An improved method for estimating human circadian phase derived from multichannel ambulatory monitoring and artificial neural networks

Recently, we developed a novel method for estimating human circadian phase with noninvasive ambulatory measurements combined with subject-independent multiple regression models and a curve-fitting approach. With this, we were able to estimate circadian phase under real-life conditions with low subject burden, i.e., without need of constant routine (CR) laboratory conditions, and without measuring standard circadian markers, such as core body temperature (CBT) or pineal hormone melatonin rhythms. The precision of ambulatory-derived estimated circadian phase was within an error of 12?±?41?min (mean?±?SD) in comparison to melatonin phase during a CR protocol. The physiological measures could be reduced to a triple combination: skin temperatures, irradiance in the blue spectral band of ambient light, and motion acceleration. Here, we present a nonlinear regression model approach based on artificial neural networks for a larger data set (25 healthy young males), including both the original data and additional data collected in the same protocol and using the same equipment. Throughout our validation study, subjects wore multichannel ambulatory monitoring devices and went about their daily routine for 1 wk. The devices collected a large number of physiological, behavioral, and environmental variables, including CBT, skin temperatures, cardiovascular and respiratory functions, movement/posture, ambient temperature, spectral composition and intensity of light perceived at eye level, and sleep logs. After the ambulatory phase, study volunteers underwent a 32-h CR protocol in the laboratory for measuring unmasked circadian phase (i.e., "midpoint" of the nighttime melatonin rhythm). To overcome the complex masking effects of many different confounding variables during ambulatory measurements, neural network-based nonlinear regression techniques were applied in combination with the cross-validation approach to subject-independent prediction of circadian phase. The most accurate estimate of circadian phase with a prediction error of -3?±?23?min (mean?±?SD) was achieved using only two types of the measured variables: skin temperatures and irradiance for ambient light in the blue spectral band. Compared to our previous linear multiple regression modeling approach, motion acceleration data can be excluded and prediction accuracy, nevertheless, improved. Neural network regression showed statistically significant improvement of variance of prediction error over traditional approaches in determining circadian phase based on single predictors (CBT, motion acceleration, or sleep logs), even though none of these variables was included as predictor. We, therefore, have identified two sets of noninvasive measures that, combined with the prediction model, can provide researchers and clinicians with a precise measure of internal time, in spite of the masking effects of daily behavior. This method, here validated in healthy young men, requires testing in a clinical or shiftwork population suffering from circadian sleep-wake disorders. (Author correspondence: vitaliy.kolodyazhniy@sbg.ac.at ).     

The statistical analysis of circadian phase and amplitude in constant-routine core-temperature data.

Accurate estimation of the phases and amplitude of the endogenous circadian pacemaker from constant-routine core-temperature series is crucial for making inferences about the properties of the human biological clock from data collected under this protocol. This paper presents a set of statistical methods based on a harmonic-regression-plus-correlated-noise model for estimating the phases and the amplitude of the endogenous circadian pacemaker from constant-routine core-temperature data. The methods include a Bayesian Monte Carlo procedure for computing the uncertainty in these circadian functions. We illustrate the techniques with a detailed study of a single subject's core-temperature series and describe their relationship to other statistical methods for circadian data analysis. In our laboratory, these methods have been successfully used to analyze more than 300 constant routines and provide a highly reliable means of extracting phase and amplitude information from core-temperature data.     

Amplitude model for the effects of mutations and temperature on period and phase resetting of the Neurospora circadian oscillator.

This paper analyzes published and unpublished data on phase resetting of the circadian oscillator in the fungus Neurospora crassa and demonstrates a correlation between period and resetting behavior in several mutants with altered periods: As the period increases, the apparent sensitivity to resetting by light and by cycloheximide decreases. Sensitivity to resetting by temperature pulses may also decrease. We suggest that these mutations affect the amplitude of the oscillator and that a change in amplitude is responsible for the observed changes in both period and resetting by several stimuli. As a secondary hypothesis, we propose that temperature compensation of period in Neurospora can be explained by changes in amplitude: As temperature increases, the compensation mechanism may increase the amplitude of the oscillator to maintain a constant period. A number of testable predictions arising from these two hypotheses are discussed. To demonstrate these hypotheses, a mathematical model of a time-delay oscillator is presented in which both period and amplitude can be increased by a change in a single parameter. The model exhibits the predicted resetting behavior: With a standard perturbation, a smaller amplitude produces type 0 resetting and a larger amplitude produces type 1 resetting. Correlations between period, amplitude, and resetting can also be demonstrated in other types of oscillators. Examples of correlated changes in period and resetting behavior in Drosophila and hamsters raise the possibility that amplitude changes are a general phenomenon in circadian oscillators.     

Estimation of human circadian phase via a multi-channel ambulatory monitoring system and a multiple regression model

Reliable detection of circadian phase in humans using noninvasive ambulatory measurements in real-life conditions is challenging and still an unsolved problem. The masking effects of everyday behavior and environmental input such as physical activity and light on the measured variables need to be considered critically. Here, we aimed at developing techniques for estimating circadian phase with the lowest subject burden possible, that is, without the need of constant routine (CR) laboratory conditions or without measuring the standard circadian markers, (rectal) core body temperature (CBT), and melatonin levels. In this validation study, subjects (N = 16) wore multi-channel ambulatory monitoring devices and went about their daily routine for 1 week. The devices measured a large number of physiological, behavioral, and environmental variables, including CBT, skin temperatures, cardiovascular and respiratory function, movement/posture, ambient temperature, and the spectral composition and intensity of light received at eye level. Sleep diaries were logged electronically. After the ambulatory phase, subjects underwent a 32-h CR procedure in the laboratory for measuring unmasked circadian phase based on the "midpoint" of the salivary melatonin profile. To overcome the complex masking effects of confounding variables during ambulatory measurements, multiple regression techniques were applied in combination with the cross-validation approach to subject-independent prediction of circadian phase. The most accurate estimate of circadian phase was achieved using skin temperatures, irradiance for ambient light in the blue spectral band, and motion acceleration as predictors with lags of up to 24 h. Multiple regression showed statistically significant improvement of variance of prediction error over the traditional approaches to determining circadian phase based on single predictors (motion acceleration or sleep log), although CBT was intentionally not included as the predictor. Compared to CBT alone, our method resulted in a 40% smaller range of prediction errors and a nonsignificant reduction of error variance. The proposed noninvasive measurement method could find applications in sleep medicine or in other domains where knowing the exact endogenous circadian phase is important (e.g., for the timing of light therapy).     

Disruptions of ultradian and circadian organization of core temperature in a rat model of African trypanosomiasis using periodogram techniques on detrended data

Periodogram techniques on detrended data were used to determine the incidence of Trypanosoma brucei brucei infection on the distribution of the core temperature of rats and the expression of temperature rhythms. In such an animal model, sudden episodic hypothermic bouts were described. These episodes of hypothermia are used here as temporal marks for the purpose of performing punctual comparisons on temperature organization. The experiment was conducted on 10 infected and 3 control Sprague-Dawley rats reared under a 24 h light-dark cycle. Core temperature was recorded continuously throughout the experiment, until the animals' death. Temperature distributions, analyzed longitudinally across the full duration of the experiment, exhibited a progressive shift from a bimodal to unimodal pattern, suggesting a weakening of the day/night core temperature differences. After hypothermic events, the robustness of the circadian rhythm substantially weakened, also affecting the ultradian components. The ultradian periods were reduced, suggesting fragmentation of temperature generation. Moreover, differences between daytime and nighttime ultradian patterns decreased during illness, confirming the weakening of the circadian component. The results of the experiments show that both core temperature distribution and temperature rhythm were disrupted during the infection. These disruptions worsened after each episode of hypothermia, suggesting an alteration of the temperature regulatory system.     

Analysis techniques for microarray time-series data.

We address possible limitations of publicly available data sets of yeast gene expression. We study the predictability of known regulators via time-series analysis, and show that less than 20% of known regulatory pairs exhibit strong correlations in the Cho/Spellman data sets. By analyzing known regulatory relationships, we designed an edge detection function which identified candidate regulations with greater fidelity than standard correlation methods. We develop general methods for integrated analysis of coarse time-series data sets. These include 1) methods for automated period detection in a predominately cycling data set and 2) phase detection between phase-shifted cyclic data sets. We show how to properly correct for the problem of comparing correlation coefficients between pairs of sequences of different lengths and small alphabets. Finally, we note that the correlation coefficient of sequences over alphabets of size two can exhibit very counterintuitive behavior when compared with the Hamming distance.     

PSEUDO-RESPONSE REGULATOR 7 and 9 are partially redundant genes essential for the temperature responsiveness of the Arabidopsis circadian clock

Environmental time cues, such as photocycles (light/dark) and thermocycles (warm/cold), synchronize (entrain) endogenous biological clocks to local time. Although much is known about entrainment of the Arabidopsis thaliana clock to photocycles, the determinants of thermoperception and entrainment to thermocycles are not known. The Arabidopsis PSEUDO-RESPONSE REGULATOR (PRR) genes, including the clock component TIMING OF CAB EXPRESSION 1/PRR1, are related to bacterial, fungal, and plant response regulators but lack the conserved Asp that is normally phosphorylated by an upstream sensory kinase. Here, we show that two PRR family members, PRR7 and PRR9, are partially redundant; single prr7-3 or prr9-1 mutants exhibit modest period lengthening, but the prr7-3 prr9-1 double mutant shows dramatic and more than additive period lengthening in the light and becomes arrhythmic in constant darkness. The prr7-3 prr9-1 mutant fails both to maintain an oscillation after entrainment to thermocycles and to reset its clock in response to cold pulses and thus represents an important mutant strongly affected in temperature entrainment in higher plants. We conclude that PRR7 and PRR9 are critical components of a temperature-sensitive circadian system. PRR7 and PRR9 could function in temperature and light input pathways or they could represent elements of an oscillator necessary for the clock to respond to temperature signals.     

Methods for estimating the parameters of a linear model for ordered categorical data.

In many empirical analyses, the response of interest is categorical with an ordinal scale attached. Many investigators prefer to formulate a linear model, assigning scores to each category of the ordinal response and treating it as continuous. When the covariates are categorical, Haber (1985, Computational Statistics and Data Analysis 3, 1-10) has developed a method to obtain maximum likelihood (ML) estimates of the parameters of the linear model using Lagrange multipliers. However, when the covariates are continuous, the only method we found in the literature is ordinary least squares (OLS), performed under the assumption of homogeneous variance. The OLS estimates are unbiased and consistent but, since variance homogeneity is violated, the OLS estimates of variance can be biased and may not be consistent. We discuss a variance estimate (White, 1980, Econometrica 48, 817-838) that is consistent for the true variance of the OLS parameter estimates. The possible bias encountered by using the naive OLS variance estimate is discussed. An estimated generalized least squares (EGLS) estimator is proposed and its efficiency relative to OLS is discussed. Finally, an empirical comparison of OLS, EGLS, and ML estimators is made.     

The endogenous melatonin profile as a marker for circadian phase position.

Several circadian rhythms have been used to assess the phase of the endogenous circadian pacemaker (ECP). However, when more than one marker rhythm is measured, results do not always agree. Questions then inevitably arise. Are there multiple oscillators? Are some markers more reliable than others? Masking is a problem for all marker rhythms. Masking of melatonin is minimized by sampling under dim light. The dim-light melatonin onset (DLMO) is particularly convenient since it can usually be obtained before sleep. However, assessing the DLMO in low melatonin producers may be problematic, particularly with the commonly used operationally defined threshold of 10 pg/ml. This study evaluates various circadian phase markers provided by the plasma melatonin profile in 14 individuals, several of whom are low melatonin producers. The amount (amplitude) of melatonin production appears to influence the phase of many points on the melatonin profile. Accordingly, when low producers are in a data set, we now prefer a lower DLMO threshold than the one previously recommended (10 pg/ml). Indeed, there are some low producers who never exceed this threshold at any time. Radioimmunoassays are now available that have the requisite sensitivity and specificity to support the use of a lower threshold. Nevertheless, the dim-light melatonin offset (DLMOff), even when operationally defined at thresholds less than 10 pg/ml, appears to be confounded by amplitude in this study; in such cases, it may be preferable to use the melatonin synthesis offset (SynOff) because it is not confounded by amplitude and because, theoretically, it is temporally closer to the endogenous mechanism signaling the offset of production. The question of whether the termination mechanism of melatonin synthesis is related to an interval timer or to a second oscillator loosely coupled to the onset oscillator is probably best answered using the SynOff rather than the DLMOff. It is hoped that these findings will make a useful contribution to the debate on the best ways to use points on the melatonin profile to assess circadian phase position in humans.     

Semiparametric method for estimating paleodemographic profiles from age indicator data.

This paper addresses the problem of estimating an age-at-death distribution or paleodemographic profile from osteological data. It is demonstrated that the classical two-stage procedure whereby one first constructs estimates of age-at-death of individual skeletons and then uses these age estimates to obtain a paleodemographic profile is not a correct approach. This is a consequence of Bayes' theorem. Instead, we demonstrate a valid approach that proceeds from the opposite starting point: given skeletal age-at-death, one first estimates the probability of assigning the skeleton into a specific osteological age-indicator stage. We show that this leads to a statistically valid method for obtaining a paleodemographic profile, and moreover, that valid individual age estimation itself requires a demographic profile and therefore is done subsequent to its construction. Individual age estimation thus becomes the last rather than the first step in the estimation procedure. A central concept of our statistical approach is that of a weight function. A weight function is associated with each osteological age-indicator stage or category, and provides the probability that a specific age indicator stage is observed, given age-at-death of the individual. We recommend that weight functions be estimated nonparametrically from a reference data set. In their entirety, the weight functions characterize the relevant stochastic properties of a chosen age indicator. For actual estimation of the paleodemographic profile, a parametric age distribution in the target sample is assumed. The maximum likelihood method is used to identify the unknown parameters of this distribution. As some components are estimated nonparametrically, one then has a semiparametric model. We show how to obtain valid estimates of individual age-at-death, confidence regions, and goodness-of-fit tests. The methods are illustrated with both real and simulated data.     

A pseudo-likelihood method for estimating misclassification probabilities in competing-risks settings when true-event data are partially observed

Outcome misclassification occurs frequently in binary-outcome studies and can result in biased estimation of quantities such as the incidence, prevalence, cause-specific hazards, cumulative incidence functions, and so forth. A number of remedies have been proposed to address the potential misclassification of the outcomes in such data. The majority of these remedies lie in the estimation of misclassification probabilities, which are in turn used to adjust analyses for outcome misclassification. A number of authors advocate using a gold-standard procedure on a sample internal to the study to learn about the extent of the misclassification. With this type of internal validation, the problem of quantifying the misclassification also becomes a missing data problem as, by design, the true outcomes are only ascertained on a subset of the entire study sample. Although, the process of estimating misclassification probabilities appears simple conceptually, the estimation methods proposed so far have several methodological and practical shortcomings. Most methods rely on missing outcome data to be missing completely at random (MCAR), a rather stringent assumption which is unlikely to hold in practice. Some of the existing methods also tend to be computationally-intensive. To address these issues, we propose a computationally-efficient, easy-to-implement, pseudo-likelihood estimator of the misclassification probabilities under a missing at random (MAR) assumption, in studies with an available internal-validation sample. We present the estimator through the lens of studies with competing-risks outcomes, though the estimator extends beyond this setting. We describe the consistency and asymptotic distributional properties of the resulting estimator, and derive a closed-form estimator of its variance. The finite-sample performance of this estimator is evaluated via simulations. Using data from a real-world study with competing-risks outcomes, we illustrate how the proposed method can be used to estimate misclassification probabilities. We also show how the estimated misclassification probabilities can be used in an external study to adjust for possible misclassification bias when modeling cumulative incidence functions.     

Separate sets of cerebral clock neurons are responsible for light and temperature entrainment of Drosophila circadian locomotor rhythms

The fruit fly Drosophila melanogaster shows a bimodal circadian locomotor rhythm with peaks at lights-on and before lights-off, which are regulated by multiple clocks in the brain. Even under light-dark cycles, the timing of the evening peak is highly dependent on temperature, starting earlier under lower ambient temperature but terminating almost at the same time. In the present study, using behavioral and immunohistochemical assays, the authors show that separate groups of clock neurons, either light-entrainable or temperature-entrainable, form a functional system driving the locomotor rhythm. When subjected to a light cycle combined with a temperature cycle advanced by 6 h relative to the light cycle, the dorsally located neurons (DNs) and lateral posterior neurons (LPNs) shifted their phase of TIMELESS expression, but the laterally located protocerebral neurons (LNs) basically maintained their original phase. Thus, the LNs seem to be preferentially light-entrainable and the DNs and LPNs to be primarily temperature-entrainable. In pdf(01) mutant flies that lack the neuropeptide PDF in the ventral groups of LNs, the onset of the evening peak was greatly advanced even under synchronized light and temperature cycles and was shifted even more than in wild-type flies in response to a 6-h phase shift of the temperature cycle, suggesting that ventral LNs have a strong impact on the phase of the other cells. It seems likely that the 2 sets of clock cells with different entrainability to light and temperature, and the coupling between them, enable Drosophila to keep a proper phase relationship of circadian activity with respect to the daily light and temperature cycles.     

New techniques for three-dimensional data analysis in histopathology.

This paper describes two three-dimensional (3D) analytical techniques based on 3D mathematical morphology that have been found useful in quantifying the 3D spatial distribution of S-phase cells in a tubular tumor of the human breast. One technique is based on determining the normalized radial distribution of the S-phase cells with respect to the central axis of the tumor. The other technique is a novel extension of the polyhedra of Voronoi to quantify the distribution. The Voronoi polyhedron of a given S-phase cell nucleus is that polyhedron of minimal volume defined by planes all of which are perpendicular bisectors of the vectors extending from the given cell to all other S-phase cells in the tumor. Methods are demonstrated for generating these polyhedra and for histogramming their volumes. An illustration is given of using the histogram to sort the S-phase cells according to their 3D positional relationships. Displays showing the sorted cells in 3D and their associated Voronoi polyhedra are provided.     

Photobiology of the Gonyaulax circadian system. I. Different phase response curves for red and blue light

Phase responses to red and blue light pulses were measured at different times during the circadian cycle (phase response curves, PRC) in the marine unicellular dinoflagellate Gonyaulaxpolyedra Stein. Pulses were given during a 24-h period of darkness; thereafter, cultures were released into constant dim red light for the assessment of phase and period. The results confirmed earlier findings that the Gonyaulax circadian system receives light signals via two distinct input pathways. During the subjective day and for the first 3 h of the subjective night, red and blue light pulses led to identical phase responses. For the rest of the circadian cycle, however, phase responses to pulses of either red or blue light differed drastically both in their amplitude and direction (advances or delays). Thus, the Gonyaulax light PRC is generated by two distinct light responses. One of these represents responses via a light input that is responsive both to red and blue light mainly producing small delays. The other represents responses of a primarily blue-sensitive input system leading to large advances restricted to the subjective night. Via feed-back, the blue-sensitive light input appears to be under the control of the circadian system. Received: 27 November 1996/Accepted: 30 January 1997     

Simultaneous telemetric monitoring of the circadian changes in core and BAT temperature in rats: Endogenous vasopressin may contribute to reduced BAT themogenesis and body temperature in the light phase of the circadian cycle

The purpose of the present study was to analyze simultaneously the temporal relationship between the changes of circadian rhythms of brown adipose tissue (BAT) thermogenesis and core temperature (T_c) by dual probe telemetric monitoring transmitters and to determine the role of endogenous arginine vasopressin (AVP) in the circadian rhythms of BAT temperature (T_BAT) and T_c in male rats. The key observations in this study are: (1) Increase in T_BAT commenced approximately 8 min before T_c increases at the start of transition from the light to dark phase. Whereas at the start of transition from the dark to light phase, decrease in T_BAT commenced approximately 3 min before T_c decreases. The data show that circadian changes of BAT thermogenesis do indeed play a significant role in the overall maintenance of the circadian rhythm of core temperature. (2) The plasma AVP level was significantly elevated when core temperature decreases during the light phase, suggesting that endogenous AVP is involved in thermoregulatory processes during the light phase. V1a receptor antagonist could elevate core and BAT temperature during the light period, suggesting that endogenous AVP, acting through V1a receptor, could be involved in tonic thermoregulatory processes.V1a receptor antagonist can increase the blood lipid metabolism, suggesting that the mechanism of endogenous AVP in tonic thermoregulatory processes during light period could involve the suppression of lipolysis in BAT and other peripheral tissues. In summary, this study demonstrated that endogenous vasopressin contributes to reduced BAT themogenesis and body temperature in the light phase of the circadian cycle.