MLE and Bayesian inference of age-dependent sensitivity and transition probability in periodic screening

This article extends previous probability models for periodic breast cancer screening examinations. The specific aim is to provide statistical inference for age dependence of sensitivity and the transition probability from the disease free to the preclinical state. The setting is a periodic screening program in which a cohort of initially asymptomatic women undergo a sequence of breast cancer screening exams. We use age as a covariate in the estimation of screening sensitivity and the transition probability simultaneously, both from a frequentist point of view and within a Bayesian framework. We apply our method to the Health Insurance Plan of Greater New York study of female breast cancer and give age-dependent sensitivity and transition probability density estimates. The inferential methodology we develop is also applicable when analyzing studies of modalities for early detection of other types of progressive chronic diseases.     

Improving estimates of the basic reproductive ratio: using both the mean and the dispersal of transition times

In both within-host and epidemiological models of pathogen dynamics, the basic reproductive ratio, R(0), is a powerful tool for gauging the risk associated with an emerging pathogen, or for estimating the magnitude of required control measures. Techniques for estimating R(0), either from incidence data or in-host clinical measures, often rely on estimates of mean transition times, that is, the mean time before recovery, death or quarantine occurs. In many cases, however, either data or intuition may provide additional information about the dispersal of these transition times about the mean, even if the precise form of the underlying probability distribution remains unknown. For example, we may know that recovery typically occurs within a few days of the mean recovery time. In this paper we elucidate common situations in which R(0) is sensitive to the dispersal of transition times about their respective means. We then provide simple correction factors that may be applied to improve estimates of R(0) when not only the mean but also the standard deviation of transition times out of the infectious state can be estimated.     

Aging, transition, and estimating the global burden of disease

Background

The World Health Organization''s Global Burden of Disease (GBD) reports are an important tool for global health policy makers, however the accuracy of estimates for countries undergoing an epidemiologic transition is unclear. We attempted to validate the life table model used to generate estimates for all-cause mortality in developing countries.

Methods and Results

Data were obtained for males and females from the Human Mortality Database for all countries with available data every ten years from 1900 to 2000. These provided inputs for the GBD life table model and served as comparison observed data. Above age sixty model estimates of survival for both sexes differed substantially from those observed. Prior to the year 1960 for males and 1930 for females, estimated survival tended to be greater than observed; following 1960 for both males and females estimated survival tended to be less than observed. Viewing observed and estimated survival separately, observed survival past sixty increased over the years considered. For males, the increase was from a mean (sd) probability of 0.22 (0.06) to 0.46 (0.1). For females, the increase was from 0.26 (0.06) to 0.65 (0.08). By contrast, estimated survival past sixty decreased over the same period. Among males, estimated survival probability declined from 0.54 (0.2) to 0.09 (0.06). Among females, the decline was from 0.36 (0.12) to 0.15 (0.08).

Conclusions

These results show that the GBD mortality model did not accurately estimate survival at older ages as developed countries transitioned in the twentieth century and may be similarly flawed in developing countries now undergoing transition. Estimates of the size of older-age populations and their attributable disease burden should be reconsidered.     

The Effect of the G 1 - S transition Checkpoint on an Age Structured Cell Cycle Model

Knowledge of how a population of cancerous cells progress through the cell cycle is vital if the population is to be treated effectively, as treatment outcome is dependent on the phase distributions of the population. Estimates on the phase distribution may be obtained experimentally however the errors present in these estimates may effect treatment efficacy and planning. If mathematical models are to be used to make accurate, quantitative predictions concerning treatments, whose efficacy is phase dependent, knowledge of the phase distribution is crucial. In this paper it is shown that two different transition rates at the - checkpoint provide a good fit to a growth curve obtained experimentally. However, the different transition functions predict a different phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is effected by the phase distribution of the population this difference may be critical in treatment planning. Using an age-structured population balance approach the cell cycle is modelled with particular emphasis on the - checkpoint. By considering the probability of cells transitioning at the - checkpoint, different transition functions are obtained. A suitable finite difference scheme for the numerical simulation of the model is derived and shown to be stable. The model is then fitted using the different probability transition functions to experimental data and the effects of the different probability transition functions on the model''s results are discussed.     

森林种群径阶转移模型中转移概率的估算方法

基于统计分析理论和微分方程理论,给出了森林种群径阶转移模型中估算转移概率的方法：第一种是在有两次样地观测数据,不考虑林分环境因子等因素的条件下估算转移概率;第二种是在已知林分环境因子条件下,不需要对样地有两次观测数据来估算转移概率．实例验证结果表明,两种估算转移概率的方法具有计算简单和实用性强的特点,对森林经营与管理有一定的理论指导和实际应用价值．     

森林种群径阶转移模型中转移概率的估算方法

基于统计分析理论和微分方程理论,给出了森林种群径阶转移模型中估算转移概率的方法：第一种是在有两次样地观测数据,不考虑林分环境因子等因素的条件下估算转移概率;第二种是在已知林分环境因子条件下,不需要对样地有两次观测数据来估算转移概率.实例验证结果表明,两种估算转移概率的方法具有计算简单和实用性强的特点,对森林经营与管理有一定的理论指导和实际应用价值.     

Spatial auto-correlation and auto-regressive models estimation from sample survey data

Maximum likelihood estimation of the model parameters for a spatial population based on data collected from a survey sample is usually straightforward when sampling and non-response are both non-informative, since the model can then usually be fitted using the available sample data, and no allowance is necessary for the fact that only a part of the population has been observed. Although for many regression models this naive strategy yields consistent estimates, this is not the case for some models, such as spatial auto-regressive models. In this paper, we show that for a broad class of such models, a maximum marginal likelihood approach that uses both sample and population data leads to more efficient estimates since it uses spatial information from sampled as well as non-sampled units. Extensive simulation experiments based on two well-known data sets are used to assess the impact of the spatial sampling design, the auto-correlation parameter and the sample size on the performance of this approach. When compared to some widely used methods that use only sample data, the results from these experiments show that the maximum marginal likelihood approach is much more precise.     

transition priors for protein hidden Markov models: an empirical study towards maximum discrimination.

Insertions and deletions in a profile hidden Markov model (HMM) are modeled by transition probabilities between insert, delete and match states. These are estimated by combining observed data and prior probabilities. The transition prior probabilities can be defined either ad hoc or by maximum likelihood (ML) estimation. We show that the choice of transition prior greatly affects the HMM's ability to discriminate between true and false hits. HMM discrimination was measured using the HMMER 2.2 package applied to 373 families from Pfam. We measured the discrimination between true members and noise sequences employing various ML transition priors and also systematically scanned the parameter space of ad hoc transition priors. Our results indicate that ML priors produce far from optimal discrimination, and we present an empirically derived prior that considerably decreases the number of misclassifications compared to ML. Most of the difference stems from the probabilities for exiting a delete state. The ML prior, which is unaware of noise sequences, estimates a delete-to-delete probability that is relatively high and does not penalize noise sequences enough for optimal discrimination.     

Few beetle species can be detected with 95% confidence using pitfall traps

False absences in wildlife surveys make it difficult to identify metapopulation processes, increase uncertainty of management decisions and bias parameter estimates in habitat models. Despite these risks, the number of species that can be detected with a certain probability in a community survey has rarely been examined. I sampled beetles over 5 months using pitfall trap grids at three rainforest locations in Tasmania, Australia. I compared detection probability for dispersed and clustered sampling schemes using a zero‐inflated binomial model and a simpler occurrence method to calculate the probability of detection. After excluding extremely rare species, I analysed 12 of 121 species. Only three to six species could be detected with 95% probability using a sampling effort that is frequently applied in ecological studies. A majority of common species had a mid summer peak in detection probability meaning that survey effort could be reduced from 5 to 2 months with only a small reduction in data quality. Most species occurred at only a proportion of sample points within locations. Despite the implied spatial structuring, three small grids within a location detected 10 of 12 species as effectively as large, dispersed grids. This study warns that as little as 5% of the beetle fauna may have a 95% probability of detection using the frequently applied pitfall trap method, highlighting a substantial limitation in our ability to accurately map the distributions of ground invertebrates. Whether very large sample sizes can overcome this limitation remains to be examined.     

Estimating abundance of mountain lions from unstructured spatial sampling

Mountain lions (Puma concolor) are often difficult to monitor because of their low capture probabilities, extensive movements, and large territories. Methods for estimating the abundance of this species are needed to assess population status, determine harvest levels, evaluate the impacts of management actions on populations, and derive conservation and management strategies. Traditional mark–recapture methods do not explicitly account for differences in individual capture probabilities due to the spatial distribution of individuals in relation to survey effort (or trap locations). However, recent advances in the analysis of capture–recapture data have produced methods estimating abundance and density of animals from spatially explicit capture–recapture data that account for heterogeneity in capture probabilities due to the spatial organization of individuals and traps. We adapt recently developed spatial capture–recapture models to estimate density and abundance of mountain lions in western Montana. Volunteers and state agency personnel collected mountain lion DNA samples in portions of the Blackfoot drainage (7,908 km²) in west-central Montana using 2 methods: snow back-tracking mountain lion tracks to collect hair samples and biopsy darting treed mountain lions to obtain tissue samples. Overall, we recorded 72 individual capture events, including captures both with and without tissue sample collection and hair samples resulting in the identification of 50 individual mountain lions (30 females, 19 males, and 1 unknown sex individual). We estimated lion densities from 8 models containing effects of distance, sex, and survey effort on detection probability. Our population density estimates ranged from a minimum of 3.7 mountain lions/100 km² (95% CI 2.3–5.7) under the distance only model (including only an effect of distance on detection probability) to 6.7 (95% CI 3.1–11.0) under the full model (including effects of distance, sex, survey effort, and distance × sex on detection probability). These numbers translate to a total estimate of 293 mountain lions (95% CI 182–451) to 529 (95% CI 245–870) within the Blackfoot drainage. Results from the distance model are similar to previous estimates of 3.6 mountain lions/100 km² for the study area; however, results from all other models indicated greater numbers of mountain lions. Our results indicate that unstructured spatial sampling combined with spatial capture–recapture analysis can be an effective method for estimating large carnivore densities. Published 2012. This article is a U.S. Government work and is in the public domain in the USA.     

Effect of count duration on abundance estimates of Black-capped Vireos

ABSTRACT.   Distance sampling applied to point count surveys (point transects) has become a common method for estimating the absolute abundance of birds. When conducting point transects, detections of focal species are typically recorded during a fixed time interval. However, count duration has varied among studies and the effect of such variation on the resulting abundance estimates is unclear. My objective was to examine the effect of count duration on abundance estimates of male Black-capped Vireos ( Vireo atricapilla ). The abundance of these vireos in a 349-ha area in central Texas was estimated using 3-, 5-, and 6-min point transects and results were then compared to actual number present as determined by banding and territory mapping. The 3-min counts provided an estimate that was 26% greater than the actual number of male Vireos present ( N = 201), but this number was within the corresponding 95% confidence interval ( N = 157–413). Confidence intervals for the 5- and 6-min counts did not include the actual number of vireos present. The shortest count duration may have provided the most accurate abundance estimate because male Black-capped Vireos are typically active, sing intermittently, and sometimes move tens of meters between songs. Thus, shorter-duration counts may also yield the most accurate abundance estimates for other species that exhibit similar behavior. However, because behavior varies among species, I recommend that investigators collect preliminary data to establish an appropriate count duration when accurate estimates of absolute, rather than relative, abundance are important.     

The relationship between the transition probability and oscillator concepts of the cell cycle and the nature of the commitment to replication

The oscillator concept of the cell cycle predicts the existence of threshold conditions within the cell which must be exceeded before replication is initiated. It is shown (a) that if the conditions are subthreshold, random disturbances can trigger a cycle of the oscillation (round of replication) and (b) that the probability of this occurring increases as the state of the system approaches the threshold. It is concluded that the oscillator concept explains the data on which the transition probability model is based. It also accounts for the ability of cells to replicate even when the mitogen is present for a limited period only.     

Comparison of methods for estimating density of forest songbirds from point counts

New analytical methods have been promoted for estimating the probability of detection and density of birds from count data but few studies have compared these methods using real data. We compared estimates of detection probability and density from distance and time-removal models and survey protocols based on 5- or 10-min counts and outer radii of 50 or 100 m. We surveyed singing male Acadian flycatchers (Empidonax virescens), cerulean warblers (Dendroica cerulea), Kentucky warblers (Oporornis formosus), Louisiana waterthrushes (Parkesia motacilla), wood thrushes (Hylocichla mustelina), and worm-eating warblers (Helmitheros vermivorum) in bottomland and upland forest across 5 states in the Central Hardwoods Bird Conservation Region during the breeding season in 2007 and 2008. Detection probabilities differed between distance and time-removal models and species detectabilities were affected differently by year, forest type, and state. Density estimates from distance models were generally higher than from time-removal models, resulting from lower detection probabilities estimated by distance models. We found support for individual heterogeneity (modeled as a finite mixture model) in the time-removal models and that 50-m radius counts generated density estimates approximately twice as high as 100-m radius counts. Users should be aware that in addition to estimating different components of detectability, density estimates derived from distance and time-removal models can be affected by survey protocol because some count durations and plot radii may better meet model assumptions than others. The choice of a method may not affect the use of estimates for relative comparisons (e.g., when comparing habitats) but could affect conclusions when used to estimate population size. We recommend careful consideration of assumptions when deciding on point-count protocol and selection of analysis methods. © 2011 The Wildlife Society.     

The permeability transition pore in cell death

The permeability transition pore (PT-pore) is a multi-component protein aggregate in mitochondria that comprises factors in the inner as well as in the outer mitochondrial membrane. This complex has two functions: firstly, it regulates the integration of oxidative phosphorylation into the cellular energy household and secondly, it induces cell death when converted into an unspecific channel. The latter causes a collapse of the mitochondrial membrane potential and activates a chain of events that culminate in the demise of the cell. It has been controversial for some time whether the PT-pore is causative for or only amplifies a signal of cell death but novel results confirm a central role of this protein complex for cell death induction. While a considerable body of data exist on its subunit composition, recent genetic knock-out experiments suggest that the identity of the core factors of the PT-pore is still unresolved. Moreover, accumulating evidence point to a much more complex composition of this protein complex than anticipated. Here, we review the current knowledge of its subunit composition, the evidence of a role in cell death, and we propose a model for the activation of the PT-pore for cell death.     

Incorporating Genotyping Error Into Non-Invasive DNA-Based Mark—Recapture Population Estimates

ABSTRACT Use of non-invasive sources of DNA, such as hair or scat, to obtain a genetic mark for population estimates is becoming commonplace. Unfortunately, with such marks, potentials for genotyping errors and for the shadow effect have resulted in use of many loci and amplification of each specimen many times at each locus, drastically increasing time and cost of obtaining a population estimate. We proposed a method, the Genotyping Uncertainty Added Variance Adjustment (GUAVA), which statistically adjusts for genotyping errors and the shadow effect, thereby allowing use of fewer loci and one amplification of each specimen per locus. Using allele frequencies and estimates of genotyping error rates, we determined, for each pair of specimens, the probability that the pair was obtained from the same individual, whether or not their observed genotypes match. Using these probabilities, we reconstructed possible capture history matrices and used this distribution to obtain a population estimate. With simulated data, we consistently found our estimates had lower bias and smaller variance than estimates based on single amplifications in which genotyping error was ignored and that were comparable to estimates based on data free of genotyping errors. We also demonstrated the method on a fecal DNA data set from a population of red wolves (Canis rufus). The GUAVA estimate based on only one amplification genotypes compares favorably to the estimate based on consensus genotypes. A program to conduct the analysis is available from the first author for UNIX or Windows platforms. Application of GUAVA may allow for increased accuracy in population estimates at reduced cost.     

Substitution-rate variation among sites and the estimation of transition bias

Substitution-rate variation among sites and differences in the probabilities of change among the four nucleotides are conflated in DNA sequence comparisons. When variation in rate exists among sites but is ignored, biases in the rates of change among nucleotides are underestimated. This paper provides a quantification of this effect when the observed proportions of transitions, P, and transversions, Q, between two sequences are used to estimate transition bias. The utility of P/Q as an estimator is examined both with and without rate variation among sites. A gamma-distributed-rates model is used to illustrate the effect that variation among sites has on estimates of transition bias, but it is argued that the basic results should hold for any pattern of rate variation. Naive estimates of the extent of transition bias, those that ignore rate variation when it is present, can seriously underestimate its true value. The extent of this underestimation increases with the amount of rate variation among sites. An example using human mitochondrial DNA shows that a simple comparison of the proportions of transitions and transversions in recently diverged sequences underestimates the level of transition bias by approximately 15%. This does not depend on the use of P/Q to estimate transition bias; maximum-likelihood methods give similar results.      

Fort Peck paddlefish population survival and abundance in the Missouri River

Excessive fishing pressure can induce population declines or complete collapse of fisheries. Unless commercial and recreational fisheries for K-selected fishes, or those with slow growth and late maturation, are carefully managed, declines in abundance or fishery collapse is probable. Paddlefish Polyodon spathula,are a K-selected species that experienced historical declines in abundance as a result of habitat degradation and overfishing. Mark-recapture studies are well-suited for long-lived fishes by providing information on population density and vital rates. For sustainable commercial or recreational fisheries targeting species such as the paddlefish, managers require accurate estimates of population vital rates including survival, abundance, and exploitation. We used a Montana Fish, Wildlife & Parks (MFWP) mark-recapture dataset and modified Jolly-Seber (POPAN) models to estimate survival, recapture, probability of entry, and abundance of 8,518 tagged paddlefish over a 25-year period. With many supporting estimates including stable survival (0.92 for females, mean of 0.82 for males), low exploitation rates (means of 2.6% for females and 2.9% for males), and stable abundance estimates (25-year mean of 12,309 individuals for both sexes), the Fort Peck paddlefish population appears to be stable and well-managed over the past 25 years. Presently, this is the only study focused on paddlefish in North America that has estimated survival and abundance for both male and female paddlefish using contemporary analyses. This research provided a unique opportunity to highlight that the effort exerted by management agencies to collect long-term field data is extremely useful to our understanding of fish populations and management.     

Stepping into adulthood: the transition period

The period of growth from late puberty to full adult maturation, termed the transition period, is important for tissue maturation. Peak bone mass, muscle mass and strength are usually attained in this period. However, it is common clinical practice in children with growth hormone deficiency (GHD) to discontinue growth hormone (GH) treatment in adolescence after attainment of final height. Therefore, patients with childhood-onset GHD that continues into adulthood and who do not receive treatment as adults may experience more severe consequences than patients who acquire GHD as an adult. Recent studies indicate that bone and muscle maturation are attenuated if GH treatment is discontinued at final height. Furthermore, these patients will also develop cardiovascular risk factors that are normally associated with GHD in adults. Much debate surrounds when retesting for GHD should be carried out and when GH treatment should be restarted in adolescents; many of these patients will not have severe GHD according to the criteria set for adults. The transition period is an appropriate time to modify GH doses. Finally, registries exist that have recorded clinical treatment experiences for children and adults. Tools that collect and analyse data provide an important opportunity to investigate issues related to transition.     

A first-order-like state transition for recombinant protein folding

Normally, proteins will aggregate and precipitate by direct folding processes. In this study, we report that quasi-static processes can restore both the structure and bio-function of two kinds of fish recombinant growth hormones (Plecoglossus altivelis and Epinephelus awoara). The conformational changes and the particle-size-distribution (PSD) of each refolding intermediate can be monitored by circular dichroism spectroscopy (CD) and dynamic light scattering (DLS), respectively. Conformation analysis of the CD spectra of the refolding intermediates indicated that the secondary structures were restored in the initial refolding intermediate. However, the tertiary interactions of the proteins were restored during the last two refolding stages, as elucidated by thermal stability tests. This is consistent with a sequential model. DLS analysis suggested that the average hydrodynamic radii of the refolding intermediates shrank to their native-like sizes after the first refolding stage. This is consistent with a collapse model. After comparison with the data on the direct folding process, it is concluded that the denaturant-containing protein folding reaction is a first-order-like state transition process.