Reporting Uncertainty in Preclinical-to-Human Predictions

From a Predictive Distribution to a Report

A preclinical-to-human prediction is not just a single number with an error bar attached. It is a distribution for a specified human quantity, under specified assumptions about the population, treatment conditions, and translation from animal evidence. A useful report makes those conditions visible, then gives a central estimate and an interval whose meaning is stated precisely. This lets readers assess the prediction without mistaking a model output for a guaranteed human outcome.

The reporting task begins by naming the target. For example, human systemic clearance for a stated population and route is different from an individual patient's clearance, and both differ from exposure under a particular regimen. A summary should identify what is predicted, for whom, under what conditions, and in what units. It should also identify whether the distribution includes uncertainty in model parameters, uncertain inputs, between-person variability, model discrepancy, or some combination. These components answer different questions and should not be silently blended.

A predictive interval is not automatically a confidence interval for a model parameter. Nor does a 90% predictive interval mean there is a 90% probability that a fixed, already-realised human outcome lies inside the interval. Its coverage statement concerns repeated predictions made under the specified predictive procedure and conditions. In a model-based analysis, the numerical distribution is conditional on the inputs and assumptions used; if those are inadequate, nominal coverage need not be achieved.

What a Decision-Ready Summary Contains

A concise report should let a reader reconstruct the meaning of the displayed numbers. At minimum, state the prediction target and units; the central estimate and its type; the interval level and endpoints; the evidence and model basis; the major assumptions; the influential uncertainties; and the scope and limits of validation. If the distribution is asymmetric, report its quantiles rather than forcing it into a symmetric estimate-plus-or-minus form.

The central estimate should suit the distribution and the question. For a right-skewed positive quantity, the median may describe a typical predictive value more clearly than the arithmetic mean. The mean may be useful when the decision concerns expected magnitude, but it can be pulled upward by a long upper tail. If both matter, report both and label them. For a lognormal distribution, for example, the median and mean are generally different.

A central interval is one choice, not the only possible summary. A central interval places equal probability in each tail under the predictive distribution. A one-sided bound may be more relevant when the concern is exceeding a threshold, but it must be identified as one-sided rather than described as a central interval. Whatever summary is used, specify its coverage level, endpoints, units, and whether the numbers are quantiles from simulation or an analytical distribution.

Quantiles, Coverage, and a Short Justification

For a continuous predictive distribution with cumulative distribution function \(F\), its \(q\)-quantile is a value \(x_q\) satisfying \(F(x_q)=q\). The central \(100(1-\alpha)\%\) predictive interval is therefore \([x_{\alpha/2},x_{1-\alpha/2}]\). Its model-implied probability is \(1-\alpha\), because:

This calculation justifies the interval under the stated distribution. It does not demonstrate that the distribution is calibrated for future human outcomes. Empirical coverage depends on whether the predictive procedure, including its assumptions and uncertainty components, behaves adequately in the relevant application domain. The distinction is central: a model can produce a mathematically correct 90% interval conditional on its own distribution and still have poor coverage against external outcomes.

Assumptions, Influential Uncertainties, and Validation

A report should distinguish assumptions that define the prediction from uncertainties that vary within those assumptions. Relevant assumptions may include the translation structure, the selected animal evidence, the form of model discrepancy, and the treatment of uncertain physiological inputs. State the ones that materially shape interpretation rather than listing every implementation detail. The earlier material on model discrepancy, sensitivity analysis, extrapolation distance, and validation provides methods for examining these issues; the summary should convey the implications that matter for this prediction.

When reporting influential uncertainties, name the uncertain quantities or structural choices and describe how they affect the prediction. A sensitivity ranking identifies what most affects the output under the analysis performed; it does not establish that the influential factor is the true cause of prediction error. Correlated inputs and interactions can complicate rankings, so state the analysis basis when it changes interpretation. Avoid describing uncertainty as “explained” by a source unless the method supports that claim.

Validation statements also need a defined scope. Report what was tested, how many validation cases were available, what prediction target and interval were assessed, and whether validation involved relevant human data or only an extrapolation proxy. Leave-one-species-out performance or external animal comparisons can inform credibility, but do not by themselves demonstrate human predictive coverage. Sparse validation evidence should be described as limited evidence, not as proof of success or failure.

Diagnostics, Alternatives, and Common Pitfalls

Before finalising a summary, check that the reported target matches the quantity generated by the model; that the central estimate is correctly labelled; that interval endpoints are ordered and in the stated units; and that the interval level and construction are explicit. Inspect the predictive distribution for skewness, multimodality, implausible tails, or boundary problems. A single median and interval can conceal separated modes or a tail that matters to a decision; in such cases, describe the shape or report additional quantiles or scenarios rather than relying on a compact summary alone.

There are several legitimate alternatives to a central interval. A mean may be preferable to a median when expected magnitude is the relevant summary. A one-sided quantile can communicate a threshold-focused concern. Scenario-specific summaries can be clearer when predictions differ substantially under distinct assumptions. These alternatives are not interchangeable: identify which quantity is reported and why. If a distribution is multimodal, a central interval may include values with little predictive density between modes, so a single interval may be an incomplete description.

A frequent mistake is to write, “There is a 90% chance that the true human clearance lies between 4.60 and 15.1 \(\mathrm{L/h}\).” This treats a realised quantity as though it were still random after observation and may also confuse a predictive interval with a parameter interval. Instead, say that the stated interval is a central 90% predictive interval under the specified model and assumptions, and qualify its intended coverage by the available calibration evidence. Another mistake is to report a prediction without its target population or conditions; the correction is to state those alongside the numbers, not in an ambiguous footnote.