Why the Prediction Horizon Matters
A competing-risk prediction is incomplete until its time horizon is stated. “The risk of event \(k\)” could mean the probability of that event within one year, five years, or another period. Those are different questions, even when they concern the same people, event definition, and prediction model. A useful horizon makes the prediction relevant to a decision and gives its probability a clear time frame.
For example, a one-year risk may inform whether to intensify monitoring during the next clinic cycle, while a five-year risk may inform a longer-term prevention strategy. The longer horizon is not automatically better: it may be less relevant to the decision, or the data may provide too little follow-up to estimate it reliably. Horizon selection is therefore part of defining the prediction target, not a cosmetic choice made after analysis.
The event definition, time origin, target population or covariate profile, and horizon jointly determine what the prediction means. A “three-year risk after diagnosis” and a “three-year risk after treatment initiation” do not have the same time origin, even if the number of years is identical. Likewise, changing from a first-event outcome to an outcome that can occur after another event changes the target and cannot be achieved merely by changing the horizon.
Choose the Horizon From the Decision
Start by specifying the decision the prediction is meant to inform. Ask when that decision is made, how far ahead its consequences matter, and whether the predicted event could plausibly occur within that period. A horizon should be long enough to capture a meaningful amount of risk for the decision, but not extended without purpose.
A practical choice is often anchored to a clinical review interval, treatment duration, follow-up schedule, policy planning cycle, or other decision deadline. The choice should also reflect the time needed for an action to have an effect. If clinicians can change a treatment only at an annual review, a risk over the next month may not answer the operational question. Conversely, a ten-year prediction may be poorly matched to a decision about immediate monitoring.
Specify who will use the prediction, what action is under consideration, which first event counts as the outcome, and what time origin begins follow-up.
Identify the date or interval by which the decision needs a risk estimate, considering clinical latency and the consequences of acting sooner or later.
Review follow-up duration, censoring, the number still under observation, and uncertainty. A nominally long follow-up maximum does not guarantee useful information at its end.
Record a primary horizon before examining outcome contrasts, state its units, and label any additional horizons as supplementary.
Why Different Horizons Mean Different Risks
For \(t_2>t_1\), the difference between two cause-\(k\) risks has a direct interpretation:
This identity follows by separating the event that defines the risk by \(t_2\) into two disjoint time intervals: occurrence by \(t_1\), and occurrence after \(t_1\) but by \(t_2\). Both require event \(k\) to be first. Therefore, the risk cannot decrease as the horizon increases, and the additional risk between horizons is the probability of event \(k\) first occurring in that interval.
This is also why a horizon is not merely a display setting. A prediction at five years includes outcomes that are absent from a one-year prediction. It may support a different decision and have different uncertainty. The definition does not imply that the risk grows at a constant rate: event occurrence can be concentrated in particular periods, and competing events affect how many people remain able to experience event \(k\) first.
Worked Example: Matching a Horizon to a Treatment Review
Suppose a hypothetical clinical service is deciding whether to offer additional monitoring at a scheduled two-year review. For a specified patient profile, a competing-risk analysis reports a cause-\(k\) prediction of 0.06 by one year and 0.14 by two years. The service's policy is to consider monitoring when the predicted risk by the review exceeds 0.10.
The two-year risk is the relevant prediction for this policy because the action is considered at the two-year review. Substituting the reported value, \(0.14>0.10\), so the profile is above the policy's stated risk threshold. The one-year prediction, \(0.06\), is below the threshold, but it answers a different question: risk by one year, not risk by the review date.
The increase over the second year is \(0.14-0.06=0.08\), or 8 percentage points. Under the cumulative-incidence definition, this is the predicted probability of event \(k\) occurring first between years one and two for this profile. It is not an annual rate, and it should not be obtained by dividing or multiplying the two-year probability by time.
This conclusion concerns the stated prediction and policy threshold; it does not establish that monitoring causes better outcomes. Before using it operationally, the service should check that the prediction is applicable to its patients and that uncertainty around 0.14 is compatible with the decision. If an uncertainty interval straddles 0.10, the decision may be sensitive to estimation uncertainty.
Check Whether the Horizon Is Supported
A decision-relevant horizon is useful only if the data can support a prediction there. Inspect the distribution of observed follow-up and censoring, along with the number of individuals still under observation near the proposed time. If few people remain observed, a point estimate may be driven by limited information and its uncertainty may be substantial. A recorded maximum follow-up time alone is not enough: one person observed very late does not provide the same support as many people followed through that period.
Estimation also relies on assumptions about incomplete follow-up. In particular, the methods used to estimate cumulative incidence require censoring to be adequately handled; a common condition is that, within the analysis groups or conditional on modeled predictors, censoring is independent of the future event process. If people with higher unobserved event risk are more likely to leave follow-up, and this dependence is not addressed, the estimated risk may be biased. A clinically chosen horizon does not repair an inadequate censoring assumption.
Check that event ascertainment and follow-up procedures remain credible through the horizon, and that the target population resembles the population providing the data. Consider whether a change in care, coding, or eligibility over time makes a long-horizon prediction difficult to interpret. These checks do not determine one universally correct cutoff; they help distinguish a defensible prediction from an extrapolation or a poorly supported estimate.
Worked Example: A Policy Horizon With Sparse Late Follow-Up
A hypothetical public-health team needs a risk estimate for a three-year funding cycle. Its analysis reports a cause-\(k\) risk of 0.12 at three years, with a 95% confidence interval from 0.08 to 0.17. At eight years, the estimated risk is 0.23, with a 95% confidence interval from 0.10 to 0.38. Only a small fraction of the cohort is still under observation near year eight.
The three-year horizon directly matches the funding cycle. Its estimated risk is 12 events per 100 people with the specified profile by three years, with an interval spanning 8 to 17 per 100. The interval expresses the uncertainty in the estimated risk; it does not mean there is a 95% probability that the fixed true risk lies inside this particular interval.
The eight-year estimate is larger, as expected for a longer cumulative horizon, but it is much less precise: its interval spans 10 to 38 per 100. Sparse late follow-up is a warning that this estimate is weakly supported. Unless an eight-year decision is also important and the analysis can justify its late-horizon estimation, it should not replace the three-year primary prediction just because it is larger.
The team should report the three-year risk as the primary policy prediction and may show the eight-year result as a qualified supplementary estimate. It should also investigate why observation becomes sparse and whether censoring is plausibly independent after accounting for the available information. The wide interval alone does not prove bias, but it signals that the late-horizon estimate carries substantial uncertainty.
One Primary Horizon or Several?
A single prespecified primary horizon makes a prediction and its evaluation easier to interpret. It reduces the temptation to emphasize whichever time point produces the most favorable risk contrast. Additional horizons can be valuable when decisions genuinely occur at several times or when the timing of risk matters; they should be labeled clearly and interpreted as separate time-specific predictions.
For multiple horizons, choose a small set with distinct purposes and explain each one. For example, an early horizon might address immediate safety monitoring and a later horizon might address longer-term planning. Do not treat values at adjacent time points as independent findings: they are calculated from overlapping follow-up and represent nested event windows. Report uncertainty at each horizon where it is relevant, and avoid presenting a dense list of numbers without explaining which decisions they inform.
A common alternative is to present an entire cumulative-incidence curve. The curve shows how estimated risk changes over time and can reveal when risk accumulates, but it does not by itself identify which time point matters for a particular decision. Conversely, a single horizon is concise and decision-focused but can conceal the timing of risk outside that point. These approaches answer complementary questions; a clinically justified primary horizon can be accompanied by a curve when the broader time pattern matters.
Another tempting choice is to use the last time at which the data produce an estimate. That is not a decision rationale, and estimates at the tail of follow-up may be unstable. Likewise, choosing the horizon after looking for the largest group difference invites selective reporting. If a horizon is changed after seeing results, disclose that fact and treat the resulting comparison as exploratory rather than as the prespecified primary analysis.
Worked Example: Avoiding Data-Driven Horizon Selection
In a hypothetical comparison of two care strategies, the estimated cause-\(k\) risks are 0.09 and 0.07 at two years, and 0.25 and 0.16 at five years. Before analysis, the clinical team had identified five years as relevant to a planned follow-up decision. The five-year risk difference is \(0.25-0.16=0.09\), or 9 percentage points; the two-year difference is \(0.09-0.07=0.02\), or 2 percentage points.
The prespecified five-year comparison is the primary result because it matches the stated decision. The two-year values may be reported as supplementary if early risk is also of interest. It would be misleading to select five years only after noticing that its difference is larger, then describe it as the primary horizon without qualification.
These are descriptive differences between predictions. They do not establish a causal effect of care strategy. A causal interpretation would require an appropriate design and assumptions beyond selecting a horizon. The horizon determines when risk is summarized; it does not by itself determine what comparison is justified.
Common Mistakes and Practical Limitations
- Leaving time unstated. “Risk is 12%” is incomplete. State the event, time origin, horizon, units, and target profile or population.
- Assuming longer is always better. Longer horizons include more possible events, but may be less relevant and less precisely estimated.
- Confusing risk with a rate. A five-year probability is not generally five times a one-year probability. Event timing and competing events make risk accumulation non-linear.
- Using the last observed time as the target by default. A horizon with sparse follow-up may be technically estimable but practically uninformative.
- Selecting the most striking time point after inspecting results. This makes the reported contrast vulnerable to selective emphasis and overstates how strongly the evidence supports that choice.
Horizon selection cannot eliminate model misspecification, poor transportability, informative censoring, or uncertainty about event classification. Nor does one horizon serve every stakeholder. If clinicians and policy makers face genuinely different decisions, they may need different predictions, each defined and justified for its intended use. A precise horizon statement makes those differences visible rather than disguising them as a single generic “risk.”
Check Your Understanding
Answer each question using the definition of cumulative incidence and the decision context.
- A clinic acts at a six-month visit. Why might a one-year prediction be less directly relevant than a six-month prediction?
- A cause-\(k\) risk is 0.11 by year two and 0.18 by year four. What probability does the difference represent?
- A prediction at ten years has a much wider interval than one at three years, and few people remain observed near year ten. Name two reasons to treat the ten-year result cautiously.
- A researcher examines many horizons and reports only the one with the largest difference between groups. What is the problem, and what is a better practice?
Solutions. (1) The six-month prediction matches the clinic's action time; the one-year prediction concerns a later period and may not answer the decision being made. (2) \(0.18-0.11=0.07\), so it is the probability of event \(k\) occurring first between years two and four, for the specified target. (3) Sparse late follow-up means limited information at that time, and the wider interval indicates substantial uncertainty; late-horizon censoring assumptions and applicability should also be checked. (4) Selecting the largest observed difference after inspection risks selective reporting. Prespecify a decision-relevant primary horizon and label other horizons as supplementary or exploratory.