Sensitivity of Pediatric Predictions to Maturation Assumptions

Why Examine Sensitivity to Maturation Assumptions?

A pediatric clearance prediction depends on the assumed course of maturation as well as on the mature clearance level. Two maturation curves can agree at one age yet differ substantially at younger or older ages. Likewise, changing a half-maturation age may have little effect in one part of the age range and a much larger effect in another. Sensitivity analysis makes these consequences visible: it asks how much the predicted clearance changes when a stated model assumption or parameter value changes, while other inputs are held fixed.

This analysis is most useful after candidate curves have been evaluated against observed data. It does not select a correct model by itself, establish that one parameter value is more probable than another, or replace evaluation of the underlying data. Its purpose here is narrower: to quantify the prediction consequences of alternative maturation assumptions.

Set Up Predictions So the Comparison Is Interpretable

To isolate maturation, consider a clearance model at a fixed reference body size:

Here \(CL(a)\) is clearance at age \(a\), \(CL_{\mathrm{mat}}\) is the clearance level after maturation is complete at that reference size, and \(M(a)\) is a maturation fraction between zero and one. Age and any age-related parameters must use consistent units. In the examples, age is measured in years and clearance in L/h. Body size is held fixed, so differences in predictions arise only from the maturation assumptions.

A common sigmoid Emax maturation function is

For \(a\geq 0\), \(TM_{50}>0\), and \(h>0\), this function rises from zero toward one. At \(a=TM_{50}\), its value is \(1/2\). The Hill coefficient \(h\) controls the steepness around that transition: larger values give a sharper transition. An alternative with the same limiting values is the exponential function

where \(k>0\) has units of inverse years when age is in years. Setting \(k=\ln(2)/TM_{50}\) makes the exponential function reach one-half at the same age as the sigmoid. Matching this single feature does not make the curves equivalent; their shapes on either side of that age can still differ.

The comparison assumes that the model forms being evaluated are meaningful over the stated age range, that the mature clearance level and reference size are held fixed, and that age is measured consistently. It also assumes the candidate parameter values are chosen deliberately and reported transparently. A sensitivity analysis cannot compensate for a maturation function that is biologically implausible or contradicted by the available observations.

Quantifying Parameter Sensitivity

A second comparison keeps the function form fixed and varies one parameter. For the sigmoid function, changing \(TM_{50}\) shifts the age at which the maturation fraction reaches one-half. A larger \(TM_{50}\) means slower maturation at any fixed positive age, so it produces a lower maturation fraction and, with all else fixed, lower clearance.

Where Does Parameter Uncertainty Matter Most?

The age at which predictions are most sensitive depends on which parameter is varied, the range of values considered, the function form, and the scale used to quantify change. The following derivation identifies the age of greatest absolute spread for one specific setup; it is not a universal rule for all maturation models.

For \(x>0\), the derivative of the factor \(x/(x^2+0.52x+0.0576)\) has the sign of

It is positive when \(x<0.24\) and negative when \(x>0.24\), so the absolute spread is largest at \(x=0.24\), or \(a=\sqrt{0.24}=0.4899\) years. This finding is specific to the selected parameter range and model. A relative difference, such as the prediction ratio, can have a different pattern and should be assessed separately when clinically relevant.

Diagnostics, Alternatives, and Limitations

A useful sensitivity analysis makes it possible to see when predictions change meaningfully, not merely to generate multiple curves. Check that the curves have the intended limits and parameter interpretation, that the age and parameter units are consistent, and that all predictions use the same mature clearance level and reference size. Tabulate predictions across the relevant age range or plot the curves with clearly identified parameter values. Look especially for unexpected curve crossings, predictions outside the intended range, or large differences concentrated where there are few observations. Such findings may indicate a coding error, an unsuitable function, or genuine extrapolation sensitivity; the calculation alone cannot distinguish among them.

The main alternatives answer related but different questions. Comparing function forms, as in the first example, tests structural sensitivity. Varying one parameter while holding the form fixed tests parameter sensitivity. Varying several assumptions together can show a combined scenario envelope, but it obscures which assumption drove the change unless additional comparisons isolate each contribution. A fitted statistical uncertainty interval instead requires an explicit probability model and uncertainty estimation; a hand-selected low-to-high scenario range does not provide that inferential interpretation.

Sensitivity results are conditional on the chosen mature clearance, body size, and candidate maturation assumptions. Holding body size constant is appropriate for isolating maturation, but it does not describe the full uncertainty of a prediction when size also varies. The values tested should be scientifically defensible and relevant to the intended population. Sparse observations at young ages, parameter correlation, misspecification, or extrapolation can all make apparently precise predictions misleading. Finally, a large difference between scenarios signals dependence on assumptions, not evidence that either scenario is correct.