Mean and Variance Modeling of Under-Dispersed and Over-Dispersed Grouped Binary Data

This article describes the R package BinaryEPPM and its use in determining maximum likelihood estimates of the parameters of extended Poisson process models for grouped binary data. These provide a Poisson process family of flexible models that can handle unlimited under-dispersion but limited over-dispersion in such data, with the binomial distribution being a special case. Within BinaryEPPM, models with the mean and variance related to covariates are constructed to match a generalized linear model formulation. Combining such under-dispersed models with standard over-dispersed models such as the beta binomial distribution provides a very general form of residual distribution for modeling grouped binary data. Use of the package is illustrated by application to several data-sets

Ovarian aging, follicular depletion, and steroidogenesis

The follicular population. Menopause occurs as a consequence of the continuous utilization of a fixed store of primordial follicles leading to almost total depletion at mid-life or sometimes earlier. The great majority of follicles that disappear are lost by atresia rather than by ovulation, and the rate of loss accelerates in the last decade of menstrual life. The numbers of growing follicles at a given age are correlated with those of the primordial stages, but there are always more being recruited than required for a single ovulation each month. The extent to which a dwindling number is responsible for the character of cycles of the menopausal transition remains unclear. Ovarian secretion. While menstrual cycles remain regular, circulating concentrations of estradiol and progesterone are relatively independent of age. On the other hand, serum levels of inhibin are substantially lower in women approaching menopausal age, probably reflecting smaller numbers of growing follicles at the beginning of the cycle. Alleviation of negative feedback on the pituitary gland results in a greater output of follicle-stimulating hormone (FSH), buthe effects of chronic superstimulation on the aging ovary ar not known. Follicular aging. Aging of long-lived oocytes could affect the developmental potential of the follicle unit as well as compromising the chances of late pregnancy. Another important field of investigation is therefore to determine the balance of responsibility between cumulated damage to molecules by toxins, on the one hand, and the effects of physiological aging and such epiphenomena as the changing hormonal or paracrine environments, on the other

Modelling predation in functional response

Functional response is important in understanding the dynamics of predator-prey systems-it is essentially the interpretation of a bio-assay system in which individual predators have access to fixed numbers of prey for a given period of time. The classical approach to the problem has entailed the use of mechanistic models to interpret the data, but more recently several papers have argued that the use of simple logistic regression is both more consistent with the nature of the data and allows for the stochastic variation inherent in the system. Nevertheless, both the classical approach and this newer interpretation focus only on the modelling of means, and ignore the variability of the data. Another overlooked difficulty is that many published data sets display over-dispersion which itself may be a function of prey density In this paper we present some models which, as well as modelling the mean response, also account for the over-dispersion. The beta-binomial is a common model for admitting extra-variation, and here we develop some variants that allow a dependency on prey density. We also develop some new models based on stochastic counting processes. These models are compared and contrasted on a strict likelihood basis. It is found that beta-binomial models provide a markedly better fit to the data than do simple binomial models. The best-fitting counting process model is almost as good (in likelihood terms) as the best-fitting beta-binomial model. We argue that the counting process models offer richer insights into the predation process than do the other more 'descriptive' models. (c) 2006 Elsevier B.V. All rights reserved

Biological bases of premature ovarian failure

The ovary is endowed at birth with a fixed number of primordial follicles, which steadily dwindles throughout life as a result of atresia and recruitment towards ovulation. In addition to age, the number varies allometrically between species, larger and longer-lived animals tending to have more follicles initially and these disappear at a slower rate. A causal relationship between follicle depletion and menopause clearly exists, and there is a gradual acceleration of follicle wastage in the human ovary beginning more than a decade before the end of menstrual life. A mathematical model has provided confirmatory evidence of this relationship, and indicates that menopause is triggered by a threshold number of follicles which varies stochastically with a mean of 1100

Comparison of two methods for attributing length of hospital stay to healthcare-acquired infection

The development of models of the cost-effectiveness of infection control programs must be informed by valid estimates of the extra length of hospital stay due to healthcare-acquired infection (HAI). The aim of this study was to compare two competing methods for attributing extra hospital stay to healthcare-acquired infection. Data were collected prospectively from two Australian hospitals. The two competing methods used to attribute extra hospital days to HAI were: (i) a matched cohort design; and (ii) a procedure for selecting predictors associated with length of stay and their subsequent inclusion in a statistical model of length of stay. There were 40 patients exposed to multiple HAIs among 4488 patients recruited over 95 days of data collection (incidence rate 0.89%). The estimates from five separate matching procedures were between 23.38 and 31.78 extra days in hospital, and the results of the statistical model suggested an exposed patient independently increased length of hospital stay by a mean of 21.0 days (95% confidence interval 17.3, 25.1). Matching studies may suffer from two potential sources of bias: the selection of exposed patients from over-matching may underestimate the true cost of HAI, and the omission of important predictors may overstate the cost of HAI. Statistical regression techniques can be used to mitigate both potential problems.\ud \u

Efficacy of a dentifrice and oral rinse containing sanguinaria extract in conjunction with initial periodontal therapy

In the treatment of periodontal disease initial therapy aims at reducing marginal inflammation so allowing assessment of residual disease and further treatment options. The aim of the present study was to determine whether the use of a dentifrice and oral rinse containing sanguinaria extract led to a more rapid resolution of gingival inflammation following initial therapy. Thirty-four subjects, randomly assigned to one of two treatment groups, took part in this randomized double-blind parallel study. All subjects received initial therapy including oral hygiene instruction and scaling and root planing as required. One group also received an active dentifrice and oral rinse containing sanguinaria extract (an antiplaque agent) and zinc chloride. The other group received a placebo dentifrice and oral rinse. The gingival index (GI), plaque index (PLI) and probing pocket depths (PD) were recorded at six sites per tooth at baseline, two weeks after initial therapy and six weeks after initial therapy. There was no significant difference between the groups for any of the parameters at the baseline examination. Two weeks following initial therapy both groups showed a statistically significant increase in the number of sites with PLI of 0 or 1 (

Markov models of mite movements

Continuous time Markov models were used to analyse data from two bioassays to investigate the influence of β-fraction, a by-product of hop processing, on the two-spotted spider mite. The models were fitted to aggregate counts of the numbers of live and dead mites on treated and untreated halves of discs cut from leaves of hop and French bean plants. Some of the rate parameters were time dependent. Although not all parameters could be estimated precisely, the analysis enabled the quantitative effects of treatment over time to be estimated with reasonable precision. The estimated treatment effects were largely insensitive to the assumed values of other parameters. The first bioassay showed a progressive initial response to increasing concentration of β-fraction, although data at the intermediate concentration appeared anomalous. The second bioassay showed similar responses on hop and French bean leaves, with a stronger repellent effect on the lower leaf surface than on the upper surface