Presentation

NLMULTIMIX program consists in estimating models for multivariate longitudinal data when various longitudinal markers are quantitative measures of an underlying latent process. This latent process is described using a linear mixed model including a Brownian motion while the link between each marker and the latent process is managed by a nonlinear transformation with marker-specific parameters to be estimated and in addition a marker-specific random intercept and independent Gaussian errors. The nonlinear transformations used in the program are Beta Cumulative Distribution Functions with two parameters.

Thus this models can analyse jointly various correlated quantitative repeated measures even if the distribution of the markers is far from a Gaussian distribution. Estimation of the parameters with confidence bands can be obtained, marginal or subject-specific predicted values of each observation and marginal standardized residual (in the latent process scale) are given in output, and the curves of the estimated transformations can also be obtained.

Characteristics of the model, the data set format and the names of the output files must be specified in the parameter file NLMULTIMIX.inf which is described below. The program and the various files involved are detailed in the user's guide.

The compacted file NLMULTIMIX_unix.zip is downloadable and contains the following files:

• NLMULTIMIX.pdf: user's guide
• NLMULTIMIX.f: source file in Fortran90
• NLMULTIMIX.inf: parameter file

Compilation

The program NLMULTIMIX is written in standard Fortran90 language and can be run on any computer with a Fortran90 compiler. Some subroutines are written in Fortran77 and options can be needed to compile both Fortran90 and Fortran77 code.

Data file

This ASCII file contains the data set and must be given in the following format. The data file is constituted in lines. It contains for each subject:

• identification number
• number of measures n_i1 for marker 1
• n_i1 vector of responses for marker 1
• n_i1 vector of measurement times for marker 1
• number of measures n_i2 for marker 2
• n_i2 vector of responses for marker 2
• n_i2 vector of measurement times for marker 2
• ...
• number of measures n_iK for marker K
• n_iK vector of responses for marker K
• n_iK vector of measurement times for marker K
• covariate 1
• covariate 2
• ...
• covariate Q

Parameter file

This file contains all the information needed to specify completely the model :

• name of the data file
• name of the output file for estimations
• name of the output file for the predictions and the residuals
• name of the output file for the estimated transformations
• number of subjects
• number K of markers
• Range of the data to use in the estimation procedure (the range must be a little larger than the real observed range)
• degree of the time polynomial
• indicator of random-effect on the time polynomial components
• number Q of covariates in the data file
• indicator that each covariate has a fixed effect (or not) in the latent process model
• indicator that each covariate has contrasts on the markers (or not)
• initial values of the transformation parameters (square roots of the parameters)
• initial values of the fixed effects in the time polynomial and the covariates (in the latent process model and then for the contrasts on the markers)
• indicator for the structure of the Variance-covariance matrix of the random-effects
• initial values of the parameters of Variance-covariance of the random-effects
• initial values of the K standard errors of the marker-specific random intercepts
• indicator for the structure of auto-correlation (Brownian motion or autoregressive process)
• initial values of the auto-correlation parameter(s) and of the K standard-errors of the Gaussian independent errors
• number of simulations for the numerical integration when computing the predictions
• real observed range of each marker

Each piece of information to specify is preceded by a line summing-up what is asked for. For each specified initial value, the user can choose to estimate the corresponding parameter or to fix it to its initial value.

Output files

• The output file for the estimations :
  it contains the main characteristics of the estimated model, the status of convergence, the final log-likelihood, the Akaike criterion, the Bayesian information criterion, estimations of the parameters with their standard-error, the Wald statistic and the 95% confidence bands.
• The output for the predictions and the residuals :
  for each observation, it contains in columns the identification number of the subject, the indicator of the marker, the indicator of the occasion, the observed value of the marker, the marginal predicted one, the subject-specific one and the marginal standardized residual in the latent process scale.
• The output for the estimated transformations :
  for each marker, it contains 100 simulated values in the real observed range of the marker and the corresponding 100 values of the estimated Beta transformation.

References

Proust C, Jacqmin-Gadda H, Taylor J, Ganiayre J, Commenges D.
A non-linear model with latent process for cognitive evolution using multivariate longitudinal data. Biometrics 2006;64(4):1014-1024.

Author

Cécile Proust
Hélène Jacqmin-Gadda
Inserm U897
146 rue Léo Saignat
33076 Bordeaux Cedex
France

Jeremy Taylor
Department of Biostatistics
University of Michigan
1420 Washington Heights
Ann Arbor
MI 48109
USA

Contact

E-mail: Daniel.Commenges@isped.u-bordeaux2.fr.
We are interested in feed-back but can not guarantee support.

Licence

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.