Testing the assumptions for the analysis of survival data arising from a prevalent cohort study with follow-up

In a prevalent cohort study with follow-up subjects identified as prevalent cases are followed until failure (defined suitably) or censoring. When the dates of the initiating events of these prevalent cases are ascertainable, each observed datum point consists of a backward recurrence time and a possibly censored forward recurrence time. Their sum is well known to be the left truncated lifetime. It is common to term these left truncated lifetimes "length biased" if the initiating event times of all the incident cases (including those not observed through the prevalent sampling scheme) follow a stationary Poisson process. Statistical inference is then said to be carried out under stationarity. Whether or not stationarity holds, a further assumption needed for estimation of the incident survivor function is the independence of the lifetimes and their accompanying truncation times. That is, it must be assumed that survival does not depend on the calendar date of the initiating event. We show how this assumption may be checked under stationarity, even though only the backward recurrence times and their associated (possibly censored) forward recurrence times are\ud observed. We prove that independence of the lifetimes and truncation times is equivalent to equality in distribution of the backward and forward recurrence times, and exploit this equivalence as a means of testing the former hypothesis. A simulation study is conducted to investigate the power and Type 1 error rate of our proposed tests, which include a bootstrap procedure that takes into account the pairwise dependence between the forward and backward recurrence times, as well as the potential censoring of only one of the members of each pair. We illustrate our methods using data from the Canadian Study of Health and Aging. We also point out an equivalence of the\ud problem presented here to a non-standard changepoint problem

The dynamics of measles in sub-Saharan Africa.

Although vaccination has almost eliminated measles in parts of the world, the disease remains a major killer in some high birth rate countries of the Sahel. On the basis of measles dynamics for industrialized countries, high birth rate regions should experience regular annual epidemics. Here, however, we show that measles epidemics in Niger are highly episodic, particularly in the capital Niamey. Models demonstrate that this variability arises from powerful seasonality in transmission-generating high amplitude epidemics-within the chaotic domain of deterministic dynamics. In practice, this leads to frequent stochastic fadeouts, interspersed with irregular, large epidemics. A metapopulation model illustrates how increased vaccine coverage, but still below the local elimination threshold, could lead to increasingly variable major outbreaks in highly seasonally forced contexts. Such erratic dynamics emphasize the importance both of control strategies that address build-up of susceptible individuals and efforts to mitigate the impact of large outbreaks when they occur

Bayesian change-point analyses in ecology

• Ecological and biological processes can change from one state to another once a threshold has been crossed in space or time. Threshold responses to incremental changes in underlying variables can characterize diverse processes from climate change to the desertification of arid lands from overgrazing. • Simultaneously estimating the location of thresholds and associated ecological parameters can be difficult: ecological data are often \u27noisy\u27, which can make the identification of the locations of ecological thresholds challenging. • We illustrate this problem using two ecological examples and apply a class of statistical models well-suited to addressing this problem. We first consider the case of estimating allometric relationships between tree diameter and height when the trees have distinctly different growth modes across life-history stages. We next estimate the effects of canopy gaps and dense understory vegetation on tree recruitment in transects that transverse both canopy and gap conditions. • The Bayesian change-point models that we present estimate both threshold locations and the slope or level of ecological quantities of interest, while incorporating uncertainty in the change-point location into these estimates. This class of models is suitable for problems with multiple thresholds and can account for spatial or temporal autocorrelation. © The Authors (2007)

Forecasting constraints on the high-z IGM thermal state from the Lyman-α\alpha forest flux auto-correlation function

The auto-correlation function of the Lyman-$\alpha$ (Ly$\alpha$) forest flux from high-z quasars can statistically probe all scales of the intergalactic medium (IGM) just after the epoch of reionization. The thermal state of the IGM, which is determined by the physics of reionization, sets the amount of small-scale power seen in the \lya forest. To study the sensitivity of the auto-correlation function to the thermal state of the IGM, we compute the auto-correlation function from cosmological hydrodynamical simulations with semi-numerical models of the thermal state of the IGM. We create mock data sets of 20 quasars to forecast constraints on $T_0$ and $\gamma$, which characterize a tight temperature-density relation in the IGM, at $5.4 \leq z \leq 6$. At $z = 5.4$ we find that an ideal data set constrains $T_0$ to 29\% and $\gamma$ to 9\%. In addition, we investigate four realistic reionization scenarios that combine temperature and ultra-violet background (UVB) fluctuations at $z = 5.8$. We find that, when using mock data generated from a model that includes temperature and UVB fluctuations, we can rule out a model with no temperature or UVB fluctuations at $>1\sigma$ level 50.5\% of the time.Comment: 18 pages, 13 figures, comments welcome. arXiv admin note: text overlap with arXiv:2208.0901

Adaptive Observers for Structural Health Monitoring of High-Rate, Time-Varying Dynamic Systems

Safe and reliable operation of hypersonic aircraft, space structures, advanced weapon systems, and other high-rate dynamic systems depends on advances in state estimators and damage detection algorithms. High-rate dynamic systems have rapidly changing input forces, rate-dependent and time-varying structural parameters, and uncertainties in material and structural properties. While current structural health monitoring (SHM) techniques can assess damage on the order of seconds to minutes, complex high-rate structures require SHM methods that detect, locate, and quantify damage or changes in the structure’s configuration on the microsecond timescale. This paper discusses the importance of microsecond structural health monitoring (μSHM) and some of the challenges that occur in development and implementation. Two model-based parameter estimators are examined for estimating the states and parameters of an example time-varying system consisting of a two degree of freedom system with a sudden change in a stiffness value that simulates structural damage. The ability of these estimators to track this stiffness change, the role of measurement noise, and the need for persistent excitation are examined