Structured Antedependence Models for Longitudinal Data

Zimmerman, Dale L.; Núñez‐Antón, Vicente

doi:10.1007/978-1-4612-0699-6_6

Cited by 40 publications

(46 citation statements)

References 13 publications

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“…As multiple longitudinal measurements collected from each woman may have been correlated, a random intercept was used to account for the covariance of measurements nested within the same participant. First-order ante-dependence structure was specified for the repeated measurements from each participant (Zimmerman and Núñez-Antón 1997). …”

Section: Methodsmentioning

confidence: 99%

Association between gaseous air pollutants and inflammatory, hemostatic and lipid markers in a cohort of midlife women

Basu

Malig

et al. 2017

Environment International

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BACKGROUND Exposures to ambient gaseous pollutants have been linked to cardiovascular diseases (CVDs), but the biological mechanisms remain uncertain. OBJECTIVES This study examined the changes in CVD marker levels resulting from elevated exposure to ambient gaseous pollutants in midlife women. METHODS Annual repeated measurements of several inflammatory, hemostatic and lipid makers were obtained from 2,306 midlife women enrolled in the longitudinal Study of Women’s Health Across the Nation (SWAN) between 1999 and 2004. Ambient carbon monoxide (CO), nitrogen dioxide (NO2), and sulfur dioxide (SO2) data were assigned to each woman based on proximity of the monitoring station to her residential address. Short- and long-term exposures were calculated, and their associations with markers were examined using linear mixed-effects regression models, adjusted for demographic, health and other factors. RESULTS Short-term CO exposure was associated with increased fibrinogen, i.e., every interquartile increase of average prior one-week exposure to CO was associated with 1.3% (95% CI: 0.6%, 2.0%) increase in fibrinogen. Long-term exposures to NO2 and SO2 were associated with reduced high-density lipoproteins and apolipoprotein A1, e.g., 4.0% (1.7%, 6.3%) and 4.7% (2.8%, 6.6%) decrease per interquartile increment in prior one-year average NO2 concentration, respectively. Fine particle (PM2.5) exposure confounded associations between CO/NO2 and inflammatory/hemostatic markers, while associations with lipoproteins were generally robust to PM2.5 adjustment. CONCLUSIONS Exposures to these gas pollutants at current ambient levels may increase thrombotic potential and disrupt cholesterol metabolism, contributing to greater risk of CVDs in midlife women. Caution should be exercised in evaluating the confounding by PM2.5 exposure.

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Section: Methodsmentioning

confidence: 99%

Association between gaseous air pollutants and inflammatory, hemostatic and lipid markers in a cohort of midlife women

Basu

Malig

et al. 2017

Environment International

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“…Next, from Section 2.5 of Zimmerman and Nuñez-Antón (2010), the correlation between and for can be expressed asThe induced correlation structure for is therefore an AR(1) structure.…”

Section: Methodsmentioning

confidence: 99%

Maximum likelihood based analysis of equally spaced longitudinal count data with first-order antedependence and overdispersion

Gamerman

Guerra²,

Shults

2016

SpringerPlus

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This manuscript implements a maximum likelihood based approach that is appropriate for equally spaced longitudinal count data with over-dispersion, so that the variance of the outcome variable is larger than expected for the assumed Poisson distribution. We implement the proposed method in the analysis of seizure data and a subset of German Socio-Economic Panel data. To demonstrate the importance of correctly modeling the over-dispersion, we make comparisons with the semi-parametric generalized estimating equations approach that incorrectly ignores any over-dispersion in the data. Our simulations demonstrate that accounting for over-dispersion results in improved small-sample efficiency and appropriate coverage probabilities. We also provide code in R so that readers can implement our approach in their own analyses.

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“…One advantage of the OUP structure built in model (3) is that

{\tilde{bold-italicH}}_{i} (ρ_{i})

can be analytically inverted and is a tridiagonal matrix, which follows by considering results available from the theory of antedependent random variables (Gabriel; 1962; Zimmerman and Núñez-Antón; 2010). Details are given in the Appendix B.…”

Section: General Model and Inferencementioning

confidence: 99%

“…It then follows that (Zimmerman and Núñez-Antón; 2010)

\begin{matrix} left \\ {\overset{H}{true} {false(ρ false)}^{- 1}}_{k, k + 1} = - \frac{r_{k}}{1 - r_{k}^{2}}, k = 1 \dots, n - 1 \\ {\overset{H}{true} {false(ρ false)}^{- 1}}_{1, 1} = \frac{1}{1 - r_{1}^{2}} \\ {\overset{H}{true} {false(ρ false)}^{- 1}}_{k, k} = \frac{1 - r_{k - 1}^{2} r_{k}^{2}}{1 - r_{k - 1}^{2} - r_{k}^{2} + r_{k - 1}^{2} r_{k}^{2}}, k = 2, \dots ., n - 1 \\ {\overset{H}{true} {false(ρ false)}^{- 1}}_{n, n} = \frac{1}{1 - r_{n - 1}^{2}} . \end{matrix}

and

{\tilde{bold-italicH} {(ρ)}^{- 1}}_{k, ℓ} = 0

otherwise. In addition, we have that

normaldet false(\overset{H}{true} false(ρ false) false) = 1 + true \sum_{i = 1}^{n - 1} {(- 1)}^{i} true \prod_{1 \leq s_{1} < s_{2} < \dots < s_{i} \leq n - 1} r_{s_{i}}^{2} .

For instance, again in the n = 4 case,

<...>

…”

Section: Figurementioning

confidence: 99%

Bayesian Nonparametric Longitudinal Data Analysis

Quintana

Johnson

Waetjen

et al. 2016

Journal of the American Statistical Association

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Practical Bayesian nonparametric methods have been developed across a wide variety of contexts. Here, we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry (CS) and autoregressive (AR) covariance structures. AR structure is often specified through the use of a Gaussian process (GP) with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart. We allow for AR structure by considering a broader class of models that incorporates a Dirichlet Process Mixture (DPM) over the covariance parameters of the GP. We are able to take advantage of modern Bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations. We also take advantage of the generality of our model, which provides for estimation of a variety of covariance structures. We observe that models that fail to incorporate CS or AR structure can result in very poor estimation of a covariance or correlation matrix. In our illustration using hormone data observed on women through the menopausal transition, biology dictates the use of a generalized family of sigmoid functions as a model for time trends across subpopulation categories.

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Structured Antedependence Models for Longitudinal Data

Cited by 40 publications

References 13 publications

Association between gaseous air pollutants and inflammatory, hemostatic and lipid markers in a cohort of midlife women

Association between gaseous air pollutants and inflammatory, hemostatic and lipid markers in a cohort of midlife women

Maximum likelihood based analysis of equally spaced longitudinal count data with first-order antedependence and overdispersion

Bayesian Nonparametric Longitudinal Data Analysis

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