Why the Treatment Rule Must Continue Beyond Initiation
A question about starting a treatment is not necessarily a question about staying on it. “What is the effect of initiating medication A rather than medication B?” leaves post-initiation use largely open. “What is the effect of starting A and continuing it for six months rather than starting B and continuing it for six months?” specifies a different intervention. A protocol that does not distinguish these questions can give a precise-sounding answer to the wrong one.
For a sustained-treatment question, the protocol must define what counts as ongoing treatment over time. It should say when treatment must begin, how much time without treatment is permitted, what happens after a long interruption, whether changing dose is allowed, and whether switching to another treatment is allowed. Each rule affects which observed treatment histories conform to the strategy and which causal effect the protocol intends to compare.
These are protocol definitions, not labels inferred from a data set after analysis. The rules should be fixed before examining outcomes. In particular, “continuous use” is not operational until the protocol defines how treatment is measured and what interruption is acceptable.
Define the Strategy and the Time Window
Begin with the population, treatment options, time zero, and follow-up horizon specified in the protocol. For each strategy, then state the permitted treatment histories from time zero through the end of follow-up. A useful description separates five decisions:
- Initiation: Must treatment start at time zero, or may it start within a specified grace period?
- Coverage: What evidence indicates ongoing use, such as days supplied, administration records, or treatment visits?
- Allowable gaps: How long may a person be without recorded treatment while still following the strategy?
- Discontinuation and restarting: Does a gap beyond the limit mark a deviation? Is restarting after that deviation permitted?
- Switching and dose changes: Are they prohibited, permitted, or allowed only under explicit conditions?
A gap rule needs a unit and a counting convention. If a dispensing record supplies medication through day \(d\), and the next supply begins on day \(r\), the uncovered gap is the number of calendar days after \(d\) and before \(r\). Under an inclusive-day convention, that count is \(r-d-1\). The protocol should also say whether overlapping supplies extend coverage, whether a gap limit applies once or repeatedly, and whether the same rule applies at the end of follow-up.
A grace period for starting treatment is not the same as an allowable gap during treatment. The first sets a deadline for initiation; the second sets a continuation rule after treatment has begun. Conflating them leaves uncertainty about whether a person who never starts treatment, or who stops after starting, follows the strategy.
Worked Example: Applying an Initiation Window and a Gap Rule
Suppose a hypothetical protocol compares two medication strategies over 180 days. Under strategy A, a person must start medication A by day 14, then remain covered by A, allowing gaps of at most 7 consecutive days. Switching is not allowed. A dispensing on day 4 supplies 30 days, including day 4, so coverage runs through day 33.
A refill begins on day 40. The uncovered days are days 34 through 39, so the gap is \(40-33-1=6\) days. Since \(6\leq 7\), this refill history remains within the specified gap rule.
Suppose the next supply begins on day 78 after coverage through day 69. The gap is \(78-69-1=8\) days. Since \(8>7\), the person has deviated from the sustained strategy under a rule that defines any gap longer than 7 days as a deviation. The protocol must state whether later restarting counts as resuming adherence; one clear option is to treat the first excessive gap as a deviation that cannot be undone by restarting.
The day-4 start meets the day-14 initiation deadline, but meeting that deadline does not establish sustained adherence. The first refill meets the gap rule; the second does not. These conclusions follow from the stated supply and counting conventions, not from an assumption that a dispensing proves medication ingestion.
Write the Causal Contrast for the Sustained Regimes
A strategy defines an intervention, and the causal contrast should compare outcomes under the interventions actually specified. Let \(g\) denote a treatment strategy and \(Y^g(\tau)\) the outcome by follow-up horizon \(\tau\) that would occur under that strategy. For a binary outcome, such as hospitalization by day 180, the risk under strategy \(g\) is \(P\{Y^g(180)=1\}\). A risk difference comparing sustained strategies \(g_A\) and \(g_B\) is:
This contrast is not automatically the effect of “ever starting A” versus “ever starting B.” Under sustained strategies, the interventions also specify what happens after initiation. In contrast, an initiation or treatment-policy question may compare starting A with starting B while leaving subsequent stopping and switching to evolve as they otherwise would. State which question is intended; do not use the word “treatment effect” as though it identified a unique contrast.
For a causal interpretation from observational data, the strategies must be sufficiently well-defined that the observed versions of treatment correspond to the interventions being compared. Identification also requires consistency, meaning that a person's observed outcome agrees with the potential outcome for the strategy actually followed; exchangeability, meaning there is no unmeasured confounding of strategy adherence and outcomes given the information used; and positivity, meaning the relevant strategies remain possible at the covariate histories being compared. These assumptions are substantive, not guaranteed by writing a detailed protocol. When adherence changes over time, baseline comparisons alone may not address confounding of later treatment decisions.
Follow-Up Is Not the Same as Time on Treatment
For the total effect of assignment to a sustained strategy, follow-up usually begins at the protocol's time zero and continues to the prespecified horizon, subject to the protocol's outcome and follow-up rules. A person does not enter follow-up only after completing a period of treatment. Nor should the horizon be shortened merely because treatment stopped: doing so changes the question and can make outcome observation depend on post-baseline treatment history.
A protocol may define a per-protocol contrast among outcomes under adherence to the assigned strategies. In observational emulation, one possible operational approach is to stop counting a person's follow-up as adherent when a prespecified strategy deviation occurs. That approach requires careful handling of the resulting selection: people who remain adherent may differ in prognosis from those who deviate. Simply restricting the analysis to people who completed treatment does not, by itself, recover the causal effect of sustained use. The assignment effect and the effect under sustained adherence are distinct targets, and the analysis must match the target.
Worked Example: An Initiation Contrast Is Not a Continuation Contrast
Consider a hypothetical 90-day comparison. Strategy I says to initiate medication A by day 7; it places no restriction on stopping A or switching after initiation. Strategy S says to initiate A by day 7, remain covered thereafter with gaps no longer than 3 days, and do not switch. Both strategies specify follow-up from day 0 through day 90.
A person starts A on day 3, has a 2-day gap in coverage, and then switches to B on day 40. This history meets the initiation requirement in both strategies. It may still be consistent with strategy I, because that strategy imposes no post-initiation restrictions. It deviates from strategy S because switching is prohibited, even though the 2-day gap is within the permitted limit.
The outcome window is day 0 through day 90 under both definitions. The strategy difference is what treatment history is required within that window, not when outcome follow-up begins. Consequently, a comparison targeting strategy I addresses initiation under subsequent use as left unspecified by the strategy; a comparison targeting strategy S addresses the specified sustained regimen. The two contrasts need not be equal.
The distinction can be stated directly in potential-outcome terms: \(Y^{g_I}(90)\) and \(Y^{g_S}(90)\) refer to outcomes under different interventions. Unless the interventions produce the same treatment histories and outcomes in the target population, there is no basis for treating these potential outcomes, or their population risks, as interchangeable.
Discontinuation, Switching, and Dose Rules
A sustained strategy should avoid treating all post-initiation changes as equivalent. Stopping medication, switching to another medication, adding a second treatment, and changing dose are different treatment histories. A protocol can prohibit these changes, allow them without restriction, or specify conditions under which they are permitted. For example, it may allow a dose adjustment within a defined range but treat a switch to a different drug as a deviation. The rule should be consistent across the strategy description, the measurement plan, and the intended estimand.
When stopping is clinically expected, a rule that requires uninterrupted treatment may describe an impractical intervention. A more realistic strategy might allow a short interruption for a specified reason or permit switching after a defined clinical event. But a reason-based exception is only reproducible if the reason can be measured consistently and its timing is clear. “Continue unless clinically necessary” is not enough unless the protocol defines how necessity is determined.
Worked Example: Making a Switching Exception Operational
Suppose a hypothetical 120-day strategy requires treatment A, allows gaps of no more than 5 days, and permits switching to B only after a documented adverse reaction. A participant is covered with A through day 50, has a 4-day gap, and begins B on day 55. The gap is \(55-50-1=4\) days, so it is within the gap limit. The switch is allowed only if the required adverse reaction was documented before day 55.
If that documentation exists before the switch, the history follows the stated exception. If the reaction is recorded only after day 55, or is absent, the protocol cannot classify the switch as permitted using the specified evidence. The conclusion does not depend on whether the switch appears reasonable in retrospect: it depends on the prospective rule and its observable inputs. This example also shows why a protocol must define whether an exception changes the intervention or merely describes a deviation.
Diagnostics, Alternatives, and Limitations
Before analysis, inspect whether the rule can be applied to the available treatment data. A useful diagnostic is to construct a small set of hypothetical histories—including late initiation, overlapping supplies, a gap exactly at the limit, a gap one day beyond it, restarting, and switching—and confirm that each receives an unambiguous classification. Then check whether the required information is recorded with adequate timing and detail. Dispensing data, for example, identify supplies rather than certain ingestion; administration records may measure use differently.
Compare the sustained-treatment question with its main alternatives before choosing a protocol:
| Target question | Post-initiation rule | What the contrast concerns |
|---|---|---|
| Initiation strategy | No continued-use requirement unless specified | Starting one option rather than another, with later treatment not constrained by the initiation rule |
| Sustained strategy | Continuation, gaps, discontinuation, and switching are specified | Following one ongoing regimen rather than another |
| Observed-use or as-treated description | Use is classified as it occurs in the data | Outcomes across observed treatment histories; this description alone does not define a causal intervention |
The table distinguishes questions, not methods that are automatically interchangeable. A sustained strategy may be closer to a clinical decision about continued therapy, but it can be difficult to emulate if adherence rules are poorly measured or if few people follow them. Conversely, an initiation strategy may be easier to define while leaving subsequent treatment behavior outside the intervention being contrasted. Neither question is universally preferable; the research aim determines the target.
Common warning signs include a gap limit with no counting convention, a discontinuation rule that omits restarting, switching rules that differ across study arms without justification, and follow-up that begins only after a person has demonstrated sustained use. Another pitfall is to call a strategy “continuous treatment” while relying on data that show only prescriptions or dispensings. State what the data measure, what the protocol requires, and where those differ.
Check Your Understanding
Answer each question using the stated protocol rules. Brief solutions follow the questions.
- A strategy permits a gap of at most 6 days. Coverage ends on day 20 and the next supply begins on day 27. Is the history within the gap rule?
- In one sentence, distinguish an initiation strategy from a sustained-treatment strategy.
- A person starts treatment by the required deadline but switches to another drug when switching is prohibited. Does meeting the initiation deadline make the full history adherent?
- Why is beginning outcome follow-up only after a participant has completed 30 days of treatment problematic for a protocol whose time zero is baseline?
- Name two pieces of information needed to make a treatment-gap rule operational.
Solutions. (1) The gap is \(27-20-1=6\) days, so it meets the limit exactly. (2) An initiation strategy specifies starting treatment, whereas a sustained strategy additionally specifies treatment use after initiation over a stated period. (3) No; the start meets the initiation rule, but the prohibited switch is a deviation from the full strategy. (4) It changes the protocol's follow-up start based on post-baseline treatment history rather than following participants from the stated time zero. (5) For example, the coverage measure and the convention for counting calendar days between the end of supply and the next supply.