Choosing an Estimand for a Clinical Scenario

Start With the Clinical Question

A clinical study can ask whether assigning a treatment changes the probability of a particular event by a specified time. But when another event can prevent that outcome from occurring, there is no single universally appropriate causal effect. The answer depends on what is meant to happen to the competing event under the comparison. A treatment-policy effect leaves it to follow its natural course under each treatment; a hypothetical-elimination effect asks what the outcome risk would be if the competing event were prevented; a controlled direct effect fixes the competing-event process to a specified regime; and a separable effect compares one component of a treatment while holding another component fixed.

Choosing among these targets is a matter of defining the scientific question, not selecting whichever estimate is easiest to calculate. Before specifying the contrast, state the target population, the treatment strategies being compared, the event of interest, and the follow-up horizon. Also describe the intervention, if any, on the competing event. The resulting estimand should answer a question that clinicians or decision-makers could interpret.

Definition: Let \(A\) denote assigned treatment, \(T\) the time to the first event, and \(J\) its type, with \(J=1\) for the event of interest and \(J=2\) for a competing event. For a target population \(Q\) and time horizon \(\tau\), a causal risk is the probability of the event of interest by \(\tau\) under a specified intervention. A causal risk contrast compares such risks under two specified interventions. The estimand must name the population, outcome, horizon, and interventions; a risk difference, risk ratio, or other scale is then chosen to summarize their contrast.

Four Ways to Specify the Competing Event

Write \(Y_\tau\) for the indicator that the event of interest occurs by time \(\tau\) before a competing event. The notation \(Y_\tau^a\) denotes the counterfactual value under assignment to treatment strategy \(a\), with other events following their natural course under that strategy. The notation \(Y_\tau^{a,g_D}\) denotes the counterfactual value under treatment \(a\) together with an intervention \(g_D\) on the competing-event process. Probabilities below refer to individuals in the target population \(Q\).

Definition: A treatment-policy effect compares \(P_Q(Y_\tau^a=1)\) with \(P_Q(Y_\tau^{a'}=1)\). The competing event is allowed to occur naturally under each treatment. A hypothetical-elimination effect compares \(P_Q(Y_\tau^{a,g_D=0}=1)\) with \(P_Q(Y_\tau^{a',g_D=0}=1)\), where \(g_D=0\) prevents the competing event throughout follow-up. A controlled direct effect compares \(P_Q(Y_\tau^{a,g_D^*}=1)\) with \(P_Q(Y_\tau^{a',g_D^*}=1)\) under the same specified competing-event regime \(g_D^*\). A separable effect compares risks under treatment components \((A_Y,A_D)\), changing one component while holding the other fixed.

The hypothetical-elimination and controlled-direct labels can overlap. If the controlled regime \(g_D^*\) is specifically “prevent the competing event throughout follow-up,” the corresponding controlled contrast is mathematically the hypothetical-elimination contrast. The distinction is useful because the labels emphasize different questions: elimination asks about an idealized absence of the event, whereas a controlled direct effect names a particular intervention on its process. A controlled regime need not eliminate the event; it could instead specify a feasible competing-event prevention or management strategy.

A separable effect requires a different structure. It is relevant when treatment can be represented by two well-defined components, \(A_Y\), acting on the event of interest, and \(A_D\), acting on the competing-event process. For example, a combination treatment might contain an antitumor component and a toxicity-reduction component. A separable contrast can compare \(P_Q(Y_\tau^{a_Y,a_D}=1)\) with \(P_Q(Y_\tau^{a_Y',a_D}=1)\), holding \(a_D\) fixed. This is not simply “adjusting for” or conditioning on the competing event. It is a contrast between interventions on treatment components.

Why the Choice Changes the Question

Under the treatment-policy estimand, treatment can affect the risk of the event of interest through multiple pathways, including by changing the competing-event process. Preventing a competing event can leave more people alive and at risk of experiencing the event of interest. Thus, a lower observed cumulative incidence of the event of interest need not mean that the treatment directly suppresses its underlying disease process.

A basic competing-risks identity makes this dependence explicit. If \(\lambda_1(t)\) is the cause-specific hazard for the event of interest and \(S(t-)\) is the probability of remaining free of either event just before \(t\), then the cumulative incidence through \(\tau\) is

P(T\leq \tau,J=1)=\int_0^\tau S(t-)\lambda_1(t)\,dt.

The event-free probability \(S(t-)\) depends on both event processes. Consequently, changing the competing-event process can change the cumulative incidence even if the cause-specific hazard \(\lambda_1(t)\) does not change. This is why an estimand that intervenes on the competing event cannot be substituted for the treatment-policy estimand without changing the question.

The potential-outcome notation also shows what each contrast holds fixed. For a treatment-policy comparison, the assigned treatment changes and the competing event is left to respond naturally. For a hypothetical or controlled comparison, the assigned treatment changes while the competing-event intervention is held fixed. For a separable comparison, one treatment component changes while the other component is held fixed. These contrasts can have different magnitudes or even different directions without contradiction: they describe different interventions.

A Practical Selection Sequence

Name the outcome and horizon.
Specify the event of interest and a time such as 30 days or 2 years. Define whether the outcome is occurrence of that event before any competing event.

Define the target population and treatment strategies.
State whose risks are being compared and what each treatment strategy entails, including relevant versions of treatment.

Ask what should happen to the competing event.
If it follows its natural course under each treatment, the target is treatment-policy. If the question explicitly imagines it prevented, consider hypothetical elimination. If a particular shared regime is specified, consider a controlled direct effect.

Check whether treatment can be decomposed.
If the scientific question concerns one component while another is held fixed, and those components define meaningful interventions, a separable effect may be appropriate.

State the contrast and the assumptions it needs.
Give the risk under each intervention and the chosen contrast scale. Separately assess whether the design and assumptions support identifying those counterfactual risks.

An estimand is conceptually defined whether or not it can be identified from available data. To interpret an estimated contrast causally, the intervention must be well-defined and consistency must be plausible; treatment and intervention assignment must satisfy the relevant exchangeability and positivity conditions; and censoring must be handled under appropriate assumptions. For a separable effect, the component interventions must be meaningful, and identification generally requires the dismissible component conditions as well as the relevant exchangeability and positivity conditions. Naming a target does not establish these assumptions. The earlier material on exchangeability, positivity, consistency, censoring, and separable effects gives the formal conditions and identification approaches.

Worked Example: Choosing a Treatment-Policy Effect

Hypothetical scenario. A randomized trial compares two cancer treatments in adults eligible for either regimen. The clinical team asks: “What is the difference in the 2-year probability of cancer progression before death under assignment to the new regimen rather than standard care?” Death before recorded progression is a competing event. Assume the target population is these eligible adults and treatment assignment is randomized, follow-up is adequate, and censoring assumptions are met.

The question asks about assignment to each treatment with death occurring as it naturally would under that assignment. It does not ask to prevent death or hold its process fixed. The appropriate target is therefore the treatment-policy risk difference:

P_Q(Y_2^{\text{new}}=1)-P_Q(Y_2^{\text{standard}}=1).

Suppose, purely for illustration, the causal 2-year risks under these strategies are 0.18 and 0.22. Then the risk difference is \(0.18-0.22=-0.04\), or \(-4.00\) percentage points. In this target population, assignment to the new regimen corresponds to 4.00 fewer percentage points of 2-year progression before death than assignment to standard care. The contrast includes any effect of treatment on the competing death process; it is not a comparison that removes death.

Worked Example: Distinguishing Elimination From a Controlled Regime

Hypothetical scenario. A study compares two preventive strategies for a disease, with non-disease death as a competing event. Investigators ask two separate questions in the same target population over 5 years. First, what would the disease risks be if non-disease death could be prevented throughout follow-up? Second, what would the risks be under a specified common supportive-care regime \(g_D^*\), designed to reduce but not eliminate non-disease death? Assume both are well-defined interventions and that the needed causal assumptions hold.

The first question defines a hypothetical-elimination contrast, \(P_Q(Y_5^{a,g_D=0}=1)-P_Q(Y_5^{a',g_D=0}=1)\). Suppose those hypothetical risks are 0.15 and 0.20. Substitution gives \(0.15-0.20=-0.05\), a 5.00-percentage-point lower disease risk under \(a\) if the competing event were prevented.

The second question defines a controlled direct contrast under the specified regime, \(P_Q(Y_5^{a,g_D^*}=1)-P_Q(Y_5^{a',g_D^*}=1)\). Suppose the corresponding risks are 0.17 and 0.19. The contrast is \(0.17-0.19=-0.02\), or 2.00 percentage points lower under \(a\) when both strategies are paired with \(g_D^*\). The two results do not conflict: one assumes no competing deaths, while the other includes deaths under the common supportive-care regime. Neither contrast is the treatment-policy effect unless the competing-event intervention matches natural experience under each treatment.

Worked Example: Defining a Separable Effect

Hypothetical scenario. Suppose a randomized combination therapy has two scientifically meaningful components: \(A_Y\), an antiviral component intended to affect disease progression, and \(A_D\), a component intended to affect fatal toxicity, a competing event. A clinical question asks about changing the antiviral component while keeping the toxicity component at its standard setting. Assume the four component combinations are well-defined and supported by the design, and assume consistency, exchangeability, positivity, and the dismissible component conditions needed for the intended separable interpretation.

The target is a separable contrast holding \(A_D=0\):

P_Q(Y_\tau^{1,0}=1)-P_Q(Y_\tau^{0,0}=1).

Suppose the hypothetical risks by \(\tau\) are 0.12 under \((A_Y,A_D)=(1,0)\) and 0.16 under \((0,0)\). The risk difference is \(0.12-0.16=-0.04\), or 4.00 percentage points lower with the antiviral component present while the toxicity component is held at its standard setting. This interpretation depends on the component intervention and assumptions; it is not automatically the effect of the observed combination therapy as a whole.

Diagnostics, Alternatives, and Limitations

A useful diagnostic is to paraphrase the estimand as an intervention. If that paraphrase does not match the clinical question, the estimand is likely wrong. “Assign either treatment and allow death to occur naturally” describes treatment-policy. “Imagine that death is prevented” describes hypothetical elimination. “Compare treatments while imposing this named competing-event regime” describes a controlled direct effect. “Change the disease-acting component but retain the other component” describes a separable effect.

Each choice has limitations. Treatment-policy effects are often closest to assignment and practice questions, but they combine pathways through the competing event and may not isolate a biological mechanism. Hypothetical elimination is an artificial intervention when the competing event cannot realistically be prevented, and it may require strong assumptions to identify. A controlled direct effect is only interpretable if the controlled regime is specified clearly and is sufficiently well-defined; vague instructions such as “hold death constant” do not define an intervention. Separable effects require a credible decomposition of treatment and assumptions that justify interpreting and identifying component-specific contrasts. If those components cannot be implemented or distinguished scientifically, the separable estimand may lack practical meaning.

These are alternatives in the sense that they answer different questions, not competing statistical estimators of one universal effect. Standardizing or weighting can target causal risks under stated assumptions, but the method does not determine the estimand. A well-chosen analysis therefore reports the counterfactual intervention in words as well as its mathematical contrast. An estimate should not be described as a direct effect merely because it adjusts for a post-treatment variable or uses a cause-specific hazard.

Common Pitfall

Wrong reasoning: “Death prevents progression from being observed, so I should remove deaths from the analysis; the resulting comparison is the treatment effect on progression.”
Correction: Removing or censoring deaths does not, by itself, define a causal intervention that prevents death. It can change the target population or induce selection. First decide whether the question concerns natural competing events, elimination, a specified controlled regime, or a treatment component; then use assumptions and an analysis appropriate to that target.

Key takeaway: State the target population, event of interest, time horizon, treatment strategies, and competing-event intervention before naming the effect. Treatment-policy, hypothetical-elimination, controlled-direct, and separable effects are distinct causal questions; the chosen label must follow the intervention the clinical question actually asks about.

Check Your Understanding

For each question, identify the estimand and explain the intervention on the competing event. Then compare your reasoning with the solutions.

A trial asks for the 1-year risk difference under assignment to two treatments, allowing competing cardiovascular death to occur naturally. Which estimand is intended?
A researcher asks what the outcome risk would be under each treatment if a named competing event were prevented throughout follow-up. Which estimand is intended?
What is the relationship between a hypothetical-elimination effect and a controlled direct effect when the specified controlled regime prevents the competing event?
A therapy has two meaningful components. The question changes the disease-targeting component but fixes the toxicity component. Which effect is being targeted, and name one important additional requirement.

Solutions. (1) Treatment-policy: the competing event follows its natural course under each treatment. (2) Hypothetical elimination, because the intervention prevents the competing event throughout follow-up. (3) They coincide mathematically when the controlled regime is exactly elimination, although the labels emphasize different framings of the question. (4) A separable effect; the components must define meaningful interventions, and identification requires appropriate assumptions, including the dismissible component conditions.