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PubMed1982

Comparing two head injury treatments by linear logistic model.

A linear logistic model is used to compare the performance of a series of head injured patients treated in Auckland with a series obtained from the International Data Bank (IDB), on head injured patients. The IDB patients were treated along conventional lines of neurosurgical management. The Auckland patients were submitted to a regime of elective artificial ventilation of the lungs and heavy sedation, directed against diffuse brain swelling. Two types of comparison were used. First, a model was constructed from the Auckland data of the relationship of outcome to factors relating to the severity of the head injury. This input-output relationship was used to predict the distributions of outcome in the IDB series. Secondly, a descriptive model on the combined Auckland and IDB data was given the option of selecting a dummy variable to indicate whether the source of the patient, Auckland or IDB, had significantly influenced outcome for a given set of other determinants. Differences between Auckland and IDB were only significant if the severity of the head injury in the IDB cases was represented by the set of scores indicating their best condition over the first 24 hours of coma. The scores indicating the condition of the Auckland patients might be comparable to either the 24 hour best or the 24 hour worst IDB scores. One cannot say whether any differences in input-output relationships between the two series arise from differences in coding the input data or from real differences in outcome for given sets of determinants of outcome.

Adolescent↗
PubMed1998

Local influence in linear mixed models.

The linear mixed model has become an important tool in modelling, partially due to the introduction of the SAS procedure MIXED, which made the method widely available to practising statisticians. Its growing popularity calls for data-analytic methods to check the underlying assumptions and robustness. Here, the problem of detecting influential subjects in the context of longitudinal data is considered, following the approach of local influence proposed by Cook.

Age Factors↗
PubMed1994

Human postmortem interval estimation from vitreous potassium: an analysis of original data from six different studies.

The investigation of the postmortem interval (PMI) by determining potassium levels in the vitreous humor (KV) has been a subject of forensic pathology research for more than a quarter of a century. The numerous studies to date have yielded a variety of linear or piecewise-linear relationships between KV and PMI, i.e., different estimated intercepts and slopes of regression line(s) as well as different reliabilities of these estimates. This lack of agreement is due in part to the variable numbers of cases reported from study to study, differing observed ranges of KV and PMI, and the unaccommodated effects of factors on potassium concentration, including age of subject, amount of urea nitrogen, ambient temperature, and presence of illness. Original data from six of these studies, for a total of 790 cases, are reanalyzed together. The relationship between KV and PMI is not completely linear, and the residual variability of KV as a function of PMI is not constant. Thus, two main assumptions of the simple linear model, linearity and constant variance, are not supported by the data. It is clearly problematic to report statistical summaries such as the slope of an estimated regression line and the reliability of that estimate based on a model with faulty assumptions. Yet even after rescaling the data in an attempt to achieve linearity in the KV-PMI relationship and to stabilize residual variation, the relationship continues to be non-linear and its variability unstable. A new approach is developed for modeling KV and PMI that accommodates non-linearities and changing residual variability. A local regression model, specifically a loess smooth curve, is fitted separately to the data from each of the six studies. The loess smooth curve adapts locally to the changing and possibly non-linear relationship between KV and PMI across their observed ranges. The data from all six studies are then combined to yield a single loess curve with 95% confidence bands. The estimated loess curve and confidence bands are used in an inverse prediction method to construct low, middle and high PMI estimates at given values of KV. The reliability of estimated PMI decreases as KV increases. Although the confidence bands surrounding the overall curve widen in the extreme high end due to there being fewer available data in that region, PMI estimates are more precise over the entire range of KV and PMI than those obtained from any single study alone. A cross-validation procedure provides an independent check of the predictive performance of the method.

Age Factors↗
PubMed2006

Implementation of a combined association-linkage model for quantitative traits in linear mixed model procedures of statistical packages.

A transmission disequilibrium test for quantitative traits which combines association and linkage analyses is currently available in several dedicated software packages. We describe how to implement such models in linear mixed model procedures that are available in widely used statistical packages such as SPSS. We also briefly mention a few extensions of the model that become naturally available once the model is implemented in such procedures.

Diseases in Twins↗
PubMed2006

Bayesian covariance selection in generalized linear mixed models.

The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of predictors that have random effects, random effects selection can be challenging, particularly when outcome distributions are nonnormal. This article proposes a fully Bayesian approach to the problem of simultaneous selection of fixed and random effects in GLMMs. Integrating out the random effects induces a covariance structure on the multivariate outcome data, and an important problem that we also consider is that of covariance selection. Our approach relies on variable selection-type mixture priors for the components in a special Cholesky decomposition of the random effects covariance. A stochastic search MCMC algorithm is developed, which relies on Gibbs sampling, with Taylor series expansions used to approximate intractable integrals. Simulated data examples are presented for different exponential family distributions, and the approach is applied to discrete survival data from a time-to-pregnancy study.

Adult↗
PubMed1995

Derivation of the optimum dose per fraction from the linear quadratic model.

The linear quadratic equation for fractionated radiotherapy has already been adapted to include a time factor for tumour repopulation: loge cell kill (E) is given as a function of dose per fraction (d), number of fractions (n), overall treatment time (T) and the clonogen doubling time (Tp). By incorporating a normal tissue isoeffect and replacing the relationship between T and n by a function f, the equation for E can be rewritten as a more complex function of d. In this form, E and d are continuous variables so that the dose per fraction (d') required to produce maximum values of E for isoeffective late normal tissue effects can be found by differential calculus. The derived equation takes the form (beta kTp-alpha Tp)d2 + 1.386fd + 0.693fk = 0 and when solved for d provides a direct estimation of the optimum dose per fraction. Where normal tissue sparing is possible and the tumour dose z is related to the normal tissue dose d, the optimum dose per fraction z' can be found by solving the equation (beta kTp-alpha gTp)z2 + 1.386fgz + 0.693fk = 0 The results show that a critical minimum dose per fraction is required to counteract rapid tumour clonogen repopulation in both conventional and accelerated radiotherapy. The calculus method is reasonably accurate for larger fraction numbers, when clonogen doubling times are 3.5 days or longer and for conventional radiotherapy given 5 days per week. The model is even more accurate for accelerated hyperfractionated radiotherapy providing that there is complete repair between successive fractions. Where greater normal tissue sparing is possible, as with focal teletherapy methods and brachytherapy, higher tumour doses per fraction can be used to increase further the tumour cell kill without exceeding normal tissue tolerance. These predicted doses per fraction are consistent with clinical experience when the given constraints in terms of frequency of treatment are considered. The model described can be used for tumours in which repopulation occurs at a constant rate throughout treatment. For tumours in which accelerated repopulation occurs, the optimum dose per fraction can be separately calculated for the initial phase of slow repopulation (for which very small doses per fraction are optimal) and also for the second phase of rapid repopulation (for which either accelerated hyperfractionated treatments or hypofractionated focal methods of treatment would be appropriate). The limitations of the model are fully discussed including the need for accurate radiobiological predictive assays. In the future such assays of pre-treatment doubling times and tumour cell radiosensitivities could be used to determine reasonable ranges for the optimum dose per fraction in experimental tumours and subsequently in clinical trails. This approach could produce major improvements in the therapeutic potential of radiotherapy.

Cell Division↗
PubMed1990

Critical determinants of endurance performance in middle-aged and elderly endurance runners with heterogeneous training habits.

The current investigation was designed to determine which factor or what combination of factors would best account for distance running performance in middle-aged and elderly runners (mean age 57.5 years SD +/- 9.7) with heterogeneous training habits. Among 35 independent variables which were arbitrarily selected as possible prerequisites in the distance running performance of these runners, oxygen uptake (VO2) at lactate threshold (LT) (r = 0.781-0.889), maximal oxygen uptake (VO2 max) (r = 0.751 approximately 0.886), and chronological age (r = -0.736-(-)0.886) were found to be the 3 predictor variables showing the highest correlations with the mean running velocity at 5 km (V5km), 10 km (V10km), and marathon (VM). When all independent variables were used in a multiple regression analysis, any 3 or 4 variables selected from among VO2 at LT, chronological age, systolic blood pressure (SBP), atherogenic index (AI), and Katsura index (KI) were found to give the best explanation of V5km, V10km, or VM in a combined linear model. Linear multiple regression equations constructed for predicting the running performances were: V5km = 0.046X1-0.026X2-0.0056X3+5.17, V10km = 0.028X1-0.028X2-0.190X4-1.34X5+6.45, and VM = -0.0400X2-0.324X4-1.16X5+7.36, where X1 = VO2 at LT (ml.min-1.kg-1), X2 = chronological age, X3 = SBP, X4 = AI, and X5 = KI.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed1990

Rates of energy processing by blowflies: the uses for a joule vary with food quality and quantity.

Data on the variation of crop volumes with time for blowflies (Phormia regina Meigen) fed various volumes and concentrations of fructose or sucrose (from Gelperin, 1966, and Edgecomb et al. 1987) were used to characterize energy processing rates to test the assumption of food energy addivity of optimal foraging theories. Six regression models (linear, square root, cube root, hyperbolic, inverse cube root and exponential) were compared for data from Edgecomb et al. (1987) with measurements of crop volumes from 10 min to 5 h after blowflies were fed 9.7 or 14.5 microliters of 0.25 moll-1 sucrose. Only the hyperbolic regression could be discriminated as statistically different, and the linear model was selected as most parsimonious for examining rates of energy processing. About the same volume bypassed the crop for flies fed 9.7 or 14.5 microliters. Volume rates of crop emptying (from Gelperin, 1966) did not change at intermediate concentrations but decreased from lowest and to highest concentrations. Energy processing patterns indicate that long-term storage rates increase with meal size and at intermediate concentrations and decrease (3.0 moll-1 fructose) or remain constant (2.0 moll-1 sucrose) at high concentrations, so the uses for a unit of energy are not additive across concentrations and meal sizes. Animals that process energy in this way should attempt to maximize meal size and include high-energy foods in their diet out of proportion to the amount of energy gained for the time spent foraging.

Animals↗
PubMedDate not supplied

A general approach to mixed effects modeling of residual variances in generalized linear mixed models.

We propose a general Bayesian approach to heteroskedastic error modeling for generalized linear mixed models (GLMM) in which linked functions of conditional means and residual variances are specified as separate linear combinations of fixed and random effects. We focus on the linear mixed model (LMM) analysis of birth weight (BW) and the cumulative probit mixed model (CPMM) analysis of calving ease (CE). The deviance information criterion (DIC) was demonstrated to be useful in correctly choosing between homoskedastic and heteroskedastic error GLMM for both traits when data was generated according to a mixed model specification for both location parameters and residual variances. Heteroskedastic error LMM and CPMM were fitted, respectively, to BW and CE data on 8847 Italian Piemontese first parity dams in which residual variances were modeled as functions of fixed calf sex and random herd effects. The posterior mean residual variance for male calves was over 40% greater than that for female calves for both traits. Also, the posterior means of the standard deviation of the herd-specific variance ratios (relative to a unitary baseline) were estimated to be 0.60 +/- 0.09 for BW and 0.74 +/- 0.14 for CE. For both traits, the heteroskedastic error LMM and CPMM were chosen over their homoskedastic error counterparts based on DIC values.

Analysis of Variance↗
PubMed1988

Prediction of donor-specific transfusion sensitization. I. A linear logistic model.

Using linear logistic regression, six factors were identified as important predictors of risk of DST sensitization in a group of 195 patients. Factors increasing the risk were: percent panel reactive antibody (PRA), previous transplants, and pregnancy; those decreasing the risk were HLA antigens matched, third-party blood transfusions, and Imuran administration. From this analysis, the magnitude of the effect of each factor on the risk of sensitization was obtained. An equation was then obtained that can be used to compute an estimated probability of sensitization (PS) for each patient. As a test of predictive ability of the model, the PS was calculated for 66 patients in an independent patient group. These observations were arranged according to the estimated probability and then divided into intervals of risk. Overall, for each interval, a very high level of agreement was found between the predicted and actual number of sensitized patients. A total of 16.13 patients were predicted to become sensitized and 17 actually did.

Azathioprine↗
PubMed1991

Application of a linear recirculation model to drug targeting.

Current interest in drug targeting has inspired theoretical considerations of its potential and problems. Previously, drug targeting has been considered in terms of more or less elaborate compartmental models. The present paper shows how an equivalent analysis of the potential advantage of drug targeting may be derived with the minimum reliance on a specific model. A linear recirculation model is used to describe the drug concentration profile at some target site and in the rest of the body. Equations for the AUCs of drug and of a drug-carrier conjugate can then be derived. These AUCs are used to define a drug targeting index (DTI), a measure of drug targeting selectivity previously derived from a specific model. It is shown that the DTI can be defined solely in terms of extraction ratios for elimination of free drug, when release of drug is confined to the target site. The expression for DTI is shown to be equivalent to that previously derived from several more model-dependent approaches.

Drug Administration Routes↗
PubMed1997

[Experimental study of response latency of visual search processes and premotor decision latency in dyslexic and non-dyslexic children. Model of linear regression: derived parametric estimates].

BACKGROUND: For some time the question of a visual impairment in dyslexic children has been a source of controversy in the literature. Depending on the method used, the findings point either to receptor or neural impairment or to a visual deficit in information processing. The question remains of whether these findings mask retardation in the motor planning and execution of a response. METHOD: In this investigation 61 children (15 dyslexic boys and 15 dyslexic girls aged 8 years 0 months to 10 years 8 months and 16 non-dyslexic boys and 15 non-dyslexic girls aged 8 years 0 months to 10 years 10 months) were tested using a computer-assisted visual display method (visual scan procedure). The results were included into a linear regression model. RESULTS: Compared to the non-dyslexic children the dyslexic children had a significant retardation in the speed of motor response (MANCOVA, Mann-Whitney U-test). For the "pure" visual process no differences in time course were found. Another important findings is the surprisingly wide range of results obtained for individual dyslexic children. In some instances there were deviations as great as 3.6 sigma (SEM). These findings indicate that we may be dealing with an individual partial impairment. It should be noted that the calculation of the linear regression model cannot be detailed for the group of dyslexic children. The prerequisites for a linear regression model are not satisfied. The comparability of the results is therefore limited. CONCLUSIONS: We cannot assume there will be a manifest visuomotor impairment in all dyslexic children when the stimulus is presented at the center and periphery of the field of vision. However, if such an impairment is present it is highly likely that the findings contain a mixture of retardation of pre-motor and visual decision latency. This would have substantial consequences for therapy, as visuomotor perception training would not be indicated in all instances. Some dyslexic children, both boys and girls, achieve completely "normal" results.

Attention↗
PubMed2002

Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials.

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator-prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator-prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1-12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of illustration we demonstrate an application of the models using real AIDS clinical trial data involving patients treated with a combination of anti-retroviral agents using a model which incorporates compliance data.

Acquired Immunodeficiency Syndrome↗
PubMed1999

Generalized linear mixed models for meta-analysis.

We examine two strategies for meta-analysis of a series of 2 x 2 tables with the odds ratio modelled as a linear combination of study level covariates and random effects representing between-study variation. Penalized quasi-likelihood (PQL), an approximate inference technique for generalized linear mixed models, and a linear model fitted by weighted least squares to the observed log-odds ratios are used to estimate regression coefficients and dispersion parameters. Simulation results demonstrate that both methods perform adequate approximate inference under many conditions, but that neither method works well in the presence of highly sparse data. Under certain conditions with small cell frequencies the PQL method provides better inference.

Humans↗
PubMed2002

Dynamic conditionally linear mixed models for longitudinal data.

We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within-subject covariance matrix using a special Cholesky decomposition. Here 'dynamic' means using past responses as covariates and 'conditional linearity' means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited.

Antidepressive Agents↗
PubMed1985

Biochemical diagnosis of alcoholism in men psychiatric patients.

A comparison was conducted of several discriminant models (linear, stepwise linear and quadratic) using two definitions of prior probability (proportional and equal) to detect alcoholism on the basis of routine blood test results. Discriminant functions were derived on a sample of men alcoholic (N = 407) and nonalcoholic (N = 1068) psychiatric patients, and were cross-validated on an independent sample of the same two populations (NS = 365 and 1020, respectively). Linear discriminant models generally outperformed quadratic models. The best classification was obtained by the equal stepwise linear model that retained SGOT, calcium, albumin, inorganic phosphate and BUN. The best quadratic model (equal) achieved good overall accuracy but weak sensitivity. The linear model was relatively accurate in terms of classification, and better sensitivity was achieved with the five best predictors than with all available measures.

Adult↗
PubMed2000

Foundation for nonlinear models with thresholds for longitudinal data.

Threshold models first appeared in the literature nearly half a century ago. Threshold segments have been added to many commonly used forms of models from linear models and generalized linear models through mixed models for the analysis of cross-sectional data. Nonlinear models with thresholds for cross-sectional data are less prevalent in the literature. Nonlinear models with thresholds for longitudinal data are new. The historical developments leading to this point are reviewed as a means of introducing terms necessary for discussing features of these newer models. Nonlinear models for longitudinal data with thresholds are presented and discussed.

Algorithms↗