Probability-Sampling Framework for Modeling the Impact of Time-Varying Covariates

描述（由申请人提供）：我们提出了一个新的基于概率的框架，用于建模时变协变量对重复离散行为事件时间的影响，以支持对涉及吸烟生态瞬时评估（EMA）的两个现有数据集建模的协作努力。EMA包括使用电子日记来监测受试者在其环境中的实时行为，避免回顾性问卷固有的回忆偏差。尽管EMA在健康科学中越来越重要，但除了我们自己的工作之外，统计文献中很少有人关注EMA。生物统计学家和心理学家提出的合作研究的具体目标是：1)开发一个一般的概率抽样框架，用于估计时变协变量对即兴吸烟模式的影响，指定戒烟日期后的寿命，以及考虑到这些吸烟事件之间的时间依赖性的香烟失效模式，并将其一般应用于生态瞬间评估；2)构建时变协变量和时间对成瘾行为影响的联合模型，考虑成瘾行为的昼夜周期；3)建立受试者在基线吸烟率、时间协变量的影响和一天中的时间方面的变化模型，从中可以识别出表现出相似吸烟行为的受试者群体；4)构建模型，其中在给定时刻吸烟的危害不仅取决于时变协变量的当前值，而且取决于这些协变量过去值的综合函数。为了更好地了解戒烟成功或失败的潜在机制，我们将构建点过程和生存模型来描述吸烟者心理状态和环境的时间变化对即兴吸烟模式、戒烟后戒烟期和戒烟后吸烟导致复发模式的影响。点过程和生存模型的一个共同特征是，完全似然涉及到采样域上时变协变量的函数（强度或风险）的积分。提出的框架将采样域视为点的总体，并假设协变量是未知但确定的时间函数。采用基于概率的设计方法对协变量进行抽样，从而得到协变量积分函数的设计无偏估计量。将这个设计无偏估计量代入似然得到一个目标函数，该函数可以被最大化，从而得到模型参数的估计量。对协变量的集成函数进行基于设计的推理，作为基于时变协变量和重复行为事件的时序联合建模的分层建模方法的替代方案。与分层方法相反，对于时变协变量，不需要模型假设。公共卫生相关性：为了更好地了解戒烟成功或失败的潜在机制，我们建议开发新的统计方法来分析两个现有的数据集，这些数据集涉及使用电子日记来实时监测吸烟者的情绪和环境。除了这里考虑的吸烟数据之外，所提出的方法在公共卫生领域也有广泛的应用，从成瘾行为的分析到哮喘发作、癫痫发作、癌症患者复发性肿瘤的调查等等。

DESCRIPTION (provided by applicant): We propose a new probability-based framework for modeling the impact of time-varying covariates on the timing of repeated discrete behavioral events to support collaborative efforts to model two existing data sets involving Ecological Momentary Assessment (EMA) of smoking. EMA involves the use of electronic diaries to monitor the real-time behavior of subjects in their environments, avoiding recall biases inherent to retrospective questionnaires. Although EMA is increasingly important in the health sciences, aside from our own work little if any attention has been given to EMA in the statistics literature. The specific aims of the proposed collaborative research between a biostatistician and a psychologist are to: 1) Develop a general probability-sampling framework for estimating the impact of time varying- covariates on the pattern of ad-lib smoking, lifetimes to lapse following a designated quit date, and the post-lapse pattern of cigarettes that takes into account temporal dependence among these smoking events with general applications to ecological momentary assessment; 2) Construct joint models for the effects of time-varying covariates and time-of-day, accounting for circadian cycles in addictive behavior; 3) Develop a model for variation among subjects with respect to baseline smoking rates, effects of time-covariates, and time of day, from which clusters of subjects showing similar smoking behaviors may be identified; and 4) Construct models in which the hazard of smoking a cigarette at a given instant in time depends not only on the current values of time-varying covariates, but also on an integrated function of past values of those covariates. To obtain a better understanding of the mechanisms underlying success or failure of attempts to quit smoking, point process and survival models will be constructed to describe the impact of temporal variation in smokers' psychological states and environments on the pattern of ad lib smoking, lifetime to lapse following smoking cessation and the post lapse pattern of cigarettes leading to relapse. A common feature of both point process and survival models is that the full likelihood involves the integration of a function (intensity or hazard) of the time- varying covariates over the sampling domain. The proposed framework treats the sampling domain as a population of points, and assumes that the covariates are an unknown but deterministic function of time. A probability-based design is used to sample the covariates, from which a design-unbiased estimator of the integrated function of the covariates may be obtained. Substituting this design-unbiased estimator into the likelihood yields an objective function that may be maximized to obtain the proposed estimator for the model parameters. Design-based inference for the integrated function of the covariates is offered as an alternative to a hierarchical modeling approach based on joint modeling of the time-varying covariates and the timing of repeated behavioral events. In contrast to the hierarchical approach, no model assumptions are required regarding the time-varying covariates. PUBLIC HEALTH RELEVANCE: To obtain a better understanding of the mechanisms underlying success or failure of attempts to quit smoking, we propose to develop new statistical methods for analyzing two existing data sets involving the use of electronic diaries to monitor the moods and environments of smokers in real time. Beyond the smoking data considered here, the proposed methods have broad applications in public health, ranging from analysis of addictive behaviors to investigations of patterns of asthma attacks, epileptic seizures, recurrent tumors in cancer patients, and more.