Comparison of Parameters from Rhythmometric Models with Multiple Components on Hybrid Data

Population multiple components is a statistical tool useful for the analysis of time-dependent hybrid data. With a small number of parameters, it is possible to model and to predict the periodic behavior of a population. In this article, we propose two methods to compare among populations rhythmometric parameters obtained by multiple component analysis. The first is a parametric method based in the usual statistical techniques for comparison of mean vectors in multivariate normal populations. The method, through MANOVA analysis, allows comparison of the MESOR and amplitude-acrophase pair of each component among two or more populations. The second is a nonparametric method, based in bootstrap techniques, to compare parameters from two populations. This test allows one to compare the MESOR, the amplitude, and the acrophase of each fitted component, as well as the global amplitude, orthophase, and bathyphase estimated when all fitted components are harmonics of a fundamental period. The idea is to calculate a confidence interval for the difference of the parameters of interest. If this interval does not contain zero, it can be concluded that the parameters from the two models are different with high probability. An estimation of p-value for the corresponding test can also be calculated. Both methods are illustrated with an example, based on clinical data. The nonparametric test can also be applied to paired data, a special situation of great interest in practice. By the use of similar bootstrap techniques, we illustrate how to construct confidence intervals for any rhythmometric parameter estimated from population multiple components models, including the orthophase, bathyphase, and global amplitude. These tests for comparison of parameters among populations are a needed tool when modeling the nonsinusoidal rhythmic behavior of hybrid data by population multiple component analysis.     

Methods for comparison of parameters from longitudinal rhythmometric models with multiple components

Multiple components linear least-squares methods have been proposed for the detection of periodic components in nonsinusoidal longitudinal time series. However, a proper test for comparison of parameters obtained from this method for two or more time series is not yet available. Accordingly, we propose two methods, one parametric and one nonparametric, to compare parameters from rhythmometric models with multiple components. The parametric method is based on techniques commonly and generally employed in linear regression analysis. The comparison of parameters among two or more time series is accomplished by the use of so-called dummy variables. The nonparametric method is based on bootstrap techniques. This approach basically tests if the difference in any given parameter obtained by fitting a model with the same periods to two different longitudinal time series differs from zero. This method calculates a confidence interval for the difference in the tested parameter. If this interval does not contain zero, it can be concluded that the parameters obtained from the two time series are different with high probability. An estimation of the p-value for the corresponding test can also be calculated. By the use of similar bootstrap techniques, confidence intervals can also be obtained for any parameter derived from the multiple component fit of several periods to nonsinusoidal longitudinal time series, including the orthophase (peak time), bathyphase (trough time), and global amplitude (difference between the maximum and the minimum) of the fitted model waveform. These methods represent a valuable tool for the comparison of rhythm parameters obtained by multiple component analysis, and they render this approach as a generally applicable one for waveform representation and detection of periodicities in nonsinusoidal, sparse, and noisy longitudinal time series sampled with either equidistant or unequidistant observations.     

Circadian chronobiology of epilepsy: murine models of seizure susceptibility and theoretical perspectives for neurology

As an integrative discipline in physiology and medical research, chronobiology renders possible the discovery of new regulation processes regarding the central mechanisms of epilepsy. In this context, the temporal fluctuations of seizure susceptibility rhythmometrically detected tend to demonstrate 1. that tonic-clonic events are circadian stage-dependent processes whose temporal characteristics (i.e. MESOR, amplitude, acrophase) and clinical parameters (e.g. neurological components, severity of motor discharges) are predictable on the basis of mathematical models, and 2. that the generalized epileptic onsets may respond to telencephalic integrations modulated by centrencephalic circadian processes of vigilance. Considering the data model assumed for our rhythmometric analyses, the circadian psychophysiological patterns of epilepsy also express dynamic biologic systems which reveal some intermodulating endogenous processes between vigilance and seizure susceptibility. The new chronophysiology investigations considered at a rhythmometric level of resolution suggest several heuristic perspectives regarding 1. the central pathophysiology of epilepsy and 2. the behavioral classification of convulsive events. Such circadian studies also show that chronobiology raises some working hypotheses in psychophysiology and permits the development of new theoretical concepts in the field of neurological science.     

On Testing an Unspecified Function Through a Linear Mixed Effects Model with Multiple Variance Components

Summary We examine a generalized F ‐test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying‐coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two‐way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F ‐test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome‐wide critical value and p ‐value of a genetic association test in a genome‐wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 10⁸ simulations) and asymptotic approximation may be unreliable and conservative.     

Pop‐Inference: An educational application to evaluate statistical differences among populations

Pop‐Inference is an educational tool designed to help teaching of hypothesis testing using populations. The application allows for the statistical comparison of demographic parameters among populations. Input demographic data are projection matrices or raw demographic data. Randomization tests are used to compare populations. The tests evaluate the hypothesis that demographic parameters differ among groups of individuals more that should be expected from random allocation of individuals to populations. Confidence intervals for demographic parameters are obtained using the bootstrap. Tests may be global or pairwise. In addition to tests on differences, one‐way life table response experiments (LTRE) are available for random and fixed factors. Planned (a priori) comparisons are possible. Power of comparison tests is evaluated by constructing the distribution of the test statistic when the null hypothesis is true and when it is false. The relationship between power and sample size is explored by evaluating differences among populations at increasing population sizes, while keeping vital rates constant.     

The daily,weekly, and seasonal cycles of body temperature analyzed at large scale

ABSTRACT

We performed large-scale analyses of circadian and infradian cycles of human body temperature, focusing on changes over the day, week, and year. Temperatures (n= 93,225) were collected using temporal artery thermometers from a Boston emergency department during 2009–2012 and were statistically analyzed using regression with cyclic splines. The overall mean body temperature was 36.7°C (98.1°F), with a 95% confidence interval of 36.7–36.7°C (98.1–98.1°F) and a standard deviation of 0.6°C (1.1°F). Over the day, mean body temperature followed a steady cycle, reaching its minimum at 6:00–8:00 and its maximum at 18:00–20:00. Across days of the week, this diurnal cycle was essentially unchanged, even though activities and sleeping hours change substantially during the weekly cycles of human behavior. Over the year, body temperatures were slightly colder in winter than summer (~0.2°C difference), consistent with most prior studies. We propose these seasonal differences might be due to ambient effects on body temperature that are not eliminated because they fall within the tolerance range of the thermoregulatory system. Over the year, bathyphase (daily time of minimum temperature) appeared to parallel sunrise times, as expected from sunrise’s zeitgeber role in circadian rhythms. However, orthophase (daily time of maximum temperature) and sunset times followed opposite seasonal patterns, with orthophase preceding nightfall in summer and following nightfall in winter. Throughout the year, bathyphase and orthophase remained separated by approximately 12 h, suggesting this interval might be conserved. Finally, although 37.0°C (98.6°F) is widely recognized as the mean or normal human body temperature, analysis showed mean temperature was <37.0°C during all times of day, days of the week, and seasons of the year, supporting prior arguments that the 37.0°C standard has no scientific basis. Overall, this large study showed robust and consistent behavior of the human circadian cycle at the population level, providing a strong example of circadian homeostasis.     

A collation of marker gene and dermatoglyphic diversity at various levels of population differentiation

The use of dermatoglyphic traits to describe interpopulational diversity among human populations at various levels of differentiation is compared with similar analysis of gene frequency data by means of nonparametric methods employing distance matrices and dendrograms, and by a partition of total variability into its between and within population components. Congruence of dermatoglyphics and gene markers appears to vary with level of population differentiation — the association remains insignificant until racial level of differentiation is considered. Different pitfalls of the data used are mentioned. The interpretation of these findings is discussed by comparison with other non-human studies.     

Computation of model-dependent tolerance bands for ambulatorily monitored blood pressure

The construction of time-specified reference limits requires systematic sampling in clinical health, particularly for those variables characterized by a circadian rhythm of large amplitude, as it is the case for blood pressure (BP). For the detection of false negatives, tolerance intervals (limits that will include at least a specified proportion of the population with a stated confidence) are important and should substitute when possible for prediction limits. We have previously described a nonparametric method for the computation of model-independent tolerance intervals that are constructed by first dividing the sampling range in several time spans in which no appreciable changes in population characteristics (namely, mean and variance) take place. The tolerance interval is then computed for each of the time spans. The limits thus computed, as well as results of any comparison of a given individual's profile against such tolerance intervals, are highly dependent on the sampling scheme of both the reference individuals and the test subject. To avoid this problem, we have developed an alternative method that allows the computation of model-dependent tolerance bands for hybrid time series. Assuming that a set X of longitudinal series monitored from a given group of reference individuals can be fitted with the same individual model, a population model C(X,t) can be also determined, as well as the deviation S(X,t) of each individual curve from the population model. The tolerance band will then have the form C(X,t) ± kS(X,t), where k is here estimated following a nonparametric approach based on bootstrap techniques. Alternatively, two different values of k can be estimated (for the lower and upper limits of the tolerance interval, respectively) in cases for which we cannot assume symmetry. The method is generally applicable for any population model describing the reference population (including the fit of multiple significant components, nonsinusoidal waveforms, and/or trends). The method was used to establish time-specified tolerance bands for time series of blood pressure monitored automatically in healthy individuals of both genders. Model-dependent intervals are preferred to the model-independent limits when reliance on a specified sampling rate needs to be avoided. These limits may serve for an objective and positive definition of health, for the screening and diagnosis of disease, and for gauging the subject's response to treatment. (Chronobiology International, 17(4), 567-582, 2000)     

Bootstrap Restricted Likelihood Ratio Test for the Detection of Rare Variants

In this paper the detection of rare variants association with continuous phenotypes of interest is investigated via the likelihood-ratio based variance component test under the framework of linear mixed models. The hypothesis testing is challenging and nonstandard, since under the null the variance component is located on the boundary of its parameter space. In this situation the usual asymptotic chisquare distribution of the likelihood ratio statistic does not necessarily hold. To circumvent the derivation of the null distribution we resort to the bootstrap method due to its generic applicability and being easy to implement. Both parametric and nonparametric bootstrap likelihood ratio tests are studied. Numerical studies are implemented to evaluate the performance of the proposed bootstrap likelihood ratio test and compare to some existing methods for the identification of rare variants. To reduce the computational time of the bootstrap likelihood ratio test we propose an effective approximation mixture for the bootstrap null distribution. The GAW17 data is used to illustrate the proposed test.     

Rest-activity circadian rhythm and sleep quality in patients with binge eating disorder

Recent findings suggest that altered rest-activity circadian rhythms (RARs) are associated with a compromised health status. RARs abnormalities have been observed also in several pathological conditions, such as cardiovascular, neurological, and cancer diseases. Binge eating disorder (BED) is the most common eating disorder, with a prevalence of 3.5% in women and 2% in men. BED and its associate obesity and motor inactivity could induce RARs disruption and have negative consequences on health-related quality of life. However, the circadian RARs and sleep behavior in patients with BED has been so far assessed only by questionnaires. Therefore, the purpose of this study was to determine RARs and sleep parameters by actigraphy in patients with BED compared to a body mass index-matched control group (Ctrl). Sixteen participants (eight obese women with and eight obese women without BED diagnosis) were recruited to undergo 5-day monitoring period by actigraphy (MotionWatch 8®, CamNtech, Cambridge, UK) to evaluate RARs and sleep parameters. In order to determine the RARs, the actigraphic data were analyzed using the single cosinor method. The rhythmometric parameters of activity levels (MESOR, amplitude and acrophase) were then processed with the population mean cosinor.

The Actiwatch Sleep Analysis Software (Cambridge Neurotecnology, Cambridge, UK) evaluated the sleep patterns. In each participant, we considered seven sleep parameters (sleep onset: S-on; sleep offset: S-off; sleep duration: SD; sleep latency: SL; movement and fragmentation index: MFI; immobility time: IT; sleep efficiency: SE) calculated over a period of five nights.

The population mean cosinor applied to BED and Ctrl revealed the presence of a significant circadian rhythm in both groups (p < 0.001). The MESOR (170.0 vs 301.6 a.c., in BED and Ctrl, respectively; p < 0.01) and amplitude (157.66 vs 238.19 a.c., in BED and Ctrl, respectively p < 0.05) differed significantly between the two groups. Acrophase was not different between BED and Ctrl, as well as all sleep parameters. Both groups displayed a low level of sleep quality (SE 80.7% and 75.7% in BED and Ctrl, respectively). These data provided the first actigraphy-based evidence of RARs disruption and sleep behavior disorder in patients with BED. However, while sleep disorders could be reasonably ascribed to overweight/obesity and the related lower daily physical activity, RARs disruption in this pathology should be ascribed to factors other than reduced physical activity. The circadian timing approach can represent a novel potential tool in the treatment of patients with eating disorders. These data provide exploratory evidence of behavioral association in a small population of patients that, if confirmed in a wider number of subjects and across different populations, may lead to a revision and enhancement of interventions in BED patients.     

Chronobiologic Evaluation of Drug Efficacy in Hypertension

Time-associated variations of blood pressure became accesible due to the modern development of pressure monitoring technology. The data collection and analysis should be standardized and formulated. Time-associated changes of pressure were evaluated not only by nonparametric and conventional but also by parametric and rhythmometric estimation. The reference data (chronodesms) are essential to define the deviant magnitude of pressure. This chronobiologic approach became feasible to quantitate the efficacy of antihypertensive agents in hypertensives.     

Assessing consistency of fish survey data: uncertainties in the estimation of mackerel icefish (<Emphasis Type="Italic">Champsocephalus gunnari</Emphasis>) abundance at South Georgia

Mackerel icefish (Champsocephalus gunnari) is a semi-pelagic finfish species inhabiting shelf areas in the Southern Ocean. The population at South Georgia is currently exploited by pelagic trawlers fishing close to the seabed. Annual catches peaked at 150,000 t in 1983 and have declined since the mid-to-late 1980s. Bottom-trawl surveys have been conducted since 1987, providing a time series of abundance and size distribution for use in assessing the status of the stock and setting quotas. Food web models suggest that estimates of the biomass from survey data are substantially lower than the amount of icefish required by the local ecosystem. The aim of this study was to assess the uncertainty around current estimates of density and variance, using alternative nonparametric stratified bootstrapping methods. The stratified rescaling bootstrap estimator was identified as the most appropriate method of those tested: in comparison with the existing method, confidence intervals and the inter-annual variability of the estimates were reduced. Numbers-at-age were estimated from mixture distribution models fitted to length-disaggregated density data in order to determine whether individual cohorts were consistently detected by the surveys. Estimates of numbers-at-age could not consistently delineate cohorts in successive years indicating that survey-based estimates of density were biased. These biases may have arisen because the trawl gear did not select individuals of all sizes equally, or because sampling was restricted to the demersal component of the stock. Estimates of abundance of the pelagic component of the stock should be derived from acoustic data to improve the assessment.     

Chronobiologic Evaluation of Drug Efficacy in Hypertension

Time-associated variations of blood pressure became accesible due to the modern development of pressure monitoring technology. The data collection and analysis should be standardized and formulated. Time-associated changes of pressure were evaluated not only by nonparametric and conventional but also by parametric and rhythmometric estimation. The reference data (chronodesms) are essential to define the deviant magnitude of pressure. This chronobiologic approach became feasible to quantitate the efficacy of antihypertensive agents in hypertensives.     

COMPUTATION OF MODEL-DEPENDENT TOLERANCE BANDS FOR AMBULATORILY MONITORED BLOOD PRESSURE

The construction of time-specified reference limits requires systematic sampling in clinical health, particularly for those variables characterized by a circadian rhythm of large amplitude, as it is the case for blood pressure (BP). For the detection of false negatives, tolerance intervals (limits that will include at least a specified proportion of the population with a stated confidence) are important and should substitute when possible for prediction limits. We have previously described a nonparametric method for the computation of model-independent tolerance intervals that are constructed by first dividing the sampling range in several time spans in which no appreciable changes in population characteristics (namely, mean and variance) take place. The tolerance interval is then computed for each of the time spans. The limits thus computed, as well as results of any comparison of a given individual's profile against such tolerance intervals, are highly dependent on the sampling scheme of both the reference individuals and the test subject. To avoid this problem, we have developed an alternative method that allows the computation of model-dependent tolerance bands for hybrid time series. Assuming that a set X of longitudinal series monitored from a given group of reference individuals can be fitted with the same individual model, a population model C(X,t) can be also determined, as well as the deviation S(X,t) of each individual curve from the population model. The tolerance band will then have the form C(X,t) ± kS(X,t), where k is here estimated following a nonparametric approach based on bootstrap techniques. Alternatively, two different values of k can be estimated (for the lower and upper limits of the tolerance interval, respectively) in cases for which we cannot assume symmetry. The method is generally applicable for any population model describing the reference population (including the fit of multiple significant components, nonsinusoidal waveforms, and/or trends). The method was used to establish time-specified tolerance bands for time series of blood pressure monitored automatically in healthy individuals of both genders. Model-dependent intervals are preferred to the model-independent limits when reliance on a specified sampling rate needs to be avoided. These limits may serve for an objective and positive definition of health, for the screening and diagnosis of disease, and for gauging the subject's response to treatment. (Chronobiology International, 17(4), 567–582, 2000)     

Age, gender and circadian or circasemidian blood pressure and heart rate variation of children.

Systolic (S) and diastolic (D) blood pressure (BP) and heart rate (HR) of clinically healthy children (24 boys and 15 girls) 3 to 7 years of age were measured with a standard mercury sphygmomanometer at 3-hour intervals for 24 hours in April 1991. The children slept and/or rested from 2100 to 0700 and napped from 1230 to 1530; they had meals at 0730, 1200 and 1800. A statistically significant circadian and about 12-hour (circasemidian) component of variation is documented for SBP and DBP of boys and girls and for HR of boys. No gender difference was found for the circadian and circasemidian components. A positive correlation with age is found for the MESOR and circadian amplitude of SBP and DBP (p < 0.05); a negative correlation with age is found for the MESOR of HR (p < 0.001).     

Rates of insufficiency and deficiency of vitamin D levels in elite professional male and female skiers: A chronobiologic approach

Vitamin D is essential for the maintenance and promotion of musculoskeletal health, for the functioning of the immune, cardiovascular and reproductive systems, and its main action is to keep calcium and phosphate plasmatic physiological concentrations at intestinal, renal and bony level. Vitamin D affects several parameters related to physical performance too and a particularly high percentage of vitamin D insufficiency and deficiency in professional athletes has been observed. Several variables are able to impair the synthesis of 25(OH)D in athletes, specifically both genetic and environmental factors, but the most probable explanation for the deficient/insufficient vitamin D levels is the insufficient ultraviolet B light (UVB) exposure during winter. To confirm this, the existence of a circannual rhythm of vitamin D in professional soccer players, highlighting a peak in summer and lowest values in winter regardless the period of the season, has been documented. Nonetheless, from what we are aware of, no other study adopted a chronobiologic approach to better understand and describe the circannual variations of serum 25(OH)D in other sport disciplines. Therefore, we studied serum vitamin D in a cohort of top-level professional skiers, during a period of three consecutive competitive seasons (2015, 2016 and 2017), in order to evaluate, with a rhythmometric approach, the vitamin D behavior along the year. The study population was composed by 152 professional Italian alpine skiers of FISI (Winter Sport Italian Federation), 63 females and 89 males (mean age: 24.1 ± 3.2 years) and a total of 298 blood drawings were carried out to determine plasma 25(OH)D. Vitamin D data were compared between genders and then processed with the population mean cosinor tests to evaluate the presence of a circannual rhythm, both for female and male athletes. In total, 77 skiers (50.7%) showed, at least once during the three competitive seasons, an insufficient level of 25(OH)D and other 45 subjects (29.6%) showed a deficient status; no differences were observed between genders (mean for females: 26.9 ± 8.1 ng/mL; mean for males: 27.4 ± 7.6 ng/mL). In addition, the rhythmometric analysis highlighted the existence of a significant circannual rhythm for both female and male professional skiers; the acrophases (Φ) occurred in July and both MESOR (M) and amplitude (A) were comparable between the two groups. Our data indicate that, despite the physical effort spent, vitamin D follows a classical season-associated rhythm with a peak in summer and a nadir in winter. Moreover, the percentage of insufficiency and deficiency is in line with that of the general population. In conclusion, our findings reinforce the hypothesis that there is no direct effect of physical activity on vitamin D metabolism and that the factors involved in the determination of vitamin D levels in the general population are valid also for athletes.     

Exploring complex fitness surfaces: multiple ornamentation and polymorphism in male guppies

Abstract.— The sexual ornamentation used by male guppies to attract females comprises many components, each of which varies considerably among males. Although natural and sexual selection have been shown to contribute to divergence among populations in male sexual ornaments, the role of sexual selection in maintaining polymorphism within populations is less clear. We used both parametric quadratic regression and nonparametric projection pursuit regression techniques to reveal the major axes of non-linear sexual selection on male ornaments. We visualized the fitness surfaces defined by these axes using thin-plate splines to allow a direct comparison of the two methodologies. Identification of the major axes of selection and their visualization was critical in determining the form and strength of nonlinear selection. Both types of analysis revealed fitness surfaces comprising three peaks, suggesting that there is more than one way to make an attractive guppy. Disruptive selection may be an important process underlying the presence of multiple sexual ornaments and may contribute to the maintenance of the high levels of polymorphism in male sexual ornaments found in guppy populations.