Revisiting nocturnal heart rate and heart rate variability in insomnia: A polysomnography-based comparison of young self-reported good and poor sleepers

Primary insomnia is often considered a disorder of 24-hr hyperarousal. Numerous attempts have been made to investigate nocturnal heart rate (HR) and its variability (HRV) as potential pathophysiological hallmarks of altered arousal levels in insomnia, with mixed results. We have aimed to overcome some of the pitfalls of previous studies by using a young, medication-free, age- and gender-matched population consisting of 43 students aged 18-30 years half with a subthreshold insomnia complaint. We employed at-home ambulatory polysomnography and compared this attenuated insomnia group to a good sleeping group. The poor sleepers had significantly higher wake after sleep onset, arousal count, mean HR in all sleep stages (with the exception of Stage 1) and lower sleep efficiency. Consistent with previous research, we also found a significant group-by-sleep stage interaction in the prediction of nocturnal HR, highlighting the insomnia group to have a lower wake-sleep HR reduction compared to good sleepers. When restricting our analyses to insomnia with objectively determined short sleep duration, we found significantly lower standard deviation of RR intervals (SDNN; a measure of HRV) compared to good sleepers. Taken together, this lends credence to the hyperarousal model of insomnia and may at least partially explain the increased prevalence of cardiovascular morbidity and mortality observed in patients with insomnia.

A kernel- and optimal transport- based test of independence between covariates and right-censored lifetimes

We propose a nonparametric test of independence, termed optHSIC, between a covariate and a right-censored lifetime. Because the presence of censoring creates a challenge in applying the standard permutation-based testing approaches, we use optimal transport to transform the censored dataset into an uncensored one, while preserving the relevant dependencies. We then apply a permutation test using the kernel-based dependence measure as a statistic to the transformed dataset. The type 1 error is proven to be correct in the case where censoring is independent of the covariate. Experiments indicate that optHSIC has power against a much wider class of alternatives than Cox proportional hazards regression and that it has the correct type 1 control even in the challenging cases where censoring strongly depends on the covariate.

On Negative Heritability and Negative Estimates of Heritability

We consider the problem of interpreting negative maximum likelihood estimates of heritability that sometimes arise from popular statistical models of additive genetic variation. These may result from random noise acting on estimates of genuinely positive heritability, but we argue that they may also arise from misspecification of the standard additive mechanism that is supposed to justify the statistical procedure. Researchers should be open to the possibility that negative heritability estimates could reflect a real physical feature of the biological process from which the data were sampled.

Statistical properties of simple random-effects models for genetic heritability

Random-effects models are a popular tool for analysing total narrow-sense heritability for quantitative phenotypes, on the basis of large-scale SNP data. Recently, there have been disputes over the validity of conclusions that may be drawn from such analysis. We derive some of the fundamental statistical properties of heritability estimates arising from these models, showing that the bias will generally be small. We show that that the score function may be manipulated into a form that facilitates intelligible interpretations of the results. We go on to use this score function to explore the behavior of the model when certain key assumptions of the model are not satisfied - shared environment, measurement error, and genetic effects that are confined to a small subset of sites. The variance and bias depend crucially on the variance of certain functionals of the singular values of the genotype matrix. A useful baseline is the singular value distribution associated with genotypes that are completely independent - that is, with no linkage and no relatedness - for a given number of individuals and sites. We calculate the corresponding variance and bias for this setting.

Derivatives of the stochastic growth rate

We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the stochastic matrix of the driving Markov chain. The derivatives of a-the "stochastic elasticities"-with respect to changes in the demographic parameters were derived by Tuljapurkar (1990). These results are here extended to a formula for the derivatives with respect to changes in the Markov chain driving the environments. We supplement these formulas with rigorous bounds on computational estimation errors, and with rigorous derivations of both the new and old formulas.

Validated analysis of mortality rates demonstrates distinct genetic mechanisms that influence lifespan

A key goal of gerontology is to discover the factors that influence the rate of senescence, which in this context refers to the age-dependent acceleration of mortality, inversely related to the morality rate doubling time. In contrast factors that influence only initial mortality rate are thought to be less relevant to the fundamental processes of aging. To resolve these two determinants of mortality rate and lifespan, initial morality rate and rate of senescence are calculated using the Gompertz equation. Despite theoretical and empirical evidence that the Gompertz parameters are most consistently and reliably estimated by maximum-likelihood techniques, and somewhat less so by non-linear regression, many researchers continue to use linear regression on the log-transformed hazard rate. The present study compares these three methods in the analysis of several published studies. Estimates of the mortality rate parameters were then used to compare the theoretical values to the actual values of the following parameters: maximal lifespan, 50% survival times, variance in control groups and agreement with the distribution of deaths. These comparisons indicate that maximum-likelihood and non-linear regression estimates provide better estimates of mortality rate parameters than log-linear regression. Of particular interest, the improved estimates indicate that most genetic manipulations in mice that increase lifespan do so by decreasing initial mortality rate, not rate of senescence, whereas most genetic manipulations that decrease lifespan surprisingly do so by increasing the rate of senescence, not initial mortality rate.

Damage segregation at fissioning may increase growth rates: a superprocess model

A fissioning organism may purge unrepairable damage by bequeathing it preferentially to one of its daughters. Using the mathematical formalism of superprocesses, we propose a flexible class of analytically tractable models that allow quite general effects of damage on death rates and splitting rates and similarly general damage segregation mechanisms. We show that, in a suitable regime, the effects of randomness in damage segregation at fissioning are indistinguishable from those of randomness in the mechanism of damage accumulation during the organism's lifetime. Moreover, the optimal population growth is achieved for a particular finite, non-zero level of combined randomness from these two sources. In particular, when damage accumulates deterministically, optimal population growth is achieved by a moderately unequal division of damage between the daughters, while too little or too much division is sub-optimal. Connections are drawn both to recent experimental results on inheritance of damage in protozoans, and to theories of aging and resource division between siblings.

Re-evaluating a test of the heterogeneity explanation for mortality plateaus

[Drapeau, M.D., Gass, E.K., Simison, M.D., Mueller, L.D., Rose, M.R., 2000. Testing the heterogeneity theory of late-life mortality plateaus by using cohorts of Drosophila melanogaster, Experimental Gerontology, 35 71-84.] tested, in populations of Drosophila melanogaster, a prediction of the heterogeneity explanation for mortality plateaus. They concluded that heterogeneity could not explain their results. We contend here that the statistical analysis was flawed. It was declared that there was no difference between the mortality plateaus of three different strains, on the basis of averaged outcomes. In fact, the results for the different strains were quite different. Most trials showed the expected lowering of the mortality plateaus for the flies selected for robustness, but these effects were washed out by a small number of very large opposing deviations. There is ample reason to believe that the opposing deviations are artifacts of fitting an overly restrictive hazard-rate model. When we fit more appropriate models, the evidence points toward a rejection of the null hypothesis (of identical plateaus), hence toward modest support for the heterogeneity explanation.

Markov mortality models: implications of quasistationarity and varying initial distributions

This paper explains some implications of Markov-process theory for models of mortality. We show that an important qualitative feature common to empirical mortality data, and which has been found in certain models-the convergence to a "mortality plateau"-is, in fact, a generic consequence of the models' convergence to a "quasistationary distribution". This phenomenon has been explored extensively in the mathematical literature. Not only does this generalization free important results from specifics of the models, it also suggests a new explanation for the convergence to constant mortality. At the same time that we show that the late behavior of these models-convergence to a finite asymptote-is almost logically immutable, we also point out that the early behavior of the mortality rates can be more flexible than has been generally acknowledged. We show, in particular, that an appropriate choice of initial conditions enables one popular model to approximate any reasonable hazard-rate data. This illustrates how precarious it can be to read a model's vindication from its consilience with a favored hazard-rate function, such as the Gompertz exponential.