Time series modeling of heroin and morphine drug action

Clinical observations and recent findings suggested different acceptance of morphine and heroin by intravenous drug users in opiate maintenance programs. We postulated that this is caused by differences in the perceived effects of these drugs, especially how desired and adverse effects of both drugs interacted.

Identifying mechanisms of treatment effects and recovery in rehabilitation of schizophrenia: longitudinal analytic methods

The longitudinal dimension of schizophrenia and related severe mental illness is a key component of theoretical models of recovery. However, empirical longitudinal investigations have been underrepresented in the psychopathology of schizophrenia. Similarly, traditional approaches to longitudinal analysis of psychopathological data have had serious limitations. The utilization of modern longitudinal methods is necessary to capture the complexity of biopsychosocial models of treatment and recovery in schizophrenia. The present paper summarizes empirical data from traditional longitudinal research investigating recovery in symptoms, neurocognition, and social functioning. Studies conducted under treatment as usual conditions are compared to psychosocial intervention studies and potential treatment mechanisms of psychosocial interventions are discussed. Investigations of rehabilitation for schizophrenia using the longitudinal analytic strategies of growth curve and time series analysis are demonstrated. The respective advantages and disadvantages of these modern methods are highlighted. Their potential use for future research of treatment effects and recovery in schizophrenia is also discussed.

Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

A Wavelet Analysis of Pliopleistocene Climate Indicators: A New View of Periodicity Evolution

Wavelet analysis offers an alternative to Fourier based time-series analysis, and is particularly useful when the amplitudes and periods of dominant cycles are time dependent. We analyse climatic records derived from oxygen isotopic ratios of marine sediment cores with modified Morlet wavelets. We use a normalization of the Morlet wavelets which allows direct correspondence with Fourier analysis. This provides a direct view of the oscillations at various frequencies, and illustrates the nature of the time-dependence of the dominant cycles.

Stable-Isotope and Trace Element Time Series from Fedchenko Glacier (Pamirs) Snow/Firn Cores

In summer 2005, two pilot snow/firn cores were obtained at 5365 and 5206 m a.s.l. on Fedchenko glacier, Pamirs, Tajikistan, the world's longest and deepest alpine glacier. The well-defined seasonal layering appearing in stable-isotope and trace element distribution identified the physical links controlling the climate and aerosol concentration signals. Air temperature and humidity/precipitation were the primary determinants of stable-isotope ratios. Most precipitation over the Pamirs originated in the Atlantic. In summer, water vapor was re-evaporated from semi-arid regions in central Eurasia. The semi-arid regions contribute to non-soluble aerosol loading in snow accumulated on Fedchenko glacier. In the Pamir core, concentrations of rare earth elements, major and other elements were less than those in the Tien Shan but greater than those in Antarctica, Greenland, the Alps and the Altai. The content of heavy metals in the Fedchenko cores is 2-14 times lower than in the Altai glaciers. Loess from Afghan-Tajik deposits is the predominant lithogenic material transported to the Pamirs. Trace elements generally showed that aerosol concentration tended to increase on the windward slopes during dust storms but tended to decrease with altitude under clear conditions. The trace element profile documented one of the most severe droughts in the 20th century.

Detecting determinism with improved sensitivity in time series: Rank-based nonlinear predictability score

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.