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PubMedDate not supplied

Use of linear models to analyze physicians' decisions.

Linear models of judgment are powerful tools for studying medical decision making. The recent increase in applications of these models to medicine reflects more available computing resources and the parallel development of clinical prediction rules derived from multivariate analysis of patient data. Psychological research into expert and novice decision making shows that linear models derived from judges' decisions usually predict future decisions more accurately than either the judge or a mechanical application of the judge's stated policies. Studies of medical decision making have shown similar results, as well as marked variation among experts in how they appear to use clinical information. Cognitive feedback, which is feedback to the learner of the judgment model derived from previous decisions, is highly effective for teaching complex judgment tasks. Many technical problems remain to be mastered in constructing linear models of medical judgment. These include how to select the correct variables, how to provide a selection of variables broad enough to accommodate individual variations in strategy, how to model intercorrelated variables, and how to characterize and aggregate individual strategies. Despite the methodologic challenges, linear models remain a powerful method for studying how physicians combine multiple items of imperfect information to make a judgment. These techniques may provide important insights into variation in physician judgments. In addition, they hold promise in teaching the appropriate integration of complex data in the day-to-day practice of medicine.

Cues↗
PubMed2000

Fitting host-parasitoid models with CV2 > 1 using hierarchical generalized linear models.

The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density-dependent heterogeneity (HDD) to be distinguished from between-patch, host density-independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well-known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.

Animals↗
PubMed2000

Biases in estimating the effect of cumulative exposure in log-linear models when estimated exposure levels are assigned.

OBJECTIVES: Exposure-response trends in occupational studies of chronic disease are often modeled via log-linear models with cumulative exposure as the metric of interest. Exposure levels for most subjects are often unknown, but can be estimated by assigning known job-specific mean exposure levels from a sample of workers to all workers. Such assignment results in (nondifferential) measurement error of the Berkson type, which does not bias the estimate of exposure effect in linear models but can result in substantial bias in log-linear models with dichotomous outcomes. This bias was explored in estimated exposure-response trends using cumulative exposure. METHODS: Simulations were conducted under the assumptions that (i) exposure level is assigned to all workers based on the job-specific means from a sample of workers, (ii) exposure level and duration are log-normal, (iii) the true exposure-response model is log-linear for cumulative exposure, (iv) the disease is rare, and (v) the variance of job-specific exposure level increases with its job-specific mean. Results Assignment of job-specific mean exposure levels from a sample of workers causes an upward bias in the estimated exposure-response trend when there is little variance in the duration of exposure but causes a downward bias when duration has a large variance. This bias can be substantial (eg, 30-50%). CONCLUSIONS: Berkson errors in exposure result in little bias in estimating exposure-response trends when the standard deviation of duration is approximately equal to its mean, which is common in many occupational studies. No bias occurs when the variance of exposure level is constant across jobs, but such conditions are probably uncommon.

Humans↗
PubMed1981

The role of linear models in psychiatric epidemiology.

The aim of this paper is to explain and to stress the importance of mathematical models and, in particular, linear models in the field of psychiatric epidemiology. An awareness of linear models is essential in contemplating the use of statistics of analyse epidemiological survey data, and in many cases the appropriate linear model is by far the most effective way of summarizing such data.

Adult↗
PubMed1989

Estimation and comparison of changes in the presence of informative right censoring: conditional linear model.

A general linear regression model for the usual least squares estimated rate of change (slope) on censoring time is described as an approximation to account for informative right censoring in estimating and comparing changes of a continuous variable in two groups. Two noniterative estimators for the group slope means, the linear minimum variance unbiased (LMVUB) estimator and the linear minimum mean squared error (LMMSE) estimator, are proposed under this conditional model. In realistic situations, we illustrate that the LMVUB and LMMSE estimators, derived under a simple linear regression model, are quite competitive compared to the pseudo maximum likelihood estimator (PMLE) derived by modeling the censoring probabilities. Generalizations to polynomial response curves and general linear models are also described.

Analysis of Variance↗
PubMed2005

Atopy, asthma, and experimental approaches based on the linear model of T cell maturation.

The linear model of maturation of IFN-gamma-producing cells from a proliferative pool of type 2 cytokine-producing T cells represents a fundamental shift in interpreting how changes in cytokine production by T cell populations are regulated. A major tenet of this model is antigen-independent, bystander proliferation of type 2 T cells and their maturation to IFN-gamma+ cells. Both clinical observations and prevailing theories of immune system development in asthma are consistent with this highly interpretative in vitro model, which allows unambiguous characterization of the modulation of the intrinsic features of T cell proliferation and differentiation by environmental and genetic factors. Hypotheses based on the linear model of T cell maturation are readily testable and should lead to a greater understanding of not only allergen-specific responses, but also the non-specific, bystander effects associated with specific responses to allergens or pathogens. Topics to be discussed in the context of the linear model of T cell maturation in this review include: (1) allergic responses to an inciting allergen that may enhance sensitivity to subsequent yet different allergens; (2) dampening the preferential accumulation of type 2 T cells during a typical immune response against viral and bacterial pathogens; (3) allergen-independent sensitization in asthmatics: (4) the 'hygiene hypothesis' for the reported increased allergy development in industrialized countries; (5) elevated IFN-gamma levels in asthmatics, in addition to the expected high levels of type 2 cytokines; (6) testing the effects of inflammatory mediators, as well as various anti-inflammation therapies on T cell maturation; and (7) testing the influence of gene variation on T cell maturation.

Asthma↗
PubMed2002

Hierarchical-likelihood approach for mixed linear models with censored data.

Mixed linear models describe the dependence via random effects in multivariate normal survival data. Recently they have received considerable attention in the biomedical literature. They model the conditional survival times, whereas the alternative frailty model uses the conditional hazard rate. We develop an inferential method for the mixed linear model via Lee and Nelder's (1996) hierarchical-likelihood (h-likelihood). Simulation and a practical example are presented to illustrate the new method.

Animals↗
PubMed1988

Light adaptation in the turtle retina: embedding a parametric family of linear models in a single nonlinear model.

A method for constructing nonlinear models for light adaptation in the retina is introduced. The components of the models are linear filters and static (instantaneous) nonlinear elements configured in a feedback arrangement. The signals in the models are combined through algebraic addition or multiplication. We apply the method to model light adaptation measured in turtle horizontal cells. Given a particular wiring diagram for the components, the functional forms of the static nonlinearities and frequency responses of the linear filters are determined by constraining the model to give temporal frequency responses (linear regime behavior) consistent with a family of linear feedback models which has been shown to provide a good description of adaptation in these cells. Two particular models, quite different in structure, are presented. Each model responds to perturbations around a mean light level as a feedback circuit in which the gain (strength) of feedback is adjusted to be proportional to the mean light level, but neither model has a separate pathway for measuring the mean light level. Thus, each of these nonlinear models embeds an entire family of linear models parametric in mean light level. Harmonic distortion in the responses of these models to sinusoidal input is found to be qualitatively consistent with physiological data. An alternative class of nonlinear models in which feedback gain is set by a separate slow pathway which tracks the mean light level is ruled out on the basis of its incorrect steady-state input-output behavior. The methods presented can be used to develop specific physical models for light adaptation based on the chemical kinetics of phototransduction or on nonlinear neural feedback. The relevance of the nonlinear models and construction techniques to modeling phototransduction is discussed.

Adaptation, Ocular↗
PubMed1999

Maximum likelihood analysis of generalized linear models with missing covariates.

Missing data is a common occurrence in most medical research data collection enterprises. There is an extensive literature concerning missing data, much of which has focused on missing outcomes. Covariates in regression models are often missing, particularly if information is being collected from multiple sources. The method of weights is an implementation of the EM algorithm for general maximum-likelihood analysis of regression models, including generalized linear models (GLMs) with incomplete covariates. In this paper, we will describe the method of weights in detail, illustrate its application with several examples, discuss its advantages and limitations, and review extensions and applications of the method.

Algorithms↗
PubMed1998

Modeling development of sleep-wake behaviors: I. Using the mixed general linear model.

The purpose of this paper is to demonstrate the use of the mixed general linear model (MixMod) for modeling development of sleep-wake behaviors in preterm infants. The mixed general linear model allows the concurrent identification of both group and individual developmental patterns in longitudinal data sets with inconsistently timed data, irregularly timed data, and randomly missing values. This statistical technique is well suited to data from preterm infants because these infants enter and leave longitudinal studies at varying times depending on their health status. One sleep organizational variable--the regularity of respiration in quiet sleep--obtained from a study of 37 preterm infants was used as an example. Seven infant characteristics were used as covariates. The various steps involved in conducting a mixed model analysis of this variable are illustrated. The strengths and limitations of this technique are discussed.

Aging↗
PubMed2005

Modeling local item dependence with the hierarchical generalized linear model.

Local item dependence (LID) can emerge when the test items are nested within common stimuli or item groups. This study proposes a three-level hierarchical generalized linear model (HGLM) to model LID when LID is due to such contextual effects. The proposed three-level HGLM was examined by analyzing simulated data sets and was compared with the Rasch-equivalent two-level HGLM that ignores such a nested structure of test items. The results demonstrated that the proposed model could capture LID and estimate its magnitude. Also, the two-level HGLM resulted in larger mean absolute differences between the true and the estimated item difficulties than those from the proposed three-level HGLM. Furthermore, it was demonstrated that the proposed three-level HGLM estimated the ability distribution variance unaffected by the LID magnitude, while the two-level HGLM with no LID consideration increasingly underestimated the ability variance as the LID magnitude increased.

Data Interpretation, Statistical↗
PubMed2006

Structural equation and log-linear modeling: a comparison of methods in the analysis of a study on caregivers' health.

BACKGROUND: In this paper we compare the results in an analysis of determinants of caregivers' health derived from two approaches, a structural equation model and a log-linear model, using the same data set. METHODS: The data were collected from a cross-sectional population-based sample of 468 families in Ontario, Canada who had a child with cerebral palsy (CP). The self-completed questionnaires and the home-based interviews used in this study included scales reflecting socio-economic status, child and caregiver characteristics, and the physical and psychological well-being of the caregivers. Both analytic models were used to evaluate the relationships between child behaviour, caregiving demands, coping factors, and the well-being of primary caregivers of children with CP. RESULTS: The results were compared, together with an assessment of the positive and negative aspects of each approach, including their practical and conceptual implications. CONCLUSION: No important differences were found in the substantive conclusions of the two analyses. The broad confirmation of the Structural Equation Modeling (SEM) results by the Log-linear Modeling (LLM) provided some reassurance that the SEM had been adequately specified, and that it broadly fitted the data.

Adaptation, Psychological↗
PubMed2004

A general linear model for MEG beamformer imaging.

A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields).

Algorithms↗
PubMed2006

Short communication: genetic evaluation of the interval from first to last insemination with survival analysis and linear models.

Sire breeding values for the interval between the first and last insemination were predicted using 4 proportional hazards models (survival analyses) and 2 linear mixed models to determine which would result in a more accurate genetic evaluation. A stochastic simulation describing the reproductive cycle of first-parity cows was conducted, in which true breeding values for conception rate were created. The model included the effects of sire and herd. The highest correlations between true breeding values for conception rate and breeding values for the interval between first and last insemination predicted by the survival analysis model and the linear model were 0.803 and 0.744, respectively. The results showed that when pregnancy status was known, survival models were more accurate than linear models to predict breeding values for conception rate when using observations on the interval between first and last insemination.

Animals↗
PubMed2004

Prediction of myelinated nerve fiber stimulation thresholds: limitations of linear models.

Computer models of neurons are used to simulate neural behavior, and are important tools for designing neural prostheses. Computation time remains an issue when simulating large numbers of neurons or applying models to real time applications. Warman et al. developed a method to predict excitation thresholds for axons using linear models and a predetermined critical voltage. We calculated threshold prediction error as a function of the location of an extracellular electrode using two different axon models to examine further threshold prediction using linear models. Threshold prediction error was low (<3% error) under the conditions examined by Warman et al., but under more general conditions, threshold prediction error was as high as 23.6%. Linear models were limited as effective tools for single fiber threshold prediction because accuracy was dependent on the nonlinear and linear models used, and any parameter that affected the extracellular potential distribution. Threshold prediction could be improved by appropriately choosing the membrane conductance of the linear model, but determination of an optimal conductance was computationally expensive. Finally, although single fiber threshold prediction error was partially masked when considering the input-output (I/O) properties of populations of axons, relatively large errors still occurred in population I/O curves generated with linear models.

Axons↗
PubMed1989

Clinical expert systems versus linear models: do we really have to choose?

This article deals with decision subsystems at the level of the organism. In recent years there has been debate as to whether linear models or clinical expert systems make clinical decisions more effectively. Previous articles in this journal have favored linear models. This article argues the opposite case. We show that expert systems are not necessarily more expensive or less accurate than linear models and that, in theory at least, they can perform many tasks that are beyond the scope of linear models. Indeed, while a linear model may serve as a subsystem of a human or computer expert system, an expert system cannot be seen as a subsystem of a linear model. We conclude that clinical expert systems and linear models are not interchangeable and users should not be forced to choose between them.

Artificial Intelligence↗
PubMed1996

Transfer factor (diffusing capacity) standardized for alveolar volume: validation, reference values and applications of a new linear model to replace KCO (TL/VA)

Transfer factor (TL) varies with alveolar volume (VA), but not in the manner implied by the carbon monoxide transfer coefficient (KCO (TL/VA)). This paper considers two other simple models (one linear and one exponential) which might standardize TL for VA, and asks the questions: 1) Is either model valid? 2) What are appropriate reference values? and 3) Will the model be useful? The relationship of TL to VA within subjects at different depths of inspiration, and between subjects having lungs of different sizes, were measured and compared. The subjects were asymptomatic, nonsmoking, Caucasian adults, including 31 males assessed in the laboratory and 503 male and female participants in population studies. The linear partial regression coefficients of TL on VA (L corrected for body temperature, atmospheric pressure and water saturation (BTPS)) standardized for height (H) in metres, were similar within- and between-subjects; the coefficients applied over a wide range of values for VA. This was not the case for the exponential model. The resulting reference equations in SI units for males and females were: TL = 11.52 H + 2.72 VA.H-2 - 0.051 Age -12.35. RSD 1.17; and TL = 4.87 H + 2.29 VA.H-2 - 0.019 Age -3.03. RSD 0.92, respectively. The residual standard deviations (RSD) about the new relationships were less than in other series. The new linear model could account for much of the variation between different published reference values for TL; it could be useful clinically, in circumstances when VA deviates from the norm. The model does not explain differences in TL associated with gender. Inclusion of VA.H-2 as a covariate in the reference equation for transfer factor, in addition to age and height, improves the accuracy of prediction of normal transfer factor compared with current reference values; its use suggests that some of the differences between published values is due to the volume term. The equations can be used clinically, and eliminate the need for carbon monoxide transfer coefficient.

Adult↗
PubMed2006

Bivariate analysis of number of services to conception and days open in Norwegian red using a censored threshold-linear model.

A bivariate censored threshold-linear model was used to study genetic parameters of number of services to conception (STC) and days open (DO) in first-lactation Norwegian Red (NRF) cows. Records of 1,454,916 NRF cows, with a first insemination from 1980 to 2004, were analyzed. It was assumed that every cow had at least a first insemination. The number of inseminations was recorded until a cow conceived or was culled, whichever occurred first. If a cow was culled before conception, it was considered censored at the number of services until culling was recorded. Twenty-one percent of cows were censored for both STC and DO. Using an univariate probit link function for STC, unobserved liabilities to STC and DO were modeled jointly as a linear function of age at first calving, month-year at first calving, herd-5-yr period, sire of cow and residual effects. Heritability of liability to STC and DO was 4% for each trait. The genetic and residual correlations between STC and DO were 0.77 and 0.68, respectively. There has been little or no genetic change for DO, whereas STC had favorable genetic and phenotypic trends.

Analysis of Variance↗