Evaluation of methods to handle nuisance covariates that are non-ignorable

Background: As the frequency of the covariate in the population tends to zero, alpha error inflates. Low frequencies may occur with some genotypes and concomitant medications. Since, (1) the presence of an effect cannot be determined accurately then these “rare” covariates are a nuisance, and (2) if rare covariates influence parameter estimates they are “non-ignorable”. The present study evaluated methods to handle nuisance and non-ignorable covariates.

Aims: (1) To calibrate the frequency of the occurrence of a covariate in terms of alpha error inflation (nuisance), (2) to calibrate the size of the covariate effect (at the frequency from (1)) which causes bias in the parameters (non-ignorability), and (3) to assess methods of dealing with nuisance and non-ignorable effects.

Methods: Simulation of the data was performed with MATLAB software (version 2012b) and estimation with NONMEM using FOCE-INTERACTION. An intravenous bolus 1-compartment PK model was used for simulation after a single unit dose administration. The between subject variability (BSV) of was assumed to be log-normal. The residual variability was additive. (1) The false positive rate was determined using a Wald test for the varying covariate frequencies with the data simulated under no covariate effect. (2) Ignorability was assessed based on the influence of the low frequency covariate on the estimates of CL and the BSV (CL) based on three simulation scenarios with weak (20% increase in CL), moderate (50% increase in CL) and strong covariate (100% increase in CL) effects. (3) After the frequency (1) and strength (2) of the covariate have been calibrated, three methods to handle these nuisance and non-ignorable effects were evaluated which included considering a heavy tail BSV distribution for CL, addition of a nuisance fixed effect parameter for the covariate effect and case deletion.

Results: (1) The false positive rate was found to be above the nominal alpha value of 0.05 when the frequency of the covariate was less than 10%. (2) Ignorability was related to frequency and strength of the covariate. For low frequency covariates (< 5%), a strong covariate effect was non-ignorable (but not weaker covariate effects). (3) Addition of a fixed effect parameter to accommodate the covariate effect resulted in elimination of bias for CL and BSV (CL). The Box-Cox transformation resulted in elimination of the bias for CL but bias for BSV (CL) remained.

Conclusions: The presence of nuisance and non-ignorable covariate effects can be effectively handled through addition of a fixed effect covariate model, but the coefficients that pertain to the covariate should not be used to make inference. The approach of allowing for a heavy tailed distribution for inclusion of the covariate through a Box-Cox transformation was found to be less effective.

Chakradhar Lagishetty