Comparisons of statistical distributions for cluster sizes in a developing pandemic.

BACKGROUND: We consider cluster size data of SARS-CoV-2 transmissions for a number of different settings from recently published data. The statistical characteristics of superspreading events are commonly described by fitting a negative binomial distribution to secondary infection and cluster size data as an alternative to the Poisson distribution as it is a longer tailed distribution, with emphasis given to the value of the extra parameter which allows the variance to be greater than the mean. Here we investigate whether other long tailed distributions from more general extended Poisson process modelling can better describe the distribution of cluster sizes for SARS-CoV-2 transmissions. METHODS: We use the extended Poisson process modelling (EPPM) approach with nested sets of models that include the Poisson and negative binomial distributions to assess the adequacy of models based on these standard distributions for the data considered. RESULTS: We confirm the inadequacy of the Poisson distribution in most cases, and demonstrate the inadequacy of the negative binomial distribution in some cases. CONCLUSIONS: The probability of a superspreading event may be underestimated by use of the negative binomial distribution as much larger tail probabilities are indicated by EPPM distributions than negative binomial alternatives. We show that the large shared accommodation, meal and work settings, of the settings considered, have the potential for more severe superspreading events than would be predicted by a negative binomial distribution. Therefore public health efforts to prevent transmission in such settings should be prioritised.

Influence of a triclosan toothpaste on periodontopathic bacteria and periodontitis progression in cardiovascular patients: a randomized controlled trial.

BACKGROUND AND OBJECTIVE: Triclosan/copolymer toothpaste is effective in controlling plaque and gingivitis and in slowing the progression of periodontitis. This study describes its influence on microbiological and clinical outcomes, over a 5-year period, in patients with established cardiovascular disease (CVD). MATERIAL AND METHODS: Four-hundred and thirty-eight patients were recruited from the Cardiovascular Unit at The Prince Charles Hospital, Brisbane, Australia, and randomized to triclosan or placebo groups. Six sites per tooth were examined annually for probing pocket depth and loss of attachment. These outcomes were analysed, using generalized linear modelling, in 381 patients who had measurements from consecutive examinations. Concurrent load of the periodontal pathogens Aggregatibacter actinomycetemcomitans, Fusobacterium nucleatum, Tannerella forsythia and Porphyromonas gingivalis was determined, using quantitative real-time PCR, in 437 patients with baseline plaque samples. Group comparisons were expressed as geometric means. The chi-square test was used to test for differences between the two groups of patients with regard to the proportion of patients with different numbers of bacterial species. RESULTS: There was no difference in general health or periodontal status between the groups at baseline. There was a significant reduction in the number of interproximal sites showing loss of attachment between examinations, by 21% on average (p < 0.01), in the triclosan group compared with the placebo group. The prevalence of patients with F. nucleatum and A. actinomycetemcomitans was high and remained relatively constant throughout the 5 years of the study. In contrast, the prevalence of T. forsythia and P. gingivalis showed more variability; however, there was no significant difference between the groups, at any time point, in the prevalence of any organism. A significant difference in the geometric means for P. gingivalis (p = 0.01) was seen at years 1 and 4, and for F. nucleatum (p = 0.01) and in the total bacterial load (p = 0.03) at year 2; however, these differences were not statistically significant following a Bonferroni correction for multiple comparisons. There was no difference between the groups in the geometric means for each organism at year 5. CONCLUSION: Within the limitations of the study, these data suggest that the use of triclosan/copolymer toothpaste significantly slowed the progression of periodontitis in patients with CVD but that it had little influence on key subgingival periodontopathic bacteria in these patients over the 5 years of the study.

The ovarian response to controlled stimulation in IVF cycles may be predictive of the age at menopause.

STUDY QUESTION: Can the number of oocytes retrieved in IVF cycles be predictive of the age at menopause? SUMMARY ANSWER: The number of retrieved oocytes can be used as an indirect assessment of the extent of ovarian reserve to provide information on the duration of the reproductive life span in women of different ages. WHAT IS KNOWN ALREADY: Menopause is determined by the exhaustion of the ovarian follicular pool. Ovarian reserve is the main factor influencing ovarian response in IVF cycles. As a consequence the response to ovarian stimulation with the administration of gonadotrophins in IVF treatment may be informative about the age at menopause. STUDY DESIGN, SIZE, DURATION: In the present cross-sectional study, participants were 1585 infertile women from an IVF clinic and 2635 menopausal women from a more general population. PARTICIPANTS/MATERIALS, SETTING, METHODS: For all infertile women, the response to ovarian stimulation with gonadotrophins was recorded. For menopausal women, relevant demographic characteristics were available for the analysis. MAIN RESULTS AND THE ROLE OF CHANCE: A cubic function described the relationship between mean numbers of oocytes and age, with all terms being statistically significant. From the estimated residual distribution of the actual number of oocytes about this mean, a distribution of the age when there would be no oocytes retrieved following ovarian stimulation was derived. This was compared with the distribution of the age at menopause from the menopausal women, showing that menopause occurred about a year later. LIMITATIONS, REASONS FOR CAUTION: The retrieved oocyte data were from infertile women, while the menopausal ages were from a more general population. WIDER IMPLICATIONS OF THE FINDINGS: In the present study, we have shown some similarity between the distributions of the age when no retrieved oocytes can be expected after ovarian stimulation and the age at menopause. For a given age, the lower the ovarian reserve, the lower the number of retrieved oocytes would be and the earlier the age that menopause would occur. STUDY FUNDING/COMPETING INTERESTS: This work was supported by a grant from the Italian Ministry of Health (GR-2009-1580036). There are no conflicts of interest.

Malaria antibody persistence correlates with duration of exposure.

BACKGROUND AND OBJECTIVES: In Australia, the risk of transfusion-transmitted malaria is managed through the identification of 'at-risk' donors, antibody screening enzyme-linked immunoassay (EIA) and, if reactive, exclusion from fresh blood component manufacture. Donor management depends on the duration of exposure in malarious regions (>6 months: 'Resident', <6 months: 'Visitor') or a history of malaria diagnosis. We analysed antibody testing and demographic data to investigate antibody persistence dynamics. To assess the yield from retesting 3 years after an initial EIA reactive result, we estimated the proportion of donors who would become non-reactive over this period. MATERIALS AND METHODS: Test results and demographic data from donors who were malaria EIA reactive were analysed. Time since possible exposure was estimated and antibody survival modelled. RESULTS: Among seroreverters, the time since last possible exposure was significantly shorter in 'Visitors' than in 'Residents'. The antibody survival modelling predicted 20% of previously EIA reactive 'Visitors', but only 2% of 'Residents' would become non-reactive within 3 years of their first reactive EIA. CONCLUSION: Antibody persistence in donors correlates with exposure category, with semi-immune 'Residents' maintaining detectable antibodies significantly longer than non-immune 'Visitors'.

Relationship of serum antimüllerian hormone concentration to age at menopause.

BACKGROUND: Serum antimüllerian hormone (AMH) levels are highly correlated with antral follicle counts, while being menstrual cycle independent and easily measurable. However, AMH, unlike antral follicle counts, has not been tested as yet as a predictor of reproductive status. By relating AMH levels to the age distribution of reproductive events like onset of menopause, we tested this hypothesis. METHODS: AMH levels were measured in 144 fertile normal volunteers and used to determine an estimate of mean AMH as a function of age. Data on the onset of menopause were obtained from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition [Prospect-EPIC] cohort. Estimation of an AMH threshold to predict menopause was done by maximum likelihood using the observed (Prospect-EPIC) distribution of age at menopause and the predictive distribution from this AMH threshold. Predictions of age at menopause follow from an individual woman's AMH relative to percentiles of the distribution of AMH for a given age, and the corresponding percentiles of the predictive distribution of age at menopause. RESULTS: There was good conformity between the observed distribution of age at menopause and that predicted from declining AMH levels. CONCLUSIONS: The similarity between observed and predictive distributions of age at menopause supports the hypothesis that AMH levels are related to onset of menopause. Results of this study suggest that AMH is able to specify a woman's reproductive age more realistically than chronological age alone.

Progression of periodontal disease and interleukin-10 gene polymorphism.

BACKGROUND AND OBJECTIVE: Interleukin-10 is a key immunoregulatory cytokine that may be of significance in the immunopathogenesis of chronic inflammatory diseases such as periodontal disease. Molecular genetic studies have defined a number of haplotypes that may be associated with differing levels of interleukin-10 secretion. The present study investigated the possible association between interleukin-10 gene polymorphism and periodontal disease progression. MATERIAL AND METHODS: Genomic DNA was obtained from 252 adults who were part of a prospective longitudinal study on the progression of periodontal disease in a general adult Australian population. Single nucleotide polymorphisms at positions -592 and -1082 in the interleukin-10 promoter were analysed using an induced heteroduplex methodology and used to determine interleukin-10 promoter haplotypes in individual samples. Periodontitis progression was assessed by measuring probing depths and relative attachment levels at regular intervals over a 5-year period. A generalized linear model was used to analyse the data, with age, gender, smoking status, interleukin-1 genotype and Porphyromonas gingivalis included as possible confounders. RESULTS: There was a significant (p approximately 0.02) main effect of interleukin-10 haplotypes, with individuals having either the ATA/ACC or the ACC/ACC genotype experiencing around 20% fewer probing depths of >or= 4 mm compared to individuals with other genotypes. Age and smoking had significant (p < 0.001) additional effects. CONCLUSION: These data suggest that the interleukin-10 genotype contributes to the progression of periodontal disease.

Markov chain modelling for geriatric patient care.

OBJECTIVES: To show that Markov chain modelling can be applied to data on geriatric patients and use these models to assess the effects of covariates. METHODS: Phase-type distributions were fitted by maximum likelihood to data on times spent by the patients in hospital and in community-based care. Data on the different events that ended the patients' periods of care were used to estimate the dependence of the probabilities of these events on the phase from which the time in care ended. The age of the patients at admission to care and the year of admission were also included as covariates. RESULTS: Differential effects of these covariates were shown on the various parameters of the fitted model, and interpretations of these effects made. CONCLUSIONS: Models based on phase-type distributions were appropriate for describing times spent in care, as the ordered phases had an interpretable structure corresponding to increasing amounts of care being given.

The Relationship Between Variation in Size of the Primordial Follicle Pool and Age at Natural Menopause.

CONTEXT: Menopause has been hypothesized to occur when the nongrowing follicle (NGF) number falls below a critical threshold. Age at natural menopause can be predicted using NGF numbers and this threshold. These predictions support the use of ovarian reserve tests, reflective of the ovarian follicle pool, in menopause forecasting. OBJECTIVE: The objective of the study was to investigate the hypothesis that age-specific NGF numbers reflect age at natural menopause. DESIGN AND SETTING: Histologically derived NGF numbers obtained from published literature (n = 218) and distribution of menopausal ages derived from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition (Prospect-EPIC) cohort (n = 4037) were combined. PARTICIPANTS: NGF data were from single ovaries that had been obtained postnatally for various reasons, such as elective surgery or autopsy. From the Prospect-EPIC cohort, women aged 58 years and older with a known age at natural menopause were selected. INTERVENTIONS: There were no interventions. MAIN OUTCOME MEASURE(S): Conformity between observed age at menopause in the Prospect-EPIC cohort and NGF-predicted age at menopause from a model for age-related NGF decline constructed using a robust regression analysis. A critical threshold for NGF number was estimated by comparing the probability distribution of the age at which the NGF numbers fall below this threshold with the observed distribution of age at natural menopause from the Prospect-EPIC cohort. RESULTS: The distributions of observed age at natural menopause and predicted age at natural menopause showed close conformity. CONCLUSION: The close conformity observed between NGF-predicted and actual age at natural menopause supports the hypothesis that that the size of the primordial follicle pool is an important determinant for the length of the individual ovarian life span and supports the concept of menopause prediction using ovarian reserve tests, such as anti-Müllerian hormone and antral follicle count, as derivatives of the true ovarian reserve.

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), but the effects of chronic superstimulation on the aging ovary are 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.

Follicle dynamics during ovarian ageing.

The human ovary is endowed at birth with a fixed number of primordial follicles which steadily declines throughout life as a result of atresia and recruitment towards ovulation. The pattern of this decline is not exponential, but more bi-exponential corresponding to a 'broken-stick' regression of logged total numbers of follicles against age. Such a model implies an abrupt change in the exponential rate of follicle loss at age 38 years, and is thus rather implausible biologically. A more refined model with an exponential rate of follicle loss that changes gradually throughout life also describes the data on declining follicle numbers but in addition leads to a distribution of age at menopause, corresponding to follicle numbers falling below a critical threshold, that shows quite remarkable agreement with independent data on menopausal ages of American women. When the follicles are classified into resting and growing stages, it is found that any changes in the consequent process of follicle development as the ovary ages relate mainly to the small resting follicles and not the larger growing ones.

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.

Ante-dependence modeling in a longitudinal study of periodontal disease: the effect of age, gender, and smoking status.

BACKGROUND: It is generally accepted that periodontal disease progresses by a series of bursts that are interspersed by periods of stability or even gain of attachment. In order to analyze longitudinal data on a patient's disease experience, it is necessary to use models which accommodate serial dependence. Ante-dependence between the results of a series of periodontal examinations over time can be modeled using a Markov chain. This model describes temporal changes in patients' levels of disease in terms of transition probabilities, which allow for both regression and progression of the disease. The aim of the present study was to demonstrate the use of a Markov chain model to analyze data from a longitudinal study investigating the progression of periodontal disease in an adult population. METHODS: The study population consisted of 504 volunteers; however, only 456 were included in the analysis because the remaining 48 subjects did not give consecutive data. Subjects were examined at baseline, 6 months, and 1, 2, and 3 years. Probing depths (PD) were recorded using an automated probe. Disease was defined as four or more sites with PD > or = 4 mm. Markov chain modeling was used to determine the effect of age, gender, and smoking on the natural progression and regression (healing) of periodontal disease. RESULTS: Smoking and increasing age had no effect on the progression of disease in this population, but did have a significant effect (P values < or = 0.05) in reducing the regression of disease; i.e., their effect on disease appears to be inhibition of the natural healing process. Gender had no significant effects. CONCLUSIONS: These results demonstrate how ante-dependence modeling of longitudinal data can reveal effects that may not be immediately apparent from the data, with smoking and increasing age being seen to inhibit the healing process rather than promote disease progression.

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 (p < 0.0001) and a statistically significant increase in the number of sites with a GI of 0 or 1 (that is, no bleeding on probing), (p < 0.0001). Also there was a statistically significant increase in the number of sites with probing depths < or = 3 mm (p < 0.0001) compared with baseline. These changes were maintained through to six weeks post therapy. There was no significant advantage to the sanguinaria group. Results demonstrate that initial therapy in the form of oral hygiene instruction, scaling and root planing leads to a significant improvement in periodontal status which is maintained at least in the short term. Further, use of a dentifrice and oral rinse containing sanguinaria did not improve the efficacy of initial therapy.

The relationship between anti-Müllerian hormone in women receiving fertility assessments and age at menopause in subfertile women: evidence from large population studies.

CONTEXT: Anti-Müllerian hormone (AMH) concentration reflects ovarian aging and is argued to be a useful predictor of age at menopause (AMP). It is hypothesized that AMH falling below a critical threshold corresponds to follicle depletion, which results in menopause. With this threshold, theoretical predictions of AMP can be made. Comparisons of such predictions with observed AMP from population studies support the role for AMH as a forecaster of menopause. OBJECTIVE: The objective of the study was to investigate whether previous relationships between AMH and AMP are valid using a much larger data set. SETTING: AMH was measured in 27 563 women attending fertility clinics. STUDY DESIGN: From these data a model of age-related AMH change was constructed using a robust regression analysis. Data on AMP from subfertile women were obtained from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition (Prospect-EPIC) cohort (n = 2249). By constructing a probability distribution of age at which AMH falls below a critical threshold and fitting this to Prospect-EPIC menopausal age data using maximum likelihood, such a threshold was estimated. MAIN OUTCOME: The main outcome was conformity between observed and predicted AMP. RESULTS: To get a distribution of AMH-predicted AMP that fit the Prospect-EPIC data, we found the critical AMH threshold should vary among women in such a way that women with low age-specific AMH would have lower thresholds, whereas women with high age-specific AMH would have higher thresholds (mean 0.075 ng/mL; interquartile range 0.038-0.15 ng/mL). Such a varying AMH threshold for menopause is a novel and biologically plausible finding. AMH became undetectable (<0.2 ng/mL) approximately 5 years before the occurrence of menopause, in line with a previous report. CONCLUSIONS: The conformity of the observed and predicted distributions of AMP supports the hypothesis that declining population averages of AMH are associated with menopause, making AMH an excellent candidate biomarker for AMP prediction. Further research will help establish the accuracy of AMH levels to predict AMP within individuals.

Prevalence of premature ovarian failure in monozygotic and dizygotic twins.

BACKGROUND: Premature ovarian failure (POF) before 40 years of age from natural causes affects approximately 1% of adult women, with minor variations between ethnic groups. A recent case of ovarian transplantation between young monozygotic (MZ) twins in which one had undergone unexplained POF at 14 years has prompted a study of the prevalence of POF. METHODS: Menopausal ages of 832 Australian and UK female twin-pairs were extracted from volunteer national twin registry databases containing medical, reproductive and lifestyle data surveyed by mail questionnaire. Surgical menopause was an exclusion criterion. RESULTS: The prevalence of POF in both MZ and dizygotic (DZ) twins was similar in both registries and 3- to 5-fold greater than the general population at age thresholds 40 and 45 years. No specific factors were found to account for the higher risk of early menopause. Some twins of both zygosities were highly discordant for menopausal age (>or=10 years). Nevertheless, there was significant intra-twin dependence, especially for MZ twins, and the average age difference at last menses was greater in DZ twin-pairs. CONCLUSION: Both MZ and DZ twins are at higher risk of POF. Despite some striking differences within MZ twin-pairs, menopausal ages were more concordant than for DZ twin-pairs, confirming that the timing of menopause has a heritable component.

Modeling the dependence between the number of trials and the success probability in binary trials.

A model for binary trials based on a bivariate generalization of the Poisson process for both the number of successes and number of trials with the transition rates dependent on the accumulating numbers of successes and trials is used to reanalyze some recently published data of Zhu, Eickhoff, and Kaiser (2003, Biometrics59, 955-961). This modeling admits alternative distributions for the numbers of trials and the numbers of successes conditional on the number of trials which generalize the Poisson and binomial distributions, without some of the restrictions apparent in the beta-binomial-Poisson mixed modeling of Zhu et al. (2003). Some quite marked differences between the results of this analysis and those described in Zhu et al. (2003) are apparent.

Nonlinear stochastic compartmental models.

Compartmental models have been widely applied to biological systems where material is transferred between compartments. The simple assumption of linear transfer functions results in a mathematically tractable system, but can underestimate the variation. Processes with some particular forms of nonlinear transfer functions are analysed, and numerical results suggest that concave transfer functions increase variability, whereas convex transfer functions decrease variability.