THETA Parameter Relative Standard Error (RSE) Calculation
It is sometimes preferable to write non-linear mixed effects models with parameters in the log domain to ensure that they remain positive or to stabilize their variance. A common use case is “mu-referencing”, e.g., the expression for CL
CL = THETA(1) * EXP(ETA(1))
can be written as
MU_1 = LOG(THETA(1))
CL = EXP(MU_1+ETA(1))
In the above example, MU_1 is the natural log of the typical value of CL. Pirana allows display of this LOG(CL) value (default), or the exp(THETA) box can be checked to back-transform the estimate to original scale.
THETA Parameter Relative Standard Error (RSE) Calculation
Percent Relative Standard Error for THETA parameters are calculated as:
RSE(%) = (SE / Estimate) * 100
where:
SE is the standard error of the estimated parameter (THETA)
Estimate is the estimated value of the parameter (THETA)
The RSE provides a measure of the precision or relative uncertainty associated with the estimated parameter. A smaller RSE indicates a more precise estimate with less uncertainty, while a larger RSE indicates a less precise estimate with higher uncertainty. It is important to note that the calculation of the RSE assumes that the standard errors and estimates follow a normal distribution and that the estimated parameter is not near zero or negative. Additionally, the RSE should be interpreted in the context of the specific parameter being estimated and the modeling assumptions and objectives of the analysis.
Note: RSE calculation depends on a successful covariance step. RSE will not be reported if SEs are not available.