Choosing The Target Population For Prediction

Why the Target Population Matters

An absolute-risk prediction is meaningful only after specifying whose risk it is intended to describe. A model may predict the cumulative incidence of an event for each covariate profile, but a single population-average risk depends on how common those profiles are in the population of interest. Standardizing to a hospital’s current patients, a regional registry, or people eligible for a planned service can therefore produce different answers—even when the fitted model and prediction horizon are unchanged.

The choice is substantive, not just computational. A prediction for a local clinical service should usually describe the people expected to use that service. A prediction intended to inform regional planning should reflect the region’s eligible population. Using the model-development sample automatically, without checking whether it matches that purpose, can answer the wrong question.

Definition: For event type $k$, time horizon $t$, and covariate profile $x$, let $F_k(t\mid x)$ denote the predicted cumulative incidence: the probability of experiencing event $k$ by time $t$, before any competing event, conditional on profile $x$. A target population is the population whose covariate distribution is used to average these profile-specific predictions. If its covariate distribution is $G$, its standardized risk is $$ R_{k,G}(t)=\int F_k(t\mid x)\,dG(x). $$

For a finite target population with profiles $x_1,\ldots,x_N$, and weights $w_i$ that sum to one, the corresponding calculation is

\widehat R_{k,G}(t)=\sum_{i=1}^{N} w_i\,\widehat F_k(t\mid x_i), \qquad \sum_{i=1}^{N}w_i=1.

With an unweighted sample representing the target population, $w_i=1/N$, so the estimate is the arithmetic mean of the individual predicted risks. With survey, calibration, or other target-population weights, use the weights appropriate to that target. The risk is still a cumulative incidence: competing events remain part of the event process rather than being treated as ordinary loss to follow-up.

State the Target Before Calculating

A useful target-population specification includes the population’s eligibility criteria, setting, and relevant calendar period, as well as the event and prediction horizon. For example, “patients eligible for this service at the regional hospitals in 2026, with 2-year risk of event 1” is more precise than “the average patient.” This description determines which people, or which covariate distribution, should contribute to the standardization.

The target is not necessarily the sample used to fit the model. That sample supplies information for estimating the profile-specific risks. The target population supplies the distribution over which those predictions are averaged. They may coincide, but they serve different roles. A chosen reference population is also not automatically a biological or statistical control group: it is the population whose average risk the prediction is intended to summarize.

Several conditions support a credible standardized prediction. The outcome definitions and time origin must be relevant to the target; the horizon must be supported by follow-up; and the fitted model must give valid conditional cumulative-incidence predictions for the target profiles. In particular, applying the model to a different population requires that the conditional relationship between the modeled covariates and event risks be sufficiently transportable. The target profiles also need adequate representation in the data used to fit the model. If important target profiles are absent or very rare, the estimate relies on extrapolation rather than well-supported prediction.

Define the use.
Specify the decision, service, or population question the risk is meant to inform, along with event type and horizon.

Describe the eligible target.
State who is included, where and when they are observed, and which covariates are needed to characterize their distribution.

Check data support.
Compare target covariate profiles with those represented in the model-fitting data; investigate sparse or absent regions before calculating a transported risk.

Choose the representation.
Use target individuals, a representative sample, or defensible population weights, and average the profile-specific predictions using that representation.

Worked Standardization Calculations

Worked Example: A Regional Target Population

Suppose a model has been judged suitable for patients in a regional service. At a 2-year horizon, it predicts event 1 cumulative incidence of 0.08 for the lower-risk profile and 0.20 for the higher-risk profile. Assume a target-population register indicates that 70% of eligible patients have the lower-risk profile and 30% have the higher-risk profile. Calculate the target’s standardized risk.

The target profile weights are $0.70$ and $0.30$, and they sum to one. Thus

\widehat R_{1,G}(2) =(0.70)(0.08)+(0.30)(0.20) =0.056+0.060 =0.116.

The estimated 2-year cumulative incidence of event 1 in this target population is 11.6%. This is not the prediction for either profile alone; it is an average using the target’s stated profile distribution. The calculation is appropriate only if the profile-specific predictions are applicable to this target and the register gives a suitable representation of its covariate distribution.

Worked Example: Using Weighted Target Profiles

Imagine a hypothetical planning exercise for a 3-year risk of event 1. A target-population survey supplies three covariate profiles with normalized weights. A model judged applicable to these profiles predicts risks of 0.04, 0.12, and 0.25. The target weights are 0.50, 0.30, and 0.20, respectively. Find the standardized risk.

The weights add to $0.50+0.30+0.20=1.00$, so they already represent a probability distribution over the target profiles. Apply each weight to its corresponding predicted risk:

\widehat R_{1,G}(3) =(0.50)(0.04)+(0.30)(0.12)+(0.20)(0.25) =0.020+0.036+0.050 =0.106.

The estimated 3-year standardized cumulative incidence is 10.6% for the population represented by those weights. The risk predictions must be paired with the correct profile weights; reordering weights without reordering profiles would calculate a different and unintended quantity.

Worked Example: When the Proposed Target Is Poorly Supported

Suppose a model was fitted using patients from urban clinics. Its 2-year event 1 predictions are supported for profiles with covariate values observed in those clinics. A planning team proposes to apply it to a rural population whose target register includes a profile with a covariate value never observed in the fitting data. For illustration, assume the register weights 80% of the target in represented profiles, with average predicted risk 0.10, and 20% in the unsupported profile. No defensible prediction has been established for that unsupported profile.

The represented contribution is calculable: $(0.80)(0.10)=0.080$. But the target standardized risk also requires the missing contribution $(0.20)\widehat F_1(2\mid x_{\mathrm{unsupported}})$. Since that profile-specific risk is not supported, the total cannot be responsibly reported as a standardization based on the available evidence. Assigning it a value of zero, dropping its 20% weight, or borrowing a prediction from a dissimilar profile would each silently change the calculation or add an unjustified assumption.

The appropriate response is to investigate whether relevant data can support that profile, revise the target only if a narrower target genuinely matches the intended decision, or report that the proposed target risk is not identified reliably from the available model and data. A numerical result is not automatically a meaningful result merely because software can produce one.

Why the Averaging Formula Works

The standardization formula follows from averaging conditional probabilities over the target distribution. Let $Y_k(t)$ indicate that event $k$ has occurred by time $t$, before a competing event. For target covariates $X$, the probability of the event in that population is

P\{Y_k(t)=1\} =\int P\{Y_k(t)=1\mid X=x\}\,dG(x) =\int F_k(t\mid x)\,dG(x).

The first equality is the law of total probability: partition the target population by covariate profile, calculate the event probability within each profile, and average over how common those profiles are. Replacing the conditional probabilities with fitted predictions and $G$ with an empirical or weighted representation yields the standardization estimator. This argument also shows why choosing $G$ is part of defining the quantity being estimated: changing $G$ changes the population average, even when $F_k(t\mid x)$ stays fixed.

Choosing and Checking a Reference Population

A practical reference population should be selected because it corresponds to the question, not because it is easiest to obtain. The model-development sample can be a reasonable reference when the aim is to describe that same source population and its sample represents it adequately. For prediction in a new service, use the eligible service population or a representative sample of it when possible. For a regional planning question, use a population register, probability sample, or appropriately constructed weights that reflect the region’s intended population.

Before trusting a standardized estimate, check:

Population alignment: Do eligibility rules, setting, calendar period, and time origin match the intended use?
Distribution alignment: Do the records or weights actually represent the target covariate distribution, including important predictors of competing events?
Overlap: Are target profiles represented in the data used to fit the model? Large portions of the target outside the observed covariate range signal extrapolation.
Weight behavior: Are weights defined and normalized for the target, and are a few records carrying an implausibly large share of the total?
Prediction validity: Are the fitted predictions suitable at the requested horizon, and are event definitions and follow-up conditions comparable?

These checks do not prove that the model transports correctly, but they can expose a mismatch that makes the intended interpretation untenable. The risk model must also handle censoring in a way that supports its conditional predictions; standardizing cannot repair biased profile-specific predictions.

Alternative Summaries and Common Pitfalls

A conditional prediction for a specified profile answers a different question from a standardized population-average risk. Likewise, averaging over the model-fitting sample describes that sample’s covariate distribution unless the sample represents another population through a defensible design or weighting scheme. Standardization is useful when the desired summary is a population risk and its covariate distribution can be represented. If there is no suitable target distribution, report profile-specific predictions or state clearly which sample distribution was used rather than implying broad population applicability.

Two standardized risks can differ without either calculation being erroneous: they may describe populations with different covariate distributions. Conversely, matching the target distribution alone is not enough to justify transport if the conditional event risks differ between settings for reasons not captured by the model. Standardized risks are descriptive predictions under the stated model and target distribution; by themselves they do not establish a causal effect or explain why populations differ.

Common mistake: “The model was fitted to this cohort, so I should always average predictions over that cohort.” The cohort distribution is appropriate only if the cohort is the intended target or suitably represents it. For a prediction intended for a different population, averaging over the development cohort answers a development-cohort question. Correction: define the intended population first, then use its covariate distribution—or explicitly say when only the development-sample distribution is being described.

Another mistake is to treat an unsupported target profile as if it were harmless because it has a small weight. Its contribution may be small, but the standardized estimate still depends on a conditional prediction that has not been validated there. State the limitation and investigate support rather than disguising extrapolation as ordinary averaging.

Key takeaway: A standardized absolute risk is an average of profile-specific cumulative-incidence predictions over a specified target covariate distribution. Choosing that distribution defines whose risk is being reported; it does not, on its own, establish that the fitted model is valid for that population.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions.

A hypothetical target population has two profiles, weighted 40% and 60%, with predicted 1-year event 1 risks of 0.05 and 0.15. What is its standardized risk?
A model-development sample is used to calculate a population-average risk, but the prediction is intended for a different region. What must be reconsidered?
Why can two correctly calculated standardized risks differ when the same fitted profile-specific predictions are used?
What is the problem with dropping target profiles that are absent from the model-fitting data and renormalizing the remaining weights?
Does a standardized risk for a target population, by itself, establish that changing a covariate would change an individual’s risk? Explain.

Solutions. (1) $(0.40)(0.05)+(0.60)(0.15)=0.020+0.090=0.110$, or 11.0% at 1 year. (2) The intended target’s eligibility, setting, period, and covariate distribution should guide the reference population and weights; model transportability and covariate overlap must also be assessed. (3) The averaging distributions differ, so the populations assign different weights to the profile-specific risks. (4) It changes the target distribution by excluding part of the target, so the result no longer represents the original target population. (5) No. The standardized value is a model-based population prediction under a stated distribution; it does not by itself identify a causal effect of changing a covariate.