Alternative Statistical Models Research Articles

Inferring the genetic basis of inbreeding depression in plants

Recent progress in the genetic analysis of inbreeding depression in plants is reviewed. While the debate over the importance of genes of dominance versus overdominance effect continues, the scope of inferences has widened and now includes such facets as the interactions between genes, the relative abundance of major versus minor genes, life cycle stage expression, and mutation rates. The types of inferences are classified into the genomic, where many genes are characterized as an average, and the genic, where individual genes are characterized. Genomic inferences can be based upon natural levels of inbreeding depression, purging experiments, the comparison of individuals of differing F (e.g., prior inbreeding), and various crossing designs. Genic inferences mainly involve mapping and characterizing loci with genetic markers, involving either a single cross or, ideally, several crosses. Alternative statistical models for analyzing polymorphic loci causing inbreeding depression should be a fruitful problem for geneticists to pursue. Key words : inbreeding depression, genetic load, self-fertilization, QTL mapping.

Use of deterministic sampling for exploring likelihoods in linkage analysis for quantitative traits

Deterministic sampling was used to numerically evaluate the expected log-likelihood surfaces of QTL-marker linkage models in large pedigrees with simple structures. By calculating the expected values of likelihoods, questions of power of experimental designs, bias in parameter estimates, approximate lower-bound standard errors of estimates and correlations among estimates, and suitability of statistical models were addressed. Examples illustrated that bracket markers around the QTL approximately halved the standard error of the recombination fraction between the QTL and the marker, although they did not affect the standard error of the QTL's effect, that overestimation of the distance between the markers caused overestimation of the distance between the QTL and marker, that more parameters in the model did not affect the accuracy of parameter estimates, that there was a moderate positive correlation between the estimates of the QTL effect and its recombination distance from the marker, and that selective genotyping did not introduce bias into the estimates of the parameters. The method is suggested as a useful tool for exploring the power and accuracy of QTL linkage experiments, and the value of alternative statistical models, whenever the likelihood of the model can be written explictly.

Subinguinal Microsurgical Varicocelectomy: A Technical Critique and Statistical Analysis of Semen and Pregnancy Data

A total of 606 modified subinguinal microscopic varicocelectomies was performed on 466 outpatients using local anesthesia and sedation. The patients selected for these procedures were infertile for at least 12 months and had at least 1 semen parameter below threshold level: less than 20 million per ml., less than 50% motility or less than 40% normal morphological forms. The lymphatics, spermatic artery and vas were preserved, whereas all refluxive veins were transected or obliterated. Postoperative complications were limited to transient epididymal discomfort in 5.5% of the patients, ecchymosis at the wound site in 3.4% and wound inflammation in 2.4%. There was only 1 permanent hydrocele. The palpable recurrence rate was 0.82% per procedure. The median values for each semen parameter were compared preoperatively and postoperatively by the Wilcoxon signed rank test. The differences in the median values were significant for all parameters. As an alternative statistical model, the average preoperative semen value was subtracted from the average postoperative semen value for each parameter. The median differences were 10.8 million sperm per ml. for sperm density, 13.9% for motility and 3.8% for normal morphological forms. These differences were significantly greater than zero by the Wilcoxon signed rank test. The intra-quartile ranges for these differences suggested that postoperatively more than 75% of the patients had a difference of greater than zero for sperm density and per cent motility, and 63% had a difference of greater than zero for normal morphology. The 1-year pregnancy rate was 35.6% for 186 varicocelectomy patients compared to 15.8% for 19 medically treated men with varicocele. The difference between the true 1-year pregnancy rates was 19.8% and the 95% confidence intervals estimated bounds of 1.91 to 37.5%. These data suggest that outpatient subinguinal microscopic varicocelectomy has minimal morbidity and recurrence, and may be beneficial for select patients.

Determination of hprt mutant frequencies in T-lymphocytes from a healthy pediatric population: statistical comparison between newborn, children and adult mutant frequencies, cloning efficiency and age

Somatic cell mutant frequencies at the hprt locus of the X-chromosome were measured with the T-lymphocyte cloning assay in a healthy pediatric population. Assays were performed on 49 subjects (29 males and 20 females) ranging in age from 0.08 to 15.2 years. A statistical analysis of the thioguanine-resistant (TG r) mutant frequency ( MF), unselected cloning efficiency ( CE) and age was performed using data obtained in this study and those previously obtained in our laboratory on 66 newborn umbilical cord blood samples and 230 adult blood samples. For statistical comparisons pediatric subjects were divided into 4 groups. Group I included cord blood samples (age 0 years); Group II were subjects between 0 and 5 years; Group III were between 6 and 11 years and Group IV were between 12 and 17 years. The ln MF of Groups I and II were significantly lower than Groups III and IV ( p < 0.05). The mean ln MF for each of Groups I–IV was significantly lower than the adult value. The cloning efficiency for Group I was significantly lower than that for Groups II–IV and adults. The relationships among the ln MF, unselected CE and age were expressed by the equations: ln ( MF) = 0.945 −2.453 CE ( p < 0.001) and ln ( MF) = 0.114 + 0.063 age ( p 0.004). The slope coefficients for unselected CE and age were significantly different from adults ( p < 0.05). Regression analysis of combined data from Groups I–IV and adults were performed using both age and unselected CE as well as terms to reflect differences in their relationships with ln MF in adults and children. The results showed that the intercept and the age coefficients differ significantly for children and adults after adjustment for CE and yielded the following equations: ln ( MF) = 0.548 −1.676 CE + 0.075 age, (Groups I–IV) and ln ( MF) = 2.263 −1.676 CE + 0.014 age (adults). An alternative statistical model using ln (age + 1), ln ( MF) = 0.381 −1.767 CE + 0.673 ln (age + 1), ( p < 0.001), describes the rapid increase in MF with age that levels off in late adolescence. These findings demonstrate the changing influence of age on mutant frequency in the pediatric population as compared to the adult populations. These studies also illustrate that the increase in background somatic mutant frequencies at the hprt locus in T-lymphocytes is not linear from birth to adolescence and is significantly different from that seen in the adult population. This model can be used to determine the possible effects of genotoxic exposures in vivo on MF in children within defined parameters such as age.

Factors involved in burn mortality: A multivariate statistical approach based on discriminant analysis

This article suggests an alternative statistical model for studying the mortality of burned patients: discriminant analysis. This model was applied to our population of 532 patients among whom 71 died. It is not the first time that this model has been applied to assess burn mortality, although it is not frequently used for that application. We found four factors that are statistically significant: age, TBSA, inhalation injury and sex (female). Discriminant analysis allowed us to demonstrate an impressive correlation between death, age and TBSA; inhalation injury by itself and sex, the two other significant factors in our study, seem to have a minor influence on the final outcome of the burned patients and their predictive value is virtually nil. The advantages of this statistical model are compared with logistic regression, the commonly chosen statistical method.

Risk Assessment for Oral Diseases

This paper seeks to achieve four goals, each of which forms the basis for a section in the presentation. First, the rationale of risk assessment is fully described. In this section, some of the necessary conditions are identified that make disease prediction worth pursuing. The second section discusses some essential background to the understanding of risk assessment in dentistry. In this segment, attention is focused on population-based and individual-based perspectives, alternative approaches to expressing health risk, and methods for comparing the predictive accuracy of alternative risk assessment models. The third section of the paper develops a conceptual framework for risk assessment in dentistry. Particular emphasis is devoted to the identification of risk factors and their incorporation into alternative statistical models. In the fourth section, empirical data are offered by which certain comparisons of the alternative risk models can be drawn. The paper concludes with a discussion that emphasizes data and technical limitations, speculates on future applications, and suggests new avenues for research.

Statistical calculation of fission decay probabilities of nuclear giant multipole resonances.

The statistical fission decay properties of the giant dipole, quadrupole, and monopole resonances in /sup 236/U are investigated with the aid of the Hauser-Feshbach model. It is found that the giant quadrupole resonance fission decay probability is as large as that of the giant dipole resonance, at energies higher than the fission barrier. At energies close to the fission barrier, the giant quadrupole resonance fission probability is found to be appreciably larger than that of the giant dipole resonance. The giant multipole resonance fission probability follows closely that of the giant quadrupole resonance. Comparison with the more commonly employed alternative statistical fission model is made.

Improved Methods of Inference in Econometrics.

Introduction. The Inferential and Decision Framework. The Measure of Performance. Some Alternative Statistical Models, Estimators and Tests. Inequality Estimation and Hypothesis Testing. Inequality Estimation and Hypothesis Testing of the Location Parameter of a Normal Random Variable. General Linear Statistical Model and a Single Linear Inequality Constraint. Inequality Restricted Estimation of Two or More Location Parameters: The Orthonormal Case. An Inequality Restricted Stein Rule Estimator. Hypothesis Testing for Two or More Inequalities: The Orthogonal Case. Inequality Restricted Estimation: General Design and Restriction Matrices. Inequality Hypothesis Testing: General Case. Some Sampling Results for the Stein Family of Estimators. Assessing the Precision of Stein's Estimator. Some Evaluations of the Sampling Performance of the Limited Translation and New Stein Estimators. Estimation Under Non-Normal Errors and Quadratic Loss. Estimation and Hypothesis Testing in the Case of Possible Heteroskedasticity. Subject Index.

ANALYZING UTTERANCES AS THE OBSERVATIONAL UNIT

If utterances are the observational unit of analysis and there are no sequential patterns to the interaction, two alternative statistical models may be applied. A hierarchical design in which utterances are nested within subjects and subjects are nested within treatment condition is considered. One method of analysis pools utterances within treatment condition; the other method collapses across utterances to obtain subject means. Inappropriate application of the pooling model instead of the subject means model can lead to Type I errors, decreased generalizability, and inflated variance estimates that attenuate univariate and multivariate correlations. The effect of utterance reliability on the apparent unidimensionality and parallelism of multiple indicators is also discussed.

Alternative statistical models for the examination of clinical positron emission tomography/fluorodeoxyglucose data.

This article describes a method for partitioning metabolic variability found in positron emission tomography/[18F]fluorodeoxyglucose studies. For the 15 subjects examined, 74.8% of the total metabolic variability could be ascribed to individual differences in global metabolic rate, whereas 15.8% of the total variability was consistent regional variation or pattern across subjects. Subsequently, the method of Q-component analysis is described for the identification of strong- and weak-pattern subjects. In addition, a standardization procedure that amplifies the observed pattern by removing systematic individual differences is described. Finally, the implications of these findings and methods for future and clinical studies are discussed.

A statistical modelling approach to community prevalence data.

Sample survey techniques are often used to assess the prevalence of illness in a community and to determine any variation with environmental, social and demographic factors. Analysis of survey data is often carried out using several elementary statistical procedures. The formulation of a statistical model is an effective way of conducting a unified analysis. The model provides a concise description of the study population and is a most effective way of summarizing community prevalence data. The testing of statistical hypotheses is equivalent to model simplification and is conveniently performed using general procedures. Two alternative statistical models are given for an investigation into the extent of minor psychiatric morbidity in Perth, Western Australia.

Statistical Model Comparison in Marketing Research

Analysis for marketing decisions often involves the consideration of several alternative statistical models. As an intermediate step prior to making policy decisions, a single model is typically selected and used to guide subsequent decisions. In this paper, Bayesian model comparison methods are shown to lead to a predictive distribution for the decision problem without the intermediate step of model selection. This approach utilizes all available information bearing on the validity of the alternative models, as well as information concerning model parameters, in order to draw inferences regarding the criterion of interest relative to the decision to be made. The procedure is illustrated in the context of an advertising budget decision in which the functional form of sales response to advertising is unknown.

A Sampling Model for Audit Tests of Composite Accounts

A typical part of the public auditor's opinion formulation process is the evaluation of composite account balances resulting from the aggregation of a large number of subsidiary components. Numerous statistical methods have been proposed as a means of assisting the auditor in estimating the total value of such accounts or, equivalently, in estimating the error in the stated book value of such accounts. These methods, for the most part, are a direct adaptation of standard classical and Bayesian statistical procedures. Recent work by Kaplan [1973b] and Neter and Loebbecke [1975] has raised serious questions about the adequacy of applying many of these methods to the auditing environment. These difficulties arise when the auditor chooses to develop a statistical inference on the total error, based upon the relationship between book value and sample audit value of the subsidiary components of the account. Because of the usual low error rates experienced in such accounting populations, these auxiliary (ratio, regression, differences, etc.) estimators all suffer from a lack of normal distribution robustness of the sampling distribution. The problem is particularly apparent within the customary range of auditing sample sizes. In this paper, we present an alternative statistical sampling model that proceeds from a different perspective and, consequently, avoids some of the assumptions made by more conventional methods. Our analysis brings together, in a Bayesian framework, the book value, audit value, and informed judgment sources of evidence that can be used to evaluate a composite account. When a noninformative prior judgment

Evaluating an Individualized College Reading Service: Alternative Criteria and Statistical Models to the Test-Retest Paradigm

Most college reading programs routinely collect demographic and test data on their student clientele and summarize this information in tables which are included in their annual reports, evaluation studies or descriptions of their service. Typically, data on student characteristics such as class, college or major, sex, grade-point averages, extent of use of the service, etc. are compiled. Table I exemplifies such data on three characteristics of students using the University of California, Berkeley Reading and Study Skills Service.

Household Surveys with Multiplicity

Abstract In the household survey with multiplicity, sample households report information about their own residents as well as about other persons who live elsewhere, such as relatives or neighbors, as specified by a multiplicity rule adopted in the survey. Although sampling errors for the multiplicity survey are not necessarily smaller than those for the conventional survey in which sample households report for their own residents only, in most instances it should be feasible to assure a substantial reduction in sampling error by selecting appropriate multiplicity rules. Using alternative statistical models, it is demonstrated that under specified conditions, sampling errors for the multiplicity survey are necessarily smaller than those for the conventional survey, and the results give insight regarding the factors contributing to the efficiency of the multiplicity survey.

Household Surveys with Multiplicity

Abstract In the household survey with multiplicity, sample households report information about their own residents as well as about other persons who live elsewhere, such as relatives or neighbors, as specified by a multiplicity rule adopted in the survey. Although sampling errors for the multiplicity survey are not necessarily smaller than those for the conventional survey in which sample households report for their own residents only, in most instances it should be feasible to assure a substantial reduction in sampling error by selecting appropriate multiplicity rules. Using alternative statistical models, it is demonstrated that under specified conditions, sampling errors for the multiplicity survey are necessarily smaller than those for the conventional survey, and the results give insight regarding the factors contributing to the efficiency of the multiplicity survey.

Statistical Model for Electron-Positron Annihilation into Hadrons

A statistical model for the production of multibody hadronic states by ${e}^{+}{e}^{\ensuremath{-}}$ annihilation is discussed. We associate the secondary hadron momentum distributions for colliding-beam processes with the exponentially failling transverse-momentum distributions in hadron-hadron collisions. The consequence of this picture is that at high energies hadron multiplicity rises linearly with c.m. energy, unlike the $\mathrm{ln}s$ behavior for the multiplicity of secondaries in hadron-hadron collisions. If the total annihilation cross section is assumed to have a power falloff $\ensuremath{\sim}{s}^{\ensuremath{-}m}$, the $n$-pion cross sections follow a Poisson distribution with the most probable multiplicity ${n}_{\ensuremath{\pi}}=\frac{{s}^{\frac{1}{2}}}{〈{E}_{\ensuremath{\pi}}〉}+3\ensuremath{-}m$ and $〈{E}_{\ensuremath{\pi}}〉\ensuremath{\sim}375$ MeV. An alternative statistical model based on jets is also briefly discussed. The storage rings now being constructed or envisaged should easily distinguish between the various possibilities.