The recovery of fertility during breast-feeding in Assiut, Egypt

A longitudinal study of twenty-six breast-feeding and twelve non-breast-feeding postpartum women was conducted in Assiut, Egypt in order to determine the time that ovulation resumed after childbirth, and the effect of breast-feeding frequency on the period of lactational anovulation. Breast-feeding women experienced the onset of follicular development, vaginal bleeding, ovulation and pregnancy significantly later than women who did not breast-feed. Ovulatory and non-ovulatory breast-feeders reported similar frequencies of breast-feeding episodes. The introduction of dietary supplements commonly preceded ovulation. An algorithm using three simple variables observable to the breast-feeding mother was found to predict up to 100% of the first ovulations. All breast-feeding women who did not give supplements and did not have a vaginal bleeding episode by 6 months postpartum were anovular by strict criteria for ovulation. Ovulation did not precede bleeding or supplementation in the women who experienced these events before 6 months, yielding a highly effective formula for preventing unplanned pregnancy by the informed use of breast-feeding.     

The Spanish tourist sector facing extreme climate events: a case study of domestic tourism in the heat wave of 2003

This research explores, by means of a questionnaire-based survey, public knowledge and perception as well as the behaviour of young Spanish tourists before, during and after the summer holiday period affected by an episode of extreme heat in 2003. The survey was administered between November and December 2004. The extraordinary heat wave of the summer of 2003 can be seen as an example of a normal episode in terms of the predicted intensity and duration of European summers towards the end of the twenty-first century. It can therefore be used as the laboratory setting for this study. In this context, the use of the climate analogue approach allows us to obtain novel perspectives regarding the future impact that this type of event could have on tourist demand, based on a real experience. Likewise, such an approach allows the strategies of adaptation implemented by the different elements in the tourist system in order to cope with the atmospheric episode to be evaluated. Such strategies could prove useful in reducing vulnerability when faced with similar episodes in the future. The main results indicate that Spanish tourists (young segment market) are flexible in adapting to episodes of extremely high temperatures. Their personal perception of the phenomenon, their behaviour and the adaptation measures implemented to a greater or lesser extent before that time, reduce the vulnerability of the sector when faced with this type of event, at least from the point of view of this young segment of the internal national market. In Spain, the episode of extreme heat of 2003 has led to the implementation or improvement of some adaptive measures after the event, especially in the fields of management, policy and education.     

Modeling the effects of a bidirectional latent predictor from multivariate questionnaire data

Researchers often measure stress using questionnaire data on the occurrence of potentially stress-inducing life events and the strength of reaction to these events, characterized as negative or positive and assigned an ordinal ranking. In studying the health effects of stress, one needs to obtain measures of an individual's negative and positive stress levels to be used as predictors. Motivated by data of this type, we propose a latent variable model, which is characterized by event-specific negative and positive reaction scores. If the positive reaction score dominates the negative reaction score for an event, then the individual's reported response to that event will be positive, with an ordinal ranking determined by the value of the score. Measures of overall positive and negative stress can be obtained by summing the reactivity scores across the events that occur for an individual. By incorporating these measures as predictors in a regression model and fitting the stress and outcome models jointly using Bayesian methods, inferences can be conducted without the need to assume known weights for the different events. We propose an MCMC algorithm for posterior computation and apply the approach to study the effects of stress on preterm delivery.     

Bayesian models for multivariate current status data with informative censoring

Multivariate current status data, consist of indicators of whether each of several events occur by the time of a single examination. Our interest focuses on inferences about the joint distribution of the event times. Conventional methods for analysis of multiple event-time data cannot be used because all of the event times are censored and censoring may be informative. Within a given subject, we account for correlated event times through a subject-specific latent variable, conditional upon which the various events are assumed to occur independently. We also assume that each event contributes independently to the hazard of censoring. Nonparametric step functions are used to characterize the baseline distributions of the different event times and of the examination times. Covariate and subject-specific effects are incorporated through generalized linear models. A Markov chain Monte Carlo algorithm is described for estimation of the posterior distributions of the unknowns. The methods are illustrated through application to multiple tumor site data from an animal carcinogenicity study.     

Semiparametric Analysis for Recurrent Event Data with Time-Dependent Covariates and Informative Censoring

Summary .  Recurrent event data analyses are usually conducted under the assumption that the censoring time is independent of the recurrent event process. In many applications the censoring time can be informative about the underlying recurrent event process, especially in situations where a correlated failure event could potentially terminate the observation of recurrent events. In this article, we consider a semiparametric model of recurrent event data that allows correlations between censoring times and recurrent event process via frailty. This flexible framework incorporates both time-dependent and time-independent covariates in the formulation, while leaving the distributions of frailty and censoring times unspecified. We propose a novel semiparametric inference procedure that depends on neither the frailty nor the censoring time distribution. Large sample properties of the regression parameter estimates and the estimated baseline cumulative intensity functions are studied. Numerical studies demonstrate that the proposed methodology performs well for realistic sample sizes. An analysis of hospitalization data for patients in an AIDS cohort study is presented to illustrate the proposed method.     

Analysis of interval‐censored recurrent event processes subject to resolution

Interval‐censored recurrent event data arise when the event of interest is not readily observed but the cumulative event count can be recorded at periodic assessment times. In some settings, chronic disease processes may resolve, and individuals will cease to be at risk of events at the time of disease resolution. We develop an expectation‐maximization algorithm for fitting a dynamic mover‐stayer model to interval‐censored recurrent event data under a Markov model with a piecewise‐constant baseline rate function given a latent process. The model is motivated by settings in which the event times and the resolution time of the disease process are unobserved. The likelihood and algorithm are shown to yield estimators with small empirical bias in simulation studies. Data are analyzed on the cumulative number of damaged joints in patients with psoriatic arthritis where individuals experience disease remission.     

The neuronal transition probability (NTP) model for the dynamic progression of non-REM sleep EEG: the role of the suprachiasmatic nucleus

Little attention has gone into linking to its neuronal substrates the dynamic structure of non-rapid-eye-movement (NREM) sleep, defined as the pattern of time-course power in all frequency bands across an entire episode. Using the spectral power time-courses in the sleep electroencephalogram (EEG), we showed in the typical first episode, several moves towards-and-away from deep sleep, each having an identical pattern linking the major frequency bands beta, sigma and delta. The neuronal transition probability model (NTP)--in fitting the data well--successfully explained the pattern as resulting from stochastic transitions of the firing-rates of the thalamically-projecting brainstem-activating neurons, alternating between two steady dynamic-states (towards-and-away from deep sleep) each initiated by a so-far unidentified flip-flop. The aims here are to identify this flip-flop and to demonstrate that the model fits well all NREM episodes, not just the first. Using published data on suprachiasmatic nucleus (SCN) activity we show that the SCN has the information required to provide a threshold-triggered flip-flop for TIMING the towards-and-away alternations, information provided by sleep-relevant feedback to the SCN. NTP then determines the PATTERN of spectral power within each dynamic-state. NTP was fitted to individual NREM episodes 1-4, using data from 30 healthy subjects aged 20-30 years, and the quality of fit for each NREM measured. We show that the model fits well all NREM episodes and the best-fit probability-set is found to be effectively the same in fitting all subject data. The significant model-data agreement, the constant probability parameter and the proposed role of the SCN add considerable strength to the model. With it we link for the first time findings at cellular level and detailed time-course data at EEG level, to give a coherent picture of NREM dynamics over the entire night and over hierarchic brain levels all the way from the SCN to the EEG.     

A Bayesian Latent Variable Mixture Model for Longitudinal Fetal Growth

Summary Fetal growth restriction is a leading cause of perinatal morbidity and mortality that could be reduced if high‐risk infants are identified early in pregnancy. We propose a Bayesian model for aggregating 18 longitudinal ultrasound measurements of fetal size and blood flow into three underlying, continuous latent factors. Our procedure is more flexible than typical latent variable methods in that we relax the normality assumptions by allowing the latent factors to follow finite mixture distributions. Using mixture distributions also permits us to cluster individuals with similar observed characteristics and identify latent classes of subjects who are more likely to be growth or blood flow restricted during pregnancy. We also use our latent variable mixture distribution model to identify a clinically meaningful latent class of subjects with low birth weight and early gestational age. We then examine the association of latent classes of intrauterine growth restriction with latent classes of birth outcomes as well as observed maternal covariates including fetal gender and maternal race, parity, body mass index, and height. Our methods identified a latent class of subjects who have increased blood flow restriction and below average intrauterine size during pregnancy. These subjects were more likely to be growth restricted at birth than a class of individuals with typical size and blood flow.     

If a population crashes in prehistory, and there is no paleodemographer there to hear it, does it make a sound?

Catastrophic episodes (e.g., epidemics, natural disasters) strike with only limited regard for age. A large percentage of catastrophic mortality in a population can lead to a death distribution that resembles the living distribution, which includes greater numbers of older children, adolescents, and young adults than typical mortality profiles. This paper examines both the population implications of a large catastrophic mortality event, based on the Black Death as it ravaged medieval Europe, and its long-term effects on age-at-death distributions. An increased prevalence of epidemic disease is a common feature of reconstructions of the shift to agriculture and the rise of urban centers. The model begins with a hypothetical Medieval living population. This population is stable and characterized by slow growth. It has fertility and mortality rates consistent with a natural-fertility, agrarian population. The effects of catastrophic episodes are simulated by projecting the model population and subjecting it to one large (30% mortality) catastrophic episode as part of a 100-year population projection. A pair of Leslie matrices forms the basis of the projection. The catastrophic episode has important, long-term effects on both the living population and the cumulative distribution of death. The living population fails to recover from plague losses; at the end of the projection, population is still less than 75% its pre-plague level. The age-at-death distribution takes on the juvenile-young adult-heavy profile characteristic of many archaeological samples. The cumulative death profile based on the projection differs from that produced by the stable model significantly (P < 0.05) for 25-50 years after the plague episode, depending on sample size.     

Rates and patterns of gene duplication and loss in the human genome

Gene duplication has certainly played a major role in structuring vertebrate genomes but the extent and nature of the duplication events involved remains controversial. A recent study identified two major episodes of gene duplication: one episode of putative genome duplication ca. 500 Myr ago and a more recent gene-family expansion attributed to segmental or tandem duplications. We confirm this pattern using methods not reliant on molecular clocks for individual gene families. However, analysis of a simple model of the birth-death process suggests that the apparent recent episode of duplication is an artefact of the birth-death process. We show that a constant-rate birth-death model is appropriate for gene duplication data, allowing us to estimate the rate of gene duplication and loss in the vertebrate genome over the last 200 Myr (0.00115 and 0.00740 Myr(-1) lineage(-1), respectively). Finally, we show that increasing rates of gene loss reduce the impact of a genome-wide duplication event on the distribution of gene duplications through time.     

A Markov model for a clinical episode of recurrent genital herpes

A time-homogeneous Markov process is proposed for modeling the clinical course of recurrent genital herpes and is used to obtain estimators for various characteristics of the disease episode. The model has a finite, discrete time parameter and discrete state space, with six transient states corresponding to the six stages a herpes lesion may enter. The healed condition is represented as an absorbing state. The number of lesions present at the onset of the clinical episode and the number of lesions appearing during the course of the episode are assumed to have negative binomial distributions. Clinical trial data are used to examine the assumptions of the model and to estimate its parameters. Estimates of clinical variables based on the model are computed and are compared with those calculated directly to assess how well the model represents the biological process of the disease.     

Joint analysis of time-to-event and multiple binary indicators of latent classes

Multiple categorical variables are commonly used in medical and epidemiological research to measure specific aspects of human health and functioning. To analyze such data, models have been developed considering these categorical variables as imperfect indicators of an individual's "true" status of health or functioning. In this article, the latent class regression model is used to model the relationship between covariates, a latent class variable (the unobserved status of health or functioning), and the observed indicators (e.g., variables from a questionnaire). The Cox model is extended to encompass a latent class variable as predictor of time-to-event, while using information about latent class membership available from multiple categorical indicators. The expectation-maximization (EM) algorithm is employed to obtain maximum likelihood estimates, and standard errors are calculated based on the profile likelihood, treating the nonparametric baseline hazard as a nuisance parameter. A sampling-based method for model checking is proposed. It allows for graphical investigation of the assumption of proportional hazards across latent classes. It may also be used for checking other model assumptions, such as no additional effect of the observed indicators given latent class. The usefulness of the model framework and the proposed techniques are illustrated in an analysis of data from the Women's Health and Aging Study concerning the effect of severe mobility disability on time-to-death for elderly women.     

Patterns of bleeding in adolescents with severe haemophilia A.

Eighty-two boys with severe haemophilia A who spent some time at Lord Mayor Treloar College during 1973-7 were studied. All episodes of bleeding that occurred during term time were recorded, along with the number of transfusions. The bleeding frequency among these boys, most of them aged 10-17 years, increased steadily from 8,31 episodes/100 days in 1973 to 12,63 episodes/100 days in 1977. At the same time there was a steady fall in bleeding frequency with age. Altogether 24% of bleeding episodes were into the elbow joint, 22% into the knee, and 15% into the ankle. As the boys grew older the proportion of bleeding episodes in the legs declined and that in the arms increased. The overall results reflect the fact that special schools now see only the severest cases of haemophilia. The pattern of bleeding during adolescence suggests that concepts of management of arm bleeding need modifying.     

Incidence and development of rhythmic episodic activity in the electroencephalogram of a large rat population under chronic conditions

689 long-term electroencephalographic recordings from 88 rats with chronically implanted electrodes were evaluated with reference to the onset and development of rhythmic spike episodes of 8-9 Hz frequency characteristic of quiet wakefulness. Episodes occurred in the recordings of 88% of the test animals. Recordings completely devoid of episodes came from selected rats highly sensitive to an acoustic epileptogenic stimulus and from 50% of rats of a Wistar-Velaz barrier breed. These two groups differed from the other animals in respect of their greater aggressiveness and restlessness in the chronic experiment. The episodes were not evoked by the surgical procedure--implantation of a cobalt-gelatin pin in the brain--or to the actual implantation of chronic electrodes in the brain. The shortest recorded latent period for the appearance of episodes was one week after the implantation of electrodes and the longest was 6 months. The animals' mean age at the time of the onset of episodes was 3.8 months and the lowest age was 2.5 months (i.e. immediately after implantation of the electrodes). The electrodes were not implanted before the age of 2.5 months. In repeated chronic recordings during the animals' life, both the number and the duration of the episodes increased. In most of the rats, the spike frequency in the episode was 8-9 Hz and was maintained at a stable value characteristic for each rat. Episodic rhythmic activity can thus occur in a state of quiet wakefulness in the electroencephalogram of all the given groups of rats (except highly sensitive animals) from early adulthood up to the age regarded in the rat as senility. The results to date indicate that the main condition for its appearance is the attainment of an optimum state of vigilance--quiet immobile wakefulness. The mechanisms leading to this stage of vigilance display both individual and group differences and are evidently related to the ability to become habituated to the experimental environment.     

Viral blip dynamics during highly active antiretroviral therapy

Although intermittent episodes of low-level viremia are often observed in well-suppressed highly active antiretroviral therapy (HAART)-treated patients, the timing and amplitude of viral blips have never been examined in detail. We analyze here the dynamics of viral blips, i.e., plasma VL measurements of >50 copies/ml, in 123 HAART-treated patients monitored for a mean of 2.6 years (range, 5 months to 5.3 years). The mean (+/- the standard deviation) blip frequency was 0.09 +/- 0.11/sample, with about one-third of patients showing no viral blips. The mean viral blip amplitude was 158 +/- 132 human immunodeficiency virus type 1 (HIV-1) RNA copies/ml. Analysis of the blip frequency and amplitude distributions suggest that two blips less than 22 days apart have a significant chance of being part of the same episode of viremia. The data are consistent with a hypothetical model in which each episode of viremia consists of a phase of VL rise, followed by two-phase exponential decay. Thus, the term "viral blip" may be a misnomer, since viral replication appears to be occurring over an extended period. Neither the frequency nor the amplitude of viral blips increases with longer periods of observation, but the frequency is inversely correlated with the CD4(+)-T-cell count at the start of therapy, suggesting that host-specific factors but not treatment fatigue are determinants of blip frequency.     

Bayesian modeling of embryonic growth using latent variables

In a growth model, individuals move progressively through a series of states in which each state is indicative of developmental status. Interest lies in estimating the rate of progression through each state while incorporating covariates that might affect the transition rates. We develop a Bayesian discrete-time multistate growth model for inference from cross-sectional data with unknown initiation times. For each subject, data are collected at only one time point at which we observe the state as well as covariates that measure developmental progress. We link the developmental progress variables to an underlying latent growth variable that can also affect the state transition rates. A subject with slow latent growth will then have relatively small developmental progress covariates and move through state transitions slowly. We then examine the association between latent growth and the probability of future events in a novel study of embryonic development and pregnancy loss. Using a Markov chain Monte Carlo (MCMC) algorithm for posterior computation, we found evidence in favor of a previously hypothesized but unproven association between slow growth early in pregnancy and increased risk of future spontaneous abortion.     

Analysis of multivariate recurrent event data with time‐dependent covariates and informative censoring

Multivariate recurrent event data are usually encountered in many clinical and longitudinal studies in which each study subject may experience multiple recurrent events. For the analysis of such data, most existing approaches have been proposed under the assumption that the censoring times are noninformative, which may not be true especially when the observation of recurrent events is terminated by a failure event. In this article, we consider regression analysis of multivariate recurrent event data with both time‐dependent and time‐independent covariates where the censoring times and the recurrent event process are allowed to be correlated via a frailty. The proposed joint model is flexible where both the distributions of censoring and frailty variables are left unspecified. We propose a pairwise pseudolikelihood approach and an estimating equation‐based approach for estimating coefficients of time‐dependent and time‐independent covariates, respectively. The large sample properties of the proposed estimates are established, while the finite‐sample properties are demonstrated by simulation studies. The proposed methods are applied to the analysis of a set of bivariate recurrent event data from a study of platelet transfusion reactions.     

Dynamics of recurrent viral infection

In chronic viral infection, low levels of viral replication and infectious particle production are maintained over long periods, punctuated by brief bursts of high viral production and release. We apply well-established principles of modelling virus dynamics to the study of chronic viral infection, demonstrating that a model which incorporates the distinct contributions of cytotoxic T lymphocytes (CTLs) and antibodies exhibits long periods of quiescence followed by brief bursts of viral production. This suggests that for recurrent viral infections, no special mechanism or exogenous trigger is necessary to provoke an episode of reactivation; rather, the system may naturally cycle through recurrent episodes at intervals which can be many years long. We also find that exogenous factors which cause small fluctuations in the natural course of the infection can trigger a recurrent episode. Our model predicts that longer periods between recurrences are associated with more severe viral episodes. Four factors move the system towards less frequent, more severe episodes: decreased viral infectivity, decreased CTL efficacy, decreased memory T cell response and increased antibody efficacy.     

Site frequency spectra from genomic SNP surveys

Genomic survey data now permit an unprecedented level of sensitivity in the detection of departures from canonical evolutionary models, including expansions in population size and selective sweeps. Here, we examine the effects of seemingly subtle differences among sampling distributions on goodness of fit analyses of site frequency spectra constructed from single nucleotide polymorphisms. Conditioning on the observation of exactly two alleles in a random sample results in a site frequency spectrum that is independent of the scaled rate of neutral substitution (θ). Other sampling distributions, including conditioning on a single mutational event in the sample genealogy or randomly selecting a single mutation from a genealogy with multiple mutations, have distinct site frequency spectra that show highly significant departures from the predictions of the biallelic model. Some aspects of data filtering may contribute to significant departures of site frequency spectra from expectation, apart from any violation of the standard neutral model.