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PubMed2005

PsN-Toolkit--a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM.

PsN-Toolkit is a collection of statistical tools for pharmacometric data analysis using the non-linear mixed effect modeling software NONMEM. The toolkit is object oriented and written in the programming language Perl using the programming library Perl-speaks-NONMEM (PsN). Five methods: the Bootstrap, the Jackknife, Log-likelihood Profiling, Case-deletion Diagnostics and Stepwise Covariate Model building are included as separate classes and may be used in user-written Perl scripts or through stand-alone command line applications. The tools are designed with the ability to cooperate and with an emphasis on common structures for workflow and result handling. Parallel execution of independent tool sections is supported on shared memory multiprocessor (SMP) computers, Mosix/openMosix clusters and distributed computing environments following the NorduGrid standard. In conclusion, PsN-Toolkit makes it easier to use the Bootstrap, the Jackknife, Log-likelihood Profiling, Case-deletion Diagnostics and Stepwise Covariate Model building in pharmacometric data analysis.

Cluster Analysis↗
PubMed2003

Combining multiple outcome measures in a meta-analysis: an application.

In meta-analysis of clinical trials published in the medical literature it is customary to restrict oneself to standard univariate fixed or random effects models. If multiple endpoints are present, each endpoint is analysed separately. A few articles have been written in the statistical literature on multivariate methods for multiple outcome measures. However, these methods were not easy to apply in practice, because self-written programs had to be used, and the examples were only two-dimensional. In this paper we consider a meta-analysis on the effect on stroke-free survival of surgery compared to conservative treatment in patients with increased risk of stroke. Three summary measures per trial are available: short-term post-operative morbidity/mortality in the surgical group; long-term event rate in the surgical group, and the event rate in the conservative group. We analyse the three outcomes jointly with a general linear MIXED model, compare the results with the standard univariate approaches and discuss the many advantages of multivariate modelling. It turns out that the general linear MIXED model is a very convenient framework for multivariate meta-analysis. All analyses could be carried out in standard general linear MIXED model software.

Disease-Free Survival↗
PubMed2006

Effect of CYP2C19 genetic polymorphism on pharmacokinetics of phenytoin and phenobarbital in Japanese epileptic patients using Non-linear Mixed Effects Model approach.

OBJECTIVE: To clarify the effect of genetic polymorphism of CYP2C19 on pharmacokinetics of phenytoin and phenobarbital using a Non-linear Mixed Effects Modelling analysis in Japanese epileptic patients. METHOD: A total of 326 serum phenytoin concentrations were collected from 132 patients, and a total of 144 serum phenobarbital concentrations were collected from 74 patients during their clinical routine care. RESULT: The maximal elimination rate of phenytoin decreased by 10.2% in patients with CYP2C19*1/*2 compared with patients with normal CYP2C19. The Michaelis-Menten constants in the patients with CYP2C19*1/*3 and the poor metabolizers of (CYP2C19*2/*2 or *2/*3 or *3/*3) were 27% and 54% higher than those for the patients with normal CYP2C19, respectively. The total body clearance of phenobarbital decreased by 19.3% in patients with CYP2C19*1/*3 or the poor metabolizers of CYP2C19 compared with patients with normal CYP2C19 or with CYP2C19*1/*2. CONCLUSION: These findings indicated that the genetic polymorphisms of CYP2C19 contribute to the pharmacokinetic variability of phenytoin and phenobarbital, the poor metabolizers of CYP2C19, which are relatively common in Asian groups.

Adult↗
PubMed2026

Associations Between Paternal Pre-Conceptional Body Mass Index and Lifestyle Factors and Offspring Weight Development.

BACKGROUND: Evidence suggests that pre-conceptional paternal factors, including BMI and diet, may influence offspring development. OBJECTIVES: We examined the associations between paternal BMI, dietary protein intake, glycemic index (GI), smoking and alcohol consumption and offspring development during the first 5 years of life. METHODS: This secondary analysis of an RCT included 162 father-child pairs from pregnancies among women with pre-pregnancy overweight or obesity. Paternal characteristics were reported at gestational week 15, reflecting the preceding 3 months. Offspring anthropometry was measured at birth, 6 and 18 months, 3 and 5 years. Associations were examined using linear mixed models and linear regression models. RESULTS: No consistent associations were found between paternal characteristics and offspring outcomes from birth to 3 years. At age 5, higher paternal BMI was associated with higher offspring BMI z-score (β = 0.07 (CI: 0.03; 0.10)), fat mass index (β = 0.07 kg/m2 (CI: 0.02; 0.12)) and fat-free mass index (β = 0.05 kg/m2 (CI: 0.01; 0.08)). Lower paternal protein intake was associated with higher offspring BMI z-score (β = 0.54 (CI: 0.07; 1.01)) and fat-free mass index (β = 0.60 kg/m2 (CI: 0.13; 1.07)), while moderately higher protein intake was associated with higher waist-to-height ratio (β = 0.03 (CI: 3.00 × 10-3; 0.05)). Higher paternal GI was associated with lower offspring BMI z-score (β = -0.04 (CI: -0.08; -2.14-10-3)) at age 5. Smoking and alcohol were not associated with offspring outcomes. CONCLUSION: Paternal BMI was associated with offspring outcomes at age 5 years, while findings for paternal dietary factors were less consistent.

Humans↗
PubMed2006

Semiparametric models for missing covariate and response data in regression models.

We consider a class of semiparametric models for the covariate distribution and missing data mechanism for missing covariate and/or response data for general classes of regression models including generalized linear models and generalized linear mixed models. Ignorable and nonignorable missing covariate and/or response data are considered. The proposed semiparametric model can be viewed as a sensitivity analysis for model misspecification of the missing covariate distribution and/or missing data mechanism. The semiparametric model consists of a generalized additive model (GAM) for the covariate distribution and/or missing data mechanism. Penalized regression splines are used to express the GAMs as a generalized linear mixed effects model, in which the variance of the corresponding random effects provides an intuitive index for choosing between the semiparametric and parametric model. Maximum likelihood estimates are then obtained via the EM algorithm. Simulations are given to demonstrate the methodology, and a real data set from a melanoma cancer clinical trial is analyzed using the proposed methods.

Algorithms↗
PubMedDate not supplied

On summary measures analysis of the linear mixed effects model for repeated measures when data are not missing completely at random.

Subjects often drop out of longitudinal studies prematurely, yielding unbalanced data with unequal numbers of measures for each subject. A simple and convenient approach to analysis is to develop summary measures for each individual and then regress the summary measures on between-subject covariates. We examine properties of this approach in the context of the linear mixed effects model when the data are not missing completely at random, in the sense that drop-out depends on the values of the repeated measures after conditioning on fixed covariates. The approach is compared with likelihood-based approaches that model the vector of repeated measures for each individual. Methods are compared by simulation for the case where repeated measures over time are linear and can be summarized by a slope and intercept for each individual. Our simulations suggest that summary measures analysis based on the slopes alone is comparable to full maximum likelihood when the data are missing completely at random but is markedly inferior when the data are not missing completely at random. Analysis discarding the incomplete cases is even worse, with large biases and very poor confidence coverage.

Computer Simulation↗
PubMed1996

Gauss or Bernoulli? A Monte Carlo comparison of the performance of the linear mixed-model and the logistic mixed-model analyses in simulated community trials with a dichotomous outcome variable at the individual level.

This Monte Carlo study compares performance of the linear and the logistic mixed-model analyses of simulated community trials having event rates of 37%, 13%, or 5%, intraclass correlations between 0.01 and 0.05, and 17 or 5 denominator degrees of freedom. Type I or Type II error rates showed no essential difference between the two analysis methods. They showed depressed error rates when the event rate or the denominator degrees of freedom were small. The authors conclude that in studies with adequate denominator degrees of freedom, the researcher may use either method of analysis but should accept negative estimates of components of variance to avoid depression of error rates.

Analysis of Variance↗
PubMed2000

Regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements.

We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.

Bias↗
PubMed2004

QT analysis: a complex answer to a 'simple' problem.

Prolongation of the QT interval on a surface electrocardiogram is a biomarker for a potentially life-threatening arrhythmia. It is used by drug developers and regulatory agencies as a measure of drug safety. Heart rate or RR interval (the inverse of heart rate) correction of the QT interval is necessary because of the QT interval shortening that accompanies physiologic decreases in the RR interval. When a drug alters the RR interval, it is important to distinguish a QT change that is due to a drug effect versus an artefact of a heart rate change. A two-step off-drug subject-specific QT correction analysis is discussed. At the first step, a linear mixed model based only on the placebo (off-drug) RR/QT data produces a correction coefficient that can be applied to a generic formula, and QT intervals are corrected for heart rate on both placebo and treatment period data using that formula. At step two, the heart rate corrected QT interval (QTc) is then compared between placebo and treatment groups at a pre-specified heart rate (usually 60 bpm) based on another linear mixed model. This two-step QT analysis implicitly assumes the slope of log(QT) versus log(RR) is unchanged by drug. Practically, it is important to understand how much this assumption can bias the QT prolongation estimates if it is not valid. We propose a one-step off-on-drug subject-specific QT correction analysis that would pool placebo and treatment period RR/QT data and derive different subject specific coefficients for the treatment and placebo data based on a linear mixed model, which can avoid the unchanged slope assumption. It is also a known unbiased and the most efficient method. The applications of both methods are demonstrated through the QT analysis of haloperidol, a neuroleptic known to prolong QTc. Both theoretical and empirical results show that, although the two-step off-drug QT correction analysis is biased, the bias is small in the case of haloperidol (0.1-0.2 ms). The two-step off-drug QT correction analysis is shown to be almost as efficient as our one-step off- and on-drug QT analysis.

Adult↗
PubMed2004

Conditional estimation for generalized linear models when covariates are subject-specific parameters in a mixed model for longitudinal measurements.

The relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest, and a relevant framework is that of a generalized linear model with covariates that are subject-specific random effects in a linear mixed model for the longitudinal measurements. Naive implementation by imputing subject-specific effects from individual regression fits yields biased inference, and several methods for reducing this bias have been proposed. These require a parametric (normality) assumption on the random effects, which may be unrealistic. Adapting a strategy of Stefanski and Carroll (1987, Biometrika74, 703-716), we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution. The methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause.

Biometry↗
PubMed2003

Assessing individual bioequivalence with high-order cross-over designs: a unified procedure.

The U.S. FDA's newly issued guidance on bioequivalence recommends the use of individual bioequivalence (IBE) for highly variable drugs and possibly for modified release dosage forms. The recommended approach to the analysis is to follow the methodology of Hyslop, Hsuan and Holder (HHH), based on a linear mixed model. A limitation of the HHH method is that it works only for uniform designs, such as RTRT/TRTR. In this paper, we present an alternative approach based on a multivariate model. The multivariate model is shown to be a strict superset of the linear mixed model and can successfully model data where the mixed model fails. Our multivariate approach coincides with the HHH method where the HHH method applies, but generalizes to any high-order cross-over design, such as the Balaam design, RTR/TRT, and TRSS/RSTT/STRR. We present numerical examples to demonstrate the proposed method, and examine its properties with a simulation study.

Analysis of Variance↗
PubMed1999

Repeated probit regression when covariates are measured with error.

This paper develops a model for repeated binary regression when a covariate is measured with error. The model allows for estimating the effect of the true value of the covariate on a repeated binary response. The choice of a probit link for the effect of the error-free covariate, coupled with normal measurement error for the error-free covariate, results in a probit model after integrating over the measurement error distribution. We propose a two-stage estimation procedure where, in the first stage, a linear mixed model is used to fit the repeated covariate. In the second stage, a model for the correlated binary responses conditional on the linear mixed model estimates is fit to the repeated binary data using generalized estimating equations. The approach is demonstrated using nutrient safety data from the Diet Intervention of School Age Children (DISC) study.

Bias↗
PubMed2005

Non-linear mixed effects modeling - from methodology and software development to driving implementation in drug development science.

Few scientific contributions have made significant impact unless there was a champion who had the vision to see the potential for its use in seemingly disparate areas-and who then drove active implementation. In this paper, we present a historical summary of the development of non-linear mixed effects (NLME) modeling up to the more recent extensions of this statistical methodology. The paper places strong emphasis on the pivotal role played by Lewis B. Sheiner (1940-2004), who used this statistical methodology to elucidate solutions to real problems identified in clinical practice and in medical research and on how he drove implementation of the proposed solutions. A succinct overview of the evolution of the NLME modeling methodology is presented as well as ideas on how its expansion helped to provide guidance for a more scientific view of (model-based) drug development that reduces empiricism in favor of critical quantitative thinking and decision making.

Algorithms↗
PubMed2005

Genetic parameters for stayability, stayability at calving, and stayability at weaning to specified ages for Hereford cows.

Genetic parameters for stayability to six ages (ST1, . . ., ST6), for five measures of stayability to calving (SC2, . . ., SC6), and for five measures of stayability to weaning (SW2, . . ., SW6), were estimated using records of 2,019 Hereford cows collected from 1964 to 1979 from a selection experiment with a control line and three lines selected for weaning weight, yearling weight, and an index of yearling weight and muscle score. The model included birth year of the cow as a fixed effect and the cow's sire as a random effect. Analyses were performed with 1) a generalized linear mixed model for binary data using a probit link with a penalized quasi-likelihood function, and 2) with a linear mixed model using REML. Genetic trends were estimated by regressing weighted means of estimated transmitting abilities (ETA) of sires by birth year of their daughters on birth year. Environmental trends were estimated by regressing solutions for year of birth on birth year. Estimates of heritability (SE) for ST were between 0.09 (0.08) and 0.30 (0.14) for threshold model and between 0.05 (0.04) and 0.19 (0.09) for linear model. Estimates of heritability from linear model analyses transformed to an underlying normal scale were between 0.09 and 0.35. Estimates of heritability (SE) for SC were between 0.29 (0.10) and 0.39 (0.11) and between 0.18 (0.09) and 0.25 (0.08) with threshold and linear models. Estimates of heritability transformed to an underlying normal scale were between 0.30 and 0.40. Estimates of heritability (SE) for SW were between 0.21 (0.14) and 0.47 (0.19) and between 0.12 (0.08) and 0.26 (0.12) with threshold and linear models, respectively. Estimates of heritability transformed to an underlying normal scale were between 0.21 and 0.50. Estimates of genetic and environmental trends for all lines were nearly zero for all traits. Correlations between ETA of sires for stayability to specific ages, for stayability to calving, and for stayability to weaning with threshold and linear models ranged from 0.09 to 0.82, from 0.68 to 0.90, and from 0.67 to 0.87, respectively. Selection for stayability would be possible in a breeding program and could be relatively effective as a result of the moderate estimates of heritability, which would allow selection of sires whose daughters are more likely to remain longer in the herd. Selection for weaning and yearling weights resulted in little correlated response for any of the measures of stayability.

Age Factors↗
PubMed2001

The relationship between disease activity, joint destruction, and functional capacity over the course of rheumatoid arthritis.

OBJECTIVE: To investigate the relationship between functional capacity, disease activity, and joint destruction over the course of rheumatoid arthritis (RA). METHODS: The followup data on 378 patients with early RA (duration <1 year), included in an open, prospective study since 1985 at the Department of Rheumatology of the University Medical Center Nijmegen, were used. Functional capacity, disease activity, and joint destruction were assessed using the Health Assessment Questionnaire disability index (HAQ DI), the Disease Activity Score (DAS), and a modification of the sharp radiographic damage score, respectively. Multiple linear regression was used to model the data collected at 0, 3, 6, and 9 years after study start, to investigate which variables influenced functional capacity during the disease course. A general linear mixed model for longitudinal data, which included the variables identified as significant in the multiple linear regression models and several interaction terms between the variables, was run. RESULTS: On average, the functional capacity of the patients, as measured by the HAQ DI, worsened over the course of the disease after an initial improvement. After an initial reduction in the extent of disease activity, the mean DAS remained more or less stable over the course of the disease. The mean modified sharp joint damage score worsened over the course of the disease, with a slower progression rate later in the disease. In the multiple linear regression at 0, 3, and 6 years after study start, disease activity was found to be an important factor influencing functional capacity, and at 6 and 9 years, joint damage had an important effect on functional capacity. Furthermore, at 6 and 9 years, there was an interaction effect of joint destruction with disease activity. In the general linear mixed model, disease activity, joint damage, and an interaction effect of disease activity and joint damage were the main factors explaining functional capacity. CONCLUSION: The effect of disease activity and joint destruction on functional capacity changes over the course of the disease. In early RA, functional capacity is most associated with disease activity, and in late disease, with joint damage.

Adult↗
PubMed2004

Genetics of osteochondral disease and its relationship with meat quality and quantity, growth, and feed conversion traits in pigs.

The main objective of this research was to estimate heritabilities of seven osteochondrosis (OC) lesions in station-tested pigs and their genetic and phenotypic correlations with four meat quality (MQ) traits, the percentage of premium cuts (PPC), daily weight gain (DWG), and feed conversion ratio (FCR). Observed OC lesions were on the head of humerus (HK), condylus medialis humeri (CMH), condylus lateralis humeri (CLH), radius and ulna proximal (RUP), distal epiphyseal cartilage of ulna (DEU), head of femur (FK), and condylus medialis femoris (CMF). Meat quality traits were i.m. fat (IMF), muscle pH at 1 h after slaughter (pH1), muscle pH at 30 h after slaughter (pH30), and light reflectance on muscle (H30). The data set comprised 2,710 animals, of which 1,291 animals had OC records. All traits were analyzed by multiple-trait linear mixed model, with the animal's genetic and common litter effects as random. Fixed effects in the model varied between traits. Each OC lesion was further analyzed by a univariate generalized linear mixed model or, equivalently, "threshold models," assuming logistic, probit (normal), and Poisson distributions of the underlying "liability" to the disease. For OC lesions, estimates of heritability were low on the original "incidence" scale (0.06 for HK to 0.16 for CLH) and moderate to high on the liability scale (0.08 to 0.42). Genetic correlations (r(g)) between OC lesions and most MQ traits and PPC were generally unfavorable. Significant r(g) were -0.44 for DWG-CMH, 0.31 for DWG-CMF, 0.40 for FCR-HK, 0.21 for PPC-CLH, 0.32 for PPC-RUP, 0.30 for PPC-CMF, -0.54 for pH1-CLH, 0.47 for pH1-DEU, -0.34 for pH30-CMH, 0.58 for pH30-DEU, -0.50 for H30-HK, -0.31 for H30-DEU, and 0.31 for H30-CMF. Genetic susceptibilities to some OC lesions within the front leg were positively related to each other (r(g) range = 0.57 to 0.69), but r(g) between front and hind leg OC lesions were mostly negative (range = -0.21 to -0.40). Estimated h2 was 0.60 for PPC, and ranged from 0.12 to 0.66 for MQ traits, 0.28 for DWG, and 0.42 for FCR. Genetic correlations among meat quality and quantity traits ranged from -0.66 to 0.37. This is the first study to report genetic and phenotypic correlations between OC lesions and several meat quality and quantity traits in pigs. These findings will be useful to pig industry, especially in designing breeding programs for robust pigs.

Aging↗
PubMed2004

Estimation of genetic and environmental factors for binary traits using family data.

While the family-based analysis of genetic and environmental contributions to continuous or Gaussian traits is now straightforward using the linear mixed models approach, the corresponding analysis of complex binary traits is still rather limited. In the latter we usually rely on twin studies or pairs of relatives, but these studies often have limited sample size or have difficulties in dealing with the dependence between the pairs. Direct analysis of extended family data can potentially overcome these limitations. In this paper, we will describe various genetic models that can be analysed using an extended family structure. We use the generalized linear mixed model to deal with the family structure and likelihood-based methodology for parameter inference. The method is completely general, accommodating arbitrary family structures and incomplete data. We illustrate the methodology in great detail using the Swedish birth registry data on pre-eclampsia, a hypertensive condition induced by pregnancy. The statistical challenges include the specification of sensible models that contain a relatively large number of variance components compared to standard mixed models. In our illustration the models will account for maternal or foetal genetic effects, environmental effects, or a combination of these and we show how these effects can be readily estimated using family data.

Cluster Analysis↗
PubMed2006

Associations between somatic cell counts at calving or prior to drying-off and future somatic cell counts, in the remaining or subsequent lactation.

Composite milk somatic cell counts (CMSCC) from four separate datasets, containing 3338, 350, 1408 and 1404 herds, were used. All herds were enrolled in the Norwegian Dairy Herd Recording System (NDHRS). The aim was to investigate associations between CMSCC at calving or prior to drying-off and future CMSCC in the remaining or subsequent lactation. CMSCC was determined using Fossomatic 5000 cell counters (Foss Electric, Hillerød, Denmark) according to IDF recommendations (International Dairy Federation, 1984) and a natural logarithmic transformation of the CMSCC data (lnCMSCC) was performed. Results obtained were arranged according to parity and lactation stage and regression models and general linear mixed models were applied, the latter model to account for clustering between herds. The best associations between CMSCC at calving or prior to drying-off and future CMSCC in the remaining or subsequent lactation were found by using at least two CMSCC test days after calving or prior to drying-off. The geometric mean of the second and third or the first three CMSCC test days explained 50% of the variation in future CMSCC in first parity cows. This information was accessible at 151 days in milk (DIM) in bimonthly tested herds, and at 87 DIM for monthly tested herds. There was not a large difference using two or three single consecutive weighted CMSCC test days compared with the geometric mean of two or three CMSCC test days. Our findings indicate the need of using at least two CMSCC test days and, if only one CMSCC test day is used, it should be obtained after 14 d post-calving or preferably after 30 DIM.

Animals↗