Predicting time to decompression illness during exercise at altitude, based on formation and growth of bubbles

For altitude decompressions, we hypothesized that reported onset times of limb decompression illness (DCI) pain symptoms follow a probability distribution related to total bubble volume [V(b.)(t)] as a function of time. Furthermore, we hypothesized that the probability of ever experiencing DCI during a decompression is associated with the cumulative volume of bubbles formed. To test these hypotheses, we first used our previously developed formation-and-growth model (Am J Physiol Regulatory Integrative Comp Physiol 279: R2304-R2316, 2000) to simulate Vb.(t) for 20 decompression profiles in which 334 human subjects performed moderate repetitive skeletal muscle exercise (827 kJ/h) in an altitude chamber. Using survival analysis, we determined that, for a controlled condition of exercise, the fraction of the subject population susceptible to DCI can be approximately expressed as a power function of the formation-and-growth model-predicted cumulative volume of bubbles throughout the altitude exposure. Furthermore, for this fraction, the probability density distribution of DCI onset times is approximately equal to the ratio of the time course of formation-and growth-modeled total bubble volume to the predicted cumulative volume.     

Alternate methods of representing single-channel data.

Clustering of dwell times in data from single-channel recordings, which is in excess of the value predicted from the probability density function (pdf) alone, provides restrictions on modeling schemes. Two methods, (a) the probability density function of the running median for groups of any size of sequential dwell times, and (b) the distribution of cumulative probabilities associated with dwell times separated by any lag, or the second cumulative probability distribution, are proposed as alternative representations of single-channel data; these methods are suitable for the detection of such clusters or modes. Simulation of three models with and without modes is done to test the efficacy of these methods. It is found that they often yield a better estimate of moding parameters than the methods of running mean pdf and autocorrelation.     

Comparison of Two New Robust Parameter Estimation Methods for the Power Function Distribution

Estimation of any probability distribution parameters is vital because imprecise and biased estimates can be misleading. In this study, we investigate a flexible power function distribution and introduced new two methods such as, probability weighted moments, and generalized probability weighted methods for its parameters. We compare their results with L-moments, trimmed L-moments by a simulation study and a real data example based on performance measures such as, mean square error and total deviation. We concluded that all the methods perform well in the case of large sample size (n>30), however, the generalized probability weighted moment method performs better for small sample size.     

Time course of ozone-induced changes in breathing pattern in healthy exercising humans.

We examined the time course of O3-induced changes in breathing pattern in 97 healthy human subjects (70 men and 27 women). One- to five-minute averages of breathing frequency (f(B)) and minute ventilation (Ve) were used to generate plots of cumulative breaths and cumulative exposure volume vs. time and cumulative exposure volume vs. cumulative breaths. Analysis revealed a three-phase response; delay, no response detected; onset, f(B) began to increase; response, f(B) stabilized. Regression analysis was used to identify four parameters: time to onset, number of breaths at onset, cumulative inhaled dose of ozone at onset of O3-induced tachypnea, and the percent change in f(B). The effect of altering O3 concentration, Ve, atropine treatment, and indomethacin treatment were examined. We found that the lower the O3 concentration, the greater the number of breaths at onset of tachypnea at a fixed ventilation, whereas number of breaths at onset of tachypnea remains unchanged when Ve is altered and O3 concentration is fixed. The cumulative inhaled dose of O3 at onset of tachypnea remained constant and showed no relationship with the magnitude of percent change in f(B). Atropine did not affect any of the derived parameters, whereas indomethacin did not affect time to onset, number of breaths at onset, or cumulative inhaled dose of O3 at onset of tachypnea but did attenuate percent change in f(B). The results are discussed in the context of dose response and intrinsic mechanisms of action.     

The Correlated Bivariate Inverted Beta Distribution

The correlated bivariate inverted beta distribution is constructed from the bivariate mixture of two independent gamma random variables whose scale parameters follow Kibble's correlated gamma distribution. Explicit expressions have been derived for the form of the joint probability density function, the joint cumulative distributive function and other statistical properties of interest. These results confirm and extend some of the conjectures of HUTCHINSON in connection with generalizations of probabilistic models of severity distribution arising from injuries sustained in two-vehicle head on collison.     

Distribution of lod scores under uncertain mode of inheritance.

We consider probability distributions of alternative lod statistics, differing in their treatment of segregation parameters when mode of inheritance is uncertain. A particular pedigree structure and a dominant genetic system displaying incomplete penetrance are analyzed. Lod scores calculated assuming an incorrect segregation model appear to conform quite well to the chi 2 distribution in the absence of linkage. In the presence of linkage, some power is lost. However, if lod scores are calculated under several different segregation models and the best one is accepted, opportunity for chance occurrence of high lod scores is enhanced. The distribution is still chi 2, but with extra degrees of freedom. These results hold over a wide range of sample sizes and segregation models, including small samples and low levels of penetrance.     

Sample size considerations in genetic polymorphism studies.

OBJECTIVES: Molecular studies for genetic polymorphisms are being carried out for a number of different applications, such as genetic disorders in different populations, pharmacogenomics, genetic identification of ethnic groups for forensic and legal applications, genetic identification of breed/stock in animals and plants for commercial applications and conservation of germ plasm. In this paper, for a random sampling scheme, we address two questions: (A) What should be the minimum size of the sample so that, with a prespecified probability, all alleles at a given locus (or haplotypes at a given set of loci) are detected? (B) What should be the sample size so that the allele frequency distribution at a given locus (or haplotype frequency distribution at a given set of loci) is estimated reliably within permissible error limits? METHODS: We have used combinatorial probabilistic arguments and Monte Carlo simulations to answer these questions. RESULTS: We found that the minimum sample size required in case A depends mainly on the prespecified probability of detecting all alleles, while in case B, it varies greatly depending on the permissible error in estimation (which will vary with the application). We have obtained the minimum sample sizes for different degrees of polymorphism at a locus under high stringency, as well as a relaxed level of permissible error. We present a detailed sampling procedure for estimating allele frequencies at a given locus, which will be of use in practical applications. CONCLUSION: Since the sample size required for reliable estimation of allele frequency distribution increases with the number of alleles at the locus, there is a strong case for using biallelic markers (like single nucleotide polymorphisms) when the available sample size is about 800 or less.     

Bayesian interval estimation of genetic relationships: application to paternity testing.

Using genetic marker data, we have developed a general methodology for estimating genetic relationships between a set of individuals. The purpose of this paper is to illustrate the practical utility of these methods as applied to the problem of paternity testing. Bayesian methods are used to compute the posterior probability distribution of the genetic relationship parameters. Use of an interval-estimation approach rather than a hypothesis-testing one avoids the problem of the specification of an appropriate null hypothesis in calculating the probability of paternity. Monte Carlo methods are used to evaluate the utility of two sets of genetic markers in obtaining suitably precise estimates of genetic relationship as well as the effect of the prior distribution chosen. Results indicate that with currently available markers a "true" father may be reliably distinguished from any other genetic relationship to the child and that with a reasonable number of markers one can often discriminate between an unrelated individual and one with a second-degree relationship to the child.     

The genetic divergence of three populations

This paper considers the effect of the genetic divergence on the genetic composition of three samples drawn from three populations at some time after the populations had split. It generalizes the two-sample case studied earlier by Watterson (1985a). Under the assumptions that (i) mating is at random, (ii) the genes at a locus can be any of infinitely many alleles and all mutants are assumed to be new alleles, and (iii) no selective differences exist, we find the probability distribution of the sample gene configurations. From this distribution the single-sample allelic distribution after one-step and two-step bottlenecks and the allelic distribution in the two-sample case can be obtained as marginal distributions. Some numerical results on the number of alleles in common in the three samples are compared with those obtained by Watterson's simulation method; the agreement is excellent. Also, the probability that the three samples are monomorphic for the same allele is found, and numerical examples are given.     

Calculation of the morbid risk in genetic-epidemiologic studies of age-dependent diseases

Distributions of age at onset are widely used in the genetic epidemiology of age-dependent diseases. Examples are estimation of recurrent risks in genetic counselling and testing genetic hypotheses in segregation and linkage analyses. In this study, morbidity parameters are defined, including age-specific morbidity rates, morbidity net risk (incidence), and cumulative incidence (population risk, an integrated measure of population susceptibility to the disease at the moment of the study). Age-specific morbidity risks are calculated from the respective morbidity rates, which are analogous to mortality rates used in demography. Population data typically used for calculation of morbidity rates are discussed. Methods of calculation of morbidity rates based on the data of single and interval epidemiological studies are described. Methods for calculating standard errors of these parameters, estimating their statistical reliability, and testing statistical hypotheses are discussed.     

On the KOLMOGOROV-SMIRNOV Test for the POISSON Distribution with Unknown Mean

The standard tables for the KOLMOGOROV -SMIRNOV test are valid only in the case of testing whether a set of observations is from a completely specified cumulative distribution, F₀(X), with all parameters known. If the parameters are unknown and must be estimated from the sample, then the tables are not valid. A table is given in this paper for use with the KOLMOGOROV -SMIRNOV statistic in the case of testing whether a set of observations is from the POISSON distribution with an unknown mean that must be estimated from the sample. The table is obtained from a Monte Carlo calculation.     

Interpretation of variation across marker loci as evidence of selection

Population structure and history have similar effects on the genetic diversity at all neutral loci. However, some marker loci may also have been strongly influenced by natural selection. Selection shapes genetic diversity in a locus-specific manner. If we could identify those loci that have responded to selection during the divergence of populations, then we may obtain better estimates of the parameters of population history by excluding these loci. Previous attempts were made to identify outlier loci from the distribution of sample statistics under neutral models of population structure and history. Unfortunately these methods depend on assumptions about population structure and history that usually cannot be verified. In this article, we define new population-specific parameters of population divergence and construct sample statistics that are estimators of these parameters. We then use the joint distribution of these estimators to identify outlier loci that may be subject to selection. We found that outlier loci are easier to recognize when this joint distribution is conditioned on the total number of allelic states represented in the pooled sample at each locus. This is so because the conditional distribution is less sensitive to the values of nuisance parameters.     

Test statistics for detecting aneuploidy and hyperdiploidy

Possible approaches to the analytical evaluation of ploidy patterns are discussed and two specific problems are considered: detection of early onset of aneuploidy and detection of moderate hyperdiploidy. A statistical model for a euploid DNA pattern is formulated in terms of a mixture distribution. A test statistic for detecting deviations from this pattern is defined, and its performance is evaluated for simulated data representing differing degrees of severity of aneuploidy. An analysis based on a discriminant function using order statistics of the sample cumulative distribution functions is proposed for detecting hyperdiploidy. This procedure has the advantage of being relatively distribution-free; its performance is evaluated for simulated data and is compared with that of its classical counterparts. Although the results reported are only preliminary, they indicate that tailor-made statistical analyses can provide early detection of aneuploidy and hyperdiploidy with known and acceptable error rates using clinically reasonable sample sizes.     

Genetic epidemiology of rheumatoid arthritis.

We conducted family studies and segregation analyses of rheumatoid arthritis (RA) that were based on consecutive patients with RA ascertained without regard to family history or known risk factors. First-degree relatives from 135 simplex and 30 multiplex families were included in the analyses. A highly penetrant recessive major gene, with a mutant allele frequency of .005, was identified as the most parsimonious genetic risk factor. Significant evidence for heterogeneity in risk for RA was observed for proband gender but not for proband age at onset. Kaplan-Meier risk analysis demonstrated significant evidence for differences in the distribution of risk among first-degree relatives. These analyses demonstrated that both proband gender and age at onset are important risk factors but that proband gender appears to be the more important determinant of risk, with relatives of male probands having the greatest cumulative risk for RA. In addition, log-linear modeling identified proband gender, familiality (multiplex or simplex), and an interaction term between these two variables as being adequate to define the distribution of risk in families. The pattern of risk for RA among susceptible individuals and its inheritance is thus heterogeneous. For future genetic analyses, families with an excess of affected males having a young age at onset may be the most informative in identifying the putative recessive gene and its modifiers.     

A pooled analysis of the Iraqi and Seychelles methylmercury studies

Several epidemiology studies have investigated the impact of maternal exposure to methylmercury (MeHg) on childhood development of the central nervous system (CNS). In the present report, data from the Iraqi episode that occurred in 1970 from contaminated grain are integrated with those from a more recent study of a population with a high fish intake in the Seychelles Islands. The latter study had many more subjects whose mercury hair levels that were much lower and more representative of levels typically found in consumers whose MeHg exposure is from fish. The age of onset of talking (AOT), the age of onset of walking (AOW) and a combined measure (CM) that integrated the two were used as common scales of MeHg effect for the two studies. The first step of the analyses involved the construction of separate two‐dimensional cumulative frequency tables for each study for different groups spanning the range of hair levels and observed effect for each measure. Models were then fit to the values in the tables that were constructed from four components: (1) A dose‐effect function that related hair MeHg to the effect measure; (2) a frequency distribution describing population variability; (3) parameters to represent dose‐independent influences on effect; and (4) parameters to represent study dependent influences on effect. When the four submodels were assembled, a series of 1092 candidate models resulted which contained 3 to 7 parameters (e.g., slope, standard‐deviation, dose‐independent age of talking) whose value could be adjusted to improve the fit. After optimizing the fit of each model, a weighting algorithm that rewards for fit and penalizes for the number of parameters in the model was used to identify the best 200 models. The same algorithm was then used to assign a probability to each model in a probability tree. A two‐dimensional Monte‐Carlo simulation using the resulting function in combination with exposure values typical of U.S. consumers yielded predicted delays in AOT, AOW, and CM attributable to fish consumption in a variable and uncertain range of 0.000 to 1 day.     

The Consideration of Latency Periods in Cumulative Damage Models

The cumulative damage model as outlined in previous papers is unable to reproduce latency periods, particularly after short-term exposures. A refinement being straightforward within the present frame of point process theory is proposed using displacement processes applied to the single damages. For the displacement distribution, the lognormal distribution has been suggested. As in the previous model, exact formula for the behaviour of the survival function after the onset and the cessation of an additional exposure can be derived. Qualitative examinations demonstrate that the thus extended model shows the relevant features known from reports on shortterm exposures. Fitting the model to data of follow-up studies should provide a measure for the impact of an environmental exposure and the parameters for the distribution of the related latency period.     

Influences of FTO gene on onset age of adult overweight

FTO affects changes in BMI during both childhood and adulthood. However, its effect on onset age of overweight in adulthood is not known. To address this question, we conducted a study to examine effects of FTO tag SNPs on censored age of overweight in the longitudinal Bogalusa Heart Study (BHS) cohort, which began in 1973–1974. Of participating subjects, 658 whites (308 males and 350 females) with genotype data were selected for the study. The FTO gene was examined by a survival analysis of 30 tag SNPs regarding their association with left, interval and right-censored adult overweight. After adjustment for birth weight and sex, SNP rs9939609 has a small nominal p value of 0.004 for the association with onset age, which has an expected proportion of false positives of 9.6?% after adjusting for multiple tests. It was estimated that genotypes AA, AT and TT have onset age (standard error) of 22.82 (1.07), 28.96 (1.04) and 27.76 (1.04)?years, respectively, for a 50?% cumulative proportion of overweight in the population. Genotypes AA, AT and TT, respectively, have estimated survival probability of 65.8, 78.7 and 76.8?% at the age of 18; and survival probability of 6.5, 11.8 and 10.7?% at the age of 60. The odds ratios of survival beyond age ≥18?years are 0.52 for AA versus AT and 0.58 for AA versus TT. We thus concluded that risk genetic variants at FTO gene can accelerate the onset age and influence the survival odds of overweight in younger adults.     

Estimating the probability for major gene Alzheimer disease.

Alzheimer disease (AD) is neuropsychiatric illness caused by multiple etiologies. Prediction of whether AD is genetically based in a given family is problematic because of censoring bias among unaffected relatives as a consequence of the late onset of the disorder, diagnostic uncertainties, heterogeneity, and limited information in a single family. We have developed a method based on Bayesian probability to compute values for a continuous variable that ranks AD families as having a major gene form of AD (MGAD). In addition, we have compared the Bayesian method with a maximum-likelihood approach. These methods incorporate sex- and age-adjusted risk estimates and allow for phenocopies and familial clustering of age at onset. Agreement is high between the two approaches for ranking families as MGAD (Spearman rank [r] = .92). When either method is used, the numerical outcomes are sensitive to assumptions of the gene frequency and cumulative incidence of the disease in the population. Consequently, risk estimates should be used cautiously for counseling purposes; however, there are numerous valid applications of these procedures in genetic and epidemiological studies.     

A general model for sample size determination for collecting germplasm

The paper develops a general model for determining the minimum sample size for collecting germplasm for genetic conservation with an overall objective of retaining at least one copy of each allele with preassigned probability. It considers sampling from a large heterogeneous 2k-ploid population under a broad range of mating systems leading to a general formula applicable to a fairly large number of populations. It is found that the sample size decreases as ploidy levels increase, but increases with the increase in inbreeding. Under exclusive selfing the sample size is the same, irrespective of the ploidy level, when other parameters are held constant. Minimum sample sizes obtained for diploids by this general formula agree with those already reported by earlier workers. The model confirms the conservative characteristics of genetic variability of polysomic inheritance under chromosomal segregation.