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E A Murphy

Publications and source records attributed to E A Murphy.

At least 91 records · Page 5Linked to original sources
PubMed1987

The bingo model of survivorship. III. Genetic principles.

The broad relationships are explored between the genetic and the phenotypic structures of the bingo-gamma model (ie, the shortest waiting time among competing, independent, multiple-hit systems). Finite algorithms are derived to compute in closed form the joint and marginal distributions; the distribution, density, and hazard functions of time to failure; the respective total probabilities of dying from failure of each competing system; and the raw and central moments. The algorithm is the computer counterpart of a generating function. The number of competing systems and their individual orders and transition parameters may be chosen at will. Classical Galton-Fisher theory does not apply: neither means nor variances are additive nor are their effects homogeneous; rather, those systems with shorter mean survival more or less mask the impact of those with longer means. Thus even huge differences among means for alleles of any one component may be almost totally concealed phenotypically; even the maximal genetic covariation may in practice remain totally unrecognized and the heritability estimated close to zero. The proportional specific mortality is a less capricious index and is naturally additive, but, though a monotonic function of the underlying parameters, it is neither linear nor homogeneous.

Humans↗
PubMed1987

Genetic ascertainment with heterogeneous risk.

Analysis of the bias of ascertainment is reformulated to deal with more general patterns commonly encountered in practice. The goal is to provide a unifying theory that will both replace the traditional, rather piecemeal, treatment of the problem and free it from certain restrictive assumptions. A compact algebraic method is furnished for analyzing the properties of the distributions by means of the probability generating function (PGF). The scope of the generalization is illustrated by applying it to the various classical patterns of bias of ascertainment. It is extended to other patterns in which the conditions of ascertainment, though more plausible, are also logically more complicated. It also accommodates cases hitherto inadequately dealt with, such as where the segregation ratios are heterogeneous (for example because of age-dependence); and cases where the ascertainment function is of arbitrary form and denies us such valuable, but demanding, assumptions as independence. Not only is the result unifying, but it leads to usable results in specific application such as diseases that depend on age or birth order. While the commonest applications are in human genetics, there are many other issues (such as the use of batteries of tests) in which it is equally important.

Age Factors↗
PubMed1987

Predicting recurrence risks under epistatic models.

We present the expected recurrence risks to a sib of an affected proband under 4 simple 2-locus epistatic models for various allele frequencies at both the disease locus and the epistatic locus. Four obvious epistatic models are considered: an autosomal recessive disease with both 1) dominant and 2) recessive masking by the epistatic locus, and an autosomal dominant disease again with both 3) dominant and 4) recessive masking. Expected recurrence risks to a sib of an affected proband and to a sib of an affected proband with another normal sib are presented in the absence of information on parental status. Similar risks are presented for the case where both parents are known to be phenotypically normal. These recurrence risks were calculated using a convenient matrix notation which allows sequential calculation of genotypic probabilities. In general, 2-locus epistatic models can give surprisingly low recurrence risks, and often these risks, especially for models of recessive diseases, fall into the range associated with a more general multifactorial model for liability.

Epistasis, Genetic↗
PubMed1987

The bingo model. IV. The statistics of survivorship in the bingo-gamma model.

The survivorship (time to death or failure) of a bingo-gamma (BG) model is defined as the minimum among the waiting times for completion among k independent gamma processes. The ith process is of order ni, with a mean rate for the occurrence of hits of ai. In this paper we address the case where, for all competing processes, the order and the rate at which hits occur are the same but both they and k are unknown. We denote by k the multiplicity, by n the order or the number of hits to failure, and by a the transition parameter. The joint maximum likelihood estimator (MLE) of the three parameters of this BG process is developed. An algorithm for calculating it has been devised and a computer program in BASIC has been written. The properties of the MLE have been explored systematically, mainly by Monte Carlo simulation. The distributions, means, variances, covariances, and correlation coefficients of the three parameters are explored for samples of size 25 and samples of size 100. Also, the simple average of the observed survival times (which gives a method of moments estimator of the mean survival) is compared with the MLE of the mean survival; the two estimators seem to be unbiased and about equally efficient.

Humans↗
PubMed1987

The bingo model of survivorship. V. The problems of conformation to the empirical evidence.

We discuss the statistical and biological problems of adapting the theoretical bingo model to the analysis of empirical data. A distinction is made between an idealized pathogenetic model, which aims to represent the disease in as much authentic detail as the present state of knowledge allows and in components that have literal interpretation, and an empirical model, which deals with those effects of the pathogenetic model that one may hope to observe clinically. We review a variety of empirical models distinguishable by the amount of data available on intermediate degrees of damage short of total destruction. The relationship of damage to time is explored, and we consider the criteria and usefulness of linearization of this relationship where the diachronic ("longitudinal") data are few and extend over a comparatively short time. Every time a patient is examined, the degree of cumulative damage is assessed in each of the body systems of interest. Thus the examination will furnish a set of measurements, which is obtained on each of several examinations, taken over a period that for preference is long relative to the survival of the system. Specific disorders discussed include dentition and enlargement of the aorta with age in the Marfan syndrome.

Aorta↗
PubMed1987

A geneticist's approach to psychiatric disease.

The pattern of the genetics of psychiatric disease is various, in detail and in kind; one cannot always expect to find simple, trustworthy explanations of what are complex relationships. There will be some diseases, mostly of the disruptive type, that will prove to be Mendelian defects; but it would be idle to expect that of most. Many disorders will be elucidated only when the nub of the problem is better defined. Mindless application of standard genetic techniques devised for quite different purposes is no substitute for articulate speculation built on sound fact and cogent testing. In this respect genetic evidence is no different from that of physiology, pathology and pharmacology, which are perhaps less unfamiliar to readers than genetics. Finally, no answer has been found unless it deals in those terms in which the question first arose. If the topic of the genetic analysis is some psychosis, the final predicate must be a statement about the psychosis, not about some arbitrary abstraction from it.

Humans↗
PubMed1987

Pulmonary function in the Marfan syndrome.

To explore the causes of reported abnormalities in pulmonary function in persons with the Marfan syndrome, we analyzed retrospective anthropometric and pulmonary function tests in 79 patients. For ten subjects, there were matched, related control subjects who did not have a connective tissue disorder. Patients had lower values of FVC and TLC than the values expected for their standing heights (83 and 91 percent). However, when sitting height was used to calculate expected spirometric values, patients free of severe deformity of the thoracic cage did not have significant spirometric abnormalities (FVC 105 percent, FEV1 92 percent). However, patients with moderate-to-severe pectus excavatum or scoliosis (common features of the Marfan syndrome) had marked reductions in total lung capacity as well as in FVC and FEV1, suggesting a restrictive ventilatory defect. The abnormalities of pulmonary function often found in clinical laboratories can be explained in most cases by inappropriate use of standing height to calculate expected values, by thoracic cage deformity, or by both. We have found no evidence from standard tests of pulmonary function for a connective tissue defect of lung parenchyma that is of clinical importance in Marfan patients who lack chest wall deformity.

Adolescent↗
PubMed1986

The genetics of quantifiable homeostasis: I. The general issues.

Some fundamental issues in developing the quantitative genetics of heritable traits are addressed. Such a trait must be capable of being represented as a quantity. Choice of the metric can be satisfactorily made only in the light of some insight into the nature of the trait and what its revealing characteristics may be. This insight is likely to change as more is known about the process, so the form and detail of the analysis is not static but perhaps continually evolving. Much has been made out of sample means and, at a more sophisticated level, Galton-Fisher theory (the analysis of the first two moments of multivariate Gaussian variates). However, at least some processes seriously violate the assumptions underlying that theory. One such group comprises traits in which the means are unvarying and the genetic message lies in other aspects of the distribution; in these circumstances the standard summary statistics such as heritability, regression, and correlation may be totally uninformative, distracting, or even misleading. This paradox is illustrated by reference to homeostasis, where the Mendelian component lies, not in the mean, but in the degree of laxity of control. Since estimating higher moments is notoriously imprecise, the suggested remedy is the familial and commonsense one of exploring the genetics of the intermediate states and underlying mechanisms and not only that of the resultant ("bottom-line") phenotype. In our chosen problem, the task of relating the outcome to the basic mechanism of inheritance calls for a detailed understanding of the homeostasis involved.

Genetic Diseases, Inborn↗
PubMed1986

Homeostasis. VII. A conspectus.

The characteristics and properties of physiological homeostasis are broadly reviewed in terms that should pave the way for definitive genetic analysis. The ideas are illustrated by common physiological and pathophysiological examples with special reference to type II diabetes mellitus.

Adaptation, Physiological↗
PubMed1986

The statistics of quantifiable homeostasis. I. Simple linear homeostasis.

The statistical properties are explored of the least-squares estimators of the parameters of a deterministic linear model for homeostasis with random, normally distributed technical errors. The parameters are: the amplitude of perturbation (A), the homing value (H), the restoration constant (B), and the lag time (L). The former two, although important in their own right, tell us nothing about the processes of biologic restitution and are thus considered "nuisance" parameters; the latter two are the "business" parameters, which tell us about the processes of biologic adjustment. The properties studied include bias and precision and their relationships to the number of data points and to the size of the technical error. Efforts have been concentrated on data points equally spaced over six lag times (which corresponds roughly to the period of observation used in loading studies, such as glucose tolerance tests). The distributions of these four estimators are studied in sets of 100 Monte Carlo simulations, each with 15, 30, and 100 data points, respectively. The estimators are virtually unbiased and all satisfactorily close to Gaussian. The residual mean-square errors (the divisor being four less than the number of data points, since four parameters are estimated) seem to be unbiased estimators of the variances of the errors. Moreover, when suitably scaled, the residual sums of squares have distributions close to the chi-square distribution for the appropriate degrees of freedom and with the corresponding means and variances. The correlations among the estimators are modest and, except where A is involved, small.

Homeostasis↗
PubMed1986

Familial aggregation in Alzheimer dementia--I. A model for the age-dependent expression of an autosomal dominant gene.

An autosomal dominant genetic etiology has been proposed for Alzheimer Dementia (AD), but many cases appear to be sporadic. Evaluation of the possible genetic transmission of AD from its familial aggregation requires consideration of (1) the proportion of index cases with genetic disease, and (2) the consequences of typically very late onset. To investigate these factors, a provisional biomathematical genetic model was developed from the empirical age-specific incidence of AD in relatives. Based upon the premise of an autosomal dominant AD gene in proband families, the modeling technique provides estimates of the proportion of genetic index cases (as opposed to phenocopies) and the parameters of age-dependent gene expression. With appropriate parameters the model accurately reflects the age-specific familial risk of AD, suggesting the appropriateness of its underlying assumptions. The estimated proportions of genetic index cases suggest that heritable disease constitutes a majority of AD. In cases ascertained by the presence of aphasia or apraxia the estimated proportion of genetic cases is 100%. The greatest likelihood of gene expression is in the ninth decade, however, suggesting that most genetically predisposed relatives will die from other causes before developing AD.

Age Factors↗
PubMed1986

Familial aggregation in Alzheimer dementia--II. Clinical genetic implications of age-dependent onset.

A biomathematical genetic model for the age-specific risk of Alzheimer Dementia (AD) was applied to two problems in the clinical genetics of this disorder. In a test of the ability of a clinical marker specifically to identify genetic AD, cases grouped by the phenotype of amnesia with aphasia or apraxia (aaa) were shown to have familial risk that suggested a pure genetic illness, and differed significantly (p = 0.006) from cases without this phenotype. The model was also used in a Bayesian paradigm to assess the probability that individual cases had hereditary disease, given their family history. Here the results were surprisingly ambiguous: Even with no affected relatives, there is a substantial likelihood that many AD cases may have a genetic illness. Hence, one cannot reliably classify individual cases as "familial" or "sporadic" from family history alone. The phenotype of aaa (or other suitable marker) appears to be more reliable than the degree of manifest familial aggregation as an indicator of genetic AD.

Age Factors↗
PubMed1984

The bingo model of survivorship. II: statistical aspects of the bingo model of multiplicity 1 with application to hereditary polyposis of the colon.

Some Mendelian disorders (Huntington chorea, hereditary polyposis coli) are not manifest at birth but show a distribution in the age of onset. Patients at risk fall into three groups. In type I, they are affected when first examined. In type II, they are not affected at one visit, but are at a later visit. Those of type III (who comprise an indistinguishable mixture of those who have, and those who have not, inherited the gene) are never found to be affected. This paper posits a model that the age of onset is logistic. (It is a degenerate bingo model in which competing causes of death may be ignored.) The statistical properties of maximum likelihood estimation (MLE) are explored by Monte Carlo simulation of this logistic function with known arbitrary parameters. Two schemes are used: point-prevalence (or synchronic) data of types I and III, and piecewise longitudinal (diachronic) data; this allows all three types to be included. Samples of various sizes between 25 and 100 are used. While estimates of the parameters are positively biased (especially with small samples), the estimate of the mean appears to be consistent, almost unbiased, and fairly precise, though somewhat larger than the estimates from the lower bound (a fact that calls for some caution in interpreting actual data). The MLE was applied to 109 patients with the Gardner syndrome (GS); measures of variability found by applying MLE to four random subsets of 25 each were compared against the asymptotic estimates. The analysis was also applied to 36 persons with familial polyposis coli (FPC). The mean age of onset in GS and FPC was similar, and since they are rather earlier than is currently believed, it is recommended that regular supervision be started at not later than 10 years of age.

Adolescent↗
PubMed1984

The dynamics of quantifiable homeostasis. III: a linear model of certain metrical diseases.

A generalization of the linear, lagged, homeostatic process shows that whether a displacement of the trait function dies out with time, continues indefinitely, or shows a steadily amplifying (wild) oscillation depends on the value assumed by the product of the lag time and the restoration constant. Moreover, it is shown that if a steady displacing force is used rather than an instantaneous displacement, a new homing value results which is given by the ratio of the displacing force to the restoration coefficient. Combining these two developments furnishes grounds for determining whether or not an overshoot will occur when administration of a drug is stopped (for instance, the rebound thrombosis on discontinuing heparin). Further developments of these ideas show how the diabetes that begins in mature patients can be wholly accounted for by the well-known prolongation of the lag in insulin response that occurs in that disorder. If wild oscillation is to be avoided as the lag time increases, the restoration constant must be weakened (evidently by a systematic reduction in insulin receptors) and this weakening means that the homing value is displaced. Thus the hyperglycemia in this diabetes is to be seen as the price paid for avoiding wild oscillation. Provided that the therapeutic use of exogenous insulin is systematic and regular, rather than cybernetic, its success where endogenous (cybernetic) insulin secretion has failed is readily understood. The point is illustrated by a familiar analogy of a car driver with slow responses. The genetic and evolutionary implications of these ideas are outlined.

Cybernetics↗