A generalized Bayesian nonlinear mixed‐effects regression model for zero‐inflated longitudinal count data in tuberculosis trials

Burger, Divan Aristo; Schall, Robert; Jacobs, Rianne; Chen, Ding‐Geng

doi:10.1002/pst.1933

Cited by 3 publications

(8 citation statements)

References 54 publications

(106 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The bactericidal activity of anti-TB drugs was characterized by the rate of decline in log 10 (CFU) count. 19,20 In particular, the bactericidal activity over a certain time interval, calculated from a log 10 (CFU) vs time profile, was expressed as follows: 21…”

Section: Previous Data Analysismentioning

confidence: 99%

“…The clinical trial's efficacy endpoints included the bactericidal activity of the three treatments quantified by overnight sputum samples. The bactericidal activity of anti‐TB drugs was characterized by the rate of decline in

\log_{10} (CFU)

count 19,20 . In particular, the bactericidal activity over a certain time interval, calculated from a

\log_{10} (CFU)

vs time profile, was expressed as follows: 21

BA (t_{1} - t_{2}) = - \frac{\hat{f} (t_{2}) - \hat{f} (t_{1})}{t_{2} - t_{1}},

where

f (t)

is the regression function for

\log_{10} (CFU)

count vs time, and

\hat{f} (t_{1})

and

\hat{f} (t_{2})

are the corresponding fitted values at Day

t_{1}

and Day

t_{2}

, respectively.…”

Section: Motivating Data and Previous Workmentioning

confidence: 99%

“…where 𝛼 ij are the random intercepts, 𝛽 1ij and 𝛽 2ij the two random slopes, 𝜅 j the change-points (or "nodes"), 𝛾 j the smoothness parameters, and o ijk are offset constants. 15,20 Like conventional Poisson and NB regression, the offset constants o ijk are implemented should it be more relevant to model the mean or median "rates" instead of the counts. In the context of our motivating dataset, an offset function may be necessary to account for the dilution of sputum samples that may have been required to count the bacteria (ie, CFU counts; see Section 6 for more details).…”

Section: Biphasic Mixed-effects Regression Modelmentioning

confidence: 99%

“…In order to accommodate potential zero‐inflation in CFU counts, Burger et al 20 extended the previous model 15 by modeling the CFU counts on the original scale based on the ZINB distribution rather than modeling the logarithmic counts. The ZINB model of Burger et al 20 was applied to the CFU dataset of Dawson et al 25 However, the ZINB distribution also models the bactericidal activity of TB treatments based on the mean count. To model the median count, replacing the ZINB distribution with the ZIDW distribution can be considered 11,26 …”

Section: Motivating Data and Previous Workmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear mixed‐effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero‐inflated discrete Weibull distribution

Burger

Lesaffre

2021

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

This article proposes a Bayesian regression model for nonlinear zero-inflated longitudinal count data that models the median count as an alternative to the mean count. The nonlinear model generalizes a recently introduced linear mixed-effects model based on the zero-inflated discrete Weibull (ZIDW) distribution. The ZIDW distribution is more robust to severe skewness in the data than conventional zero-inflated count distributions such as the zero-inflated negative binomial (ZINB) distribution. Moreover, the ZIDW distribution is attractive because of its convenience to model the median counts given its closed-form quantile function. The median is a more robust measure of central tendency than the mean when the data, for instance, zero-inflated counts, are right-skewed.In an application of the model we consider a biphasic mixed-effects model consisting of an intercept term and two slope terms. Conventionally, the ZIDW model separately specifies the predictors for the zero-inflation probability and the counting process's median count. In our application, the two latent class interpretations are not clinically plausible. Therefore, we propose a marginal ZIDW model that directly models the biphasic median counts marginally. We also consider the marginal ZINB model to make inferences about the nonlinear mean counts over time. Our simulation study shows that the models have good properties in terms of accuracy and confidence interval coverage. K E Y W O R D SBayesian, marginal zero-inflated discrete Weibull, marginal zero-inflated negative binomial, median counts, nonlinear mixed-effects 5078

show abstract

Section: Previous Data Analysismentioning

confidence: 99%

\log_{10} (CFU)

count 19,20 . In particular, the bactericidal activity over a certain time interval, calculated from a

\log_{10} (CFU)

vs time profile, was expressed as follows: 21

BA (t_{1} - t_{2}) = - \frac{\hat{f} (t_{2}) - \hat{f} (t_{1})}{t_{2} - t_{1}},

where

f (t)

is the regression function for

\log_{10} (CFU)

count vs time, and

\hat{f} (t_{1})

and

\hat{f} (t_{2})

are the corresponding fitted values at Day

t_{1}

and Day

t_{2}

, respectively.…”

Section: Motivating Data and Previous Workmentioning

confidence: 99%

Section: Biphasic Mixed-effects Regression Modelmentioning

confidence: 99%

Section: Motivating Data and Previous Workmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear mixed‐effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero‐inflated discrete Weibull distribution

Burger

Lesaffre

2021

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

show abstract

“…The deviance information criterion (DIC) statistics conditional on the random effects of the regression models, and compound Laplace‐Metropolis marginal likelihoods (CLMMLs) were calculated to discriminate between the candidate regression models.…”

Section: Bayesian Mixed Effects Regression Modelsmentioning

confidence: 99%

A robust Bayesian mixed effects approach for zero inflated and highly skewed longitudinal count data emanating from the zero inflated discrete Weibull distribution

Burger

Schall

Ferreira

et al. 2020

Statistics in Medicine

Self Cite

View full text Add to dashboard Cite

This article proposes a Bayesian mixed effects zero inflated discrete Weibull (ZIDW) regression model for zero inflated and highly skewed longitudinal count data, as an alternative to mixed effects regression models that are based on the negative binomial, zero inflated negative binomial, and conventional discrete Weibull (DW) distributions. The mixed effects ZIDW regression model is an extension of a recently introduced model based on the DW distribution and uses the log‐link function to specify the relationship between the linear predictors and the median counts. The ZIDW approach offers a more robust characteristic of central tendency, compared to the mean count, when there is skewness in the data. A matrix generalized half‐t (MGH‐t) prior distribution is specified for the random effects covariance matrix as an alternative to the widely used Wishart prior distribution. The methodology is applied to a longitudinal dataset from an epilepsy clinical trial. In a data contamination simulation study, we show that the mixed effect ZIDW regression model is more robust than the competing mixed effects regression models when the data contain excess zeros or outliers. The performance of the ZIDW regression model is also assessed in a simulation study under the specification of, respectively, the MGH‐t and Wishart prior distributions for the random effects covariance matrix. It turns out that the highest posterior density intervals under the MGH‐t prior for the fixed effects maintain nominal coverage when the true variability between random slopes over time is small, whereas those under the Wishart prior are generally conservative.

show abstract

Evaluating the Performance of Mixed Zero-Inflated Poisson Regression Models with Time-dependent and Time-independent Covariates

Alomair

2024

BAS-SJKFU

View full text Add to dashboard Cite

One of the issues that researchers may encounter in count data is having many zeros. One of the solutions to model these data is using zero-inflated Poisson (ZIP) regression models. Recently, researchers have started to model longitudinal count data with time-dependent covariates. However, it has not been considered whether a model with time-dependent covariates provides a better fit than a model with time-independent covariates. In this paper, the fit between a mixed ZIP model with time-dependent covariates and a mixed ZIP model with time-independent covariates is compared using simulation. Using the deviance information criterion as a measure of fit, we found that the model with time-dependent covariates exhibits a better fit than the model with time-independent covariates. KEYWORDS correlated data, count data, excess zeros, longitudinal, mixed models, model fit

show abstract

A generalized Bayesian nonlinear mixed‐effects regression model for zero‐inflated longitudinal count data in tuberculosis trials

Cited by 3 publications

References 54 publications

Nonlinear mixed‐effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero‐inflated discrete Weibull distribution

Nonlinear mixed‐effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero‐inflated discrete Weibull distribution

A robust Bayesian mixed effects approach for zero inflated and highly skewed longitudinal count data emanating from the zero inflated discrete Weibull distribution

Evaluating the Performance of Mixed Zero-Inflated Poisson Regression Models with Time-dependent and Time-independent Covariates

Contact Info

Product

Resources

About