What a Treatment-Policy Effect Asks
An assigned treatment strategy can change what happens after assignment. Some people discontinue, switch treatments, or do not adhere as planned; a competing event may also occur before the event of interest. A treatment-policy effect asks about the contrast between assigned strategies while allowing those subsequent events and treatment changes to follow their natural course under each assignment. It does not ask what the effect would have been if everyone had adhered perfectly.
For a competing-risk outcome, the endpoint must specify both the event of interest and the time horizon. For example, one may compare the probability of a particular disease-related event by 2 years under assignment to strategy 1 versus strategy 0. A person who experiences a competing event first has not experienced the event of interest by that horizon. That competing event is part of the observed event process, not a reason to remove the person from the assignment group.
The assignment strategies need to be described concretely: for example, assignment to an offer of a specified drug plus usual follow-up versus assignment to usual care. The estimand is not automatically the effect of taking the drug continuously. Its interpretation includes the adherence and subsequent-care patterns that would arise under each assignment in the target population.
Define the Estimand Before Choosing an Analysis
A complete treatment-policy estimand specifies the target population, the assigned strategies being compared, the outcome and horizon, how post-assignment events are handled, and the summary contrast. For competing risks, the outcome definition is especially important: \(Y_k^a(\tau)\) is one if event \(k\) occurs first by \(\tau\), and zero otherwise. Thus it is zero if a different event type occurs first or if no event occurs by \(\tau\).
The treatment-policy strategy for adherence-related events means that outcomes are still counted according to initial assignment after discontinuation or switching. It does not mean that missing outcomes are automatically known, nor does it turn a competing event into a censoring time. Loss to follow-up is a separate data problem and requires assumptions or methods to address incomplete observation.
Worked Example: Comparing Assigned Strategies With Natural Adherence
Consider a hypothetical randomized trial with 100 people assigned to each of two strategies. During follow-up to 2 years, 20 people assigned to strategy 0 have the target event, 10 have a competing event first, and 70 have neither event by 2 years. In the strategy 1 group, 16 have the target event, 8 have a competing event first, and 76 have neither event by 2 years. Several people in both groups discontinue or switch, but their outcomes are still ascertained.
With complete event ascertainment through 2 years, the treatment-policy risks are the numbers with the target event divided by the numbers assigned:
The estimated risk difference is \(0.16-0.20=-0.04\), or a 4-percentage-point lower risk under assignment to strategy 1. The estimated risk ratio is \(0.16/0.20=0.80\). These estimates compare assignment strategies as implemented, including the discontinuation and switching that occurred. They do not by themselves show the effect of adhering continuously to strategy 1.
The competing events remain in the denominators because each person was assigned to a strategy and each competing event is part of that strategy’s outcome experience. They are not counted as target events; they contribute zero to \(Y_k^a(2)\).
Identification and Estimation
In a randomized study, the causal interpretation of the assignment contrast follows from random assignment, consistency, and adequate outcome follow-up. Consistency means that a person assigned to \(a\) has the outcome \(Y_k^a(\tau)\) defined for that assignment strategy; the strategy must be specific enough that materially different versions are not silently treated as identical. Randomization makes assignment independent of the potential outcomes, and positivity requires a nonzero probability of assignment to each strategy in the trial’s target population. If there is interference between participants, the usual individual-level potential-outcome interpretation also needs modification; the standard formulation assumes no such interference.
In an observational study, assignment is not randomized. Identification then additionally requires conditional exchangeability: given measured baseline covariates \(L\), assignment is independent of the potential outcomes. Positivity requires that each strategy has a positive probability for covariate patterns represented in the target population. Consistency and no interference are still required. These assumptions concern assignment to the strategies; they do not require post-assignment adherence to be randomized.
A short justification makes clear why this identifies the treatment-policy effect. Under consistency, among people assigned \(a\), their observed outcome is their potential outcome under \(a\). Under exchangeability, that potential outcome has the same distribution in the assigned-\(a\) group as in the target population, or within baseline-covariate strata in an observational study. Averaging the resulting risks over the target population gives \(F_k^a(\tau)\). Subtracting or taking the ratio of the two identified risks yields the chosen causal contrast.
With complete follow-up to \(\tau\), the risk in a randomized arm can be estimated by the proportion assigned to that arm who experience event \(k\) by \(\tau\). With right censoring before \(\tau\), that proportion generally undercounts events if censored participants are simply treated as event-free. A standard estimator is the Aalen–Johansen cumulative incidence estimator. At each event time, it adds the estimated probability of still being free of any event just before that time multiplied by the estimated conditional probability of event type \(k\) at that time:
Here \(Y_j\) is the number still under observation and event-free just before event time \(t_j\), \(d_{kj}\) is the number of type-\(k\) events at that time, and \(d_m\) is the number of events of any type. The formula accounts for competing events by reducing the estimated probability of remaining free of all events after they occur. It requires that censoring be independent of the event process within the groups or covariate strata used for estimation, or independent conditional on the variables used to adjust the analysis. In a randomized study, estimate each strategy’s risk and contrast them; in an observational study, adjust for baseline confounders and standardize to the target population.
Worked Example: Cumulative Incidence With Right Censoring
Suppose a hypothetical randomized study has 50 participants assigned to each strategy. In strategy 0, at day 30 there are 2 target events and 2 competing events among 50 at risk. Seven of the 46 remaining participants are censored before day 90. At day 90, there are 2 target events and 4 competing events among the 39 still at risk. In strategy 1, there are 4 target events and 1 competing event at day 30; five of the 45 remaining participants are censored before day 90; at day 90, there are 2 target events and 3 competing events among 40 at risk. Assume, for this calculation, that censoring is independent of the event process within each assignment group.
For strategy 0, the event-free probability just before day 90 is \(1-(2+2)/50=0.92\). The two increments for the target-event cumulative incidence are:
For strategy 1, the event-free probability just before day 90 is \(1-(4+1)/50=0.90\), giving:
The estimated treatment-policy risk difference at day 90, strategy 1 minus strategy 0, is \(0.1250-0.08718=0.03782\), or about 3.78 percentage points higher under assignment to strategy 1. This is an estimate of the difference in target-event cumulative incidence under the stated censoring assumption. The calculations do not treat the competing events as censored: they reduce the event-free probability available for later target events.
Why the Assignment Contrast Matters
The treatment-policy estimand is often appropriate when the question concerns the effect of adopting or offering a treatment strategy in practice, where discontinuation and switching are expected. It preserves the comparison defined by assignment and avoids making adherence a condition for inclusion in the primary contrast. If adherence is affected by prognosis, restricting an analysis to adherent participants can select groups that differ in their underlying risk. The resulting comparison is not generally the treatment-policy effect and does not become a causal effect merely by excluding people who changed treatment.
Other analyses answer different questions. An as-treated comparison groups people by treatment actually received and can be confounded by reasons for switching or discontinuing. A per-protocol question concerns adherence to specified regimens and requires a separate estimand and appropriate assumptions and methods. A hypothetical strategy that removes discontinuation or a competing event also targets a different counterfactual question. By contrast, the treatment-policy contrast retains each person under initial assignment and allows subsequent events to occur naturally.
A cause-specific hazard analysis and a cumulative-incidence risk contrast also summarize different features of the data. The treatment-policy risk difference here is an absolute probability contrast by a specified time. It does not describe an instantaneous event rate. The risk ratio is a relative contrast in cumulative incidence, not a hazard ratio. Reporting the estimand and its time horizon makes these distinctions explicit.
Worked Example: Why an Adherer-Only Comparison Is Different
In a hypothetical trial, 100 people are assigned to strategy 1. Eighty adhere throughout follow-up; among them, 8 experience the target event and 4 experience a competing event first. The other 20 discontinue or switch; among them, 8 experience the target event and 4 experience a competing event first. In the 100 people assigned to strategy 0, 20 have the target event and 10 have a competing event first. Assume complete outcome follow-up and random assignment.
The treatment-policy risk for strategy 1 is based on everyone assigned to it: \((8+8)/100=0.16\). The strategy 0 risk is \(20/100=0.20\), so the assignment-based risk difference is \(0.16-0.20=-0.04\), or 4 percentage points lower under assignment to strategy 1.
The risk among strategy 1 adherers alone is \(8/80=0.10\). Comparing that 10% with the 20% in all of strategy 0 would not estimate the treatment-policy effect: it uses different populations and conditions on post-assignment adherence. The 10% figure is descriptive of the adherers in this example; interpreting it as a causal per-protocol effect would require additional design and analysis assumptions.
Diagnostics, Limitations, and Common Mistakes
Before interpreting an estimate, check that the analysis follows the estimand. Confirm that participants remain grouped by assignment after treatment changes, that competing events are coded as competing events rather than ordinary censoring, and that the target event and time horizon are specified. Examine the amount and timing of loss to follow-up in each group. If censoring is substantial or plausibly related to prognosis, an unadjusted independent-censoring assumption may be implausible; covariate adjustment or censoring weights may be needed, with their own modeling and positivity requirements.
In an observational analysis, also inspect whether baseline covariate overlap supports the comparison. Sparse or absent treatment options within covariate strata undermine positivity and make standardized risks depend heavily on extrapolation. In a randomized study, randomization supports exchangeability at assignment, but it does not repair informative loss to follow-up or poor outcome ascertainment. The treatment-policy interpretation also depends on a meaningful, sufficiently specified assignment strategy; the effect of an ill-defined “usual care” strategy may be difficult to transport.
- Mistake: censoring a participant at treatment discontinuation. That removes post-discontinuation outcomes and changes the question. For a treatment-policy estimand, continue outcome follow-up and retain the participant in the assigned group.
- Mistake: treating a competing event as ordinary censoring. A competing event prevents the target event from being the first event by the horizon. It must enter the competing-risk calculation, not be treated as if the participant’s later target-event status were simply unobserved.
- Mistake: calling an adherer-only contrast the effect of assignment. Adherence occurs after assignment and may be related to prognosis. The correction is to estimate the assignment contrast using all assigned participants, or to define and justify a different estimand.
- Mistake: interpreting a risk difference as a hazard contrast. A risk difference is an absolute difference in probabilities by a specified time; always state the event, horizon, assignment strategies, and units (such as percentage points).
Check Your Understanding
Answer each question, then compare your reasoning with the brief solutions.
- In a randomized study, a participant assigned to strategy 1 switches treatment and later has the target event. Does that event contribute to the treatment-policy risk under strategy 1? Why?
- By 1 year, an assigned participant experiences a competing event before the target event. What value does this give to \(Y_k^a(1)\), and should the competing event be treated as ordinary censoring?
- In an observational study, name two key assumptions beyond consistency that support identifying risks under each assigned strategy.
- Why can the risk among adherers alone differ from the treatment-policy risk?
- What does a risk difference of \(-0.03\) at 2 years mean if it compares strategy 1 with strategy 0?
Solutions. (1) Yes. The participant remains in the strategy 1 assignment group, and the observed target event contributes to that group’s risk. (2) \(Y_k^a(1)=0\), because the target event did not occur first by 1 year; the competing event is part of the event process, not ordinary censoring. (3) Conditional exchangeability given measured baseline covariates and positivity, in addition to consistency and the usual no-interference formulation. (4) Adherence is post-assignment and may select people with different prognoses; an adherer-only comparison also changes the population being compared. (5) The estimated target-event risk by 2 years is 3 percentage points lower under assignment to strategy 1 than under assignment to strategy 0; it is not a hazard difference or a guarantee about an individual.