Gene regulatory, signal transduction and metabolic networks are major areas of interest in the newly emerging field of systems biology. In living cells, stochastic dynamics play an important role; however, the kinetic parameters of biochemical reactions necessary for modelling these processes are often not accessible directly through experiments. The problem of estimating stochastic reaction constants from molecule count data measured, with error, at discrete time points is considered. For modelling the system, a hidden Markov process is used, where the hidden states are the true molecule counts, and the transitions between those states correspond to reaction events following collisions of molecules. Two different algorithms are proposed for estimating the unknown model parameters. The first is an approximate maximum likelihood method that gives good estimates of the reaction parameters in systems with few possible reactions in each sampling interval. The second algorithm, treating the data as exact measurements, approximates the number of reactions in each sampling interval by solving a simple linear equation. Maximising the likelihood based on these approximations can provide good results, even in complex reaction systems.
BackgroundMental health professionals have a pivotal role in suicide prevention. However, they also often have intense emotional responses, or countertransference, during encounters with suicidal patients. Previous studies of the Therapist Response Questionnaire-Suicide Form (TRQ-SF), a brief novel measure aimed at probing a distinct set of suicide-related emotional responses to patients found it to be predictive of near-term suicidal behavior among high suicide-risk inpatients. The purpose of this study was to validate the TRQ-SF in a general outpatient clinic setting.MethodsAdult psychiatric outpatients (N = 346) and their treating mental health professionals (N = 48) completed self-report assessments following their first clinic meeting. Clinician measures included the TRQ-SF, general emotional states and traits, therapeutic alliance, and assessment of patient suicide risk. Patient suicidal outcomes and symptom severity were assessed at intake and one-month follow-up. Following confirmatory factor analysis of the TRQ-SF, factor scores were examined for relationships with clinician and patient measures and suicidal outcomes.ResultsFactor analysis of the TRQ-SF confirmed three dimensions: (1) affiliation, (2) distress, and (3) hope. The three factors also loaded onto a single general factor of negative emotional response toward the patient that demonstrated good internal reliability. The TRQ-SF scores were associated with measures of clinician state anger and anxiety and therapeutic alliance, independently of clinician personality traits after controlling for the state- and patient-specific measures. The total score and three subscales were associated in both concurrent and predictive ways with patient suicidal outcomes, depression severity, and clinicians’ judgment of patient suicide risk, but not with global symptom severity, thus indicating specifically suicide-related responses.ConclusionThe TRQ-SF is a brief and reliable measure with a 3-factor structure. It demonstrates construct validity for assessing distinct suicide-related countertransference to psychiatric outpatients. Mental health professionals’ emotional responses to their patients are concurrently indicative and prospectively predictive of suicidal thoughts and behaviors. Thus, the TRQ-SF is a useful tool for the study of countertransference in the treatment of suicidal patients and may help clinicians make diagnostic and therapeutic use of their own responses to improve assessment and intervention for individual suicidal patients.
Life history theory (LHT) predicts a trade-off between reproductive effort and the pace of biological aging. Energy invested in reproduction is not available for tissue maintenance, thus having more offspring is expected to lead to accelerated senescence. Studies conducted in a variety of non-human species are consistent with this LHT prediction. Here we investigate the relationship between the number of surviving children born to a woman and telomere length (TL, a marker of cellular aging) over 13 years in a group of 75 Kaqchikel Mayan women. Contrary to LHT’s prediction, women who had fewer children exhibited shorter TLs than those who had more children (p = 0.045) after controlling for TL at the onset of the 13-year study period. An “ultimate” explanation for this apparently protective effect of having more children may lay with human’s cooperative-breeding strategy. In a number of socio-economic and cultural contexts, having more chilren appears to be linked to an increase in social support for mothers (e.g., allomaternal care). Higher social support, has been argued to reduce the costs of further reproduction. Lower reproductive costs may make more metabolic energy available for tissue maintenance, resulting in a slower pace of cellular aging. At a “proximate” level, mechanisms involved may include the actions of the gonadal steroid estradiol, which increases dramatically during pregnancy. Estradiol is known to protect TL from the effects of oxidative stress as well as increase telomerase activity, an enzyme that maintains TL. Future research should explore the potential role of social support as well as that of estradiol and other potential biological pathways in the trade-offs between reproductive effort and the pace of cellular aging within and among human as well as in non-human populations.
This paper is motivated by the work of Albert et al. who consider lesion count data observed on multiple sclerosis patients, and develop models for each patient's data individually. From a medical perspective, adequate models for such data are important both for describing the behaviour of lesions over time, and for designing efficient clinical trials. In this paper, we discuss some issues surrounding the hidden Markov model proposed by these authors. We describe an efficient estimation method and propose some extensions to the original model. Our examples illustrate the need for models which describe all patients' data simultaneously, while allowing for inter-patient heterogeneity.
BackgroundCortisol is frequently used as a marker of physiologic stress levels. Using cortisol for that purpose, however, requires a thorough understanding of its normal longitudinal variability. The current understanding of longitudinal variability of basal cortisol secretion in women is very limited. It is often assumed, for example, that basal cortisol profiles do not vary across the menstrual cycle. This is a critical assumption: if cortisol were to follow a time dependent pattern during the menstrual cycle, then ignoring this cyclic variation could lead to erroneous imputation of physiologic stress. Yet, the assumption that basal cortisol levels are stable across the menstrual cycle rests on partial and contradictory evidence. Here we conduct a thorough test of that assumption using data collected for up to a year from 25 women living in rural Guatemala.MethodologyWe apply a linear mixed model to describe longitudinal first morning urinary cortisol profiles, accounting for differences in both mean and standard deviation of cortisol among women. To that aim we evaluate the fit of two alternative models. The first model assumes that cortisol does not vary with menstrual cycle day. The second assumes that cortisol mean varies across the menstrual cycle. Menstrual cycles are aligned on ovulation day (day 0). Follicular days are assigned negative numbers and luteal days positive numbers. When we compared Models 1 and 2 restricting our analysis to days between −14 (follicular) and day 14 (luteal) then day of the menstrual cycle did not emerge as a predictor of urinary cortisol levels (p-value >0.05). Yet, when we extended our analyses beyond that central 28-day-period then day of the menstrual cycle become a statistically significant predictor of cortisol levels.SignificanceThe observed trend suggests that studies including cycling women should account for day dependent variation in cortisol in cycles with long follicular and luteal phases.
Summary. In this article, we propose a graphical technique for assessing the goodness-of-fit of a stationary hidden Markov model (HMM). We show that plots of the estimated distribution against the empirical distribution detect lack of fit with high probability for large sample sizes. By considering plots of the univariate and multidimensional distributions, we are able to examine the fit of both the assumed marginal distribution and the correlation structure of the observed data. We provide general conditions for the convergence of the empirical distribution to the true distribution, and demonstrate that these conditions hold for a wide variety of time-series models. Thus, our method allows us to compare not only the fit of different HMMs, but also that of other models as well. We illustrate our technique using a multiple sclerosis data set.Key words: Goodness-of-fit; Hidden Markov model; Model selection; Multiple sclerosis; Probability plot; Stationary time series. IntroductionHidden Markov models (HMMs) describe the relationship between two stochastic processes: an observed process and an underlying "hidden" (unobserved) process. These models have been applied to a wide array of problems involving longitudinal data, including speech recognition (e.g., Levinson, Rabiner, and Sondhi, 1983), gene profiling and recognition (e.g., Krogh, 1998), and precipitation modeling (Hughes and Guttorp, 1994).Magnetic resonance imaging (MRI) scans of relapsingremitting multiple sclerosis (MS) patients are another source of data that may be appropriately modeled by HMMs. Patients afflicted with this disease have symptoms that worsen and then improve in alternating periods of relapse and remission. One such symptom is lesions in the brain; it is now believed that exacerbations are associated with increased numbers of lesions. Thus, it may be reasonable to assume that the distribution of the lesion counts depends on the patient's (unobserved) disease state, i.e., whether the patient is in relapse or remission. Additionally, we might expect to see autocorrelation in this sequence of disease states. Indeed, Albert et al. (1994) use this idea in the development of an HMM for individual relapsing-remitting MS patients.We will give the definition of a stationary HMM in the context of these MS/MRI data. In particular, for a given patient, we let Y t be the observed lesion count and Z t be the hidden disease state at time t, t = 1, . . . , n. We assume, for convenience, that these time points are equally spaced; however, this assumption is not strictly necessary. The process {Y t } is a stationary HMM if the following two conditions hold:
Objective: To evaluate putative links between birth sex ratios (BSR = male:female births) and maternal age in a traditional, agricultural, natural fertility population. Metabolic energy, social support, and the costs and benefits associated with producing sons versus daughters can affect BSR. These variables fluctuate with maternal age. Most studies evaluating links between maternal age and BSR have been based on industrialized populations, which differ importantly from traditional indigenous communities in terms of the aforementioned socio-ecological variables.Materials and methods: We analyze data from 108 mothers and their 603 children living in an agricultural, pronatalist, Kakchiquel Mayan community.Results: A logistic regression model, including linear and quadratic maternal age terms and women-specific random effects, shows a nonmonotonic (p = .028) relationship between log BSR and maternal age. For maternal age ≤ 22, the upper bound of the 95% confidence interval (CI) for BSR is <1, suggesting a bias toward girls. The probability of birthing a son increased early during the average mother's reproductive career, peaked at age 31.3 (approximately 95% CI = 27.1, 35.5), and decreased as she approached her perimenopausal period (p = .014).Discussion: No changes in mating system, population sex ratio, mortality patterns, natural disasters, social risk, or toxic exposures were observed and thus are unlikely to explain our results. At this point, age-related changes in metabolic energy, social support, and costs and benefits associated with offspring sex cannot be excluded as possible explanations. BSR can affect growth, morbidity, and mortality. Thus, our results are relevant to numerous fields, including anthropology, ecology, demography, and public health. K E Y W O R D Sbirth order, maternal age, maternal fitness, sex ratio
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