Model Risk From Decision Consequence and Model Influence

Why Decision Consequence and Model Influence Are Separate

A PBPK prediction can be uncertain without creating substantial decision risk. If plausible changes in the prediction would not change the action, the decision may be relatively insensitive to the model. Conversely, a small prediction error can matter greatly when the decision rule is close to a threshold and the resulting action has serious consequences. Risk assessment therefore needs two distinct questions: how serious would a wrong decision be, and how strongly does the action depend on the model prediction?

The context of use identifies the decision being supported and the population, drug, and conditions involved. For this assessment, take that context and its decision rule as specified. The task is not to assign a single label to a model in every possible use; it is to understand risk for the particular decision at hand.

The reference prediction may be the prediction that would be obtained if the relevant model inputs or structure were correct, or another defensible reference specified for the analysis. In practice, the truth is usually not observed directly. Analysts can therefore examine plausible error scenarios, rather than claim that \(E\), \(D\), or \(W\) is known with certainty.

Consequence describes the severity of an incorrect decision, using a context-appropriate measure such as clinical harm, loss of efficacy, or a meaningful operational cost. Model influence describes how much the selected action depends on the model prediction. One probabilistic expression of error-conditional influence is \(P(D\mid E)\). It is not the probability of a wrong decision: it includes action changes that may still lead to the appropriate action.

Connecting Error, Influence, and Harm

A useful way to organize the reasoning is to trace the route from prediction error to decision. First, specify what counts as a material prediction error. Next, apply the same decision rule to the reference and erroneous predictions to determine whether the action changes. Finally, evaluate the changed action against the true state or an appropriate decision criterion. Each step answers a different question.

This identity follows from the probability chain rule, provided the conditional probabilities are defined for events with nonzero probability. It does not assume independence. \(P(E)\) is the probability of a materially erroneous prediction under the scenarios or probability model being considered. \(P(D\mid E)\) is the probability that such an error changes the action. \(P(W\mid E,D)\) is the probability that the changed action is wrong, conditional on an error that changed the action. Their product is the probability of the combined event that all three occur.

This combined probability is not, by itself, a complete measure of harm. The severity of a wrong decision can vary across scenarios. Also, a changed action that is wrong may not increase harm if the reference action would have been wrong as well. For an attributable comparison, let \(L(a,\theta)\) denote the loss under action \(a\) and true state \(\theta\). The loss increase caused by an error-induced action change is:

A positive \(\Delta L\) means the changed action has greater loss than the reference action for that state; a negative value means the changed action has lower loss. When probabilities and losses are defensible, an expected incremental loss can be calculated across scenarios as the average of \(\Delta L\). When they are not, a qualitative assessment of consequence and influence is more honest than a numerical risk score.

How to Judge Model Influence

Model influence is decision-specific. It depends on the prediction, the decision rule, and the range and direction of plausible prediction errors. A prediction can be highly influential if small plausible changes cross a decision boundary. A large numerical error can have little influence if all plausible values lead to the same action. Therefore, prediction error measured only by its absolute size does not establish decision influence.

For a threshold rule, compare the reference and perturbed predictions with the threshold. For a rule selecting among several actions, apply the rule to each plausible prediction and record whether the selected action changes. Hold other information \(z\) fixed when isolating the model’s contribution; if \(z\) also varies, state that and assess the combined scenarios. The error scenarios should be relevant to the intended use, rather than arbitrary perturbations.

A practical influence assessment should include whether the model is near a decision boundary, whether plausible errors cross that boundary, and whether errors in different directions lead to different actions. If every plausible scenario produces the same action, the decision is locally robust to the examined errors. This does not prove that the model is accurate: the scenarios may omit an important error or may not cover the relevant uncertainty.

Consequence: Severity Is Not the Same as Probability

Consequence concerns what follows if the decision is wrong, not how likely the model is to be wrong. Consider the magnitude, duration, reversibility, and distribution of potential harm where these are relevant to the use. A wrong decision affecting a single, readily monitored choice may have a different consequence from a wrong decision that could expose many patients to serious harm. Consequence should be described in terms meaningful for the specified decision, not inferred from prediction error alone.

Putting the Two Dimensions Together

A useful qualitative classification keeps consequence and model influence visible as separate judgments. For consequence, state the plausible severity of a wrong decision and why it matters. For influence, state whether plausible material errors can change the action, how often they do so if that can be estimated, and whether the action is near a boundary. The combination identifies where model-related decision risk deserves particular attention without pretending that unlike quantities are automatically commensurate.

This comparison is not a scoring formula. A high-consequence decision with low observed influence is not automatically safe: influence may be underestimated if the error scenarios are too narrow. Likewise, high influence does not by itself mean high harm. A change in action can be appropriate, and an action can remain wrong even when the model prediction is accurate.

When numerical probabilities are available, state how they were obtained and what scenarios they represent. When they are not, describe the basis for qualitative judgments and the uncertainty around them. Avoid multiplying ordinal labels such as “high” and “medium” as if they were measured probabilities or loss values.

Diagnostics, Alternatives, and Limitations

Warning signs include defining material error only after seeing which errors change the decision; applying different decision rules to reference and perturbed predictions; treating every action change as harmful; and reporting a probability without specifying its event and conditioning. Check that the prediction quantity, error criterion, decision rule, and consequence measure all correspond to the same context of use.

Alternative analyses answer related but different questions. Prediction-error summaries describe model discrepancy but do not alone show whether actions change. Sensitivity analysis examines how predictions respond to inputs or assumptions; it is informative about influence only when linked to the decision rule. Expected-loss analysis can combine probabilities and consequences when both can be justified, while qualitative review is preferable when reliable numerical inputs are unavailable. None of these substitutes for stating what decision is being supported.

The assessment is limited by imperfect knowledge of prediction error, the true state, and the consequences of actions. Probabilities from a scenario set depend on its weighting and coverage. A decision rule may omit relevant clinical judgment, and a stated loss scale may simplify heterogeneous outcomes. Report these limitations rather than treating a classification as a guarantee of safety or model validity.

A Short Decision-Risk Review

The central discipline is to keep three questions separate: can the prediction be materially wrong, can that error change the action, and would the changed action be wrong or more harmful? Consequence adds a further question about the severity of that outcome. Keeping these distinctions explicit makes a risk judgment interpretable and prevents model influence from being mistaken for harm.