Jonathan Raz

Semiparametric Stochastic Mixed Models for Longitudinal Data

Abstract We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within-subject correlation using random effects and a stationary or nonstationary stochastic process. We derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function. The resulting estimator of the nonparametric function is a smoothing spline. We propose and compare frequentist inference and Bayesian inference on these model components. We use restricted maximum likelihood to estimate the smoothing parameter and the variance components simultaneously. We show that estimation of all model components of interest can proceed by fitting a modified linear mixed model. We illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations.

Neuroendocrine and psychophysiologic responses in PTSD : A symptom provocation study

Biological research on post-traumatic stress disorder (PTSD) has focused on autonomic, sympatho-adrenal, and hypothalamo-pituitary-adrenal (HPA) axis systems. Interactions among these response modalities have not been well studied and may be illuminating. We examined subjective, autonomic, adrenergic, and HPA axis responses in a trauma-cue paradigm and explored the hypothesis that the ability of linked stress-response systems to mount integrated responses to environmental threat would produce strong correlations across systems. Seventeen veterans with PTSD, 11 veteran controls without PTSD, and 14 nonveteran controls were exposed to white noise and combat sounds on separate days. Subjective distress, heart rate, skin conductance, plasma catecholamines, ACTH, and cortisol, at baseline and in response to the auditory stimuli, were analyzed for group differences and for patterns of interrelationships. PTSD patients exhibited higher skin conductance, heart rate, plasma cortisol, and catecholamines at baseline, and exaggerated responses to combat sounds in skin conductance, heart rate, plasma epinephrine, and norepinephrine, but not ACTH. The control groups did not differ on any measure. In canonical correlation analyses, no significant correlations were found between response systems. Thus, PTSD patients showed heightened responsivity to trauma-related cues in some, but not all, response modalities. The data did not support the integrated, multisystem stress response in PTSD that had been hypothesized. Individual response differences or differing pathophysiological processes may determine which neurobiological system is affected in any given patient.

Automatic statistical analysis of bivariate nonstationary time series

We propose a new method for analyzing bivariate nonstationary time series. The proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span to be used to obtain the smoothed estimates of the time-varying spectra and coherence. It is based on the smooth localized complex exponential (SLEX) transform, which forms a library of orthogonal complex-valued transforms that are simultaneously localized in time and frequency. We show that the smoothed SLEX periodograms are consistent estimators, report simulation results, and apply the method to a two-channel electroencephalogram dataset recorded during an epileptic seizure.

Progression of coronary artery calcification: a pilot study.

OBJECTIVE To describe individual changes in the quantity of coronary artery calcification (CAC) measured by electron beam computed tomography (CT) and determine the rate of change in the quantity of CAC during a 3.5-year period. MATERIAL AND METHODS Eighty-eight consecutive participants (51 men at least 30 years of age and 37 women at least 40 years of age) from a community-based CAC study were invited for a follow-up examination. Established coronary artery disease risk factors were studied at baseline. CAC score was measured by electron beam CT at baseline and follow-up. RESULTS Of the 88 invited participants, 82 (93%) returned for a follow-up examination. Considerable variation existed among the participants in the extent of CAC score change. On average, CAC score increased over time by an estimated 24% each year (P<0.05). The relative increase in CAC score over time was significantly lower for older than for younger participants but did not vary significantly by sex. CONCLUSION The ability to recruit follow-up participants in this pilot study and to detect significant change in CAC score over time provides evidence that electron beam CT is useful for studying progression of CAC in a sample and may be a valuable procedure for assessing the effectiveness of clinical interventions designed to retard progression of coronary atherosclerosis.

The SLEX Model of a Non-Stationary Random Process

We propose a new model for non-stationary random processes to represent time series with a time-varying spectral structure. Our SLEX model can be considered as a discrete time-dependent Cramér spectral representation. It is based on the so-called Smooth Localized complex EXponential basis functions which are orthogonal and localized in both time and frequency domains. Our model delivers a finite sample size representation of a SLEX process having a SLEX spectrum which is piecewise constant over time segments. In addition, we embed it into a sequence of models with a limit spectrum, a smoothly in time varying “evolutionary” spectrum. Hence, we develop the SLEX model parallel to the Dahlhaus (1997, Ann. Statist., 25, 1–37) model of local stationarity, and we show that the two models are asymptotically mean square equivalent. Moreover, to define both the growing complexity of our model sequence and the regularity of the SLEX spectrum we use a wavelet expansion of the spectrum over time. Finally, we develop theory on how to estimate the spectral quantities, and we briefly discuss how to form inference based on resampling (bootstrapping) made possible by the special structure of the SLEX model which allows for simple synthesis of non-stationary processes.

Confidence intervals for the signal-to-noise ratio when a signal embedded in noise is observed over repeated trials

The problem of estimating the signal-to-noise ratio (SNR) when repeated measurements are made of a deterministic signal embedded in random noise is considered. An estimator is described, its asymptotic distribution is derived, and a method for constructing confidence intervals is proposed. The performance of the method is evaluated using simulated evoked potential data, and an application to real evoked potential data is presented.<<ETX>>

Linear mixed models with heterogeneous within-cluster variances.

This paper describes an extension of linear mixed models to allow for heterogeneous within-cluster variances in the analysis of clustered data. Unbiased estimating equations based on quasilikelihood/pseudolikelihood and method of moments are introduced and are shown to give consistent estimators of the regression coefficients, variance components, and heterogeneity parameter under regularity conditions. Cluster-specific random effects and variances are predicted by the posterior modes. The method is illustrated through an analysis of menstrual diary data and its properties are evaluated in a simulation study.

EEG spectra in dyslexic and normal readers during oral and silent reading

EEGs of extensively screened dyslexics and normal readers were recorded while they read easy and difficult texts silently and orally, and during two other verbal tasks which also differed in overt speaking but had no reading component: narrative speaking and listening to a story. Mid-temporal, central and parietal leads were referenced to linked ears and to Cz. Large differences between tasks and between groups were found. With the linked ears reference, power was higher in all bands in oral reading than in silent reading, with the largest change occurring in the temporal leads. In the theta and low beta bands the difference between oral and silent reading was greater for controls than for dyslexics. These effects were not accounted for by differences in reading speed or in difficulty. Similar results were found in two cohorts of subjects. The difference between groups in theta was found only in the reading tasks. In contrast, the group difference in low beta was also found in the change from listening to speaking. This implies that the oral-silent group difference in theta is related to some aspect of the reading tasks other than the presence or absence of overt speaking, and that the low beta group difference is related to some aspect of overt speaking rather than to reading per se. With the Cz reference no group differences were found. It is suggested that the groups differ in the reading strategies they use, and the degree to which they shift strategy between the silent and oral tasks. We hypothesize that these cognitive differences are reflected in the theta activity from the temporal lobe. While there were many differences between the tasks in alpha power and asymmetry, no group differences involving alpha were found.

Analysis of repeated measurements using nonparametric smoothers and randomization tests.

The mixed-model analysis of variance (ANOVA), which is commonly applied to repeated measurements taken over time, depends on specialized assumptions about the error distribution and fails to exploit information contained in the ordering of the data points over time. This paper describes a procedure that overcomes these disadvantages while preserving familiar features of the mixed-model ANOVA. Group profiles are estimated by nonparametric smoothing of observed mean profiles. Group and time main effects, and the group by time interaction effect, are tested using randomization tests. Results of Zerbe (1979, Journal of the American Statistical Association 74, 215-221) are used to construct F-test approximations for the randomization tests of the group and group by time effects. A new approximate F-test for time effect is proposed. A simulation study demonstrates that the approximations perform well and that smoothing increases the power of the tests for time main effect and group by time interaction. The procedure is applied to data on hormone levels in cows.

Intra-hemispheric alpha coherence decreases with increasing cognitive impairment in HIV patients

Inter-hemispheric and intra-hemispheric canonical coherences in the alpha range between EEG signals collected from frontal and posterior groups of electrodes were estimated for 38 HIV positive subjects and 23 uninfected controls. Neuropsychological testing was used to categorize the degree of cognitive impairment evident in each of the subjects. A linear regression analysis provided evidence that intra-hemispheric coherence decreased with increasing cognitive impairment in impaired HIV+ subjects, as measured by a Global Impairment Score (GIS). There was no evidence that cognitively unimpaired HIV+ subjects differed in coherence when compared to uninfected control subjects. Severely impaired HIV+ subjects showed significantly decreased coherence compared to uninfected controls. These data contradict previous work demonstrating increased intra-hemispheric and inter-hemispheric alpha coherence in impaired HIV subjects. In addition, they provide evidence that intra-hemispheric (and possibly inter-hemispheric) disconnection is associated with cognitive impairment in HIV.