What result files are generated by Monolix?

Monolix generates a lot of different output files depending on the tasks done by the user. Here is a complete listing of the files, along with the condition for creation and their content.

Task: population parameter estimation (SAEM)
Task: Fisher Information Matrix calculation
Task: Individual parameter estimation (using conditional mode and or mean)
Task: Log-likelihood calculation
Tables using the “Output to save” window

Task: Population parameter estimation (SAEM)

pop_parameters.txt

Description: summary file.
Delimiter: (variable)
Outputs:

Header: project file name, date and time of run, Monolix version
Estimation of the population parameters: Estimated population parameters & computation time

estimates.txt

Description: estimated population parameters.
Delimiter: semicolon
Outputs:

First column (no name): contains the parameter names (e.g ‘V_pop’ and ‘omega_V’).
Column ‘parameter’: contains the estimated parameter values.

Task: Fisher Information Matrix calculation

pop_parameters.txt

Description: summary file.
Delimiter: (variable)
Outputs:

Header: project file name, date and time of run, Monolix version (outputted population parameter estimation task)
Estimation of the population parameters: Estimated population parameters & computation time (outputted population parameter estimation task). Standard errors and relative standard errors are added.
Correlation matrix of the estimates: correlation matrix by block, eigenvalues and computation time

estimates.txt

Description: estimated population parameters, associated standard errors and p-value.
Delimiter: semicolon
Outputs:

First column (no name): contains the parameter names (outputted population parameter estimation task)
Column ‘parameter’: contains the estimated parameter values (outputted population parameter estimation task)
s.e._lin / s.e._sa: contains the standard errors (s.e.) for the (untransformed) parameter, obtained by linearization of the system (lin) or stochastic approximation (sa).
r.s.e._lin / r.s.e._sa: contains the parameter relative standard errors (r.s.e.) in % (param_r.s.e. = 100*param_s.e./param), obtained by linearization of the system (lin) or stochastic approximation (sa).
pvalues_lin / pvalues_sa: for beta parameters associated to covariates, the line contains the p-value obtained from a Wald test of whether beta=0. If the parameter is not a beta parameter, ‘NaN’ is displayed.

Notice that if the Fisher Information Matrix is difficult to invert, some parameter’s standard error can maybe not be computed leading to NaN in the corresponding columns.

correlationEstimates_sa.txt and/or correlationEstimates_lin.txt

Description: correlation matrix for the (untransformed) parameters
Delimiter: semicolon
Outputs: matrix with the project parameters as lines and columns. First column contains the parameter names.

The correlation matrix is calculated as:

$corr(\theta_i,\theta_j)=\frac{covar(\theta_i,\theta_j)}{\sqrt{var(\theta_i)}\sqrt{var(\theta_j)}}$

This implies that the diagonal is unitary. The variance-covariance matrix for the untransformed parameters $\theta$ is obtained from the inverse of the Fisher Information Matrix and the jacobian. See below for the formula.

fimTransPop_sa.txt and/or fimTransPop_lin.txt

Description: inverse of the Fisher Information Matrix (i.e the variance-covariance matrix) for the transformed normally distributed parameters
Delimiter: semicolon
Outputs: matrix with the project parameters as lines and columns. First column contains the parameter names.

The variance-covariance matrix $\Gamma$ for the transformed normally distributed parameters $\zeta$ can be multiplied by the jacobian $J$ (which elements are defined by $J_{ij}=\frac{\partial\theta_i}{\partial\zeta_j}$ , see jacobian.txt) to obtain the variance-covariance matrix $\tilde{\Gamma}$ for the untransformed parameters $\theta$ :

$\tilde{\Gamma}=J^T\Gamma J$ .

jacobian.txt

Description: jacobian (i.e derivatives of the untransformed parameters $\theta$ w.r.t the transformed and normally distributed parameters $\zeta$ )
Delimiter: semicolon
Outputs: matrix with the project parameters as lines and columns. First column and first row contain the parameter names.

The elements of the jacobian $J$ are defined by:

$J_{ij}=\frac{\partial\theta_i}{\partial\zeta_j}$

with $\theta$ the untransformed parameters and $\zeta$ the transformed and normally distributed parameters. Note that only the fixed effects get transformed by Monolix, while the standard deviations ‘omega’ are not (the diagonal elements are therefore 1 for those parameters).

Task: Individual parameters estimation by conditional mode and/or mean

indiv_parameters.txt

Description: Individual parameter (mode and/or mean of the conditional distribution)
Delimiter: tab
Outputs:

ID: subject name and occasion (if applicable). If there is one type of occasion, the syntax will be 1#2 for individual 1, occasion 2 for instance. For several types of occasions, 1#(1,2) for instance.
parameterName_mode (if conditional mode was computed): individual parameter estimated by the conditional mode task, i.e mode of the conditional distribution $p(\psi_i|y_i;\hat{\theta})$
parameterName_mean (if conditional mean was computed) or parameterName_mean*: individual parameter estimated by the conditional mode task, i.e mean of the conditional distribution $p(\psi_i|y_i;\hat{\theta})$ (or in case of ‘*’: mean over the parameters drawn during the last iterations of the SAEM algorithm, if the conditional mean task has not been run)
parameterName_sd (if conditional mean was computed) or parameterName_sd*: standard deviation of the conditional distribution $p(\psi_i|y_i;\hat{\theta})$ calculated during the conditional mean task (or in case of ‘*’: standard deviation of the parameters drawn during the last iterations of the SAEM algorithm, if the conditional mean task has not been run)
COVname: continuous covariates values corresponding to all data set columns tagged as “COV”
CATname_CATmodality: modalities associated to the covariate (except the reference) used in the covariate model. If for example, the CAT is country with USA as reference modality and France and England as other modalities, it will propose Country_France and Country_England columns. For each modality, 0 or 1 is used to define which modality was used.
P(ZM=i|Y) (in case of latent covariate): probability for the individual of being in category i, calculated either as $P(ZM=i|\hat{\psi}_i,y_i,\hat{\theta})$ (when option “Cond. mode” is used) with $\hat{\psi}_i$ the estimated individual parameter (conditional mode) and $\hat{\theta}$ the estimated population parameters, or as the empirical probability resulting from the draws of the MCMC.
SAEM_lcat_i (in case of latent covariate): 1 if the last MCMC draw during the SAEM task was ZM=i, and 0 otherwise. Note that there is one column less than the number of latent categories.
condmode_SAEM_lcat_i (in case of latent covariate): 1 if $\textrm{argmax }(p(z_i|y_i,\psi_i^{(k)},\hat{\theta}))=i$ with $\hat{\theta}$ the estimated population parameters, $z_i$ the latent covariate and $\psi_i^{(k)}$ the individual parameter from the last MCMC draw of the SAEM task, and 0 otherwise
condmode_ZM (in case of latent covariate): index of the category, obtained during the conditional mode task as $(\hat{\psi}_i,\hat{z}_i)=\textrm{argmax }p(\psi_i,z_i|y_i,\hat{\theta})$ .

indiv_eta.txt

Description: individual random effect, calculated using the population parameters, the covariates and the conditional mode or conditional mean. For instance if we have a parameter defined as $k_i=k_{pop}+\beta_{k,WT}WT_i+\eta_i$ , we calculate $\eta_i=k_i - k_{pop}-\beta_{k,WT}WT_i$ with $k_i$ the estimated individual parameter (mode or mean of the conditional distribution), $WT_i$ the individual’s covariate, and $k_{pop}$ and $\beta_{k,WT}$ the estimated population parameters.
Delimiter: tab
Outputs:

ID: subject name and occasion (if applicable). If there is one type of occasion, the syntax will be 1#2 for individual 1, occasion 2 for instance. For several types of occasions, 1#(1,2) for instance.
eta_parameterName_mode (if conditional mode was computed): random effect calculated using the conditional mode as individual parameter
eta_parameterName_mean (if conditional mean was computed) or eta_parameterName_mean*: random effect calculated using the conditional mean as individual parameter (from individual parameter estimation task or calculated over the last iterations of the SAEM algorithm, in case of ‘*’)
eta_parameterName_sd (if conditional mean was computed) or eta_parameterName_sd*: standard deviation of the random effect, calculated using the conditional mean as individual parameter (from individual parameter estimation task or calculated over the last iterations of the SAEM algorithm, in case of ‘*’)
COVname: continuous covariates values corresponding to all data set columns tagged as “COV”
CATname_CATmodality: modalities associated to the covariate (except the reference) used in the covariate model. If for example, the CAT is country with USA as reference modality and France and England as other modalities, it will propose Country_France and Country_England columns. For each modality, 0 or 1 is used to define which modality was used.
P(ZM=i|Y) (in case of latent covariate): probability for the individual of being in category i, calculated either as $P(ZM=i|\hat{\psi}_i,y_i,\hat{\theta})$ (when option “Cond. mode” is used) with $\hat{\psi}_i$ the estimated individual parameter (conditional mode) and $\hat{\theta}$ the estimated population parameters, or as the empirical probability resulting from the draws of the MCMC.
SAEM_lcat_i (in case of latent covariate): 1 if the last MCMC draw during the SAEM task was ZM=i, and 0 otherwise. Note that there is one column less than the number of latent categories.
condmode_SAEM_lcat_i (in case of latent covariate): 1 if $\textrm{argmax }(p(z_i|y_i,\psi_i^{(k)},\hat{\theta}))=i$ with $\hat{\theta}$ the estimated population parameters, $z_i$ the latent covariate and $\psi_i^{(k)}$ the individual parameter from the last MCMC draw of the SAEM task, and 0 otherwise
condmode_ZM (in case of latent covariate): index of the category, obtained during the conditional mode task as $(\hat{\psi}_i,\hat{z}_i)=\textrm{argmax }p(\psi_i,z_i|y_i,\hat{\theta})$ .

Task: Log-Likelihood calculation

pop_parameters.txt

Description: summary file.
Delimiter: (variable)
Outputs:

Header: project file name, date and time of run, Monolix version (outputted population parameter estimation task)
Estimation of the population parameters: Estimated population parameters & computation time (outputted population parameter estimation task). Standard errors and relative standard errors are added.
Correlation matrix of the estimates: correlation matrix by block, eigenvalues and computation time
Log-likelihood Estimation: -2*log-likelihood, AIC and BIC values, together with the computation time

Tables using the “Output to save” window

The tables selected in the “Output to save” window will be saved at the end of the graphics generation task.

predictions.txt

Description: predictions and residuals at the observation times
Delimiter: tab
Outputs:

ID: subject name and occasion (if applicable). If there is one type of occasion, the syntax will be 1#2 for individual 1, occasion 2 for instance. For several types of occasions, 1#(1,2) for instance.
time: Time from the data set.
MeasurementName: Measurement from the data set.
RegressorName: Regressor value.
popPred: prediction using the population parameters and the covariates, e.g $V_i=V_{pop}\left(\frac{WT_i}{70}\right)^{\beta}$ (without random effects)
meanPred: mean of predictions with different draws of the individual parameters, i.e $\mathbb{E}(f(t_{ij},\psi_i))$
indPred_mean*: prediction using the mean of the conditional distribution, calculated using the last iterations of the SAEM algorithm.
indPred_mean (if conditional mean was computed): prediction using the mean of the conditional distribution, calculated in the “Cond. mean and s.d” task
indPred_mode (if conditional mode was computed): prediction using the mean of the conditional distribution, calculated in the “Cond. mode” task
popWRes: weighted residuals $pWRES_{ij}=\frac{y_{ij}-f(t_{ij},\xi_i)}{g(t_{ij},\xi_i)}$ with $\xi_i$ the individual parameter obtained from population parameters and the covariates, e.g $V_i=V_{pop}\left(\frac{WT_i}{70}\right)^{\beta}$ (without random effects)
meanWRES (if residual figure generated): weighted residuals $PWRES_{ij}$ as defined here.
indWRes_mean*: weighted residuals $IWRES_{ij}=\frac{y_{ij}-f(t_{ij},\psi_i)}{g(t_{ij},\psi_i)}$ with $\psi_i$ the mean of the conditional distribution, calculated using the last iterations of the SAEM algorithm
indWRes_mean (if conditional mean was computed): weighted residuals $IWRES_{ij}=\frac{y_{ij}-f(t_{ij},\psi_i)}{g(t_{ij},\psi_i)}$ with $\psi_i$ the mean of the conditional distribution, calculated in the “Cond. mean and s.d” task
indWRes_mode (if conditional mode was computed): weighted residuals $IWRES_{ij}=\frac{y_{ij}-f(t_{ij},\psi_i)}{g(t_{ij},\psi_i)}$ with $\psi_i$ the mode of the conditional distribution, calculated in the “Cond. mode” task
NPDE (if residual figure generated): normalized prediction distribution errors as defined here.

Notice that in case of several outputs, Monolix generates predictions1.txt, predictions2.txt, …

If additional outputs have been added to the table list in the model file, the corresponding values will also be outputted in the predictions.txt file, with suffix ‘_mean’, ‘_mean*’, ‘_mode’ or ‘_pop’.

finegrid.txt

Description: predictions on a regular fine grid.
Delimiter: tab
Outputs:

ID: subject name and occasion (if applicable). If there is one type of occasion, the syntax will be 1#2 for individual 1, occasion 2 for instance. For several types of occasions, 1#(1,2) for instance.
time: time on a regular grid. The number of point is the same for each individual and set to the value in “Settings/Results/Grid size” of the interface. The grid depends on the individual and goes over [tmin -(tmax-tmin)/10 , tmax + (tmax-tmin)/10].
RegressorName: regressor value.
popPred: prediction using the population parameters and the covariates, e.g $V_i=V_{pop}\left(\frac{WT_i}{70}\right)^{\beta}$ (without random effects)
indPred_mean*: prediction using the mean of the conditional distribution, calculated using the last iterations of the SAEM algorithm
indPred_mean (if conditional mode task computed): prediction using the mean of the conditional distribution, calculated in the “Cond. mean and s.d” task
indPred_mode (if conditional mode task computed): prediction using the mean of the conditional distribution, calculated in the “Cond. mode” task

Notice that in case of several outputs, Monolix generates finegrid1.txt, finegrid2.txt, …

If additional outputs have been added to the table list in the model file, the corresponding values will also be outputted in the finegrid.txt file, with suffix ‘_mean’, ‘_mean*’, ‘_mode’ or ‘_pop’.

fulltimes.txt

Description: predictions at all times present in the data set (doses and measurements)
Delimiter: tab
Outputs: Same as finegrid.txt.

Notice that in case of several outputs, Monolix generates fulltimes1.txt, fulltimes2.txt, …

If additional outputs have been added to the table list in the model file, the corresponding values will also be outputted in the fulltimes.txt file, with suffix ‘_mean’, ‘_mean*’, ‘_mode’ or ‘_pop’.

individualContributionToLL.txt

The file appears only if the log-likelihood task has been run.

Description: Log-likelihood for each subject.
Delimiter: tab
Outputs:

Subject: subject name.
Linearization (if LL computed by linearization): log-likelihood of the subject, obtained by linearization of the system.
Importance Sampling (if LL computed by importance sampling): log-likelihood of the subject, obtained by importance sampling.

covariateSummary.txt

The file appears only if covariates columns are present in the data set.

Description: summary of the covariate model.
Delimiter: variable
Outputs:

Continuous covariate: mean, median, std, min, max.
Categorical covariate: modalities, number and % of appearance of each modality.