Why Model Resolution Is a Decision Choice
A model can report a population average, a prediction for a particular patient, a complete time course, or a single summary such as total exposure. It can also report results for one broad population or for several narrowly defined subgroups. These are different levels of resolution: they determine what distinctions the model output preserves.
The appropriate level is not automatically the most detailed one. It is the least coarse level that still gives the information needed for the intended decision. Begin with the decision rule: what quantity is compared with what threshold, for whom, and over what period? Then select predictions that preserve those distinctions. A decision based on a population-average exposure may not need patient-specific predictions; a decision about whether any patient exceeds a safety limit may need them.
This choice complements the earlier material on linking model outputs to decision rules and matching data to the intended use. It concerns the form and granularity of the output, not which model class to use or how complex its implementation should be.
Three Resolution Choices
For an outcome \(Y_i(t)\), where \(i\) identifies a person and \(t\) denotes time, resolution can be considered along three related dimensions.
- Individual or population. An individual-level prediction concerns a particular person, usually conditional on that person’s relevant characteristics and information. A population-level prediction describes a target population, for example through its mean, distribution, or proportion meeting a criterion. A population mean is not itself a prediction for every member of that population.
- Time course or summary. A time-course output represents how an outcome changes over time. A summary measure compresses that course into a quantity such as maximum concentration, total exposure over a stated interval, or a value at a specified time. A summary is useful only if it retains the information relevant to the decision.
- Fine or broad subgroups. A broad analysis may combine people into one target population or a few large groups. A finer analysis distinguishes characteristics such as renal-function categories or age bands. Subgroups are useful when the distinction could change the decision and can be meaningfully supported by the evidence.
These dimensions can be combined. A decision might require a population distribution of maximum concentration, stratified by renal-function category, rather than a single population mean or a full time course for every person. State the required output precisely enough that someone can tell what is averaged, across whom, and over what time interval.
Start With the Decision Rule
A practical way to choose resolution is to work backward from the consequence of the decision. Identify the quantity the rule uses, the unit and time window, the relevant population or person, and any subgroup-specific criteria. Then ask what would be lost by summarizing or pooling the predictions. If the discarded detail could change which action the rule selects, the output is too coarse.
Specify the outcome, population, time window, and decision threshold or comparison that matters.
Decide whether the rule applies to an individual, a population summary, or a distribution of individual outcomes.
Use a time course if the decision depends on when or how an outcome changes; use a summary if the rule is defined in terms of that summary.
Retain distinctions that could lead to different decisions, and check that the available evidence can support those distinctions.
Worked Example: Individual Risk Versus a Population Mean
Hypothetical scenario. A dose decision uses a safety threshold of 5 units for a patient-specific exposure measure. Two hypothetical patients have model-predicted exposures of 6.2 and 3.1 units. Assume that these predictions refer to the same exposure definition and time interval, and that the stated rule applies to each patient separately.
The patient-level comparisons are direct: \(6.2 > 5\), so the first prediction exceeds the threshold, while \(3.1 < 5\), so the second does not. The arithmetic mean is
The mean, 4.65 units, is below 5 units. But applying the threshold to this mean does not answer the patient-specific question: one of the two individual predictions is above the threshold. The mean may be relevant to a decision defined for average exposure; it cannot replace individual predictions when the rule is applied separately to each patient. In a real application, uncertainty in the predictions would also need consideration, but it does not change this distinction between the decision unit and the average.
When a Time Course Can Be Summarized
A time course preserves when an outcome rises, falls, or reaches a peak. A summary discards some or all of that ordering. For example, area under a concentration–time curve (AUC) summarizes cumulative exposure over a specified interval, whereas maximum concentration (\(C_{\max}\)) summarizes the highest concentration in that interval. Neither is universally more informative: the decision rule determines which is relevant.
A summary is adequate when the decision is defined using that summary, or when the relationship between the summary and the decision is established for the intended use. If a decision concerns a peak-related safety limit, equal AUC does not imply equal peak concentration. If it concerns cumulative exposure, a single concentration at one time may not represent the relevant quantity. The calculation of a summary also depends on the time interval and, for observed or simulated points, the method used to obtain it.
Worked Example: Equal AUC Does Not Mean Equal Peak
Hypothetical scenario. Two concentration–time profiles are specified at times 0, 2, 4, 6, and 8 hours, with concentrations in mg/L. Assume linear change between successive points, and estimate AUC from 0 to 8 hours with the trapezoidal rule. Suppose a separate decision rule flags a profile if its maximum concentration exceeds 9 mg/L.
| Time (hours) | Profile A (mg/L) | Profile B (mg/L) |
|---|---|---|
| 0 | 0 | 0 |
| 2 | 8 | 2 |
| 4 | 6 | 10 |
| 6 | 3 | 5 |
| 8 | 0 | 0 |
For equally spaced times, each trapezoid has width 2 hours, so each area is the width times the average of its two endpoint concentrations. For Profile A,
For Profile B,
Both profiles have an estimated AUC of 34 mg·h/L, but their maxima differ: Profile A has \(C_{\max}=8\) mg/L, whereas Profile B has \(C_{\max}=10\) mg/L. Under the stated peak rule, Profile A does not exceed 9 mg/L and Profile B does. AUC alone cannot distinguish their decisions; the peak or relevant time-course detail must be retained. This conclusion assumes the specified interpolation and that the rule is applied to these profiles; it does not establish that either profile predicts a clinical outcome.
Choosing Subgroup Granularity
Pooling people can make results easier to communicate and may be appropriate when the decision applies uniformly to the whole target population. But a pooled result can conceal different outcomes among subgroups. Conversely, splitting into many narrow groups can produce unstable estimates or groups for which the data provide little information. The relevant question is not simply whether groups differ; it is whether distinguishing them is necessary for the decision and supportable by the available evidence.
Worked Example: A Pooled Result Hides a Subgroup Below the Target
Hypothetical scenario. A development team evaluates whether a predicted response reaches a minimum target of 4 units in two renal-function subgroups. Assume that the hypothetical target population comprises 80% of people in the first subgroup and 20% in the second, and that predicted subgroup mean responses are 6 and 2 units, respectively. The decision is to check whether each subgroup reaches the target.
The population-weighted mean is
The pooled mean of 5.2 units exceeds the target of 4 units. However, the first subgroup mean is 6 units, above target, and the second subgroup mean is 2 units, below target. A rule that checks each subgroup would therefore reach a different conclusion from a rule that checks only the pooled mean. The weighting assumptions and the subgroup means are part of this example; changing the target population weights could change the pooled mean, but would not change the stated subgroup comparisons.
This example supports a finer subgroup distinction because the decision explicitly asks whether each subgroup meets the target. If the decision instead concerned only the target-population average, the weighted mean could be the relevant output. Neither choice is universally correct apart from the decision it is meant to support.
Diagnostics, Alternatives, and Limitations
A resolution mismatch often appears as a mismatch between the quantity reported and the quantity used by the rule. Check whether a population average is being used to answer an individual question; whether a summary hides a time-specific threshold crossing; and whether pooling combines groups for which different actions may be warranted. Also verify that the target population, subgroup definitions, measurement units, and time interval match the decision statement.
| Decision need | Potentially suitable output | What may be lost if made coarser |
|---|---|---|
| Average outcome in a defined target population | Population mean or another specified population summary | Variation or the fraction of people in an important range |
| Whether a particular patient crosses a threshold | Individual prediction, with relevant uncertainty | Differences between patients |
| Whether a peak or timing rule is met | Time course or peak and timing summaries | When the outcome occurs or how high it rises |
| Whether distinct groups require different decisions | Predictions stratified by decision-relevant groups | Subgroup differences hidden by pooling |
No single output resolves every question. Individual-level outputs do not by themselves guarantee reliable predictions for a particular person; the evidence may support only population-level statements. A fine subgroup breakdown may be poorly supported if few data inform a group or if the group is not adequately characterized. A summary measure may be easier to interpret but may discard features needed for another decision. The appropriate response to these limits is to state what the evidence supports, not to imply that unreported detail is known.
A common mistake is to say, “The population mean is below the safety threshold, so every patient is below it.” That conclusion does not follow: an average can be below a threshold even when some individual values exceed it. The correction is to match the output to the rule—use the mean for a mean-based decision, and an individual prediction or a suitable distributional summary for a decision about individual exceedance. A related mistake is to assume that the most detailed output is automatically best. Extra detail is useful only when it addresses a decision-relevant distinction and can be supported by evidence.
Check Your Understanding
For each question, identify the resolution that matches the stated decision and compare your reasoning with the solutions.
- A rule asks whether the target-population mean exposure is below 20 mg·h/L. Is an individual-level output required by that rule?
- A peak safety rule applies to each patient. Two hypothetical predicted peak concentrations are 7 and 13 mg/L, and the threshold is 10 mg/L. What does their mean imply, and what does it fail to answer?
- A decision compares AUC over 24 hours with a specified limit. Is a full concentration–time course always required as the reported decision output? State one condition for using AUC.
- A pooled response exceeds a target, but the rule requires each renal-function subgroup to meet the target. What subgroup resolution is needed?
Solutions. (1) No. The rule is explicitly about the target-population mean, so a suitable population-mean prediction is the relevant output; it does not establish that every individual is below 20 mg·h/L. (2) The mean is \((7+13)/2=10\) mg/L, equal to the threshold. That mean does not answer the patient-specific rule: one prediction is below 10 mg/L and the other is above it. (3) Not necessarily. AUC can be the decision output if the rule is defined in terms of AUC over that same 24-hour interval and the method used to estimate it is appropriate. A time course may still be needed for a different question, such as a peak threshold. (4) Predictions must preserve the renal-function subgroup distinction, because the rule checks each subgroup rather than only the pooled response.