اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA generalized linear mixed model for longitudinal binary data with a marginal logit link function
65
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Longitudinal studies of a binary outcome are common in the health, social, and behavioral sciences. In general, a feature of random effects logistic regression models for longitudinal binary data is that the marginal functional form, when integrated over the distribution of the random effects, is no longer of logistic form. Recently, Wang and Louis [Biometrika 90 (2003) 765--775] proposed a random intercept model in the clustered binary data setting where the marginal model has a logistic form. An acknowledged limitation of their model is that it allows only a single random effect that varies from cluster to cluster. In this paper we propose a modification of their model to handle longitudinal data, allowing separate, but correlated, random intercepts at each measurement occasion. The proposed model allows for a flexible correlation structure among the random intercepts, where the correlations can be interpreted in terms of Kendalls $tau$. For example, the marginal correlations among the repeated binary outcomes can decline with increasing time separation, while the model retains the property of having matching conditional and marginal logit link functions. Finally, the proposed method is used to analyze data from a longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women.
قيم البحث
اقرأ أيضاً
This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions that enabl
e the marginal likelihood of such class of models to be expressed in closed-form. Illustrations are provided using the Gaussian, Poisson, binomial and gamma distributions. These models are unified under a single umbrella of conjugate generalized linear mixed models, where conjugate refers to the fact that the marginal likelihood can be expressed in closed-form, rather than implying inference via the Bayesian paradigm. Having an explicit marginal likelihood means that these models are more computationally convenient, which can be important in big data contexts. Except for the binomial distribution, these models are able to achieve simultaneous conjugacy, and thus able to accommodate both unit and group level covariates.
Segmented regression is a standard statistical procedure used to estimate the effect of a policy intervention on time series outcomes. This statistical method assumes the normality of the outcome variable, a large sample size, no autocorrelation in t
he observations, and a linear trend over time. Also, segmented regression is very sensitive to outliers. In a small sample study, if the outcome variable does not follow a Gaussian distribution, then using segmented regression to estimate the intervention effect leads to incorrect inferences. To address the small sample problem and non-normality in the outcome variable, including outliers, we describe and develop a robust statistical method to estimate the policy intervention effect in a series of longitudinal data. A simulation study is conducted to demonstrate the effect of outliers and non-normality in the outcomes by calculating the power of the test statistics with the segmented regression and the proposed robust statistical methods. Moreover, since finding the sampling distribution of the proposed robust statistic is analytically difficult, we use a nonparametric bootstrap technique to study the properties of the sampling distribution and make statistical inferences. Simulation studies show that the proposed method has more power than the standard t-test used in segmented regression analysis under the non-normality error distribution. Finally, we use the developed technique to estimate the intervention effect of the Istanbul Declaration on illegal organ activities. The robust method detected more significant effects compared to the standard method and provided shorter confidence intervals.
Data scientists across disciplines are increasingly in need of exploratory analysis tools for data sets with a high volume of features. We expand upon graph mining approaches for exploratory analysis of high-dimensional data to introduce Sirius, a vi
sualization package for researchers to explore feature relationships among mixed data types using mutual information and network backbone sparsification. Visualizations of feature relationships aid data scientists in finding meaningful dependence among features, which can engender further analysis for feature selection, feature extraction, projection, identification of proxy variables, or insight into temporal variation at the macro scale. Graph mining approaches for feature analysis exist, such as association networks of binary features, or correlation networks of quantitative features, but mixed data types present a unique challenge for developing comprehensive feature networks for exploratory analysis. Using an information theoretic approach, Sirius supports heterogeneous data sets consisting of binary, continuous quantitative, and discrete categorical data types, and provides a user interface exploring feature pairs with high mutual information scores. We leverage a backbone sparsification approach from network theory as a dimensionality reduction technique, which probabilistically trims edges according to the local network context. Sirius is an open source Python package and Django web application for exploratory visualization, which can be deployed in data analysis pipelines. The Sirius codebase and exemplary data sets can be found at: https://github.com/compstorylab/sirius
Imaging in clinical oncology trials provides a wealth of information that contributes to the drug development process, especially in early phase studies. This paper focuses on kinetic modeling in DCE-MRI, inspired by mixed-effects models that are fre
quently used in the analysis of clinical trials. Instead of summarizing each scanning session as a single kinetic parameter -- such as median $ktrans$ across all voxels in the tumor ROI -- we propose to analyze all voxel time courses from all scans and across all subjects simultaneously in a single model. The kinetic parameters from the usual non-linear regression model are decomposed into unique components associated with factors from the longitudinal study; e.g., treatment, patient and voxel effects. A Bayesian hierarchical model provides the framework in order to construct a data model, a parameter model, as well as prior distributions. The posterior distribution of the kinetic parameters is estimated using Markov chain Monte Carlo (MCMC) methods. Hypothesis testing at the study level for an overall treatment effect is straightforward and the patient- and voxel-level parameters capture random effects that provide additional information at various levels of resolution to allow a thorough evaluation of the clinical trial. The proposed method is validated with a breast cancer study, where the subjects were imaged before and after two cycles of chemotherapy, demonstrating the clinical potential of this method to longitudinal oncology studies.
The mixed-logit model is a flexible tool in transportation choice analysis, which provides valuable insights into inter and intra-individual behavioural heterogeneity. However, applications of mixed-logit models are limited by the high computational
and data requirements for model estimation. When estimating on small samples, the Bayesian estimation approach becomes vulnerable to over and under-fitting. This is problematic for investigating the behaviour of specific population sub-groups or market segments with low data availability. Similar challenges arise when transferring an existing model to a new location or time period, e.g., when estimating post-pandemic travel behaviour. We propose an Early Stopping Bayesian Data Assimilation (ESBDA) simulator for estimation of mixed-logit which combines a Bayesian statistical approach with Machine Learning methodologies. The aim is to improve the transferability of mixed-logit models and to enable the estimation of robust choice models with low data availability. This approach can provide new insights into choice behaviour where the traditional estimation of mixed-logit models was not possible due to low data availability, and open up new opportunities for investment and planning decisions support. The ESBDA estimator is benchmarked against the Direct Application approach, a basic Bayesian simulator with random starting parameter values and a Bayesian Data Assimilation (BDA) simulator without early stopping. The ESBDA approach is found to effectively overcome under and over-fitting and non-convergence issues in simulation. Its resulting models clearly outperform those of the reference simulators in predictive accuracy. Furthermore, models estimated with ESBDA tend to be more robust, with significant parameters with signs and values consistent with behavioural theory, even when estimated on small samples.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
