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的时间的影响，以支持合作努力，以对涉及吸烟的生态瞬时评估(EMA)的两个现有数据集进行建模。EMA涉及使用电子日记来监控受试者在其环境中的实时行为，避免回溯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外，统计文献中对EMA的关注很少。生物统计学家和心理学家提议的合作研究的具体目的是：1)开发一个通用的概率抽样框架，以估计时变协变量对临时吸烟模式、指定戒烟日期后的寿命和香烟后的吸烟模式的影响，其中考虑到这些吸烟事件之间的时间相关性，并将其广泛应用于生态瞬时评估；2)构建时变协变量和一天中的时间的影响的联合模型，以解释成瘾行为的昼夜周期；3)建立了受试者之间关于基线吸烟率、时间协变量的影响和一天中的时间的变化的模型，从该模型中可以识别出表现出相似吸烟行为的受试者群；以及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的过去值的综合函数。为了更好地了解戒烟成功或失败的机制，将构建点过程和生存模型，以描述吸烟者心理状态和环境的时间变化对即兴吸烟模式、戒烟后的生命周期和导致复吸的香烟后模式的影响。点过程模型和生存模型的一个共同特征是，完全似然涉及时变协变量在采样域上的函数(强度或风险)的积分。该框架将采样域视为点的总体，并假设协变量是时间的一个未知但确定的函数。使用基于概率的设计对协变量进行采样，由此可以得到协变量的积分函数的设计无偏估计。将这种设计无偏估计代入似然估计，可以得到一个目标函数，该目标函数可以被最大化，以获得所建议的模型参数估计。作为基于时变协变量和重复行为事件的定时的联合建模的分层建模方法的替代方案，提供了对协变量的集成功能的基于设计的推理。与分层方法不同的是，不需要关于时变协变量的模型假设。与公共健康相关：为了更好地了解戒烟尝试成功或失败的机制，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，建议的方法在公共卫生中有广泛的应用，从成瘾行为的分析到哮喘发作、癫痫发作、癌症患者的复发肿瘤等模式的调查。

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.