What was the baseline period of the study?

The randomization of epilepsy patients took place after a 12-week baseline period that served to stabilize the use of AED’s, and duringwhich the number of seizures were counted.

What is the binomial probability of a given case?

The binomial probability, conditional on the random effects, is:P(yi | ξ , bi) = ni∏ j=1 λ yij ij (1 − λij)(1−yij), (27)where λij is defined by Equation (10).

What is the corresponding scale parameter for the Weibull-normal (W-N)?

The Weibull-normal (W-N) and Weibull-gamma-normal (WGN) models are considered, with scale parameter λ = 1, and linear predictor ηij = ξ0 + bi + ξ1Ti, where Ti is an indicator for treatment and bi ∼ N(0, d).

What is the advantage of the numerical approach?

The advantage of this approach is straightforward implementation for the models considered here but also for other models with perturbation scheme (19) for the log-likelihood, provided that the score and Hessian functions are numerically available.

Open AccessJournal Article10.1080/02664763.2015.1117594

Local influence diagnostics for incomplete overdispersed longitudinal counts

Trias Wahyuni Rakhmawati, +3 more

- 17 Feb 2016

- Journal of Applied Statistics

- Vol. 43, Iss: 9, pp 1722-1737

TL;DR: This paper developed local influence diagnostics to detect influential subjects when generalized linear mixed models are fitted to incomplete longitudinal overdispersed count data, focusing on the influence stemming from the dropout model specification.

Abstract: We develop local influence diagnostics to detect influential subjects when generalized linear mixed models are fitted to incomplete longitudinal overdispersed count data. The focus is on the influence stemming from the dropout model specification. In particular, the effect of small perturbations around an MAR specification are examined. The method is applied to data from a longitudinal clinical trial in epileptic patients. The effect on models allowing for overdispersion is contrasted with that on models that do not.

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Most frequently asked questions

1. What are the contributions mentioned in the paper "Local influence diagnostics for generalized linear mixed models with overdispersion" ?

Given the model ’ s nonlinear structure, these authors did not derive interpretable components but rather focused on a graphical depiction of influence.. In this paper, the authors consider GLMMs for binary, count, and time-to-event data, with the additional feature of accommodating overdispersionwhenever necessary.. Unlike when case deletion is used, this leads to interpretable components, allowing not only to identify influential subjects, but also to study the cause thereof.

2. What is the common method for analyzing hierarchical data?

Next to linear mixed models (LMMs) for hierarchical Gaussian data [26], generalized linear mixed models (GLMMs; [2,19,28]) have become a standard tool for the analysis of hierarchical data of a variety of data types.

3. What is the frequently used random-effects model?

The GLMM [2,11,28] is arguably the most frequently used random-effects model in the context of (non-)Gaussian repeatedmeasurements, extending both GLMMs for univariate outcomes and LMMs [26].

4. How many people were randomized to weight training?

The study of two treatment modalities was aimed at reducing the occurrence of muscle soreness among 400 middle-aged men in the beginning of weight training.

Citations

Journal Article•10.1080/02664763.2018.1510476

Application of sensitivity analysis to incomplete longitudinal CD4 count data

Abdul-Karim Iddrisu, +1 more

- 12 Mar 2019

- Journal of Applied Statistics

TL;DR: The analyses showed that the inferences from the MAR are robust to the NMAR assumption and influential subjects do not overturn the study conclusions about treatment effects and the dropout mechanism and the missing CD4 count measurements are likely to be MAR.

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Hierarchical models with normal and conjugate random effects: a review (invited article)

Geert Molenberghs, +2 more

- 01 Jan 2017

- Sort-statistics and Operations Research ...

TL;DR: A unified treatment of the model framework and key extensions is provided and the basic models and several extensions are illustrated using a set of key examples, one per data type (count, binary, multinomial, ordinal, and time-to-event).

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A joint transition model for evaluating eGFR as biomarker for rejection after kidney transplantation

Maarten Coemans, +2 more

- 14 Oct 2021

- Statistical Modelling

TL;DR: A joint model is built which combines characteristics of transition models and shared parameter models to carry over information from one biopsy to the next, taking into account the longitudinal information of eGFR collected in between, and concludes that a negative deviation from the mean eGfr slope increases the probability of rejection in indication biopsies, but that, on top of the biopsy history, there is little benefit in using the eG FR profile for diagnosing rejection.

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Journal Article•10.1080/02664763.2018.1531978

Sensitivity analysis of longitudinal count responses: a local influence approach and application to medical data

Alejandra Tapia, +3 more

- 26 Apr 2019

- Journal of Applied Statistics

TL;DR: In this article, a negative binomial mixed model was used to analyze longitudinal count responses under over-dispersion, and the model was shown to be better described with a Poisson mixed model.

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Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

Stefanie Schoenen, +10 more

- 02 Mar 2024

- Orphanet Journal of Rare Diseases

TL;DR: The iSTORE project aims to improve rare disease clinical trials in limited populations by developing innovative statistical methodologies for natural history course modeling, subgroup similarity identification, and multiple endpoint analysis to enhance trial planning and evidence level.

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References

•Book

Statistical Analysis with Missing Data

Roderick J. A. Little, +1 more

- 01 Jan 1987

TL;DR: This work states that maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse and large-Sample Inference Based on Maximum Likelihood Estimates is likely to be high.

...read moreread less

18.3K

Journal Article•10.1198/TECH.2003.S167

Statistical Analysis With Missing Data

Nicole A. Lazar

- 01 Nov 2003

- Technometrics

TL;DR: Generalized Estimating Equations is a good introductory book for analyzing continuous and discrete correlated data using GEE methods and provides good guidance for analyzing correlated data in biomedical studies and survey studies.

...read moreread less

10.6K

Journal Article•10.1093/BIOMET/63.3.581

Inference and missing data

Donald B. Rubin

- 01 Dec 1976

- Biometrika

TL;DR: In this article, it was shown that ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are missing at random and the observed data are observed at random, and then such inferences are generally conditional on the observed pattern of missing data.

...read moreread less

10K

Journal Article•10.1080/01621459.1993.10594284

Approximate inference in generalized linear mixed models

Norman E. Breslow, +1 more

- 01 Mar 1993

- Journal of the American Statistical Asso...

TL;DR: In this paper, generalized linear mixed models (GLMM) are used to estimate the marginal quasi-likelihood for the mean parameters and the conditional variance for the variances, and the dispersion matrix is specified in terms of a rank deficient inverse covariance matrix.

...read moreread less

4.6K

•Book

Linear Mixed Models for Longitudinal Data

Geert Verbeke, +1 more

- 26 Mar 2013

TL;DR: Using data of 955 men, Brant et al showed that the average rates of increase of systolic blood pressure (SBP) are smallest in the younger age groups, and greatest in the older agegroups, and that obese individuals tend to have a higher SBP than non-obese individuals.

...read moreread less

4.1K

...

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Local influence diagnostics for incomplete overdispersed longitudinal counts

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AI Agents for this Paper

Most frequently asked questions

1. What are the contributions mentioned in the paper "Local influence diagnostics for generalized linear mixed models with overdispersion" ?

2. What is the common method for analyzing hierarchical data?

3. What is the frequently used random-effects model?

4. How many people were randomized to weight training?

5. What was the baseline period of the study?

6. What is the binomial probability of a given case?

7. What is the corresponding scale parameter for the Weibull-normal (W-N)?

8. What is the advantage of the numerical approach?

Citations

Application of sensitivity analysis to incomplete longitudinal CD4 count data

Hierarchical models with normal and conjugate random effects: a review (invited article)

A joint transition model for evaluating eGFR as biomarker for rejection after kidney transplantation

Sensitivity analysis of longitudinal count responses: a local influence approach and application to medical data

Istore: a project on innovative statistical methodologies to improve rare diseases clinical trials in limited populations

References

Statistical Analysis with Missing Data

Statistical Analysis With Missing Data

Inference and missing data

Approximate inference in generalized linear mixed models

Linear Mixed Models for Longitudinal Data

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