| Type | Journal Article |
|---|---|
| Author | David J. Lunn |
| Author | Jon Wakefield |
| Author | Amy Racine-Poon |
| URL | https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.922 |
| Volume | 20 |
| Issue | 15 |
| Pages | 2261-2285 |
| Publication | Statistics in Medicine |
| ISSN | 1097-0258 |
| Date | 2001 |
| Extra | _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.922 |
| DOI | 10.1002/sim.922 |
| Accessed | 10/21/2021, 9:08:27 AM |
| Library Catalog | Wiley Online Library |
| Language | en |
| Abstract | Ordered categorical data arise in numerous settings, a common example being pain scores in analgesic trials. The modelling of such data is intrinsically more difficult than the modelling of continuous data due to the constraints on the underlying probabilities and the reduced amount of information that discrete outcomes contain. In this paper we discuss the class of cumulative logit models, which provide a natural framework for ordinal data analysis. We show how viewing the categorical outcome as the discretization of an underlying continuous response allows a natural interpretation of model parameters. We also show how covariates are incorporated into the model and how various types of correlation among repeated measures on the same individual may be accounted for. The models are illustrated using longitudinal allergy data consisting of sneezing scores measured on a four-point scale. Our approach throughout is Bayesian and we present a range of simple diagnostics to aid model building. Copyright © 2001 John Wiley & Sons, Ltd. |
| Short Title | Cumulative logit models for ordinal data |
| Date Added | 10/21/2021, 9:08:27 AM |
| Modified | 10/21/2021, 9:11:10 AM |
Has an example where variance of random effects is greatly reduced when modeling serial dependence using a Markov model vs. using the ordinary random effects model, stating that within-subject variation is mostly explained by serial correlation.
| Type | Journal Article |
|---|---|
| Author | Orestis Efthimiou |
| Author | Nicky Welton |
| Author | Myrto Samara |
| Author | Stefan Leucht |
| Author | Georgia Salanti |
| URL | https://onlinelibrary.wiley.com/doi/abs/10.1002/pst.1794 |
| Rights | Copyright © 2016 The Authors Pharmaceutical Statistics Published by John Wiley & Sons Ltd. |
| Volume | 16 |
| Issue | 2 |
| Pages | 122-132 |
| Publication | Pharmaceutical Statistics |
| ISSN | 1539-1612 |
| Date | 2017 |
| Extra | _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/pst.1794 |
| DOI | https://doi.org/10.1002/pst.1794 |
| Accessed | 5/2/2021, 3:52:14 PM |
| Library Catalog | Wiley Online Library |
| Language | en |
| Abstract | Missing outcome data constitute a serious threat to the validity and precision of inferences from randomized controlled trials. In this paper, we propose the use of a multistate Markov model for the analysis of incomplete individual patient data for a dichotomous outcome reported over a period of time. The model accounts for patients dropping out of the study and also for patients relapsing. The time of each observation is accounted for, and the model allows the estimation of time-dependent relative treatment effects. We apply our methods to data from a study comparing the effectiveness of 2 pharmacological treatments for schizophrenia. The model jointly estimates the relative efficacy and the dropout rate and also allows for a wide range of clinically interesting inferences to be made. Assumptions about the missingness mechanism and the unobserved outcomes of patients dropping out can be incorporated into the analysis. The presented method constitutes a viable candidate for analyzing longitudinal, incomplete binary data. |
| Date Added | 5/2/2021, 3:52:14 PM |
| Modified | 5/2/2021, 3:52:58 PM |
| Type | Journal Article |
|---|---|
| Author | Alberto Pasanisi |
| Author | Shuai Fu |
| Author | Nicolas Bousquet |
| URL | http://arxiv.org/abs/1009.1216 |
| Volume | 56 |
| Issue | 9 |
| Pages | 2609-2625 |
| Publication | Computational Statistics & Data Analysis |
| ISSN | 01679473 |
| Date | 9/2012 |
| Extra | arXiv: 1009.1216 |
| Journal Abbr | Computational Statistics & Data Analysis |
| DOI | 10.1016/j.csda.2012.02.027 |
| Accessed | 5/2/2021, 3:47:02 PM |
| Library Catalog | arXiv.org |
| Abstract | The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable. A review of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied. |
| Date Added | 5/2/2021, 3:47:02 PM |
| Modified | 5/2/2021, 3:50:02 PM |
Comment: 26 pages - preprint accepted in 20th February 2012 for publication in Computational Statistics and Data Analysis (please cite the journal's paper)
| Type | Journal Article |
|---|---|
| Author | Yu Luo |
| Author | David A. Stephens |
| Author | Aman Verma |
| Author | David L. Buckeridge |
| URL | http://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13261 |
| Rights | © 2020 The International Biometric Society |
| Volume | 77 |
| Issue | 1 |
| Pages | 78-90 |
| Publication | Biometrics |
| ISSN | 1541-0420 |
| Date | 2021 |
| Extra | _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/biom.13261 |
| DOI | https://doi.org/10.1111/biom.13261 |
| Accessed | 3/10/2021, 7:22:51 AM |
| Library Catalog | Wiley Online Library |
| Language | en |
| Abstract | Large amounts of longitudinal health records are now available for dynamic monitoring of the underlying processes governing the observations. However, the health status progression across time is not typically observed directly: records are observed only when a subject interacts with the system, yielding irregular and often sparse observations. This suggests that the observed trajectories should be modeled via a latent continuous-time process potentially as a function of time-varying covariates. We develop a continuous-time hidden Markov model to analyze longitudinal data accounting for irregular visits and different types of observations. By employing a specific missing data likelihood formulation, we can construct an efficient computational algorithm. We focus on Bayesian inference for the model: this is facilitated by an expectation-maximization algorithm and Markov chain Monte Carlo methods. Simulation studies demonstrate that these approaches can be implemented efficiently for large data sets in a fully Bayesian setting. We apply this model to a real cohort where patients suffer from chronic obstructive pulmonary disease with the outcome being the number of drugs taken, using health care utilization indicators and patient characteristics as covariates. |
| Date Added | 3/10/2021, 7:22:51 AM |
| Modified | 3/10/2021, 7:23:47 AM |
| Type | Journal Article |
|---|---|
| Author | Isabelle L. Smith |
| Author | Jane E. Nixon |
| Author | Linda Sharples |
| URL | http://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8882 |
| Rights | © 2021 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. |
| Volume | n/a |
| Issue | n/a |
| Publication | Statistics in Medicine |
| ISSN | 1097-0258 |
| Date | 2021 |
| Extra | _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.8882 |
| DOI | https://doi.org/10.1002/sim.8882 |
| Accessed | 2/12/2021, 11:20:57 AM |
| Library Catalog | Wiley Online Library |
| Language | en |
| Abstract | For clinical trials where participants pass through a number of discrete health states resulting in longitudinal measures over time, there are several potential primary estimands for the treatment effect. Incidence or time to a particular health state are commonly used outcomes but the choice of health state may not be obvious and these estimands do not make full use of the longitudinal assessments. Multistate models have been developed for some diseases and conditions with the purpose of understanding their natural history and have been used for secondary analysis to understand mechanisms of action of treatments. There is little published on the use of multistate models as the primary analysis method and potential implications on design features, such as assessment schedules. We illustrate methods via analysis of data from a motivating example; a Phase III clinical trial of pressure ulcer prevention strategies. We clarify some of the possible estimands that might be considered and we show, via a simulation study, that under some circumstances the sample size could be reduced by half using a multistate model based analysis, without adversely affecting the power of the trial. |
| Date Added | 2/12/2021, 11:20:57 AM |
| Modified | 2/25/2021, 8:34:44 AM |
| Type | Journal Article |
|---|---|
| Author | Shaun Bender |
| Author | Victoria Gamerman |
| Author | Peter P. Reese |
| Author | Daniel Lloyd Gray |
| Author | Yimei Li |
| Author | Justine Shults |
| URL | http://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8883 |
| Rights | © 2021 John Wiley & Sons, Ltd. |
| Volume | n/a |
| Issue | n/a |
| Publication | Statistics in Medicine |
| ISSN | 1097-0258 |
| Date | 2021 |
| Extra | _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.8883 |
| DOI | https://doi.org/10.1002/sim.8883 |
| Accessed | 2/12/2021, 11:18:56 AM |
| Library Catalog | Wiley Online Library |
| Language | en |
| Abstract | We consider longitudinal discrete data that may be unequally spaced in time and may exhibit overdispersion, so that the variance of the outcome variable is inflated relative to its assumed distribution. We implement an approach that extends generalized linear models for analysis of longitudinal data and is likelihood based, in contrast to generalized estimating equations (GEE) that are semiparametric. The method assumes independence between subjects; first-order antedependence within subjects; exponential family distributions for the first outcome on each subject and for the subsequent conditional distributions; and linearity of the expectations of the conditional distributions. We demonstrate application of the method in an analysis of seizure counts and in a study to evaluate the performance of transplant centers. Simulations for both studies demonstrate the benefits of the proposed likelihood based approach; however, they also demonstrate better than anticipated performance for GEE. |
| Date Added | 2/12/2021, 11:18:56 AM |
| Modified | 2/12/2021, 11:20:18 AM |
| Type | Journal Article |
|---|---|
| Author | Noorian, Sajad |
| Author | Ganjali, Mojtaba |
| URL | https://www.academia.edu/30796618/Bayesian_Analysis_of_Transition_Model_for_Longitudinal_Ordinal_Response_Data_Application_to_Insomnia_Data |
| Volume | 1 |
| Issue | 2 |
| Pages | 148-161 |
| Publication | International Journal of Statistics in Medical Research |
| ISSN | 1929-6029 |
| Date | 2012 |
| Accessed | 12/22/2020, 8:21:14 AM |
| Library Catalog | www.academia.edu |
| Language | en |
| Abstract | Bayesian Analysis of Transition Model for Longitudinal Ordinal Response Data: Application to Insomnia Data |
| Short Title | Bayesian Analysis of Transition Model for Longitudinal Ordinal Response Data |
| Date Added | 12/22/2020, 8:21:14 AM |
| Modified | 1/24/2021, 7:21:47 AM |
Bayesian inference for Goodman-Kruskal gamma rank correlation using multinomial distribution and Dirichlet prior. Markov proportional odds model with priors for intercepts that are ordered t distribution variates. Also uses a sequential-conditioning Markov-like prior for the coefficients of previous states. Methods don't scale to high number of Y levels. Dataset used is not a very good one as it categorized an ordinal measurement into a very crude ordinal measurement. Transition model is categorical in previous Y level.
| Type | Journal Article |
|---|---|
| Author | Larry R. Muenz |
| Author | Lawrence V. Rubinstein |
| URL | http://www.jstor.org/stable/2530646 |
| Volume | 41 |
| Issue | 1 |
| Pages | 91-101 |
| Publication | Biometrics |
| ISSN | 0006-341X |
| Date | 1985 |
| Extra | Publisher: [Wiley, International Biometric Society] |
| DOI | 10.2307/2530646 |
| Accessed | 12/27/2020, 10:27:53 AM |
| Library Catalog | JSTOR |
| Abstract | Suppose that a heterogeneous group of individuals is followed over time and that each individual can be in state 0 or state 1 at each time point. The sequence of states is assumed to follow a binary Markov chain. In this paper we model the transition probabilities for the 0 to 0 and 1 to 0 transitions by two logistic regressions, thus showing how the covariates relate to changes in state. With p covariates, there are 2(p + 1) parameters including intercepts, which we estimate by maximum likelihood. We show how to use transition probability estimates to test hypotheses about the probability of occupying state 0 at time i (i = 2, ..., T) and the equilibrium probability of state 0. These probabilities depend on the covariates. A recursive algorithm is suggested to estimate regression coefficients when some responses are missing. Extensions of the basic model which allow time-dependent covariates and nonstationary or second-order Markov chains are presented. An example shows the model applied to a study of the psychological impact of breast cancer in which women did or did not manifest distress at four time points in the year following surgery. |
| Date Added | 12/27/2020, 10:27:53 AM |
| Modified | 1/22/2021, 5:44:04 PM |
Not clear on why dual models are need. I think I'm content with P(0 -> 1) = expit(alpha + beta*x) and P(1 -> 0) = expit(-alpha -beta*x - gamma) where gamma is the coefficient of Y(t-1) in the logistic model.
Covers median time until entering a state.
Table 4 states that b'x = d'x is equivalent to independence of binary sequences for a specific clear. Not clear on this.
Covers missing responses.
Has matrix exponent form of occupation probabilities.
| Type | Journal Article |
|---|---|
| Author | Fei Yu |
| Author | Hal Morgenstern |
| Author | Eric Hurwitz |
| Author | Thomas R Berlin |
| URL | https://doi.org/10.1191/0962280203sm321ra |
| Volume | 12 |
| Issue | 4 |
| Pages | 321-331 |
| Publication | Statistical Methods in Medical Research |
| ISSN | 0962-2802 |
| Date | August 1, 2003 |
| Extra | Publisher: SAGE Publications Ltd STM |
| Journal Abbr | Stat Methods Med Res |
| DOI | 10.1191/0962280203sm321ra |
| Accessed | 1/3/2021, 9:06:24 AM |
| Library Catalog | SAGE Journals |
| Language | en |
| Abstract | In a randomized clinical trial to assess the effectiveness of different strategies for treating low-back pain in a managed-care setting, 681 adult patients presenting with low-back pain were randomized to four treatment groups: medical care with and without physical therapy; and chiropractic care with and without physical modalities. Follow-up information was obtained by questionnaires at two and six weeks, six, 12 and 18 months and by a telephone interview at four weeks. One outcome measurement at each follow-up is the patient’s self-report on the perception of low-back pain improvement from the previous survey, recorded as ‘A lot better,’ ‘A little better,’ ‘About the same’ and ‘Worse.’ Since the patient’s perception of improvement may be influenced by past experience, the outcome is analysed using a transition (first-order Markov) model. Although one could collapse categories to the point that logistic regression analysis with repeated measurements could be used, here we allow for multiple categories by relating transition probabilities to covariates and previous outcomes through a polytomous logistic regression model with Markov structure. This approach allows us to assess not only the effects of treatment assignment and baseline characteristics but also the effects of past outcomes in analysing longitudinal categorical data. |
| Date Added | 1/3/2021, 9:06:25 AM |
| Modified | 1/22/2021, 4:56:08 PM |
Polytomous Markov logistic model; made no use of the ordinal nature of Y. Shows how to use Cox or Poisson regression to do polytomous regression.
| Type | Journal Article |
|---|---|
| Author | A. Azzalini |
| URL | + http://dx.doi.org/10.1093/biomet/81.4.767 |
| Volume | 81 |
| Issue | 4 |
| Pages | 767-775 |
| Publication | Biometrika |
| Date | 1994 |
| Extra | Citation Key: azz94log tex.citeulike-article-id= 14413457 tex.citeulike-attachment-1= azz94log.pdf; /pdf/user/harrelfe/article/14413457/1115540/azz94log.pdf; 756c07ab51f065630cc1f5ec267153565bdaa110 tex.citeulike-linkout-0= http://dx.doi.org/10.1093/biomet/81.4.767 tex.citeulike-linkout-1= + http://dx.doi.org/10.1093/biomet/81.4.767 tex.eprint= /oup/backfile/content\_public/journal/biomet/81/4/10.1093/biomet/81.4.767/2/81-4-767.pdf tex.posted-at= 2017-08-12 22:56:09 tex.priority= 2 |
| DOI | 10.1093/biomet/81.4.767 |
| Date Added | 7/7/2018, 1:38:33 PM |
| Modified | 1/4/2021, 9:54:00 AM |
See section 3.1 where the authors imply that if there are gaps in measurements one can merely replace 1-step transition probabilities with gap-step probabilities.
The paper's aim is to reparameterize the model so that an effect is on the unconditional (on previous times) probability Y=1. The author did not comment on the fact that one can use the simple parameterization and uncondition the estimates to get marginal quantities.
| Type | Journal Article |
|---|---|
| Author | Paul S. Albert |
| URL | http://www.jstor.org/stable/2533196 |
| Volume | 50 |
| Issue | 1 |
| Pages | 51-60 |
| Publication | Biometrics |
| ISSN | 0006-341X |
| Date | 1994 |
| Extra | Publisher: [Wiley, International Biometric Society] |
| DOI | 10.2307/2533196 |
| Accessed | 1/3/2021, 9:28:18 AM |
| Library Catalog | JSTOR |
| Abstract | Many chronic diseases follow a course with multiple relapses into periods with severe symptoms alternating with periods of remission; experimental allergic encephalomyelitis, the animal model for multiple sclerosis, is an example of such a disease. A finite Markov chain is proposed as a model for analyzing sequences of ordinal data from a relapsing-remitting disease. The proposed model is one in which the state space is expanded to include information about the relapsing-remitting status as well as the ordinal severity score, and a reparameterization is suggested that reduces the number of parameters needed to be estimated. The Markov model allows for a wide range of relapsing-remitting behavior, provides an understanding of the stochastic nature of the disease process, and allows for efficient estimation of important characteristics of the disease course (such as mean first passage times, occupation times, and steady-state probabilities). These methods are applied to data from a study of the effect of a treatment (transforming growth factor-β1) on experimental allergic encephalomyelitis. |
| Date Added | 1/3/2021, 9:28:18 AM |
| Modified | 1/3/2021, 9:28:52 AM |
Joint model for relapse and disease severity. Not clear why this needs to be two models. For equally spaced measurements.
| Type | Journal Article |
|---|---|
| Author | J. K. Lindsey |
| Author | B. Jones |
| Author | A. F. Ebbutt |
| URL | http://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0258%2819971230%2916%3A24%3C2873%3A%3AAID-SIM675%3E3.0.CO%3B2-D |
| Rights | Copyright © 1997 John Wiley & Sons, Ltd. |
| Volume | 16 |
| Issue | 24 |
| Pages | 2873-2882 |
| Publication | Statistics in Medicine |
| ISSN | 1097-0258 |
| Date | 1997 |
| Extra | _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291097-0258%2819971230%2916%3A24%3C2873%3A%3AAID-SIM675%3E3.0.CO%3B2-D |
| DOI | https://doi.org/10.1002/(SICI)1097-0258(19971230)16:24<2873::AID-SIM675>3.0.CO;2-D |
| Accessed | 1/3/2021, 9:22:28 AM |
| Library Catalog | Wiley Online Library |
| Language | en |
| Abstract | In contrast to other models for ordinal data, the continuation ratio model can be fitted with standard statistical software. This makes it particularly appropriate for large clinical trials with ordinal response variables. In addition, when the trials are longitudinal, this model can be applied to individual responses instead of frequencies in contingency tables. Dependence can be incorporated by conditioning on the previous response, yielding a form of Markov chain. This approach is applied to the analysis of a large seasonal rhinitis trial, where patients were observed over 28 days and six symptoms recorded as ordinal responses. © 1997 John Wiley & Sons, Ltd. |
| Date Added | 1/3/2021, 9:22:28 AM |
| Modified | 1/3/2021, 9:22:59 AM |
Uses continuation ratio model, which requires stringing ot the data doubly (over categories and over time) but is flexible. Does not cover irregular times. States that if an observation is missing in the middle it will require ignoring the next non-missing observation.
| Type | Journal Article |
|---|---|
| Author | Kathryn Bartimote-Aufflick |
| Author | Peter C. Thomson |
| URL | https://doi.org/10.1080/02664763.2010.529885 |
| Volume | 38 |
| Issue | 9 |
| Pages | 1883-1897 |
| Publication | Journal of Applied Statistics |
| ISSN | 0266-4763 |
| Date | September 1, 2011 |
| Extra | Publisher: Taylor & Francis _eprint: https://doi.org/10.1080/02664763.2010.529885 |
| DOI | 10.1080/02664763.2010.529885 |
| Accessed | 1/3/2021, 8:47:54 AM |
| Library Catalog | Taylor and Francis+NEJM |
| Abstract | While standard techniques are available for the analysis of time-series (longitudinal) data, and for ordinal (rating) data, not much is available for the combination of the two, at least in a readily-usable form. However, this data type is common place in the natural and health sciences where repeated ratings are recorded on the same subject. To analyse these data, this paper considers a transition (Markov) model where the rating of a subject at one time depends explicitly on the observed rating at the previous point of time by incorporating the previous rating as a predictor variable. Complications arise with adequate handling of data at the first observation (t=1), as there is no prior observation to use as a predictor. To overcome this, it is postulated the existence of a rating at time t=0; however it is treated as ‘missing data’ and the expectation–maximisation algorithm used to accommodate this. The particular benefits of this method are shown for shorter time series. |
| Date Added | 1/3/2021, 8:47:54 AM |
| Modified | 1/3/2021, 8:48:25 AM |
Imputation and E-M for handling missing first observation; does not cover other missings or irregular time points
Emphasis of paper is on the case where the first observation of Y is a response, and one wants to impute the time zero state.
Points to Diggle et al 2nd edition 2002 as primary reference for Markov ordinal models.
Discusses interacting covariates with previous state but doesn't use that in their examples.
| Type | Journal Article |
|---|---|
| Author | Richard H. Jones |
| Author | Stanley Xu |
| Author | Gary K. Grunwald |
| Volume | 48 |
| Issue | 3 |
| Pages | 411-419 |
| Publication | Biometrical Journal. Biometrische Zeitschrift |
| ISSN | 0323-3847 |
| Date | 2006-06 |
| Extra | PMID: 16845905 |
| Journal Abbr | Biom J |
| DOI | 10.1002/bimj.200510224 |
| Library Catalog | PubMed |
| Language | eng |
| Abstract | Longitudinal data usually consist of a number of short time series. A group of subjects or groups of subjects are followed over time and observations are often taken at unequally spaced time points, and may be at different times for different subjects. When the errors and random effects are Gaussian, the likelihood of these unbalanced linear mixed models can be directly calculated, and nonlinear optimization used to obtain maximum likelihood estimates of the fixed regression coefficients and parameters in the variance components. For binary longitudinal data, a two state, non-homogeneous continuous time Markov process approach is used to model serial correlation within subjects. Formulating the model as a continuous time Markov process allows the observations to be equally or unequally spaced. Fixed and time varying covariates can be included in the model, and the continuous time model allows the estimation of the odds ratio for an exposure variable based on the steady state distribution. Exact likelihoods can be calculated. The initial probability distribution on the first observation on each subject is estimated using logistic regression that can involve covariates, and this estimation is embedded in the overall estimation. These models are applied to an intervention study designed to reduce children's sun exposure. |
| Date Added | 1/1/2021, 8:54:07 AM |
| Modified | 1/1/2021, 8:54:41 AM |
Explicit handling of continuous time through an exponential decay. Likelihood involves a combination of logit and complementary log-log links, so is a bit complex and doesn't clearly extend to ordinal Y.
| Type | Journal Article |
|---|---|
| Author | GARRETT M. FITZMAURICE |
| Author | NAN M. LAIRD |
| URL | https://doi.org/10.1093/biomet/80.1.141 |
| Volume | 80 |
| Issue | 1 |
| Pages | 141-151 |
| Publication | Biometrika |
| ISSN | 0006-3444 |
| Date | March 1, 1993 |
| Journal Abbr | Biometrika |
| DOI | 10.1093/biomet/80.1.141 |
| Accessed | 12/27/2020, 10:22:24 AM |
| Library Catalog | Silverchair |
| Abstract | In this paper, we discuss a likelihood-based method for analysing correlated binary responses based on a multivariate model. It is related to the pseudo-maximum likelihood approach suggested recently by Zhao & Prentice (1990). Their parameterization results in a simple pairwise model, in which the association between responses is modelled in terms of correlations, while the present paper uses conditional log odds-ratios. With this approach, higher-order associations can be incorporated in a natural way. One important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence. We describe an iterative two-stage procedure for obtaining the maximum likelihood estimates. Two examples are presented to illustrate this methodology. |
| Date Added | 12/27/2020, 10:22:24 AM |
| Modified | 12/27/2020, 10:22:56 AM |
odds ratios as dependence parameters; dependence structures more general than Markov including compound symmetry-type models. General model uses a matrix of all pairwise co-occurrences. The paper starts with a general multivariate distribution for all the binary responses for one subject.
| Type | Journal Article |
|---|---|
| Author | M. Mandel |
| Author | R. Betensky |
| Publication | Biostatistics |
| Date | 2008 |
| DOI | 10.1093/biostatistics/kxn008 |
| Library Catalog | Semantic Scholar |
| Abstract | Longitudinal ordinal data are common in many scientific studies, including those of multiple sclerosis (MS), and are frequently modeled using Markov dependency. Several authors have proposed random-effects Markov models to account for heterogeneity in the population. In this paper, we go one step further and study prediction based on random-effects Markov models. In particular, we show how to calculate the probabilities of future events and confidence intervals for those probabilities, given observed data on the ordinal outcome and a set of covariates, and how to update them over time. We discuss the usefulness of depicting these probabilities for visualization and interpretation of model results and illustrate our method using data from a phase III clinical trial that evaluated the utility of interferon beta-1a (trademark Avonex) to MS patients of type relapsing-remitting. |
| Short Title | Estimating time-to-event from longitudinal ordinal data using random-effects Markov models |
| Date Added | 12/22/2020, 8:16:15 AM |
| Modified | 12/22/2020, 8:17:19 AM |
| Type | Journal Article |
|---|---|
| Author | M. Olschewski |
| Author | M. Schumacher |
| Volume | 9 |
| Pages | 749-763 |
| Publication | Stat Med |
| Date | 1990 |
| Extra | Citation Key: ols90sta tex.citeulike-article-id= 13264642 tex.posted-at= 2014-07-14 14:09:39 tex.priority= 0 |
| Date Added | 7/7/2018, 1:38:33 PM |
| Modified | 11/8/2019, 8:01:59 AM |
| Type | Journal Article |
|---|---|
| Author | Guillermo Marshall |
| Author | Richard H. Jones |
| Volume | 14 |
| Pages | 1975-1983 |
| Publication | Stat Med |
| Date | 1995 |
| Extra | Citation Key: mar95mul tex.citeulike-article-id= 13264580 tex.posted-at= 2014-07-14 14:09:38 tex.priority= 0 |
| Date Added | 7/7/2018, 1:38:33 PM |
| Modified | 11/8/2019, 8:01:59 AM |
| Type | Journal Article |
|---|---|
| Author | B. E. Hansen |
| Author | J. Thorogood |
| Author | J. Hermans |
| Author | R. J. Ploeg |
| Author | J. H. van Bockel |
| Author | J. C. van Houwelingen |
| Volume | 13 |
| Pages | 2517-2529 |
| Publication | Stat Med |
| Date | 1994 |
| Extra | Citation Key: han94mul tex.citeulike-article-id= 13264211 tex.posted-at= 2014-07-14 14:09:31 tex.priority= 0 |
| Date Added | 7/7/2018, 1:38:33 PM |
| Modified | 11/8/2019, 8:01:59 AM |
| Type | Journal Article |
|---|---|
| Author | Hussein R. al-Khalidi |
| Author | Daniel J. Schnell |
| Volume | 31 |
| Pages | 607-613 |
| Publication | Drug Info J |
| Date | 1997 |
| Extra | Citation Key: alk97app tex.citeulike-article-id= 13263686 tex.posted-at= 2014-07-14 14:09:21 tex.priority= 0 |
| Date Added | 7/7/2018, 1:38:33 PM |
| Modified | 11/8/2019, 8:01:59 AM |