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Statistical models for trisomic phenotypes.

Certain genetic disorders are rare in the general population but more common in individuals with specific trisomies, which suggests that the genes involved in the etiology of these disorders may be located on the trisomic chromosome. As with all aneuploid syndromes, however, a considerable degree of variation exists within each phenotype so that any given trait is present only among a subset of the trisomic population. We have previously presented a simple gene-dosage model to explain this phenotypic variation and developed a strategy to map genes for such traits. The mapping strategy does not depend on the simple model but works in theory under any model that predicts that affected individuals have an increased likelihood of disomic homozygosity at the trait locus. This paper explores the robustness of our mapping method by investigating what kinds of models give an expected increase in disomic homozygosity. We describe a number of basic statistical models for trisomic phenotypes. Some of these are logical extensions of standard models for disomic phenotypes, and some are more specific to trisomy. Where possible, we discuss genetic mechanisms applicable to each model. We investigate which models and which parameter values give an expected increase in disomic homozygosity in individuals with the trait. Finally, we determine the sample sizes required to identify the increased disomic homozygosity under each model. Most of the models we explore yield detectable increases in disomic homozygosity for some reasonable range of parameter values, usually corresponding to smaller trait frequencies. It therefore appears that our mapping method should be effective for a wide variety of moderately infrequent traits, even though the exact mode of inheritance is unlikely to be known.

Abortion, Spontaneous↗

Statistical model building and model criticism for human circadian data.

Mathematical models have played an important role in the analysis of circadian systems. The models include simulation of differential equation systems to assess the dynamic properties of a circadian system and the use of statistical models, primarily harmonic regression methods, to assess the static properties of the system. The dynamical behaviors characterized by the simulation studies are the response of the circadian pacemaker to light, its rate of decay to its limit cycle, and its response to the rest-activity cycle. The static properties are phase, amplitude, and period of the intrinsic oscillator. Formal statistical methods are not routinely employed in simulation studies, and therefore the uncertainty in inferences based on the differential equation models and their sensitivity to model specification and parameter estimation error cannot be evaluated. The harmonic regression models allow formal statistical analysis of static but not dynamical features of the circadian pacemaker. The authors present a paradigm for analyzing circadian data based on the Box iterative scheme for statistical model building. The paradigm unifies the differential equation-based simulations (direct problem) and the model fitting approach using harmonic regression techniques (inverse problem) under a single schema. The framework is illustrated with the analysis of a core-temperature data series collected under a forced desynchrony protocol. The Box iterative paradigm provides a framework for systematically constructing and analyzing models of circadian data.

Adult↗

Statistical models of outcome in malpractice lawsuits involving death or neurologically impaired infants.

The objective was to determine whether factors could be identified in medical and legal records that are associated with the successful defense of obstetrical malpractice cases involving the death or neurological impairment of infants. Obstetrical claims (169) closed by PROMUTUAL between January 1, 1990, and December 31, 1994, were retrospectively abstracted and analyzed to identify associations between medical and legal factors, and the medicolegal outcome. Multivariable analysis identifies that the use of pitocin, diagnosis of asphyxia, a delay in delivery, and the use of multiple defense expert witnesses decreased the chances of a successful defense. Two statistical models explaining indemnity payment were developed. The first, based on medical outcome, showed an increased indemnity payment when a case involved major neurological deficits, diagnosis of asphyxia, newborn seizures, later year of delivery, and participation of a particular defense firm. Perinatal or childhood death and the use of pitocin were indicators of a decrease in payment. The second model was based on long-term care requirements. In this model, indicators of increased indemnity payment were: nonreassuring intrapartum fetal heart rate tracing, later year of delivery, intensity of long-term care required, and participation of a particular defense law firm. Perinatal or childhood death, the use of pitocin, and settlement date increasingly removed from the occurrence date were the determinants of decreased payments in this model. Finally, the presence of major neurological deficits, the prolongation of a case, and the involvement of multiple law firms and defense witnesses increased the expense charged to and paid by the insurance company. Using the medical, legal, and financial data relevant to 169 obstetrical cases closed by one malpractice insurance carrier between 1990 and 1994, statistical models with potential predictive values for future malpractice claims involving neurologically impaired infants were constructed. These models may help determine in advance the chance a future case has for successful defense and the likely amount of expense and indemnity dollars that will be paid out to settle and defend it.

Adolescent↗

Statistical modelling of general practice medicine for computer assisted data entry in electronic medical record systems.

Electronic medical record (EMR) systems have much potential, however, there are still a number of issues that need to be resolved before EMRs are widely accepted. One of these issues is the data input task, a potentially serious practical barrier to on-line medical computer usage. This paper reports the empirical modelling of data input requirements for physicians who use a problem-orientated medical record system. Three statistical models (Bayesian conditional probability, multiple linear regression and discriminant analysis) to predict drug treatment given problem diagnoses are derived from EMRs of 2500 general Practice encounters. Two metrics are used to measure the predictive power of the models considering both the number of drugs correctly predicted and the strength with which the models predict them. The models are tested on 500 unseen records from the same patient-physician population and the data used to build the models. The Bayesian model produces the best predictions on unseen data and is also the easiest model to compute. A prototype interface that enables new patient cases to be entered is constructed to demonstrate how the predictive power of the model can translate into benefits in the data entry task.

Bayes Theorem↗

A physician-based architecture for the construction and use of statistical models.

Physicians need specially tailored computer tools to take advantage of published research results. We present a knowledge-based computer framework--the physician-based (PB) architecture--for constructing such tools, and we use the problem of physicians' interpretation of two-arm parallel randomized clinical trials (TAPRCT) as a working example. Statistical models are represented by influence diagrams. The interpretation of influence-diagram elements are mapped into users' language in a domain-specific, physician-based user interface, called a patient-flow diagram. Statistical-model transformations that maintain the semantic relationships of the model and that embody clinical-epidemiological knowledge are encoded in a mediating structure called the cohort-state diagram. The algorithm that coordinates the interactions among the knowledge representations uses modular actions called construction steps. This architecture has been implemented in a Bayesian system, called THOMAS, that supports physician decision making in light of TAPRCT data. This support entails assessing clinical significance, prior beliefs, and methodological concerns. We suggest that the PB architecture applies to a wide range of statistical tools and users.

Algorithms↗

A multi-variate statistical model integrating passive sampler and meteorology data to predict the frequency distributions of hourly ambient ozone (O3) concentrations.

A multi-variate, non-linear statistical model is described to simulate passive O3 sampler data to mimic the hourly frequency distributions of continuous measurements using climatologic O3 indicators and passive sampler measurements. The main meteorological parameters identified by the model were, air temperature, relative humidity, solar radiation and wind speed, although other parameters were also considered. Together, air temperature, relative humidity and passive sampler data by themselves could explain 62.5-67.5% (R(2)) of the corresponding variability of the continuously measured O3 data. The final correlation coefficients (r) between the predicted hourly O3 concentrations from the passive sampler data and the true, continuous measurements were 0.819-0.854, with an accuracy of 92-94% for the predictive capability. With the addition of soil moisture data, the model can lead to the first order approximation of atmospheric O3 flux and plant stomatal uptake. Additionally, if such data are coupled to multi-point plant response measurements, meaningful cause-effect relationships can be derived in the future.

Air Pollutants↗

Efficient statistical modelling of longitudinal data.

A new class of statistical models is proposed for the analysis of longitudinal data, especially those from growth studies. The models are all derived from a simple univariate two-level polynomial model. It is shown that they make efficient use of available data, and can handle a very wide range of problems. They have several important advantages over existing procedures.

Age Factors↗

Statistical models for prevalent cohort data.

In prospective cohort studies individuals are sometimes recruited according to a certain cross-sectional sampling criterion. A prevalent cohort is defined as a group of individuals who have a certain disease at enrollment into the study. Statistical models for the analysis of prevalent cohort data are considered when the onset or diagnosis time of the disease is known. The incident proportional hazards model, where the time scale is duration with disease, is compared to the prevalent proportional hazards model, where the fundamental time scale is follow-up time. In certain cases the time of enrollment may coincide with another event (such as the initiation of treatment). This situation is also considered and its limitations highlighted. To illustrate the methodological ideas discussed in the paper, the analysis of data from an observational study of zidovudine (ZVD) in patients with the acquired immunodeficiency syndrome (AIDS) is presented.

Acquired Immunodeficiency Syndrome↗

Different statistical models used in the calculation of the prevalence of insulin-dependent diabetes mellitus according to the polymorphism of the HLA-DQ region.

The use of three statistical models yielded different estimates of the odds ratio relative to the association between the polymorphism in the HLA-DQ region and insulin-dependent diabetes mellitus (IDDM). The models used were: (1) the allele-dosage model which assumes that the number of susceptibility alleles has a linear effect on the logarithm of the odds; (2) the reference cell coding method used with alleles of susceptibility as a risk factor; or (3) a model that uses a classification of alpha/beta heterodimers as a susceptibility factor. We suggest that models which imply a log-linear relationship between a susceptibility marker and disease such as the first model are not appropriate in the assessment of the HLA-IDDM association. In contrast, although both latter models are valid, the third model is more compatible with current hypotheses of the pathological process of the disease. Once an estimation of the odds ratio is chosen, we use such an estimation to calculate an approximation of the prevalence of IDDM according to the polymorphism in HLA-DQ region using the iterative procedure of Newton-Raphson. These approaches are illustrated with data from a case-control study previously conducted in the city of Santiago, Chile.

Alleles↗

A statistical model examining repetitive criminal behavior in acts of violence.

A simple statistical model for examining repetitive criminal behavior in acts of violence is described. The units, called "parameters," are nonquestionable data concerning environment of the crime, personal properties, and postmortem findings of the victim, obtained by double-blind investigation performed by two forensic pathologists. Parameters shared by two or more criminal acts allegedly committed by the same assailant were compared with the same parameters recorded from 50 or 100 other mutually independent criminal acts committed by other known assailants. This allowed an evaluation of the probability (p) of a crime pattern expressed as a parameter score to recur in mutually independent cases. The distribution of the score, when plotted on a logarithmic scale in all examples, showed an approximately normal distribution. The relation between probability (p), the estimated mean (means), and standard deviation (SD) yielded a normal curve. Different patterns of action by different perpetrators and patterns indicating repetitive behavior could be obtained. The method is applicable during investigation of crimes in which the perpetrator acts in a repetitive manner, as in serial murders.

Crime↗

A statistical model of infant mortality.

"We have developed here a statistical model for describing infant deaths. Even though the model is tested with Canadian data, it will be a good approximation of the relationship between infant deaths and age in any population. The model needs improvement when high risk populations are studied."

Age Factors↗

Predicting outcome in coronary disease. Statistical models versus expert clinicians.

To study the accuracy with which long-term prognosis can be predicted in patients with coronary artery disease, prognostic predictions from a data-based multivariable statistical model were compared with predictions from senior clinical cardiologists. Test samples of 100 patients each were selected from a large series of medically treated patients with significant coronary disease. Using detailed case summaries, five senior cardiologists each predicted one- and three-year survival and infarct-free survival probabilities for 100 patients. Fifty patients appeared in multiple samples for assessing interphysician variability. Cox regression models, developed using patients not in the test samples, predicted corresponding outcome probabilities for each test patient. Overall, model predictions correlated better with actual patient outcomes than did the doctors' predictions. For three-year survival, rank correlations were 0.61 (model) and 0.49 (doctors). For three-year infarct-free survival predictions, correlations with outcome were 0.48 (model) and 0.29 (doctors). Comparisons by individual doctor revealed Cox model three-year survival predictions were better than those of four of five doctors (model predictions added significant [p less than 0.05] prognostic information to the doctor's predictions, whereas the converse was not true). For infarct-free survival, the Cox model was superior to all five doctors. Where predictions were made by multiple doctors, the interphysician variability was substantial. In coronary artery disease, statistical models developed from carefully collected data can provide prognostic predictions that are more accurate than predictions of experienced clinicians made from detailed case summaries.

Coronary Disease↗

A statistical model to optimize indirect sandwich enzyme-linked immunosorbent assay parameters of antigen and antibody: a microcomputer program.

A new computer software program "AVCRV" was developed using a statistical model to analyze the data from the indirect sandwich enzyme-linked immunosorbent assay (ELISA). The software program calculates a sigmoid type of regression analysis and can be run on most microcomputers in the laboratory. The program permits those who are not familiar with computers to complete this type of analysis in a few seconds without a large mainframe computer or complicated software. This statistical model for a sigmoid type of regression analysis of ELISA data may improve the analysis of research data for various avian pathogens from several different experiments.

Animals↗

The frequency of ion-pair substructures in proteins is quantitatively related to electrostatic potential: a statistical model for nonbonded interactions.

A statistical analysis of ion pairs in protein crystal structures shows that their abundance with respect to uncharged controls is accurately predicted by a Boltzmann-like function of electrostatic potential. It appears that the mechanisms of protein folding and/or evolution combine to produce a "thermal" distribution of local nonbonded interactions, as has been suggested by statistical-mechanical theories. Using this relationship, we develop a maximum likelihood methodology for estimation of apparent energetic parameters from the data base of known structures, and we derive electrostatic potential functions that lead to optimal agreement of observed and predicted ion-pair frequencies. These are similar to potentials of mean force derived from electrostatic theory, but departure from Coulombic behavior is less than has been suggested.

Biological Evolution↗

Statistical models for discerning protein structures containing the DNA-binding helix-turn-helix motif.

A method for discerning protein structures containing the DNA-binding helix-turn-helix (HTH) motif has been developed. The method uses statistical models based on geometrical measurements of the motif. With a decision tree model, key structural features required for DNA binding were identified. These include a high average solvent-accessibility of residues within the recognition helix and a conserved hydrophobic interaction between the recognition helix and the second alpha helix preceding it. The Protein Data Bank was searched using a more accurate model of the motif created using the Adaboost algorithm to identify structures that have a high probability of containing the motif, including those that had not been reported previously.

Binding Sites↗

A statistical model for estimating donor postdonation platelet counts after plateletpheresis.

BACKGROUND: To avoid the need, in serial apheresis donors, either to delay plateletpheresis until a predonation platelet count is completed or to obtain a postdonation count after each procedure, a statistical model has been developed to predict the postdonation platelet count from the donor predonation platelet count, weight, and hematocrit. STUDY DESIGN AND METHODS: Predonation and postdonation platelet counts were measured in two groups of approximately 100 consecutive donors (Group A to test the model and Group B to validate it), and the postdonation counts were calculated with the model. Using stepwise multiple linear regression from donor data, estimated postdonation platelet counts were found to be comparable to the postdonation platelet counts actually measured. RESULTS: Estimated postdonation platelet counts x 10(9) per L (mean +/- SD) for each group, respectively, were Group A, 195 +/- 35, versus actual platelet counts of 195 +/- 39 (p = 0.43), and Group B, 183 +/- 36, versus actual platelet counts of 189 +/- 34 (p = 0.14). Sensitivity and specificity, respectively, were Group A, 57 and 99 percent and Group B, 62 and 99 percent. CONCLUSION: For most serial apheresis donors, application of this predictor model should preclude the need to obtain an extra postdonation platelet count.

Blood Donors↗

Gene-environment interaction and the mapping of complex traits: some statistical models and their implications.

The manifestation of many complex diseases or traits is very likely the result of an inextricable interplay of the biological and the environmental. Yet the role of environmental effect has traditionally been played down, for various reasons. In this paper, some simple statistical models that incorporate gene-environment interaction (GEI) have been proposed and their behavior and implications investigated. These implications concern the conditional independence assumption in likelihood calculation of pedigree data, the fine-tuning of the sib pair method for mapping quantitative traits, apportioning of disease or trait variation due to specific causes. In addition, they concern properties of gene mapping methods that do not take GEI into account, and they bring into question the utility of commonly used measures of genetic effects such as recurrence risk ratio for relative pairs, twin concordance rates, and heritability coefficients. In the presence of GEI, all these measures are functions not only of genetic effects and gene frequency, but also of environmental effects, the distribution of environmental factors in the population, and of GEI. Above all, these measures are all measures of familial aggregation, since they can be significant even in the absence of any genetic component of the disease. Thus their use as indicators of the genetic basis of complex diseases is cast into doubt.

Chromosome Mapping↗

Angioarchitecture associated with haemorrhage in cerebral arteriovenous malformations: a prognostic statistical model.

The overall haemorrhagic risk of a cerebral arteriovenous malformation (cAVM) is 2-4% per year. However, the individual risk of haemorrhage has never been determined. This study was undertaken to assess the haemorrhage risk of an individual cAVM. Neuroangiographic findings of 160 cAVM were analysed retrospectively, looking at 30 angiographic features. A statistical model was established by logistic regression to evaluate the risk of an individual cAVM. We statistically correlated 15 parameters with the haemorrhage risk. The statistical model includes five independent parameters. Four are unfavourable: exclusively deep drainage, venous stenoses, venous reflux and the radio of afferent to efferent systems; one is favourable: venous recruitment. This model quantifies the individual risk of haemorrhage. When this model is applied to the population studied, the error rate is 5%. This model can contribute to therapeutic strategy, and to a better understanding of the natural history of cAVM.

Adolescent↗