failure was caused by infection by the smut fungus. Infected capsules which constitute 10–30% of the capsules produced in the subpopulations were filled with ustilospores instead of seeds. In the subpopulation that escaped flower damage byEusphalerum beetles and smut fungal infection, seed sets of both pin and thrum flowers were much higher than in the other subpopulations. The spatial restriction of individual antagonistic agents to a part of subpopulations suggest that dispersal of the agents, as well as the mode of spatial subdivision of the plant population would be important for determining the overall effects of antagonistic interactions on plant performances at the metapopulation level.     

Identification of drug‐induced toxicity biomarkers for treatment determination

Drug‐induced organ toxicity (DIOT) that leads to the removal of marketed drugs or termination of candidate drugs has been a leading concern for regulatory agencies and pharmaceutical companies. In safety studies, the genomic assays are conducted after the treatment so that drug‐induced adverse effects can occur. Two types of biomarkers are observed: biomarkers of susceptibility and biomarkers of response. This paper presents a statistical model to distinguish two types of biomarkers and procedures to identify susceptible subpopulations. The biomarkers identified are used to develop classification model to identify susceptible subpopulation. Two methods to identify susceptibility biomarkers were evaluated in terms of predictive performance in subpopulation identification, including sensitivity, specificity, and accuracy. Method 1 considered the traditional linear model with a variable‐by‐treatment interaction term, and Method 2 considered fitting a single predictor variable model using only treatment data. Monte Carlo simulation studies were conducted to evaluate the performance of the two methods and impact of the subpopulation prevalence, probability of DIOT, and sample size on the predictive performance. Method 2 appeared to outperform Method 1, which was due to the lack of power for testing the interaction effect. Important statistical issues and challenges regarding identification of preclinical DIOT biomarkers were discussed. In summary, identification of predictive biomarkers for treatment determination highly depends on the subpopulation prevalence. When the proportion of susceptible subpopulation is 1% or less, a very large sample size is needed to ensure observing sufficient number of DIOT responses for biomarker and/or subpopulation identifications. Copyright © 2015 John Wiley & Sons, Ltd.