Population modeling run options

The following options are displayed in the Run Options tab when the Population? checkbox is checked.

Not all run options are applicable for every run method. Some options are made available or unavailable depending on the selected run method. For detailed explanations of Maximum Likelihood Models run options, see “Run modes”.

In the Algorithm menu, select one of seven run methods:

FOCE L-B (First-Order Conditional Estimation, Lindstrom-Bates)
FOCE ELS (FOCE Extended Least Squares)
FO (First Order)
Laplacian
Naive pooled
IT2S-EM (Iterated two-stage expectation-maximization)
QRPEM (Quasi-Random Parametric Expectation Maximization)

In the N Iter field, type the maximum number of iterations to use with each modeling run (the default is 1000).
Check the NonParametric checkbox to use the NonParametric engine for producing nonparametric results in the output. This option is available for FOCE L-B, FOCE ELS, Laplacian, IT2S-EM, and QRPEM methods.

•If the NonParametric checkbox is selected, then the N NonPar field is made available.

•In the N NonPar field, type the maximum number of iterations of nonparametric computations to complete during the modeling process.

Check the Sort Input? checkbox (the default) to sort the input by subject and time values. (Refer to the Sort Input? description in the Individual Modeling section for additional information.)
Select the local or remote machine or grid on which to execute the job from the Execute on menu.

The contents of this menu can be edited, refer to “Compute Grid preferences”.

Note:When a grid is selected, loading the grid can take some time and it may seem that the application has stopped working.

Note:Make sure that you have adequate disk space on the grid for execution of all jobs. A job will fail on the grid if it runs out of disk space.

In the Max ODE menu, select one of the ODE (ordinary differential equations) solver methods. For more on ODE methodology, see “Differential equations in NLME”.
Check the Synthetic Gradients? checkbox to allow synthetic gradients in the model.

When this is selected in population modeling, the engine computes and makes use of analytic gradients with respect to etas. In some cases, with differential equation models, one or more gradient components can be computed by integrating the sensitivity equations along with the original model system using a numerical differential equation solver. For reasonably sized models, selecting Synthetic Gradients can help speed and accuracy.
In the Stderr menu, select the form of standard error to compute. (Refer to the Stderr description in the Individual Modeling section for additional information.)

none (no standard error calculations are performed)
Central Diff, that uses the form:

Forward Diff, that uses the form:

Select the Method of computing the standard errors from the menu:

Hessian: The Hessian method of parameter uncertainty estimation evaluates the uncertainty matrix as R-1, where R-1 is the inverse of the second derivative matrix of the -2*Log Likelihood function. This is the only method available for individual models.

Sandwich: The sandwich method has both advantages and disadvantages relative to the Hessian method. The main advantage is that, in simple cases, the sandwich method is robust for covariance model misspecification, but not for mean model misspecification. The main disadvantage is that it can be less efficient than the simpler Hessian-based method when the model is correctly specified.

Fisher Score: The Fisher Score method is fast and robust, but less precise than the Sandwich and Hessian methods.

Auto-detect: When selected, NLME automatically chooses the standard error calculation method. Specifically, if both Hessian and Fisher score methods are successful, then it uses the Sandwich method. Otherwise, it uses either the Hessian method or the Fisher score method, depending on which method is successful. The user can check the Core Status text output to see which method is used.

In the Confidence Level % field, enter the confidence interval percentage or use the default.
In the N AGQ field, enter the maximum number of integration points for the Adaptive Gaussian Quadrature. This field is available for FOCE ELS and Laplacian methods.
In the ISAMPLE field, enter the number of sample points or use the default. For each subject, the joint likelihood, the mean, and the covariance integrals will all be evaluated with this number of samples from the designated importance sampling distribution. Increasing this number improves the accuracy of the integrals. This option is available for the QRPEM method.
Check the PCWRES? checkbox to generate the predictive check weighted residuals in the results. This option is available for FOCE L-B, FOCE ELS, FO, Laplacian, and IT2S-EM methods. It is unchecked by default. When checked, then the nrep field becomes available. Enter the number of replicates or use the default for predictive check weighted results. The maximum number of replicates is 1001, a number higher than this is automatically reduced, by the system, to 1001 and a warning appears in the Core Status tab.

PCWRES is an adaptation of France Mentre’ et al.'s normalized predictive error distribution method. Each observation for each individual is converted into a nominally normal N(0,1) random value. It is similar to WRES and CWRES, but computed with a different covariance matrix. The covariance matrix for PCWRES is computed from simulations using the time points in the data.
Check the MAP-NP Start? checkbox to perform Maximum A Posteriori initial Naive Pooling. This option is available for FOCE L-B, FOCE ELS, FO, Laplacian, QRPEM and IT2S-EM methods. If selected, an Iterations field appears requesting the number of iterations to apply MAP-NP.

This process is designed to improve the initial fixed effect solution with relatively minor computational effort before a main engine starts. It consists of alternating between a Naive pooled engine computation, where the random effects (etas) are fixed to a previously computed set of values, and a MAP computation to calculate the optimal MAP eta values for the given fixed effect values that were identified during the Naive Pooled step.

On the first iteration, MAP-NP applies the standard Naive pooled engine with all etas frozen to zero to find the maximum likelihood estimates of all the fixed effects. The fixed effects are then frozen and a MAP computation of the modes of the posterior distribution for the current fixed effects parameters is then performed. This cycle of a Naive pooled followed by MAP computation is performed for the number of requested iterations. Note that, throughout the MAP-NP iteration sequence, the user-specified initial values of an eps and Omega are kept frozen.
Check the FOCEHess? checkbox to use FOCE Hessian. This option is available for Laplacian and IT2S-EM methods.
Click Advanced to toggle access to advanced run options for population models (only).

All engines have the following Advanced options.

•In the LAGL nDig field, enter the number of significant decimal digits for the LAGL algorithm to use to reach convergence. Used with FOCE ELS and Laplacian Run methods. LAGL, or LaPlacian General Likelihood, is a top level log likelihood optimization that applies to a log likelihood approximation summed over all subjects.

•In the SE Step field, enter the standard error numerical differentiation step size. SE Step is the relative step size to use for computing numerical second derivatives of the overall log likelihood function for model parameters when computing standard errors. This value affects all Run methods except IT2S-EM, which does not compute standard errors.

•In the BLUP nDig field, enter the number of significant decimal digits for the BLUP estimation to use to reach convergence. Used with all run methods except Naive pooled. BLUP, or Best Linear Unbiased Predictor, is an inner optimization that is done for a local log likelihood for each subject. BLUP optimization is done many times over during a modeling run.

•In the Modlinz Step field, enter the model linearization numerical differentiation step size. Modlinz Step is the step size used for numerical differentiation when linearizing the model function in the FOCE approximation. This option is used by the FOCE ELS and FOCE L-B Run methods, the IT2S-EM method when applied to models with Gaussian observations, and the Laplacian method when the FOCEhess option is selected and the model has Gaussian observations.

•In the ODE Rel. Tol. field, enter the relative tolerance value for the Max ODE.

•In the ODE Abs. Tol. field, enter the absolute tolerance value for the Max ODE.

•In the ODE max step field, enter the maximum number of steps for the Max ODE.

The following are additional advanced options available only for the QRPEM method.

Check the MAP Assist checkbox to perform a maximization of the joint log likelihood before each evaluation of the underlying integrals in order to find the mode. The importance sampling distribution is centered at this mode value. (If MAP Assist is not selected, the mode finding optimization is only done on the first iteration and subsequent iterations use the mean of the conditional distribution as found on the previous iteration.) If the MAP Assist checkbox is checked, enter the periodicity for MAP assist in the period field. (For example, a value of two specifies that MAP assist should be used every other iteration.)
Select the importance sampling distribution type from the Imp Samp Type pull-down menu.

normal: Multivariate normal (MVN)

double-exponential: Multivariate Laplace (MVL). The decay rate is exponential in the negative of the sum of absolute values of the sample components. The distribution is not spherically symmetric, but concentrated along the axes defined by the eigenvectors of the covariance matrix. MVL is much faster to compute than MVT.

direct: Direct sampling.

T: Multivariate t (MVT). The MVT decay rate is governed by the degrees of freedom: lower values correspond to slower decay and fatter tails. Enter the number of degrees of freedom in the Imp Samp DOF field. A value between four and 10 is recommended, although any value between three and 30 is valid.

mixture-2: Two-component defensive mixture. (See T. Hesterberg, “Weighted average importance sampling and defensive mixture distributions,” Tech. report no. 148, Division of Biostatistics, Stanford University, 1991). Both components are Gaussian, have equal mixture weights of 0.5, and are centered at the previous iteration estimate of the posterior mean. both components have a variance covariance matrix, which is a scaled version of the estimated posterior variance covariance matrix from the previous iteration. One component uses a scale factor of 1.0, while the other uses a scale factor determined by the acceptance ratio.

mixture-3: Three-component defensive mixture. Similar to the two-component case, but with equal mixture weights of 1/3 and scale factors of 1, 2, and the factor determined by the acceptance ratio.

Check the MCPEM checkbox to use Monte-Carlo sampling instead of Quasi-Random. Although the default is recommended, using Monte-Carlo sampling may be necessary if the most direct comparison possible with other MCPEM algorithms is desired.
Check the Run all checkbox to execute all requested iterations, ignoring the convergence criteria.
In the # SIR Samp field, enter the number of samples per subject used in the Sampling Importance Re-Sampling algorithm to determine the number of SIR samples taken from the empirical discrete distribution that approximates the target conditional distribution.

The # SIR Samp from each subject are merged to form the basis for a log-likelihood optimization that allows fixed effects that are not paired with random effects to be estimated. The # SIR Samp is usually far smaller than the number that would be used if the SIR algorithm were not used.

The default of 10 is usually adequate, unless the number of subjects is extremely small. If necessary, # SIR Samp can be increased up to a maximum of ISAMPLE.
In the # burn-in Iters field, type the number of QRPEM burn-in iterations to perform at startup to adjust certain internal parameters. During a burn-in iteration, importance sampling is performed and the three main integrals are evaluated, but no changes are made to the parameters to be estimated or the likelihood. The default is zero, in which case the QRPEM algorithm starts normally. Typical values, other than zero, are 10 to 15.
Check the Frozen omega burn-in checkbox to freeze the omega but not theta for the number of iterations entered in the # burn-in Iters field. If this checkbox is not checked, then both omega and theta are frozen during the burn-in.
Check the Use previous posteriors checkbox to start the model up from the posteriors and eta-means saved from a previous run. Checking this box allows the QRPEM engine to be restarted from a previous run using the final posteriors from that run as initial posteriors in the restart, thus allowing the run to resume from exactly where it left off. To do this, press Accept All Fixed+Random in the Parameters tab to accept the final parameter estimates from the first run as initial parameter estimates for the new run, then run QRPEM with the Use previous posteriors box checked.
In the Acceptance ratio field, enter a decimal value for the acceptance ratio (default is 0.1). As this value is reduced below 0.1, the importance sampling distribution becomes broader relative to the conditional density.

Note:ISAMPLE, Imp Samp Type, and Acceptance ratio can all be used to increase or decrease the coverage of the tails of the target conditional distribution by the importance sampling distribution.

Select the Quasi-Random scrambling method to use from the Scramble menu: none, Owen, or TF (Tezuka-Faur).