Increasing the efficiency of the covariate search algorithm in the SCM
E. Niclas Jonsson and Kajsa Harling
Pharmetheus AB, Uppsala, Sweden
Objectives: To compare the efficiency of the legacy SCM covariate search algorithm  to the new SCM+ algorithm.
Methods: The SCM+ algorithm was implemented as a wrapper on top of PsN's SCM program . SCM+ seeks to reduce the legacy SCM run times for covariate searches by adaptive scope reduction (ASR), constrained number of function evaluations, and the CTYPE=4 termination option in NONMEM.
Briefly, ASR uses the outcome from prior search steps to reduce the search scope by removing parameter-covariate combinations with low potential of being included in the final model. When the forward search is finished and before the backward exclusion phase starts, the removed parameter-covariate combinations are re-tested.
To avoid situations with excessive run times without any real progression in the objective function value (OFV) towards convergence, the allowed maximum number of function evaluations (MAXEVAL) in NONMEM is reduced. The reduction in MAXEVAL is based on the number of function evaluations required in the base model without any covariates.
In a similar spirit, the CTYPE=4 option in NONMEM is used, which bases the termination only on OFV (and not the default combination of OFV and parameter gradients, etc). The rationale for the reduction of MAXEVAL and the use of CTYPE=4 is that the SCM algorithm is driven solely by differences in OFV and any factor that increases run-times without impacting OFV should be avoided.
Two real data examples were used to compare the efficiency of the algorithms. Both are phase 3 pharmacokinetic data sets, including data from 1628 and 370 subjects, respectively. In the latter example, the data set was a subset of the original data set to manage run-times. The first model, which has previously been published , was implemented using differential equations and the second model included inter-occasion variability from 9 occasions.
Performance was measured as the required total number of function evaluations and total run-times under assumptions of different degrees of computational resource constraints. The search scope for the two data sets included 24 and 57 parameter-covariate relationships,respectively.
Results: Both search algorithms resulted in the same final covariate models. Overall, the SCM+ algorithm required 54% less function evaluations (both examples), compared to the legacy SCM, to establish the final model. Assuming single threaded NONMEM execution, the SCM+ searches required 56% and 49% less time for each of the two data sets, respectively, compared to the legacy SCM searches. Without computational resource constraints, a situation which is maximally beneficial for the legacy SCM search, the SCM+ searches still required less time (43% and 45% less time).
Conclusions: The SCM+ algorithm has the potential to reduce the run-time requirements of covariate searches by more than 50% compared to the legacy SCM search algorithm. This is accomplished by reducing the number of times that non-significant parameter-covariate combinations are tested and by accepting that the covariate selection decisions are based on slightly different, but for the task at hand more relevant, convergence criteria, compared to the default criteria in NONMEM.
 Jonsson EN and Karlsson MO, Automated covariate model building within NONMEM, PharmRes (15), 1998.
 Lindbom L, Ribbing J and Jonsson EN. Perl-speaks-NONMEM (PsN) - a Perl module for NONMEM related programming. Comp Meth Prog Biomed 75 (2), 2004.
 Jonsson EN et al, Population pharmacokinetics of tanezumab in phase 3 clinical trials for osteoarthritis pain. Br J Clin Pharm 81 (4) 2015.