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PubMed2004

SAS macros for estimation of the cumulative incidence functions based on a Cox regression model for competing risks survival data.

When considering competing risks survival data, the cause specific hazard functions are often modelled by the proportional hazards Cox regression model. First, we present how to estimate the parameters in this model when some of the covariates are allowed to have exactly the same effect on several causes of failure. In many cases, the focus is not on the parameter estimates, but rather on the probability of observing a failure from a specific cause for individuals with specified covariate values. These probabilities, the cumulative incidences, are not simple functions of the parameters and they are, so far, not provided by the standard statistical software packages. We present two SAS macros: a SAS macro named CumInc for estimation of the cumulative incidences and a SAS macro named CumIncV for estimation of the cumulative incidences and the variances of the estimated cumulative incidences. The use of the macros is demonstrated through an example.

Proportional Hazards Models↗

PubMed2003

Use of a random coefficient regression (RCR) model to estimate growth parameters.

We used a random coefficient regression (RCR) model to estimate growth parameters for the time series of observed serum glucose levels in the Replicate 1 of the Genetic Analysis Workshop 13 simulated data. For comparison, a two time-point interval was also selected and the slope between these two observations was calculated. This process yielded four phenotypes: the RCR growth phenotype, a two time-point slope phenotype, and Time 1 and Time 2 serum glucose level phenotypes. These four phenotypes were used for linkage analyses on simulated chromosomes 5, 7, 9, and 21, those chromosomes that contained loci affecting the growth course for serum glucose levels. The linkage analysis of the RCR-derived phenotype showed overwhelming evidence for linkage at one locus (LOD 65.78 on chromosome 5), while showing elevated but nonsignificant LOD scores for two other loci (LOD 1.25 on chromosome 7, LOD 1.10 on chromosome 9), and no evidence of linkage for the final locus. The two time-point slope phenotype showed evidence for linkage at one locus (LOD 4.16 on chromosome 5) but no evidence for linkage at any of the other loci. A parallel cross-sectional approach, using as input phenotypes the endpoints of the two-point slope phenotype, gave strong linkage results for the major locus on chromosome 5 (maximal LOD scores of 17.90 and 27.24 for Time 1 and Time 2, respectively) while showing elevated but nonsignificant linkage results on chromosome 7 (maximal LOD scores of 1.71 and 1.48) and no evidence for linkage at the two remaining loci. The RCR growth parameter showed more power to detect linkage to the major locus than either the cross-sectional or two-point slope approach, but the cross-sectional approach gave a higher maximal LOD score for one of the minor loci.

Adult Children↗

PubMed2004

New hybrid stochastic-deterministic technique for fast registration of dermatological images.

Digital image processing in the medical field has become very popular in recent years owing to the significant advantages it offers over conventional techniques of visual or analogue image analysis. One of the most significant aspects in medical image processing has been that of image registration, which deals with the task of registering two images taken under different conditions. Image registration is considered an important issue in the field of dermatology, as pictures of a lesion taken in different periods need to be compared and quantitatively analysed. A hybrid image registration scheme was developed and evaluated for dermatological applications. The method splits the parameter estimation problem into two, with a combination of deterministic and iterative estimation techniques. The scaling and rotation parameters are estimated using a cross-correlation of image invariant image descriptors algorithm, whereas the two translation parameters are estimated with a non-parametric similarity criterion and a hill-climbing optimisation scheme. The efficacy of the method has been validated for the registration and comparison of malignant melanoma images. Determination of rotation and scaling parameters was performed using the log-polar transformation technique, which proved to be very accurate, even when high rotation and scaling values were imposed. Deviations for the rotation parameter estimations were less than 0.5%, whereas, for the scaling factor, differences were on average less than 2.5%, with a maximum difference estimated to be 4.5%. Translation parameter estimation was performed using integer similarity measures namely the stochastic sign change, the deterministic sign change (DSC) and the window value range, the performance of which has been assessed and, in all cases, was found to be highly effective. A novel hill-climbing optimisation algorithm has been proposed and, in combination with the DSC similarity criterion, was evaluated and proved to successfully estimate translation parameters. Thus the proposed hybrid registration technique can successfully estimate problem parameters in a time-efficient manner.

Algorithms↗

PubMed2005

A computer program to estimate the parameters of covariate dependent higher order Markov model.

This paper presents a computer program developed in S-plus to estimate the parameters of covariate dependent higher order Markov Chain and related tests. The program can be applied for two states Markov Chain with any order and any number of covariates depending on the PC capabilities. The program provides the maximum likelihood estimates of the parameters, together with their estimated standard error, t-value and significance level. It also produces the test results for likelihood ratio and model chi-square. To illustrate the program we have used a longitudinal data set on maternal morbidity of rural women in Bangladesh. The occurrences of haemorrhage, convulsion, or fits at different follow-ups were used as outcome variable. Economic status, wanted pregnancy, ages at marriage, and education of women were used as covariates.

Algorithms↗

PubMed1987

Model selection for ventricular mechanics: a sensitivity analysis approach.

Quantitative characterization of left ventricle pump properties has been recognized as being of great significance for both physiological and clinical purposes. Several descriptions have been proposed in the past to this end, where the ventricle is viewed as an isovolumic pressure generator coupled to an internal impedance, considered as either only viscous, only elastic or viscoelastic. Though these models have been used widely, the respective advantages and limits have not been fully elucidated. In this paper, six models for the left ventricular pumping function, of the viscoelastic type, are compared using both simulated and experimental data in a typical parameter estimation approach. Elastic and viscous parameters are estimated starting from ventricular pressure and aortic flow, together with the isovolumic pressure at the same preload. The basis for the comparison is the well-established criterion relating the fit obtained from collected data and the covariance matrix of the parameter estimates. The latter allows evaluation of the so-called indifference region in the parameter space, which is represented by an ellipse if both elastic and viscous elements are present. The properties of the indifference region are synthetically represented by two indices linked to the area and the eccentricity of the ellipse: the first represents the mean accuracy of the parameter estimate, the second gives information about the different sensitivities to variation of single parameters. This comparison, in both simulated and experimental cases, generally leads to preference for a model where elastance and viscosity vary with time in linear proportion to the isovolumically developed ventricular pressure. Appropriate description of the elastic effect reveals it to be very crucial while the viscous effect, though improving the fitting of data, is less critical.

Animals↗

PubMed1978

Recent advances in EEG data processing.

It is argued that the most interesting advances in EEG signal processing are with methods based on descriptive mathematical models of the process. Formulation of auto-regressive (AR) and mixed autoregressive and moving average (ARMA) models is reviewed for the scalar and the multidimensional cases and extensions to allow time-varying coefficients are pointed out. Data processing with parametric models, DPPM, involves parameter estimation and a large number of algorithms are available. Emphasis is put on those that are simple to apply and require a modest amount of computation. A recursive algorithm by Levinson, Robinson and Durbin is well suited for estimation of the coefficients in the AR model and for tests of model order. It is applicable to both the scalar and multidimensional cases. The ARMA model can be handled by approximation of an AR model or by nonlinear optimization. Recursive estimation with AR and ARMA models is reviewed and the connection with the Kalman filter pointed out. In this way processes with time-varying properties may be handled and a stationarity index is defined. The recursive algorithms can deal with AR or ARMA models in the same way. A reformulation of the algorithm to include sparsely updated parameter estimates significantly speeds up the calculations. It will allow several EEG channels to be handled simultaneously in real time on a modern minicomputer installation. DPPM has been particularly successful in the areas of spectral analysis and detection of short transients such as spikes and sharp waves. Recently some interesting attempts have been made to apply classification algorithms to estimated parameters. A brief review is made of the main results in these areas.

Electroencephalography↗

PubMed2006

Developing a realistic sexual network model of chlamydia transmission in Britain.

BACKGROUND: A national chlamydia screening programme is currently being rolled out in the UK and other countries. However, much of the epidemiology remains poorly understood. In this paper we present a stochastic, individual based, dynamic sexual network model of chlamydia transmission and its parameterisation. Mathematical models provide a theoretical framework for understanding the key epidemiological features of chlamydia: sexual behaviour, health care seeking and transmission dynamics. RESULTS: The model parameters were estimated either directly or by systematic fitting to a variety of appropriate data sources. The fitted model was representative of sexual behaviour, chlamydia epidemiology and health care use in England. We were able to recapture the observed age distribution of chlamydia prevalence. CONCLUSION: Estimating parameters for models of sexual behaviour and transmission of chlamydia is complex. Most of the parameter values are highly correlated, highly variable and there is little empirical evidence to inform estimates. We used a novel approach to estimate the rate of active treatment seeking, by combining data sources, which improved the credibility of the model results. The model structure is flexible and is broadly applicable to other developed world settings and provides a practical tool for public health decision makers.

Adolescent↗

PubMed2001

Dual-[11C]tracer single-acquisition positron emission tomography studies.

The ability to study multiple physiologic processes of the brain simultaneously within the same subject would provide a new means to explore the interactions between neurotransmitter systems in vivo. Currently, examination of two distinct neuropharmacologic measures with positron emission tomography (PET) necessitates performing two separate scans spaced in time to allow for radionuclide decay. The authors present results from a dual-tracer PET study protocol using a single dynamic-scan acquisition where the injections of two tracers are offset by several minutes. Kinetic analysis is used to estimate neuropharmacologic parameters for both tracers simultaneously using a combined compartmental model configuration. This approach results in a large reduction in total study time of nearly 2 hours for carbon-11-labeled tracers. As multiple neuropharmacologic measures are obtained at nearly the same time, interventional protocols involving a pair of dual-tracer scans become feasible in a single PET session. Both computer simulations and actual human PET studies were performed using combinations of three different tracers: [11C]flumazenil, N-[11C]methylpiperidinyl propionate, and [ 11 C]dihydrotetrabenazine. Computer simulations of tracer-injection separations of 10 to 30 minutes showed the feasibility of the approach for separations down to 15 to 20 minutes or less. Dual-tracer PET studies were performed in 32 healthy volunteers using injection separations of 10, 15, or 20 minutes. Model parameter estimates for each tracer were similar to those obtained from previously performed single-injection studies. Voxel-by-voxel parametric images were of good quality for injections spaced by 20 minutes and were nearly as good for 15-minute separations, but were degraded noticeably for some model parameters when injections were spaced by only 10 minutes. The authors conclude that dual-tracer single-scan PET is feasible, yields accurate estimates of multiple neuropharmacologic measures, and can be implemented with a number of different radiotracer pairs.

Brain↗

PubMed1998

Inferential statistical method for analysis of nonsinusoidal hybrid time series with unequidistant observations.

Most variables of interest in laboratory medicine show predictable changes with several frequencies in the span of time investigated. The waveform of such nonsinusoidal rhythms can be well described by the use of multiple components rhythmometry, a method that allows fitting a linear model with several cosine functions. The method, originally described for analysis of longitudinal time series, is here extended to allow analysis of hybrid data (time series sampled from a group of subjects, each represented by an individual series). Given k individual series, we can fit the same linear model with m different frequencies (harmonics or not from one fundamental period) to each series. This fit will provide estimations for 2m + 1 parameters, namely, the amplitude and acrophase of each component, as well as the rhythm-adjusted mean. Assuming that the set of parameters obtained for each individual is a random sample from a multivariate normal population, the corresponding population parameter estimates can be based on the means of estimates obtained from individuals in the sample. Their confidence intervals depend on the variability among individual parameter estimates. The variance-covariance matrix can then be estimated on the basis of the sample covariances. Confidence intervals for the rhythm-adjusted mean, as well as for the amplitude-acrophase pair, of each component can then be computed using the estimated covariance matrix. The p-values for testing the zero-amplitude assumption for each component, as well as for the global model, can finally be derived using those confidence intervals and the t and F distributions. The method, validated by a simulation study and illustrated by an example of modeling the circadian variation of heart rate, represents a new step in the development of statistical procedures in chronobiology.

Biometry↗

PubMed2007

A kinetic model describing Shewanella oneidensis MR-1 growth, substrate consumption, and product secretion.

Aerobic growth of Shewanella oneidensis MR-1 in minimal lactate medium was studied in batch cultivation. Acetate production was observed in the middle of the exponential growth phase and was enhanced when the dissolved oxygen (DO) concentration was low. Once the lactate was nearly exhausted, S. oneidensis MR-1 used the acetate produced during growth on lactate with a similar biomass yield as lactate. A two-substrate Monod model, with competitive and uncompetitive substrate inhibition, was devised to describe the dependence of biomass growth on lactate, acetate, and oxygen and the acetate growth inhibition across a broad range of concentrations. The parameters estimated for this model indicate interesting growth kinetics: lactate is converted to acetate stoichiometrically regardless of the DO concentration; cells grow well even at low DO levels, presumably due to a very low K(m) for oxygen; cells metabolize acetate (maximum specific growth rate, micro(max,A) of 0.28 h(-1)) as a single carbon source slower than they metabolize lactate (micro(max,L) of 0.47 h(-1)); and growth on acetate is self-inhibiting at a concentration greater than 10 mM. After estimating model parameters to describe growth and metabolism under six different nutrient conditions, the model was able to successfully estimate growth, oxygen and lactate consumption, and acetate production and consumption under entirely different growth conditions.

Acetates↗

PubMed2000

Optimal image sampling schedule for both image-derived input and output functions in PET cardiac studies.

Optimal sampling schedule (OSS) design for both image-derived input and output functions in tracer kinetic modeling with positron emission tomography (PET) is investigated. This problem is very important in noninvasive PET dynamic cardiac studies where both the input function, i.e., the plasma time-activity curve (PTAC), and the output function, i.e., the tissue time-activity curve (TTAC), are obtained simultaneously from the same sequence of PET images. The integral PET measurement is used in this study. The spillover correction for the cross contaminations in cardiac studies is incorporated into the OSS design procedure. A new target function based on the D-optimal criterion involving both the input and output sensitivity functions is proposed. The fluorodeoxyglucose (FDG) model and a six-parameter PTAC model are used to illustrate the simultaneous OSS design for both the PTAC and TTAC. An OSS design consisting of six different scanning intervals is derived. Computer simulations are performed based on the estimated parameters from real studies to evaluate the effectiveness of the OSS. The double modeling approach is used in parameter estimation to simultaneously estimate the parameters involved. The results have shown that, for a wide range of parameter variations, the OSS is as effective as a conventional sampling schedule (CSS) and comparable parameter estimates can be obtained. Compared with the use of the CSS, the use of the OSS leads to an approximately 70% reduction in the storage space and data processing time.

Computer Simulation↗

PubMed2007

Curvature-adjusted optimal design of sampling times for the inference of pharmacokinetic compartment models.

In pharmacokinetics, compartment models are often used to describe the time course of blood concentration after the administration of a drug. In this article, we propose an optimal design criterion for precise estimation of parameters included in the compartment model and illustrate the non-sequential design of sampling times of blood drug concentration data in individual pharmacokinetics. The proposed optimal design criterion minimizes the determinant of the mean-squared error matrix of the parameter estimator that is quadratically approximated by the curvature array. Therefore, the proposed criterion considers the intrinsic and parameter-effects nonlinearity underlying the compartment model, and so is applicable in a pharmacokinetic experiment where the sample size of the blood drug concentration data is quite small.

Biological Availability↗

PubMed2006

Using SAS to conduct nonparametric residual bootstrap multilevel modeling with a small number of groups.

In multilevel modeling, researchers often encounter data with a relatively small number of units at the higher levels. As a result, of this and/or non-normality of the residuals, model parameter estimates, particularly the variance components and standard errors of parameter estimates at the group level, may be biased, thus the corresponding statistical inferences may not be trustworthy. This problem can be addressed by using bootstrap methods to estimate the standard errors of the parameter estimates for significance testing. This study illustrates how to use statistical analysis system (SAS) to conduct nonparametric residual bootstrap multilevel modeling. Specific SAS programs for such modeling are provided.

Models, Statistical↗

PubMedDate not supplied

Trimethoprim-sulfamethoxazole pharmacokinetics in trauma patients.

STUDY OBJECTIVES: To characterize the pharmacokinetic profile of trimethoprim-sulfamethoxazole (TMP-SMX) in trauma patients and to compare these parameter estimates with those obtained in nontrauma patients. DESIGN: Open-label, multidose, pharmacokinetic study. SETTING: Trauma intensive care unit of a level 1 trauma center located within a regional medical center. PATIENTS: Fifteen adult trauma patients with serious gram-negative infections. All patients were studied on day 1 of treatment, nine on day 3, three on day 5, and two on day 7. One patient was discontinued from the study because of a possible drug-induced rash. INTERVENTIONS: Study patients received TMP 4 mg/kg and SMX 20 mg/kg intravenously every 12 hours. Serial blood sampling was performed up to 4 times per patient between treatment days 1 and 7. Serum was assayed for TMP-SMX using high-performance liquid chromatography. A one-compartment model was fit to the data using maximum likelihood estimation. MEASUREMENTS AND MAIN RESULTS: Mean (SD) baseline parameter estimates for TMP were volume 2.1 (0.65) L/kg, half-life 9.7 (3.0) hours, and clearance 2.6 (0.80) ml/min/kg. Estimates for SMX were volume 0.51 (0.10) L/kg, half-life 7.8 (2.0) hours, and clearance 0.80 (0.29) ml/min/kg. Both volume (p < 0.01) and clearance (p < 0.001) for SMX were significantly higher and half-life (p < 0.05) significantly shorter than previously reported estimates in nontrauma patients. No significant differences in TMP parameter estimates were found. Neither TMP nor SMX clearance was significantly correlated with estimated creatinine clearance (p > 0.05). CONCLUSION: The results indicate that the pharmacokinetics of SMX in trauma patients differ significantly from nontrauma patients, which may result in lower than expected concentrations using standard dosing guidelines.

Accidents↗

PubMed2006

Bayesian methods for pharmacokinetic models in dynamic contrast-enhanced magnetic resonance imaging.

This paper proposes a new method for estimating kinetic parameters of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) based on adaptive Gaussian Markov random fields. Kinetic parameter estimates using neighboring voxels reduce the observed variability in local tumor regions while preserving sharp transitions between heterogeneous tissue boundaries. Asymptotic results for standard errors from likelihood-based nonlinear regression are compared with those derived from the posterior distribution using Bayesian estimation with and without neighborhood information. Application of the method to the analysis of breast tumors based on kinetic parameters has shown that the use of Bayesian analysis combined with adaptive Gaussian Markov random fields provides improved convergence behavior and more consistent morphological and functional statistics.

Algorithms↗

PubMed2005

Quantile regression models with multivariate failure time data.

As an alternative to the mean regression model, the quantile regression model has been studied extensively with independent failure time data. However, due to natural or artificial clustering, it is common to encounter multivariate failure time data in biomedical research where the intracluster correlation needs to be accounted for appropriately. For right-censored correlated survival data, we investigate the quantile regression model and adapt an estimating equation approach for parameter estimation under the working independence assumption, as well as a weighted version for enhancing the efficiency. We show that the parameter estimates are consistent and asymptotically follow normal distributions. The variance estimation using asymptotic approximation involves nonparametric functional density estimation. We employ the bootstrap and perturbation resampling methods for the estimation of the variance-covariance matrix. We examine the proposed method for finite sample sizes through simulation studies, and illustrate it with data from a clinical trial on otitis media.

Biometry↗

PubMed2002

A new approach to closed-loop linear system identification via a vector autoregressive model.

A new vector autoregressive (VAR) model algorithm is developed for closed-loop identification. The new VAR approach is an extension of a recently developed algorithm, named the optimal parameter search (OPS), thus, we call the new technique VOPS, for vector OPS. Monte Carlo simulations of closed-loop systems were performed to compare the performance of VOPS to the widely utilized vector least squares (VLS) and vector fast orthogonal search (VFOS) approaches. In addition, we examined the effect on parameter estimates obtained via open-loop identification techniques, when using data from closed-loop systems. Comparative results show that both the VOPS and VFOS algorithms produce far more accurate parameter estimates than does the VLS. Furthermore, open-loop identification via univariate OPS and to a lesser extent univariate FOS for closed-loop systems, does not adversely affect the accuracy of the parameter estimates. An open-loop identification via the univariate least-squares method for closed-loop systems showed the most deleterious effect on the accuracy of the parameter estimates. In addition to developing the VOPS algorithm, we also developed approaches termed constrained OPS (COPS) and constrained FOS (CFOS). For closed-loop systems considered in this paper, both COPS and CFOS resulted in more accurate parameter estimates (less biased and more efficient) than did VLS, VFOS, and VOPS.

Algorithms↗

PubMed2003

Modelling approaches to compare sorption and degradation of metsulfuron-methyl in laboratory micro-lysimeter and batch experiments.

Results of laboratory batch studies often differ from those of outdoor lysimeter or field plot experiments--with respect to degradation as well as sorption. Laboratory micro-lysimeters are a useful device for closing the gap between laboratory and field by both including relevant transport processes in undisturbed soil columns and allowing controlled boundary conditions. In this study, sorption and degradation of the herbicide metsulfuron-methyl in a loamy silt soil were investigated by applying inverse modelling techniques to data sets from different experimental approaches under laboratory conditions at a temperature of 10 degrees C: first, batch-degradation studies and, second, column experiments with undisturbed soil cores (28 cm length x 21 cm diameter). The column experiments included leachate and soil profile analysis at two different run times. A sequential extraction method was applied in both study parts in order to determine different binding states of the test item within the soil. Data were modelled using ModelMaker and Hydrus-1D/2D. Metsulfuron-methyl half-life in the batch-experiments (t1/2 = 66 days) was shown to be about four times higher than in the micro-lysimeter studies (t1/2 about 17 days). Kinetic sorption was found to be a significant process both in batch and column experiments. Applying the one-rate-two-site kinetic sorption model to the sequential extraction data, it was possible to associate the stronger bonded fraction of metsulfuron-methyl with its kinetically sorbed fraction in the model. Although the columns exhibited strong significance of multi-domain flow (soil heterogeneity), the comparison between bromide and metsulfuron-methyl leaching and profile data showed clear evidence for kinetic sorption effects. The use of soil profile data had significant impact on parameter estimates concerning sorption and degradation. The simulated leaching of metsulfuron-methyl as it resulted from parameter estimation was shown to decrease when soil profile data were considered in the parameter estimation procedure. Moreover, it was shown that the significance of kinetic sorption can only be demonstrated by the additional use of soil profile data in parameter estimation. Thus, the exclusive use of efflux data from leaching experiments at any scale can lead to fundamental misunderstandings of the underlying processes.

Adsorption↗