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PubMed1995

Multivariate contingency tables and the analysis of exchangeability.

There are settings in the social and health sciences where it is natural to question whether a collection of discrete random variables is exchangeable. In this paper the inter-relationships between parameter symmetry, parameter invariance, and exchangeable discrete random variables are investigated within the log-linear models framework. We demonstrate how log-linear models can be used to formulate and test hypotheses of various forms of exchangeability, and to characterize departures from exchangeability. Conditions under which the observed cross-classification collapses into a lower dimensional cross-classification, while preserving the essential probability structure of the higher dimensional cross-classification, and the model structure of this lower dimensional cross-classification are presented. The development is sufficiently general to allow for subsetting the variables into classes, which is important for some applications. For example, in studying the spatial clustering of periodontal disease, there is interest in studying differences among disease patterns between the upper and lower arches in terms of parameter symmetry, parameter invariance, and exchangeability. Cross-sectional periodontal disease data from a study of Pima Indians residing in the Gila River Indian Community are used to illustrate how log-linear models may be used to examine for exchangeability, and for specific departures from exchangeability.

Adolescent↗

PubMed2002

Wavelet-generalized least squares: a new BLU estimator of linear regression models with 1/f errors.

Long-memory noise is common to many areas of signal processing and can seriously confound estimation of linear regression model parameters and their standard errors. Classical autoregressive moving average (ARMA) methods can adequately address the problem of linear time invariant, short-memory errors but may be inefficient and/or insufficient to secure type 1 error control in the context of fractal or scale invariant noise with a more slowly decaying autocorrelation function. Here we introduce a novel method, called wavelet-generalized least squares (WLS), which is (to a good approximation) the best linear unbiased (BLU) estimator of regression model parameters in the context of long-memory errors. The method also provides maximum likelihood (ML) estimates of the Hurst exponent (which can be readily translated to the fractal dimension or spectral exponent) characterizing the correlational structure of the errors, and the error variance. The algorithm exploits the whitening or Karhunen-Loéve-type property of the discrete wavelet transform to diagonalize the covariance matrix of the errors generated by an iterative fitting procedure after both data and design matrix have been transformed to the wavelet domain. Properties of this estimator, including its Cramèr-Rao bounds, are derived theoretically and compared to its empirical performance on a range of simulated data. Compared to ordinary least squares and ARMA-based estimators, WLS is shown to be more efficient and to give excellent type 1 error control. The method is also applied to some real (neurophysiological) data acquired by functional magnetic resonance imaging (fMRI) of the human brain. We conclude that wavelet-generalized least squares may be a generally useful estimator of regression models in data complicated by long-memory or fractal noise.

Adult↗

PubMed2006

Nonlinear effects on solvation dynamics in simple mixtures.

The authors applied the time dependent density functional method (TDDFM) and a linear model to solvation dynamics in simple binary solvents. Changing the solute-solvent interactions at t=0, the authors calculated the time evolution of density fields for solvent particles after the change (t>0) by the TDDFM and linear model. First, the authors changed the interaction of only one component of solvents. In this case, the TDDFM showed that the solvation time decreased monotonically with a mole fraction of the solvent strongly interacting with the solute. The monotonical decreases agreed with experimental results, while the linear model did not reproduce these results. The authors also calculated the solvation time by changing the interaction of both components. The calculation showed that the mole fraction dependence had the peak. The TDDFM presented a much higher peak than the linear model. The difference between the TDDFM and the linear model was caused by a nonlinear effect on an exchange process of solvent particles.

Journal Article↗

PubMed1999

Computing minimum description length for robust linear regression model selection.

A minimum description length (MDL) and stochastic complexity approach for model selection in robust linear regression is studied in this paper. Computational aspects and implementation of this approach to practical problems are the focuses of the study. Particularly, we provide both algorithms and a package of S language programs for computing the stochastic complexity and proceeding with the associated model selection. A simulation study is then presented for illustration and comparing the MDL approach with the commonly used AIC and BIC methods. Finally, an application is given to a physiological study of triathlon athletes.

Algorithms↗

PubMed1995

Have sperm counts been reduced 50 percent in 50 years? A statistical model revisited.

OBJECTIVE: To reanalyze data that were used in a linear model to predict that mean sperm counts have been reduced globally by approximately 50% in the last 50 years. DESIGN: The mean sperm counts and their temporal distribution were reanalyzed via several different statistical models (quadratic, spline fit, and stairstep). CONCLUSION: There are several reasons why a published linear regression model is inappropriate to infer a 50% reduction in mean sperm counts in the last 50 years. These include [1] the potential selection biases that may have occurred with the 61 assembled studies such that they are not representative of their underlying populations; [2] the likely variability in collection methods, in particular, the lack of adherence to a minimum prescribed abstinence period, as has been stated for the largest study, which contained 29.7% of all the subjects included in the analysis; [3] the paucity of data in the first 30 years of the 50-year trend analysis; [4] the fact that if the last 20 years of data are examined, which contains 78.7% of all the studies and 88.1% of the total number of subjects, there is no decrease in sperm counts, in fact, sperm counts were observed to have increased; [5] the conflicting data from a large individual laboratory, which was not prone to the collection variability that likely occurred between the 61 studies, that did not suggest a decline in mean sperm count or seminal volume during a comparable time period, even though this laboratory published the data that were largely responsible for the high historical values in the linear model; and, most importantly, [6] the variety of other mathematical models that perform statistically better at describing the recent data than the linear model and thus offer substantially different hypotheses. The data are only robust during the last 20 years of the analysis, in which all the models, except the linear model, suggest constant or slightly increasing sperm counts.

Female↗

PubMedDate not supplied

Multivariate linear mixed models for multiple outcomes.

We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of exposure across outcomes. In contrast to the Sammel-Ryan model, the MLMM separates the mean and correlation parameters so that the mean estimation will remain reasonably robust even if the correlation is misspecified. The model is applied to birth defects data, where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls.

Abnormalities, Drug-Induced↗

PubMed2000

Estimation of regression parameters and the hazard function in transformed linear survival models.

An estimator of the regression parameters in a semiparametric transformed linear survival model is examined. This estimator consists of a single Newton-like update of the solution to a rank-based estimating equation from an initial consistent estimator. An automated penalized likelihood algorithm is proposed for estimating the optimal weight function for the estimating equations and the error hazard function that is needed in the variance estimator. In simulations, the estimated optimal weights are found to give reasonably efficient estimators of the regression parameters, and the variance estimators are found to perform well. The methodology is applied to an analysis of prognostic factors in non-Hodgkin's lymphoma.

Analysis of Variance↗

PubMed2001

Linear mixed models with flexible distributions of random effects for longitudinal data.

Normality of random effects is a routine assumption for the linear mixed model, but it may be unrealistic, obscuring important features of among-individual variation. We relax this assumption by approximating the random effects density by the seminonparameteric (SNP) representation of Gallant and Nychka (1987, Econometrics 55, 363-390), which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may be carried out using standard optimization techniques. We demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simulation and using longitudinal data from the Framingham study.

Biometry↗

PubMed1999

[Analysis of longitudinal Gaussian data with missing data on the response variable].

BACKGROUND: Using an application and a simulation study we show the bias induced by missing data in the outcome in longitudinal studies and discuss suitable statistical methods according to the type of missing responses when the variable under study is gaussian. METHOD: The model used for the analysis of gaussian longitudinal data is the mixed effects linear model. When the probability of response does not depend on the missing values of the outcome and on the parameters of the linear model, missing data are ignorable, and parameters of the mixed effects linear model may be estimated by the maximum likelihood method with classical softwares. When the missing data are non ignorable, several methods have been proposed. We describe the method proposed by Diggle and Kenward (1994) (DK method) for which a software is available. This model consists in the combination of a linear mixed effects model for the outcome variable and a logistic model for the probability of response which depends on the outcome variable. RESULTS: A simulation study shows the efficacy of this method and its limits when the data are not normal. In this case, estimators obtained by the DK approach may be more biased than estimators obtained under the hypothesis of ignorable missing data even if the data are non ignorable. Data of the Paquid cohort about the evolution of the scores to a neuropsychological test among elderly subjects show the bias of a naive analysis using all available data. Although missing responses are not ignorable in this study, estimates of the linear mixed effects model are not very different using the DK approach and the hypothesis of ignorable missing data. CONCLUSION: Statistical methods for longitudinal data including non ignorable missing responses are sensitive to hypotheses difficult to verify. Thus, it will be better in practical applications to perform an analysis under the hypothesis of ignorable missing responses and compare the results obtained with several approaches for non ignorable missing data. However, such a strategy requires development of new softwares.

Data Interpretation, Statistical↗

PubMed2002

In vivo detection of striatal dopamine release during reward: a PET study with [(11)C]raclopride and a single dynamic scan approach.

A new simple method is proposed to detect, using PET and [(11)C]raclopride, changes in striatal extracellular dopamine concentration during a rewarded effortful task. This approach aimed to increase the sensitivity in detection of these effects. It requires a single-dynamic PET study and combines the classic kinetic compartmental model with the general linear model of SPM to provide statistical inference on changes in [(11)C]raclopride time-activity curve due to endogenous dopamine release during two short periods of activation. Kinetic simulations predicted that 100% dopamine increase during two 5-min periods starting at 30 and 60 min after the injection can be detected. Moreover the effects of dopamine release on the [(11)C]raclopride time-activity-curve are different from those induced by CBF increase. These simulated curves were used to construct the statistical linear model and to test voxel-by-voxel in healthy subjects the hypothesis that dopamine is released in the ventral striatum during periods of unexpected monetary gains, but not during periods of unexpected monetary loss. The experimental results are in line with the expected results although the amplitude of the effects due to dopamine release is moderate. The advantages and the limits of this method as well as the relevance of the results for dopamine involvement in reward processing are discussed.

Adult↗

PubMed1991

Predictors of outcome in children hospitalized with maxillofacial infections: a linear logistic model.

The purpose of this study was to determine factors predictive of clinical outcome for pediatric patients with maxillofacial infections. Using linear logistic regression, four important variables, age, admission temperature, admission white blood cell count, and source of infection, were identified. Relevant study variables were abstracted from the records of all children less than 15 years old admitted to San Francisco General Hospital (SFGH) with facial infections between 1982 and 1986 (n = 105). An unfavorable clinical outcome was defined as a length of hospital stay (LOS) greater than or equal to 4 days and/or the need for an operation to resolve the infection. A favorable outcome was a LOS less than 4 days and no operation. To develop and validate the linear logistic model, the original group of patients (n = 105) was divided into index and validation sets. The index set was created by randomly selecting 80 of the original patients. The model was then applied to a validation set of the 25 remaining children. The model predicted that 13.95 of the patients in the validation set would have an unfavorable outcome. The actual number of unfavorable outcomes was 16. To further test the model's validity, a third data set was collected. It was composed of pediatric patients admitted to SFGH between January 1, 1987 and June 30, 1989 (n = 24). The model predicted that 15.99 of these patients would have an unfavorable outcome; 17 patients actually did have an unfavorable outcome.(ABSTRACT TRUNCATED AT 250 WORDS)

Bacterial Infections↗

PubMed2004

[Analysis on the trend of long-term change of blood pressure in hypertensive patients treated with benazepril].

OBJECTIVE: To introduce the application of mixed linear model in the analysis of secular trend of blood pressure under antihypertensive treatment. METHODS: A community-based postmarketing surveillance of benazepril was conducted in 1831 essential hypertensive patients (age range from 35 to 88 years) in Shanghai. Data of blood pressure was analyzed every 3 months with mixed linear model to describe the secular trend of blood pressure and changes of age-specific and gender-specific. RESULTS: The changing trends of systolic blood pressure (SBP) and diastolic blood pressure (DBP) were found to fit the curvilinear models. A piecewise model was fit for pulse pressure (PP), i.e., curvilinear model in the first 9 months and linear model after 9 months of taking medication. Both blood pressure and its velocity gradually slowed down. There were significant variation for the curve parameters of intercept, slope, and acceleration. Blood pressure in patients with higher initial levels was persistently declining in the 3-year-treatment. However blood pressures of patients with relatively low initial levels remained low when dropped down to some degree. Elderly patients showed high SBP but low DBP, so as with higher PP. The velocity and sizes of blood pressure reductions increased with the initial level of blood pressure. CONCLUSION: Mixed linear model is flexible and robust when applied to the analysis of longitudinal data but with missing values and can also make the maximum use of available information.

Adult↗

PubMed2003

Recursive prediction of broiler growth response to feed intake by using a time-variant parameter estimation method.

The objective of this study was to explore whether time-variant parameter estimation procedures allow modeling and predicting the dynamic growth response of broiler chickens to feed intake in real time. A recursive linear model was used that estimated the model parameters every 24 h based on a fixed number of actual and past measurements (i.e., time window). Based on 48 datasets, it was concluded that the mean relative prediction error (MRPE) of the recursive linear modeling approach had a minimum for a window size of 5 d. Weight of the birds could be predicted during the growth process 3 to 7 d ahead with a mean relative prediction error of 5% or less. In comparison with the prediction results of three static empirical growth models (one linear and two nonlinear models), the recursive modeling technique had a similar accuracy to the nonlinear empirical models (MRPE of 1.4% to 2.3% vs. 1.1% to 2.8%), but it was less accurate for larger prediction horizons (2 to 7 d). The compact recursive linear model was more accurate than the static linear growth model for prediction horizons of one up to 4 d, depending on the feeding strategy. Since such recursive modeling approach allows the prediction of broiler growth without any prior knowledge of the system and takes into account the time-variant (nonlinear) nature of the growth process based on only a small window of measured information, it is suitable for real-time integration in process management.

Animal Nutritional Physiological Phenomena↗

PubMed2003

Sleep disordered breathing may not be an independent risk factor for diabetes, but diabetes may contribute to the occurrence of periodic breathing in sleep.

OBJECTIVE(S): (a) To determine if self-reported diabetes mellitus is independently associated with sleep-disordered breathing (SDB); (b) to determine if diabetes mellitus is specifically associated with central sleep apnea including periodic breathing (Cheyne-Stokes breathing pattern) during sleep. STUDY POPULATION: The study population reflected participants in the on-going Sleep Heart Health Study (SHHS). Analyses were conducted utilizing data obtained from 4872 SHHS participants without prevalent cardiovascular disease (CVD) and 1002 participants with self-reported CVD, defined as hospitalization for non-fatal coronary heart disease, congestive heart failure, myocardial infarction, coronary artery bypass graft, and stroke. METHODS: SHHS methodologies have been previously reported and include performance of overnight, in-home polysomnography (PSG), which recorded variables reflecting sleep architecture and breathing, permitting identification of obstructive and central apneas, hypopneas, periodic breathing and oxyhemoglobin saturation (SpO(2)). Anthropomorphic metrics as well as systemic blood pressure measurements were obtained at the time of PSG. Other health data were available from questionnaires and the data sets of the parent cohorts from whom SHHS participants were recruited. The investigators assessed and compared breathing parameters, sleep architecture and CVD variables in diabetic and non-diabetic participants. The relationships between diabetes and the various study parameters, independent of potential confounders, were examined by multivariable modeling. Linear regression modeling was employed to examine the relationship between continuously distributed variables such as respiratory disturbance index log (RDI). The relationships between diabetes and dichotomous outcome variables such as central apnea index (CAI), obstructive apnea index (OAI), periodic breathing and the percentage of time spent at various levels below SpO(2) 90% were examined by the logistic regression model. Age, gender, race, BMI and neck circumference were forced into all multivariable analyses since these factors are associated with both diabetes mellitus and SDB. RESULTS: The investigators reported that the prevalence of CVD risk factors including increased BMI, waist circumference, neck circumference, triglycerides, reduced HDL cholesterol and hypertension was greater in diabetic than non-diabetic participants. Native Americans represented a disproportionately high percentage of the diabetic population. Unadjusted data obtained from participants without prevalent CVD indicated that the mean RDI was higher in the diabetic participants. Moreover, there was a greater percentage of diabetic participants in the higher RDI categories (e.g. 23.8% of the 470 diabetics and 15.6% of the 4402 non-diabetics had RDI>15, P<0.001). Similarly, the unadjusted data indicated that a significantly greater proportion of the diabetic participants spent >5% and >10% of sleep time below SpO(2) 90%, compared with the non-diabetic participants. The unadjusted data from participants without prevalent CVD indicated that the diabetic and non-diabetic participants did not differ with regard to distribution by category of OAI severity (e.g. > or =2 events/h, > or =3 events/h, or > or =4 events/h). On the other hand, although the prevalence of central apneas was low, a significantly greater proportion of diabetic participants were in the CAI categories (> or =2 events/h and > or =3 events/h) than non-diabetic subjects. There was no difference between diabetic and non-diabetic individuals with regard to CAI prevalence in the > or =4 events/h category. Of note, a greater percentage of diabetic patients exhibited periodic breathing (3.8% vs. 1.8%, diabetic and non-diabetic participants, respectively, P=0.002). Repeating the above analyses with inclusion of the participants with prevalent CVD did not change these relationships, and in fact, the differences between diabetic and non-diabetic participants with respect to central events and periodic breathing became more evident (the data forre evident (the data for this were not provided in the paper). Linear regression analyses demonstrated that BMI, age and male gender were independently related to increased RDI among participants without prevalent CVD. Furthermore, after adjusting for age, gender, race, BMI and neck circumference, there was no difference in geometric mean RDI between the diabetic and non-diabetic participants. The adjusted odds of having RDI> or =15 and the adjusted odds for spending> or =5% or > or =10% of sleep time with SpO(2) <90% did not differ between the diabetic and non-diabetic individuals. The investigators also examined sleep architecture in the study cohort. There were no differences between the diabetic and non-diabetic groups with regard to the adjusted proportion of time spent in non-REM sleep stages, although the mean percent time spent in REM sleep was 1.1% less in the diabetic individuals. The findings were the same with or without inclusion of participants with known CVD. Even after adjustment for potential confounders, in a sample without or with prevalent CVD, diabetic participants had increased adjusted odds for periodic breathing odds ratio (1.8, 95% confidence interval (CI) with a range of 1.02--3.15 in diabetic participants without prevalent CVD vs. 1.74, 95% CI with a range of 1.16--2.62 in diabetic participants with prevalent CVD). There was a suggestion of increased odds for CAI in diabetic subjects when analyzing populations with and without prevalent CVD. CONCLUSION: The authors concluded that diabetes mellitus is associated with sleep apnea but that this association is largely explained by risk factors in common for both disorders, most notably obesity. After adjusting for confounding factors there was no difference between diabetic and non-diabetic participants with regard to obstructive events. However, even after adjusting for potential confounders, there was a greater prevalence of periodic breathing in diabetic subjects. Although not reaching statistical significance, there was a suggestion of an increased prevalence of central events in the diabetic population, particularly when the sample included participants with known CVD. The investigators believed it unlikely that the findings were attributable to underlying congestive heart failure in as much as the diabetic subjects without prevalent CVD exhibited increased prevalence of periodic breathing and possibly increased central events. The authors proposed that diabetes mellitus might be a cause of SDB, mediated through autonomic neuropathy that may alter ventilatory control mechanisms. In this context, the authors commented that autonomic neuropathy may cause perturbations in ventilatory control by altering chemoreceptor gain or altering cardiovascular function (although the authors discounted underlying congestive heart failure as an explanation for the higher prevalence of periodic breathing in diabetic participants). To reinforce their conclusions, the authors cited the literature indicating increased prevalence of sleep apnea in diabetic patients with autonomic dysfunction, as well as the association between Shy--Drager syndrome, in which autonomic insufficiency is a constitutive element, and central sleep apnea.

Journal Article↗

PubMed2007

An autoregressive linear mixed effects model for the analysis of longitudinal data which show profiles approaching asymptotes.

In longitudinal data, a continuous response sometimes shows a profile approaching an asymptote. For such data, we propose a new class of models, autoregressive linear mixed effects models in which the current response is regressed on the previous response, fixed effects, and random effects. Asymptotes can shift depending on treatment groups, individuals, and so on, and can be modelled by fixed and random effects. We also propose error structures that are useful in practice. The estimation methods of linear mixed effects models can be used as long as there is no intermittent missing.

Azathioprine↗

PubMed2004

Modelling of cardiac imaging data with spatial correlation.

Cardiac imaging with single photon emission computed tomography (SPECT) is a common approach for quantifying myocardial perfusion. Fusing serial SPECT studies allows detection and quantification of changes in myocardial perfusion such as those resulting from disease progression or successful treatment therapy for patients with coronary artery disease. The abundance of data for each subject along with the inherent intra-subject correlation due to spatial proximity of multiple perfusion measurements present special analytical challenges. We utilize a standard physiological model of the left ventricle (LV) to construct a general statistical model for cardiac perfusion that incorporates spatial correlation. We illustrate the use of mixed effects models and linear models with correlated errors to estimate myocardial perfusion counts and to compare these counts across serial studies. We address different types of spatial correlation among perfusion measurements in the LV, and we consider various parametric structures for these correlations. We apply the model to data from serial SPECT studies conducted while subjects were in both restful and stressful states approximately two days and one year following a myocardial infarction.

Coronary Circulation↗

PubMed1989

Pharmacodynamic modeling of digoxin-induced bradycardia.

Digoxin-induced bradycardia in dogs was used to evaluate several pharmacodynamic models. Digoxin plasma concentrations and response were monitored in beagle dogs administered either 0.05 or 0.025 mg/kg of digoxin iv as an infusion over 5 min. The models investigated were the linking model, the linear model, the effect compartment model, and the inhibitory model. Regression procedures for investigating the effect compartment model were conducted with Emax (the maximal response, where response was the percentage decrease in heart rate) as a variable with an upper bound of 100%, with a constant value of 100%, or alternately with a constant value equal to the maximal observed response. Based on statistical criteria the effect model using Emax as a variable was found to be the best model for describing digoxin-induced bradycardia. For the effect compartment model, CPss(50) (concentration at steady state that will produce 50% of the maximal response) ranged from 3.8-9.8 ng/ml; delta (exponent describing the steepness of the concentration-response relationship) ranged from 0.6-7.1. The implication of these models in understanding concentration-effect relationships are discussed.

Animals↗

PubMed2005

Real-time ocular artifact suppression using recurrent neural network for electro-encephalogram based brain-computer interface.

The paper presents an adaptive noise canceller (ANC) filter using an artificial neural network for real-time removal of electro-oculogram (EOG) interference from electro-encephalogram (EEG) signals. Conventional ANC filters are based on linear models of interference. Such linear models provide poorer prediction for biomedical signals. In this work, a recurrent neural network was employed for modelling the interference signals. The eye movement and eye blink artifacts were recorded by the placing of an electrode on the forehead above the left eye and an electrode on the left temple. The reference signal was then generated by the data collected from the forehead electrode being added to data recorded from the temple electrode. The reference signal was also contaminated by the EEG. To reduce the EEG interference, the reference signal was first low-pass filtered by a moving averaged filter and then applied to the ANC. Matlab Simulink was used for real-time data acquisition, filtering and ocular artifact suppression. Simulation results show the validity and effectiveness of the technique with different signal-to-noise ratios (SNRs) of the primary signal. On average, a significant improvement in SNR up to 27 dB was achieved with the recurrent neural network. The results from real data demonstrate that the proposed scheme removes ocular artifacts from contaminated EEG signals and is suitable for real-time and short-time EEG recordings.

Artifacts↗