Setting the control limit at release for stability assurance.

A common task in quality control is to determine a control limit for a product at the time of release that incorporates its risk of degradation over time. Such a limit for a given quality measurement will be based on empirical stability data, the intended shelf life of the product and the stability specification. The task is particularly important when the registered specifications for release and stability are equal. We discuss two relevant formulations and their implementations in both a frequentist and Bayesian framework. The first ensures that the risk of a batch failing the specification is comparable at release and at the end of shelf life. The second is to screen out batches at release time that are at high risk of failing the stability specification at the end of their shelf life. Although the second formulation seems more natural from a quality assurance perspective, it usually renders a control limit that is too stringent. In this paper we provide theoretical insight in this phenomenon, and introduce a heat-map visualisation that may help practitioners to assess the feasibility of implementing a limit under the second formulation. We also suggest a solution when infeasible. In addition, the current industrial benchmark is reviewed and contrasted to the two formulations. Computational algorithms for both formulations are laid out in detail, and illustrated on a dataset.

Unbiased estimation of Langevin dynamics from time series with application to hippocampal field potentials in vitro.

The last decade showed an increased interest in Langevin equations for modeling time series recorded from complex dynamical systems. These equations allow to discriminate between deterministic (drift) and stochastic (diffusion) components of the recorded time series. In practice, the estimation of drift and diffusion is often based on approximations of the models' dynamics that are valid only for high sampling frequencies. Also, model assessment is not or only indirectly performed, potentially leading to false claims. In this study we compare the performance of an asymptotically unbiased estimation method with a generally used approximate method, demonstrating the necessity of using (asymptotically) unbiased estimators. Furthermore, we describe how confidence intervals for the unknown parameters can be constructed and how model assessment can be carried out. We apply the methodology to local field potentials recorded in vitro from mouse hippocampus from eight genetically different strains. The recorded field potentials turn out to be well described by linearly damped Langevin equations with parabolic diffusion. The modeling enables a dynamical interpretation of the spectral power of the field potentials. It reveals that observed spectral power differences in the field potentials across hippocampal regions are associated with differences in the deterministic component of the system, and it reveals transiently active current dipoles, which are not detectable by conventional methods. Also, all estimated parameters have significant heritabilities, which suggests that the Langevin equations capture biological relevant aspects of electrical hippocampal activity.

Dynamics underlying spontaneous human alpha oscillations: a data-driven approach.

Although the cognitive and clinical correlates of spontaneous human alpha oscillations as recorded with electroencephalography (EEG) or magnetoencephalography (MEG) are well documented, the dynamics underlying these oscillations is still a matter of debate. This study proposes a data-driven method to reveal the dynamics of these oscillations. It demonstrates that spontaneous human alpha oscillations as recorded with MEG can be viewed as noise-perturbed damped harmonic oscillations. This provides evidence for the hypothesis that these oscillations reflect filtered noise and hence do not possess limit-cycle dynamics. To illustrate the use of the model, we apply it to two data-sets in which a decrease in alpha power can be observed across conditions. The associated differences in the estimated model parameters show that observed decreases in alpha power are associated with different kinds of changes in the dynamics. Thus, the model parameters are useful dynamical biomarkers for spontaneous human alpha oscillations.

Gamma frailty model for linkage analysis with application to interval-censored migraine data.

For many diseases, it seems that the age at onset is genetically influenced. Therefore, the age-at-onset data are often collected in order to map the disease gene(s). The ages are often (right) censored or truncated, and therefore, many standard techniques for linkage analysis cannot be used. In this paper, we present a correlated frailty model for censored survival data of siblings. The model is used for testing heritability for the age at onset and linkage between the loci and the gene(s) that influence(s) the survival time. The model is applied to interval-censored migraine twin data. Heritability (obtained from the frailties rather than actual onset times) was estimated as 0.42; this value was highly significant. The highest lod score, a score of 1.9, was found at the end of chromosome 19.

Correcting missing-data bias in historical demography.

Studies on population history are often based on incomplete records of life histories. For instance, in studies using data obtained from family reconstitution, the date of death is right censored (by migration) and the censoring time is never observed. Several methods for the correction of mortality estimates are proposed in the literature, most of which first estimate the number of individuals at risk and then use standard techniques to estimate mortality. Other methods are based on statistical models. In this paper all methods are reviewed, and their merits are compared by applying them to simulated and to seventeenth-century data from the English parish of Reigate. An ad hoc method proposed by Ruggles performs reasonably well. Methods based on statistical models, provided they are sufficiently realistic, give comparable accuracy and allow the estimation of several other quantities of interest, such as the distribution of migration times.

[Growth charts for height, weight and body-mass index of twins during infancy]. / Groeidiagrammen voor lengte, gewicht en 'body mass index' van tweelingen in de peutertijd.

OBJECTIVE: To determine the magnitude of the growth retardation in Dutch monozygotic and dizygotic twins during infancy in comparison with the Dutch reference growth charts for general population infants from 1997 and to construct reference growth charts for twins. DESIGN: Descriptive. METHOD: The growth of twins was studied using longitudinal data on over 4000 Dutch twin pairs from birth until 2.5 years of age. The LMS method was used to obtain growth charts for height, weight and body-mass index (BMI) for twin pairs during infancy. Centiles were estimated by the Box-Cox power curve (L), the median curve (M) and the coefficient of variation curve (S). RESULTS: From birth until the age of half a year, the average height and weight of twin pairs were at about the 10th percentile of the Dutch reference population. One year later this difference had decreased to about the 25th percentile, and when the twin pairs were between 1.5 and 2.5 years of age the difference was further decreased to the 35th percentile. The BMI deviated less from that of the reference population: during the first half a year the BMI of twin pairs was at about the 25th percentile. Subsequently, the BMI improved, but remained slightly below the median of the reference population at the age of about two years. Approximately half (50% for height, 58% for weight) of the growth retardation from birth until 1.5 years was attributable to gestational age. Between 1.5 years and 2.5 years of age, this difference was reduced to one third: 33% for both height and weight. Thus, a substantial part of the growth difference could not be explained by gestational age. CONCLUSION: Correcting for gestational age alone is not sufficient to make possible a comparison of the growth of twin pairs with the growth of general population infants. The development of twins can, however, be followed by means of the reference growth charts designed by the authors.