Jakob Ribbing and Niclas Jonsson
Uppsala University
Identification and quantification of covariate relationships is an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modeling. The covariate model is often built in a stepwise manner. With such methods, selection bias may be a problem, if the covariate model is selected based on the same data as used for estimating the model parameters. Competition between multiple covariates could further increase selection bias [1], especially when there is a high correlation between the covariates, and could result in a loss of power to find the true covariates.
The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and some states of nature (se below).
Data sets with 20 to 1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation (r=0, 0.15, 0.50 and 0.85, respectively) to the other four covariates. Data sets, in which each individual had 2 or 3 PK observations, were simulated using a one compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter individual variability in the structural model parameters was also introduced to the simulation model. 7,400 replications were simulated independently, for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified p-value) the different covariates, along with the estimated covariate coefficient was recorded.
The results show that selection bias is very high for small datasets (50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to twice its true value, rendering the covariate model useless for predictive purposes. Surprisingly, all though competition from false covariates caused substantial loss in the power of selecting the true covariate, selection bias increased only marginally if statistical significance was required. Without the competition, there was a clear link from the power of selecting a true covariate to bias and predictive performance of the selected covariate model.
Reference:
[1] Miller, A. J. (1984). “Selection of Subsets of Regression Variables.” Journal of the Royal Statistical Society. Series A (General) 147(3): 389-425.
Reference: PAGE 12 (2003) Abstr 382 [www.page-meeting.org/?abstract=382]
Poster: poster