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OBJECTIVES Postpartum amenorrhea (PA) affects the length of interbirth intervals and thus is intimately related to human life history strategies. PA duration appears to be influenced by maternal energetic status. In humans, as in other mammals, sons are costlier than daughters. Thus, we hypothesize that, in energetically constrained environments, a newborn's sex should be associated with PA duration. METHODS We analyzed data from two natural fertility populations in which mothers have differing energy budgets: Qom women (n = 121) from a periurban village in Argentina, who have a comparatively calorically dense diet and are sedentary (prepregnancy mean BMI = 24.8 ± 4.5 kg/m2 in 1997), and agropastoral Kaqchikel Maya women (n = 88), who have a comparatively calorically restricted diet and high physical activity levels (mean BMI = 21.8 ± 3.7 kg/m2 ). We predict that (a) mothers of sons exhibit longer PA duration than mothers of daughters and (b) this association between offspring sex and PA duration is stronger in the Maya, who have smaller energy budgets. RESULTS Maya mothers with sons exhibited estimated mean and median PA durations that were 1.34 times the estimated mean and median PA duration of mothers with daughters (p = 0.02). Among the Qom, mean, and median PA duration did not differ significantly in relation to offspring sex (p = 0.94). CONCLUSIONS Maya mothers with sons exhibited longer PA duration than those with daughters. This phenomenon was not observed in the well-nourished Qom, possibly due to "buffering" effects from larger energy budgets. Offspring sex may influence birth spacing and maternal life history strategies in energetically constrained environments.

Rainfall in Guanacaste, Costa Rica, has marked wet/dry phases: the rainy season is punctuated by a short midsummer drought, and the dry season frequently has months of no rain. In this region, spring and summer rainfall peaks are important for local rain-fed agriculture and annual total for groundwater recharge and hydroelectricity production. We propose a novel model of rainfall in this region, the double-Gaussian model, which uses monthly total rainfall data collected from 1980 to 2020 from two meteorological observation stations. Our model provides an intuitive way of describing the seasonality of rainfall, the inter-annual variability of the cycle, and variability due to the monthly Oceanic Niño Index, ONI. We also consider two alternative models, a regression model with ARMA errors and a Tweedie model, as a means of assessing the robustness of our conclusions to violations of the assumptions of the double-Gaussian model. We found that the data provide strong evidence of an increase/decrease in rainfall in both temporal maxima during La Niña/El Niño (negative/positive ONI) conditions but no evidence of a decade-scale trend after accounting for ONI effects. Finally, we investigated the problem of forecasting future rainfall based on our three models. We found that when ONI is incorporated as a predictor variable, our models can produce substantial gains in prediction accuracy of spring, summer, and annual totals over naive methods based on monthly sample means or medians.

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

Variation in the durations of exclusive breastfeeding (exBF) and any breastfeeding (anyBF) is associated with socioecological factors. This plasticity in breastfeeding behavior appears adaptive, but the mechanisms involved are unclear. With this concept in mind, we investigated whether durations of exBF and anyBF in a rural Maya population covary with markers of a form of socioecological change—market integration—and whether individual factors (individual learning, physiological plasticity) and/or learning from others in the community (social learning, norm adherence) mediate these changes. Using data from 419 mother-child pairs from two Guatemalan Maya villages, we fit a bivariate linear mixed model. The model compared exBF and anyBF among children from households of varying degrees of market integration whose mothers follow what we inferred to be local infant-feeding norms. It controlled for other factors expected to affect breastfeeding durations. We found evidence that exBF is associated with whether mothers follow their population’s infant feeding norms, but no evidence that exBF is associated with the household’s level of market integration. Conversely, anyBF is significantly associated with the household’s market integration, but not with the villages’ inferred norms. Because deviations from exBF norms are likely to result in infant mortality and reduced fitness, we hypothesize that the incentive to conform is relatively strong. Relatively greater individual plasticity in anyBF allows mother-child pairs to tailor it to socioecological conditions. Deviations from anyBF norms may be tolerated because they may provide later-life health/fitness payoffs, while posing few risks to infant survival.

The grouped relative risk model (GRRM) is a popular semi-parametric model for analyzing discrete survival time data. The maximum likelihood estimators (MLEs) of the regression coefficients in this model are often asymptotically efficient relative to those based on a more restrictive, parametric model. However, in settings with a small number of sampling units, the usual properties of the MLEs are not assured. In this paper, we discuss computational issues that can arise when fitting a GRRM to small samples, and describe conditions under which the MLEs can be ill-behaved. We find that, overall, estimators based on a penalized score function behave substantially better than the MLEs in this setting and, in particular, can be far more efficient. We also provide methods of assessing the fit of a GRRM to small samples.

Objectives The causes of variation in breastfeeding duration in humans are poorly understood, but life history factors related to maternal energetics drive much of the variation in lactation duration in nonhuman animals. With this in mind, we investigated whether four energy-related factors influence variation in breastfeeding duration in a non-industrial human population: (1) mortality risk during mother's development (assessed via mother's adult height), (2) reliance on nutrient-dense weaning foods, (3) access to and need for help with infant feeding and care (“allomaternal care”), and (4) maternal tradeoffs between current and future reproduction (measured via child's birth order). Materials and methods The data pertain to 51 Kakchiquel-speaking Maya mothers and 283 children from a village in rural Guatemala. We developed a linear mixed model to evaluate the relationships between breastfeeding duration and the energy-related factors. Results Duration of breastfeeding was associated with two of the energy-related factors in the ways we predicted but not with the other two. Contrary to predictions, taller mothers breastfed for shorter periods and we found no evidence that weanling diet quality impacts breastfeeding duration. As predicted, women who had more help with infants breastfed for shorter periods, and later-born infants breastfed longer than earlier-born ones. Discussion The results regarding allomaternal care suggest that help reduces mothers' lactation demands. The energy saved may be redirected to increasing fecundity or investment in other children. The birth order result suggests that children born to mothers nearing reproductive senescence receive higher levels of investment, which likely impacts children's fitness.

Psychological challenges, including traumatic events, have been hypothesized to increase the age-related pace of biological aging. Here we test the hypothesis that psychological challenges can affect the pace of telomere attrition, a marker of cellular aging, using data from an ongoing longitudinal-cohort study of Kaqchikel Mayan women living in a population with a high frequency of child mortality, a traumatic life event. Specifically, we evaluate the associations between child mortality, maternal telomere length and the mothers’ hypothalamic-pituitary-adrenal axis (HPAA), or stress axis, activity. Child mortality data were collected in 2000 and 2013. HPAA activity was assessed by quantifying cortisol levels in first morning urinary specimens collected every other day for seven weeks in 2013. Telomere length (TL) was quantified using qPCR in 55 women from buccal specimens collected in 2013. Results: Shorter TL with increasing age was only observed in women who experienced child mortality (p = 0.015). Women with higher average basal cortisol (p = 0.007) and greater within-individual variation (standard deviation) in basal cortisol (p = 0.053) presented shorter TL. Non-parametric bootstrapping to estimate mediation effects suggests that HPAA activity mediates the effect of child mortality on TL. Our results are, thus, consistent with the hypothesis that traumatic events can influence cellular aging and that HPAA activity may play a mediatory role. Future large-scale longitudinal studies are necessary to confirm our results and further explore the role of the HPAA in cellular aging, as well as to advance our understanding of the underlying mechanisms involved.

Background: Economic transitions expose indigenous populations to a variety of ecological and cultural challenges, especially regarding diet and stress. These kinds of challenges are predicted by evolutionary ecological theory to have fitness consequences (differential reproduction) and, indeed, are often associated with changes in fertility dynamics. It is currently unclear whether international immigration might impact the nature of such an economic transition or its consequences for fertility. Aim: To examine measures of fertility, diet and stress in two economically transitioning Maya villages in Guatemala that have been differentially exposed to immigration by Westerners. Subjects and methods: This study compared Maya women’s ages at first birth and birth rates between villages and investigated whether these fertility indicators changed through time. It also explored whether the villages differed in relation to diet and/or a proxy of stress. Results: It was found that, in the village directly impacted by immigration, first births occurred earlier, but birth rate was slower. In both villages, over the sampled time window, age at first birth increased, while birth rate decreased. The villages do not differ significantly in dietary indicators, but the immigration-affected village scored higher on the stress proxy. Conclusion: Immigration can affect fertility in host communities. This relationship between immigration and fertility dynamics may be partly attributable to stress, but this possibility should be evaluated prospectively in future research.

Magnetic resonance imaging (MRI) data are routinely collected at multiple time points during phase 2 clinical trials in multiple sclerosis. However, these data are typically summarized into a single response for each patient before analysis. Models based on these summary statistics do not allow the exploration of the trade-off between numbers of patients and numbers of scans per patient or the development of optimal schedules for MRI scanning. To address these limitations, in this paper, we develop a longitudinal model to describe one MRI outcome: the number of lesions observed on an individual MRI scan. We motivate our choice of a mixed hidden Markov model based both on novel graphical diagnostic methods applied to five real data sets and on conceptual considerations. Using this model, we compare the performance of a number of different tests of treatment effect. These include standard parametric and nonparametric tests, as well as tests based on the new model. We conduct an extensive simulation study using data generated from the longitudinal model to investigate the parameters that affect test performance and to assess size and power. We determine that the parameters of the hidden Markov chain do not substantially affect the performance of the tests. Furthermore, we describe conditions under which likelihood ratio tests based on the longitudinal model appreciably outperform the standard tests based on summary statistics. These results establish that the new model is a valuable practical tool for designing and analyzing multiple sclerosis clinical trials. Copyright © 2011 John Wiley & Sons, Ltd.

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.

Hidden Markov models (HMMs) are a useful tool for capturing the behavior of overdispersed, autocorrelated data. These models have been applied to many different problems, including speech recognition, precipitation modeling, and gene finding and profiling. Typically, HMMs are applied to individual stochastic processes; HMMs for simultaneously modeling multiple processes—as in the longitudinal data setting—have not been widely studied. In this article I present a new class of models, mixed HMMs (MHMMs), where I use both covariates and random effects to capture differences among processes. I define the models using the framework of generalized linear mixed models and discuss their interpretation. I then provide algorithms for parameter estimation and illustrate the properties of the estimators via a simulation study. Finally, to demonstrate the practical uses of MHMMs, I provide an application to data on lesion counts in multiple sclerosis patients. I show that my model, while parsimonious, can describe the...

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.

To the Editor .— We are surprised that the journal’s review process of the school-randomized trial reported by MacKelvie et al1 did not insist on an analysis appropriate to the group-randomized design or at least require stronger justification of the assumptions involved in ignoring the randomization design in the analysis. Randomizing intact social groups is a common approach outside the clinic because it is often easier, and possibly only feasible, to intervene with a whole class, troop, church, or community rather than to work with individuals. Members within intact social groups tend to be more like each other than they are like members in other groups, making for some redundancy of information and increased variance compared with the same number of subjects individually randomized. As a general rule, group-randomized trials that are analyzed by using methods appropriate for individual-level trials will overestimate the significance of the effects. Twenty-five years ago, Cornfield2 warned clearly that “randomization by cluster accompanied by an analysis appropriate to randomization by individual is an exercise in self-deception and should be discouraged.” Methodological reviews (eg, Donner et al,3 Simpson et al,4 and Smith et al5) show that Cornfield’s message is not well heeded and point to neglect in the review process for insisting on appropriate attention to the analytic issues incurred by the choice of a group-randomized trial. When randomization is by group but analyzed by individual, chance differences between the …

Background: Sample sizes for magnetic resonance imaging (MRI)-based clinical trials in multiple sclerosis (MS) generally assume that lesion counts are reasonably described by the negative binomial (NB) model. Objective: This study aimed to assess the appropriateness of the NB model for lesion count data and to provide sample sizes for placebo-controlled, MRI-based clinical trials in relapsing–remitting MS using a more realistic model. Methods: The fit of the NB model in each arm of five MS clinical trials was assessed using Pearson’s chi-squared statistic. Required sample sizes associated with various tests of treatment effect were estimated by simulating data from a new, longitudinal model for repeated lesion count data on individual patients. Results: Evidence ( p < 0.05) against the NB model was found in at least one arm of four of the five trials. If a trial is designed using this model but the resulting clinical data do not follow its assumptions then this trial can be seriously under-powered for assessing differences in mean lesion counts. Conclusion: Sample sizes based on the longitudinal model are more realistic and often smaller than those previously reported using the NB model.

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.

Background Cortisol 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. Methodology We 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. Significance The observed trend suggests that studies including cycling women should account for day dependent variation in cortisol in cycles with long follicular and luteal phases.