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 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.

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.

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.

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'.

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.

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.

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.

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.

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.

Acquisition and loss of Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia over a 5-year period: effect of a triclosan/copolymer dentifrice.

OBJECTIVES: The present study describes the natural history of Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia over a 5-year period and the effect of a triclosan/copolymer dentifrice on these organisms in a normal adult population. MATERIAL AND METHODS: Subgingival plaque samples were collected from 504 adult volunteers. Probing pocket depths (PPD) and relative attachment levels were measured using an automated probe. Participants were matched for disease status (CPI), plaque index, age and gender, and allocated to receive either a triclosan/copolymer or placebo dentifrice. Re-examination and subgingival plaque sampling was repeated after 1, 2, 3, 4 and 5 years. P. gingivalis, A. actinomycetemcomitans and P. intermedia were detected and quantitated using an enzyme linked immunosorbent assay. Logistic regression and generalised linear modelling were used to analyse the data. RESULTS: This 5-year longitudinal study showed considerable volatility in acquisition and loss (below the level of detection) of all three organisms in this population. Relatively few subjects had these organisms on multiple occasions. While P. gingivalis was related to loss of attachment and to PPD >/=3.5 mm, there was no relationship between A. actinomycetemcomitans or P. intermedia and disease progression over the 5 years of the study. Smokers with P. gingivalis had more PPD >/=3.5 mm than smokers without this organism. There was no significant effect of the triclosan dentifrice on P. gingivalis or A. actinomycetemcomitans. Subjects using triclosan were more likely to have P. intermedia than those not using the dentifrice; however this did not translate into these subjects having higher levels of P. intermedia and its presence was uniform showing no signs of increasing over the course of the study. CONCLUSION: The present 5-year longitudinal study has shown the transient nature of colonisation with P. gingivalis, A. actinomycetemcomitans and P. intermedia in a normal adult population. The use of a triclosan-containing dentifrice did not lead to an overgrowth of these organisms. The clinical effect of the dentifrice would appear to be independent of its antimicrobial properties.

The effect of a triclosan-containing dentifrice on the progression of periodontal disease in an adult population.

OBJECTIVES: The aim of the present study was to determine the effect of unsupervised, long-term use of a 0.3% triclosan/2% copolymer dentifrice on the progression of periodontal disease in a general adult population. METHODS: Five hundred and four volunteers were enrolled in a double-blind, controlled clinical trial. Participants were matched for disease status, plaque index, age and gender. At the baseline examination, probing pocket depths and relative attachment levels were recorded and participants were assigned to either the test or control group. Re-examinations took place after 6, 12, 24, 36, 48 and 60 months. Subgingival plaque samples were collected at each examination and assayed for Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia. A generalised linear model was used to analyse the data, with a number of covariates thought to influence the responses included as the possible confounding effects. RESULTS: The triclosan/copolymer dentifrice had a significant effect in subjects with interproximal probing depths > or =3.5 mm, where it significantly reduced the number of sites with probing depths > or =3.5 mm at the following examination, when compared with the control group (p<0.001). Furthermore, this effect increased with increasing numbers of affected sites. There was no effect of the triclosan/copolymer dentifrice in individuals without probing depths > or =3.5 mm at the previous examination. Other factors significantly affecting probing pocket depths (PPD) included increasing age, smoking and presence of P. gingivalis. PPD > or =3.5 mm were positively associated with loss of attachment some 2 years later. CONCLUSION: This study showed that in a normal adult population, unsupervised use of a triclosan/copolymer dentifrice is effective in slowing the progression of periodontal disease.

A longitudinal study of interleukin-1 gene polymorphisms and periodontal disease in a general adult population.

BACKGROUND: Cross-sectional studies have demonstrated that a specific polymorphism (allele 2 of both IL-1A +4845 and IL-1B +3954) in the IL-1 gene cluster has been associated with an increased susceptibility to severe periodontal disease and to an increased bleeding tendency during periodontal maintenance. The aim of the present study was to investigate the relationship between IL-1 genotype and periodontitis in a prospective longitudinal study in an adult population of essentially European heritage. METHODS: From an ongoing study of the Oral Care Research Programme of The University of Queensland, 295 subjects consented to genotyping for IL-1 allele 2 polymorphisms. Probing depths and relative attachment levels were recorded at baseline, 6, 12, 24, 36, 48 and 60 months using the Florida probe. Periodontitis progression at a given site was defined as attachment loss > or =2 mm at any observation period during the 5 years of the study and the extent of disease progression determined by the number of sites showing attachment loss. Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia were detected using ELISA. RESULTS: 38.9% of the subjects were positive for the composite IL-1 genotype. A relationship between the IL-1 positive genotype and increased mean probing pocket depth in non-smokers greater than 50 years of age was found. Further, IL-1 genotype positive smokers and genotype positive subjects with P. gingivalis in their plaque had an increase in the number of probing depths > or =3.5 mm. There was a consistent trend for IL-1 genotype positive subjects to experience attachment loss when compared with IL-1 genotype negative subjects. CONCLUSION: The results of this study have shown an interaction of the IL-1 positive genotype with age, smoking and P. gingivalis which suggests that IL-1 genotype is a contributory but non-essential risk factor for periodontal disease progression in this population.

Likelihood-based modeling and analysis of data underdispersed relative to the Poisson distribution.

By using a generalization of the Poisson process, distributions can be constructed that show appropriate amounts of underdispersion relative to the Poisson distribution that may be apparent from observed data. These are then used to examine the differences between the distributions of numbers of fetal implants in mice corresponding to different doses of the herbicide 2,4,5-T.

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.

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.

Estimations of the efficacy and reliability of paternity assignments from DNA microsatellite analysis of multiple-sire matings.

It is important for bovine DNA testing laboratories to provide the cattle industry with accurate estimates of the efficacy and reliability of DNA tests offered so that end users of this technology can adequately assess the cost-benefits of testing. To address these issues for bovine paternity testing, paternity exclusion probability estimates were obtained from breed panel data and were predictive of the efficacy of the DNA tests used in 39 multiple-sire mating groups, involving 5960 calves and 505 bulls. Paternity testing of these mating groups has demonstrated that the majority involve a variable proportion of unknown sires and this impacts on the reliability of sire allocation. Mathematical models based on binomial or beta-binomial probability distributions were used to estimate the reliability of single-sire allocations from multiple-sire matings involving unknown sires. Reliability of 98-99% is achieved when the exclusion probability is 0.99 or greater, after allowing for up to 20% unknown sires. When the exclusion probability drops below 0.90 and there are 20% unknown sires, the reliability is poor, bringing into question the benefits of testing. This highlights the need for DNA testing laboratories to offer paternity tests with an exclusion power of at least 99%.