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Predictors of refraction prediction error after cataract surgery: a shared parameter model to account for missing post-operative measurements

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STATISTICAL METHODS AND APPLICATIONS 2022年第2期31卷 343-364页

作者： Miller, D. Claire MaWhinney, Samantha Patnaik, Jennifer L. Christopher, Karen L. Lynch, Anne M. Wagner, Brandie D. Colorado Sch Publ Hlth Dept Biostat & Informat Aurora CO 80045 USA Univ Colorado Dept Ophthalmol Sch Med Aurora CO 80045 USA

Cataract surgery is a common procedure that involves removing the cataractous lens of the eye and implanting a new clear plastic lens, with a goal of improving vision and often changing the refraction of the eye. Unexpected refractive outcomes, or refraction prediction error (PE), may be more likely to occur among patients with certain preexisting ocular conditions. However, longitudinal refractive measurements are often missing after surgery, making it difficult to accurately assess which ocular comorbidities lead to increased PE. Moreover, patients with ideal refractive outcomes in one or both eyes may be less likely to return to the clinic, thus more likely to have missing measurements that are missing not at random (MNAR). Despite this potential complication to data analysis, very few studies evaluating PE address the missing data mechanism and the effect it may have on the results. We propose the application of a shared parameter model to reduce bias in situations of MNAR data and compare this to a linear mixed model that is not able to account for this mechanism. We also conduct a simulation study to better understand the most plausible missing mechanism in our study and to characterize situations in which the shared parameter model may be necessary. Applied to the cataract surgery data, the shared parameter model gives similar results as the linear mixed model, finding that a history of LASIK, PRK, RK, high myopia, hyperopia, astigmatism, or combined surgery lead to increased PE. In addition, the simulations confirm that under certain scenarios, a shared parameter model will greatly reduce bias in situations of MNAR.

关键词： Joint model shared parameter model Missing not at random Refraction prediction error Cataract surgery outcomes

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Using joint models for longitudinal and time-to-event data to investigate the causal effect of salvage therapy after prostatectomy

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STATISTICAL METHODS IN MEDICAL RESEARCH 2024年第5期33卷 894-908页

作者： Rizopoulos, Dimitris Taylor, Jeremy M. G. Papageorgiou, Grigorios Morgan, Todd M. Erasmus MC Dept Biostat POB 2040 NL-3000 CA Rotterdam Netherlands Erasmus MC Dept Epidemiol Rotterdam Netherlands Univ Michigan Dept Biostat Ann Arbor MI USA Univ Michigan Dept Urol Ann Arbor MI USA

Prostate cancer patients who undergo prostatectomy are closely monitored for recurrence and metastasis using routine prostate-specific antigen measurements. When prostate-specific antigen levels rise, salvage therapies are recommended in order to decrease the risk of metastasis. However, due to the side effects of these therapies and to avoid over-treatment, it is important to understand which patients and when to initiate these salvage therapies. In this work, we use the University of Michigan Prostatectomy Registry Data to tackle this question. Due to the observational nature of this data, we face the challenge that prostate-specific antigen is simultaneously a time-varying confounder and an intermediate variable for salvage therapy. We define different causal salvage therapy effects defined conditionally on different specifications of the longitudinal prostate-specific antigen history. We then illustrate how these effects can be estimated using the framework of joint models for longitudinal and time-to-event data. All proposed methodology is implemented in the freely-available R package JMbayes2.

关键词： Decision making observational data time-varying confounding time-varying treatment shared parameter model survival analysis

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Improved retention analysis in freemium role-playing games by jointly modelling players' motivation, progression and churn

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY 2022年第1期185卷 102-133页

作者： Karmakar, Bikram Liu, Peng Mukherjee, Gourab Che, Hai Dutta, Shantanu Univ Florida Dept Stat Gainesville FL 32611 USA Santa Clara Univ Dept Mkt Santa Clara CA 95053 USA Univ Southern Calif Dept Data Sci & Operat Los Angeles CA 90007 USA UC Riverside Dept Mkt Riverside CA USA Univ Southern Calif Dept Mkt Los Angeles CA 90007 USA

We consider user retention analytics for online freemium role-playing games (RPGs). RPGs constitute a very popular genre of computer-based games that, along with a player's gaming actions, focus on the development of the player's in-game virtual character through a persistent exploration of the gaming environment. Most RPGs follow the freemium business model in which the gamers can play for free but they are charged for premium add-on amenities. As with other freemium products, RPGs suffer from the curse of high dropout rates. This makes retention analysis extremely important for successful operation and survival of their gaming portals. Here, we develop a disciplined statistical framework for retention analysis by modelling multiple in-game player characteristics along with the dropout probabilities. We capture players' motivations through engagement times, collaboration and achievement score at each level of the game, and jointly model them using a generalized linear mixed model (glmm) framework that further includes a time-to-event variable corresponding to churn. We capture the interdependencies in a player's level-wise engagement, collaboration, achievement with dropout through a shared parameter model. We illustrate interesting changes in player behaviours as the gaming level progresses. The parameters in our joint model were estimated by a Hamiltonian Monte Carlo algorithm which incorporated a divide-and-recombine approach for increased scalability in glmm estimation that was needed to accommodate our large longitudinal gaming data-set. By incorporating the level-wise changes in a player's motivations and using them for dropout rate prediction, our method greatly improves on state-of-the-art retention models. Based on data from a popular action based RPG, we demonstrate the competitive optimality of our proposed joint modelling approach by exhibiting its improved predictive performance over competitors. In particular, we outperform aggregate statistics based

关键词： consumer engagement divide and recombine dropout freemium games joint modelling player motivation retention analysis role-playing games scalable glmm shared parameter model social contagion

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modeling of correlated cognitive function and functional disability outcomes with bounded and missing data in a longitudinal aging study

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BEHAVIOR RESEARCH METHODS 2022年第6期54卷 2949-2961页

作者： Agogo, George O. Mwambi, Henry Shi, Xiaoming Liu, Zuyun StatsDecide Analyt & Consulting Ltd POB 17438-20100 Nakuru Kenya Univ KwaZulu Natal Sch Math Stat & Comp Sci Pietermaritzburg Campus Pietermaritzburg South Africa Chinese Ctr Dis Control & Prevent Natl Inst Environm Hlth Beijing 100021 Peoples R China Zhejiang Univ Sch Med Dept Big Data Hlth Sci Hangzhou Peoples R China Zhejiang Univ Sch Med Ctr Clin Big Data & Analyt Sch Publ Hlth Hangzhou Peoples R China Zhejiang Univ Sch Med Affiliated Hosp 2 Hangzhou Peoples R China

Longitudinal studies of correlated cognitive and disability outcomes among older adults are characterized by missing data due to death or loss to follow-up from deteriorating health conditions. The Mini-Mental State Examination (MMSE) score for assessing cognitive function ranges from a minimum of 0 (floor) to a maximum of 30 (ceiling). To study the risk factors of cognitive function and functional disability, we propose a shared parameter model to handle missingness, correlation between outcomes, and the floor and ceiling effects of the MMSE measurements. The shared random effects in the proposed model handle missingness (either missing at random or missing not at random) and correlation between these outcomes, while the Tobit distribution handles the floor and ceiling effects of the MMSE measurements. We used data from the Chinese Longitudinal Healthy Longevity Survey (CLHLS) and a simulation study. By ignoring the MMSE floor and ceiling effects in the analyses of the CLHLS, the association of systolic blood pressure with cognitive function was not significant and the association of age with cognitive function was lower by 16.6% (from -6.237 to -5.201). By ignoring the MMSE floor and ceiling effects in the simulation study, the relative bias in the estimated association of female gender with cognitive function was 43 times higher (from -0.01 to -0.44). The estimated associations obtained with data missing at random were smaller than those with data missing not at random, demonstrating how the missing data mechanism affects the analytic results. Our work underscores the importance of proper model specification in longitudinal analysis of correlated outcomes subject to missingness and bounded values.

关键词： Correlated outcomes Joint modeling Mini-Mental State Examination Missing data shared parameter model Tobit regression

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A shared parameter location scale mixed effect model for EMA data subject to informative missing

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HEALTH SERVICES AND OUTCOMES RESEARCH METHODOLOGY 2018年第4期18卷 227-243页

作者： Lin, Xiaolei Mermelstein, Robin Hedeker, Donald Univ Chicago Dept Publ Hlth Sci Chicago IL 60637 USA Univ Illinois Inst Hlth Res & Policy Chicago IL USA

In this paper, we address the problem of accounting for informative missing in the context of ecological momentary assessment studies (sometimes referred to as intensive longitudinal studies), where each study unit gets measured intensively over time and intermittent missing is usually present. We present a shared parameter modeling approach that links the primary longitudinal outcome with potentially informative missingness by a common set of random effects that summarize a subjects' specific traits in terms of their mean (location) and variability (scale). The primary outcome, conditional on the random effects, are allowed to exhibit heterogeneity in terms of both the mean and within subject variance. Unlike previous methods which largely rely on numerical integration or approximation, we estimate the model by a full Bayesian approach using Markov Chain Monte Carlo. An adolescent mood study example is illustrated together with a series of simulation studies. Results in comparison to more conventional approaches suggest that accounting for the common but unobserved random subject mean and variance effects, shared between the primary outcome and missingness models, can significantly improve the model fit, and also provide the benefit of understanding how missingness can affect the inference for the primary outcome.

关键词： Ecological momentary assessments Informative missing Mixed effects shared parameter model

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Assessing importance of biomarkers: A Bayesian joint modelling approach of longitudinal and survival data with semi-competing risks

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STATISTICAL modelLING 2021年第1-2期21卷 30-55页

作者： Zhang, Fan Chen, Ming-Hui Cong, Xiuyu Julie Chen, Qingxia Pfizer Inc Groton CT 06340 USA Univ Connecticut Dept Stat Storrs CT 06269 USA Everest Med Shanghai Peoples R China Vanderbilt Univ Dept Biostat 221 Kirkland Hall Nashville TN 37235 USA

Longitudinal biomarkers such as patient-reported outcomes (PROs) and quality of life (QOL) are routinely collected in cancer clinical trials or other studies. Joint modelling of PRO/QOL and survival data can provide a comparative assessment of patient-reported changes in specific symptoms or global measures that correspond to changes in survival. Motivated by a head and neck cancer clinical trial, we develop a class of trajectory-based models for longitudinal and survival data with disease progression. Specifically, we propose a class of mixed effects regression models for longitudinal measures, a cure rate model for the disease progression time (T-P) and a Cox proportional hazards model with time-varying covariates for the overall survival time (T-D) to account for T-P and treatment switching. Under the semi-competing risks framework, the disease progression is the non-terminal event, the occurrence of which is subject to a terminal event of death. The properties of the proposed models are examined in detail. Within the Bayesian paradigm, we derive the decompositions of the deviance information criterion (DIC) and the logarithm of the pseudo-marginal likelihood (LPML) to assess the fit of the longitudinal component of the model and the fit of each survival component, separately. We further develop Delta DIC as well as Delta LPML to determine the importance and contribution of the longitudinal data to the model fit of the T-P and T-D data.

关键词： cure rate model DIC decomposition Markov chain Monte Carlo Patient-reported outcome shared parameter model time-varying covariates

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Joint modelling of competing risks and current status data: an application to a spontaneous labour study

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS 2019年第4期68卷 1167-1182页

作者： Lee, Youjin Wang, Mei-Cheng Grantz, Katherine L. Sundaram, Rajeshwari Johns Hopkins Sch Publ Hlth Baltimore MD USA Eunice Kennedy Shriver Natl Inst Child Hlth & Hum Bethesda MD USA

The second stage of labour begins when the cervix is fully dilated and pushing begins until the fetus is delivered. A Caesarean delivery (CD) or operative vaginal delivery (OVD) is typically encouraged after the recommended time set by 'expert consensus'. This recommended time has been set out of concern for an increased chance of maternal and neonatal morbidities due to a prolonged second stage of labour, but without thorough consideration of heterogeneous risks for spontaneous vaginal delivery (SVD) and morbidities among women. To provide quantitative evidence for the recommendation, the first step is to compare the risks for SVD, CD or OVD, and the risks of maternal or neonatal morbidities simultaneously across the duration of the second stage of labour. To address such risk comparisons statistically, one needs to study the joint distribution for the time to delivery due to each mode and time to maternal or neonatal morbidity given information provided for each individual. We introduce a joint model which combines the competing risks data for delivery time and current status data for any type of maternal or neonatal morbidity given each woman's baseline characteristics. These two processes are assumed dependent through individual-specific frailty under the joint model. Our numerical studies include a simulation that reflects the structure of observed real data and a detailed real data analysis based on nearly 12000 spontaneous labours. Our finding indicates the necessity to incorporate maternal characteristic such as age or body mass index in assessing the probability for delivery due to SVD, CD or OVD and the onset of morbidities across the second stage of labour.

关键词： Competing risks model Current status data Random effect shared parameter model

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Joint longitudinal and time-to-event models for multilevel hierarchical data

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STATISTICAL METHODS IN MEDICAL RESEARCH 2019年第12期28卷 3502-3515页

作者： Brilleman, Samuel L. Crowther, Michael J. Moreno-Betancur, Margarita Novik, Jacqueline Buros Dunyak, James Al-Huniti, Nidal Fox, Robert Hammerbacher, Jeff Wolfe, Rory Monash Univ Dept Epidemiol & Prevent Med Sch Publ Hlth & Prevent Med Melbourne Vic Australia Victorian Ctr Biostat ViCBiostat Melbourne Vic Australia Univ Leicester Dept Hlth Sci Biostat Res Grp Leicester Leics England Murdoch Childrens Res Inst Clin Epidemiol & Biostat Unit Melbourne Vic Australia Univ Melbourne Melbourne Sch Populat & Global Hlth Melbourne Vic Australia Icahn Sch Med Mt Sinai Dept Genet & Genom Sci New York NY 10029 USA AstraZeneca Quantitat Clin Pharmacol IMED Biotech Unit Waltham MA USA Med Univ South Carolina Dept Microbiol & Immunol Charleston SC 29425 USA

Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper, we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient may have more than one lesion, and each lesion is tracked over time, the data have a three-level hierarchical structure: repeated measurements taken at time points (level 1) clustered within lesions (level 2) within patients (level 3). We jointly model the lesion-specific longitudinal trajectories and patient-specific risk of death or disease progression by specifying novel association structures that combine information across lower level clusters (e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide user-friendly software for fitting the model under a Bayesian framework. Lastly, we discuss alternative situations in which additional clustering factor(s) occur at a level higher in the hierarchy than the patient-level, since this has implications for the model formulation.

关键词： Longitudinal survival joint model shared parameter model hierarchical multilevel cancer

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Bayesian quantile regression for analyzing ordinal longitudinal responses in the presence of non-ignorable missingness

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METRON-INTERNATIONAL JOURNAL OF STATISTICS 2018年第3期76卷 321-348页

作者： Ghasemzadeh, Siamak Ganjali, Mojtaba Baghfalaki, Taban Shahid Beheshti Univ Fac Math Sci Dept Stat Tehran Iran Tarbiat Modares Univ Fac Math Sci Dept Stat Tehran Iran

In this paper, we develop a quantile regression model for analyzing ordinal longitudinal responses with random effects in the presence of non-ignorable and non-monotone missing data. The ordinal responses are related to underlying latent variables which are considered to have asymmetric Laplace distribution. For modeling the missing data mechanism an ordinary probit model is used via specifying another latent variable. In order to consider non-ignorable missing data, a shared parameter model is used for joint modeling of ordinal longitudinal responses and missing data mechanism. We use a Bayesian approach via Markov chain Monte Carlo method for analyzing the proposed joint model. Especially to estimate unknown parameters, a Gibbs sampler algorithm is used. Moreover, we use the Schizophrenia data set to illustrate an application of the proposed model.

关键词： Asymmetric Laplace distribution Quantile regression Ordinal longitudinal data shared parameter model Gibbs sampler

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A shared parameter model for the estimation of longitudinal concomitant intervention effects

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BIOSTATISTICS 2011年第4期12卷 737-749页

作者： Wu, Colin O. Tian, Xin Jiang, Wenhua NHLBI Off Biostat Res Bethesda MD 20892 USA

We investigate a change-point approach for modeling and estimating the regression effects caused by a concomitant intervention in a longitudinal study. Since a concomitant intervention is often introduced when a patient's health status exhibits undesirable trends, statistical models without properly incorporating the intervention and its starting time may lead to biased estimates of the intervention effects. We propose a shared parameter change-point model to evaluate the pre- and postintervention time trends of the response and develop a likelihood-based method for estimating the intervention effects and other parameters. Application and statistical properties of our method are demonstrated through a longitudinal clinical trial in depression and heart disease and a simulation study.

关键词： Change-point model Concomitant intervention Likelihood Longitudinal study shared parameter model

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