Why Adherence Rules Must Be Explicit
A treatment strategy is not fully specified by naming a drug or procedure. The protocol must also state when treatment must begin, what counts as continuing it, which changes are permitted, and how long those requirements apply. Without these rules, two analysts can classify the same treatment history differently and thereby estimate different causal effects.
For example, “initiate treatment A” might mean receiving the first dose on the day of eligibility, starting within a 14-day grace period, or filling a prescription within that period. These are not interchangeable definitions. Similarly, a brief medication gap might count as discontinuation under one rule but not another. The adherence definition should be chosen before inspecting outcome patterns and should reflect the intended intervention as well as what the data can measure.
The introductory material on target-trial protocols establishes that strategies, time zero, follow-up, and the causal contrast must be aligned. Here the focus is narrower: operationalizing adherence to those strategies. The rules below concern treatment behavior; eligibility, outcome ascertainment, and ordinary loss to follow-up still require their own definitions.
Turn Each Strategy Into Observable Rules
For each strategy, write down the required actions, deadlines, allowable alternatives, and observation period. At a minimum, distinguish the following components:
- Initiation: the event that establishes treatment start, such as administration, dispensing, or a recorded procedure, and the latest permitted start time.
- Discontinuation: the rule for when treatment is considered to have stopped. It may be based on a recorded stop date or a prespecified gap after expected supply runs out.
- Switching: whether moving to another treatment is allowed, prohibited, or allowed only under stated conditions.
- Nonadherence: any other failure to follow a treatment requirement, such as missing a required dose or exceeding a permitted dose range, when that behavior is observable and relevant to the strategy.
- Duration: the dates or event that end the adherence requirement. A rule that applies through day 30 is different from one that applies through the end of follow-up.
The definition should be operational in the available data. A prescription fill is evidence of dispensing, not proof that a patient swallowed each dose. If adherence can only be measured through dispensing records, the protocol should describe it as such rather than claiming to observe ingestion. Likewise, a gap rule needs a precise threshold and a rule for days’ supply, overlapping fills, and any permitted grace interval. These choices determine which treatment histories are classified as adherent.
A strategy can specify initiation without specifying maintenance. In that case, later discontinuation is not automatically a deviation. Conversely, if a strategy requires starting and continuing treatment, a participant who starts on time and then stops may adhere to the initiation component but deviate from the continuation component. The protocol must say which interpretation applies.
Worked Example: Writing a Medication Strategy as Rules
Suppose a hypothetical target trial compares two strategies among eligible adults at time zero. Strategy A is “initiate drug A within 14 days and continue it through day 90.” Strategy B is “initiate drug B within 14 days and continue it through day 90.” For this example, dispensing records identify initiation, days’ supply is recorded, gaps of at most 7 consecutive uncovered days are allowed, and dispensing a different study drug counts as switching.
Under Strategy A, an A dispensing on day 10 meets the initiation deadline. If the supply ends on day 39, a refill on day 46 leaves days 40 through 45 uncovered: that is a 6-day gap and is allowed by the stated rule. If the refill instead occurs on day 47, the 7 uncovered days from day 40 through day 46 remain within the allowed maximum. A refill on day 48 creates 8 uncovered days, so the participant deviates when the gap exceeds 7 days. Dispensing B before day 90 is also a deviation because switching is prohibited.
Under Strategy B, the corresponding initiation and continuation rules apply to B. A person who never initiates either drug by day 14 deviates from both strategies at the deadline, not on day 1: until the deadline, initiation remains possible. If the protocol had specified initiation only and said nothing about continuation, stopping after an on-time start would not violate that narrower strategy.
The example shows why “adherent” cannot be assigned from a treatment label alone. It requires the deadline, observable treatment event, gap threshold, switching rule, and end of the adherence period.
Deviation, Follow-Up, and the Estimand
A deviation does not have one universal consequence. The consequence depends on the estimand and prespecified analysis. An assignment-based or treatment-policy contrast compares outcomes according to the strategy assigned at baseline, regardless of later deviations. Under that approach, a deviation does not itself end follow-up: outcomes continue to be counted according to the protocol’s outcome and follow-up rules. In an observational emulation, this contrast requires a well-defined assignment analogue and appropriate control of confounding; simply grouping people by treatment they eventually received does not create a randomized assignment.
A per-protocol contrast instead asks about outcomes under adherence to the specified strategies. A common emulation approach artificially censors a participant or strategy-specific clone at the first deviation from that strategy. Artificial censoring is an analysis operation, not a claim that the person stopped being observed or became ineligible for the outcome. Their later outcomes may still exist in the source data, but they no longer contribute directly to the adherent follow-up for that strategy. Because deviation may depend on prognosis, analyses often need methods such as inverse-probability-of-censoring weighting to address selection induced by this censoring.
For grace-period strategies, the deadline matters. A strategy requiring initiation by day 14 is not violated merely because treatment has not started on day 5. A participant can remain compatible with that strategy while the deadline is open. If a participant starts the competing treatment on day 5 and the strategy prohibits it, however, that action can be a deviation immediately. This is especially important when a person is represented by clones assigned to different strategies: each clone is assessed against its own rules, not against a single retrospective label for the person.
Worked Example: Locating the Deviation in a Grace Period
Consider two hypothetical strategy-specific clones at time zero. Clone A must initiate A by day 14; Clone B must initiate B by day 14. Either strategy prohibits initiating the competing drug before the required initiation. A hypothetical participant initiates B on day 6 and never initiates A.
For Clone A, the participant has not violated the deadline merely by being untreated on day 5. On day 6, however, initiating B violates the rule prohibiting the competing drug. Clone A is artificially censored at that deviation, day 6. It is not necessary to wait until day 14, because the observed action has already made adherence to A impossible under the protocol.
For Clone B, initiation of B on day 6 satisfies the initiation rule. If B continuation is also required, adherence is then assessed against the continuation rules through the specified end date. If the protocol required only initiation, the later treatment history would not create a continuation deviation. Thus the same event can be a deviation for one clone and adherence for another.
This classification follows the protocol’s timing and rules. It does not use future outcomes to decide when the participant “really” entered a strategy.
A Short Justification for Weighting After Artificial Censoring
Artificially censoring at deviation can select a noncomparable subset. For instance, if worsening health makes discontinuation more likely and also predicts the outcome, the remaining adherent participants may have better prognosis even apart from treatment. Weighting can, under assumptions, re-create a population in which adherence-related censoring is independent of potential outcomes conditional on measured history.
In a simple two-interval illustration, suppose an individual remains adherent through interval 1 with conditional probability 0.80 and through interval 2 with conditional probability 0.75, given the measured history used in the model. The probability of remaining uncensored through both intervals is the product \(0.80 \times 0.75 = 0.60\). The corresponding inverse-probability weight is:
The weight represents the contribution of an observed adherent history relative to its probability under the modeled adherence process; it is not a literal number of people. With time-varying histories, weights are formed from conditional probabilities across intervals, and practical analyses often use stabilized weights and assess their distribution. This illustration is not a guarantee that weighting works: the adherence model must be appropriate, relevant predictors of both adherence and outcome must be measured, and there must be a positive probability of remaining adherent for the histories being analyzed.
The justification is that, if measured history suffices to make censoring conditionally independent of the potential outcome and the conditional adherence probabilities are correctly specified, weighting by the inverse probability of remaining uncensored counteracts the over- or under-representation created by that censoring. If either condition fails, the weighted analysis need not identify the per-protocol effect.
Worked Example: Calculate a Two-Interval Weight
In a hypothetical analysis, the estimated conditional probabilities of adhering through the first and second intervals are 0.80 and 0.75 for a particular measured history. The individual adheres through both intervals. Calculate the unstabilized inverse-probability weight.
Step 1: Find the probability of remaining uncensored. By the multiplication rule for sequential conditional probabilities, it is \(0.80 \times 0.75 = 0.60\).
Step 2: Take the inverse. The weight is \(1/0.60 = 1.6667\), or approximately 1.667. Equivalently, \(1/(0.80 \times 0.75)=1/0.60=1.667\).
The result is consistent with the unrounded probabilities. It would be misleading to multiply rounded reciprocals and report a different value: the weight is calculated as the inverse of the product of the stated probabilities. This single calculation illustrates the construction; it does not establish that the assumptions needed for causal interpretation hold.
Diagnostics, Alternatives, and Limits
Before analysis, check whether the adherence definition can actually be applied to the data. Look for dates that are missing or inconsistent, implausible days’ supply, treatment records that cannot distinguish initiation from continuation, and gaps that cannot be classified. Tabulate deviations by type and time, and compare how many participants remain adherent under each strategy. In weighted analyses, inspect the adherence probabilities and weight distribution; very small probabilities can produce extreme weights and unstable estimates. These checks can reveal sparse support or a poorly operationalized rule, but they do not prove absence of bias.
The main alternatives answer different questions. A treatment-policy analysis retains follow-up after deviation and targets the effect of assignment or initial strategy, if that assignment contrast is identifiable. A per-protocol analysis targets adherence to the specified strategies and may use artificial censoring with weighting or another appropriate adjustment. An as-treated analysis classifies people by treatment actually received; unless carefully defined and adjusted, it can be confounded by the reasons people start, stop, or switch. These analyses are not interchangeable repairs for one another.
Important limitations remain. Misclassified initiation or gaps can make artificial censoring occur at the wrong time. Unmeasured predictors of both deviation and outcome can leave informative censoring uncontrolled. Positivity can fail when some measured histories almost always lead to deviation, so the data contain little information about continued adherence for those histories. Finally, defining adherence more strictly often reduces the number of contributing observations and may change the target intervention itself. Sensitivity analyses can explore plausible alternative definitions, but they cannot make an ambiguous protocol precise after the fact.
Common Mistakes
- Calling every post-initiation stop a deviation. That is incorrect if the strategy only required initiation. Add a continuation requirement and duration if stopping is meant to violate the strategy.
- Censoring at the first untreated day of a grace period. If initiation is allowed through day 14, being untreated on day 5 is still compatible with the strategy. Censor only when a stated rule is actually violated or the deadline passes without initiation.
- Treating artificial censoring as ordinary loss to follow-up. It is a strategy-specific analysis rule. The person may remain observed in the data, and censoring must be handled consistently with the chosen estimand.
- Assuming a weighted per-protocol analysis is automatically unbiased. Weighting relies on adequate measurement, correct modeling, and positivity; it cannot adjust for unmeasured causes of deviation and outcome.
Check Your Understanding
Answer each question using the protocol rules stated in the question. Brief solutions follow.
- A strategy requires a first dispensing of drug C by day 10 and says nothing about later use. A participant starts C on day 8 and stops on day 20. Is stopping a deviation from this strategy?
- A strategy permits initiation of drug D through day 7 and prohibits drug E. A participant is untreated on day 4 and starts E on day 5. When does the participant first deviate?
- In a per-protocol analysis, the probability of remaining adherent is 0.90 in interval 1 and 0.80 in interval 2, conditional on the modeled history. What is the two-interval unstabilized inverse-probability weight?
- Why might a treatment-policy analysis retain follow-up after switching, while a per-protocol analysis censors at switching?
Solutions. (1) No. The stated strategy requires initiation only; it imposes no continuation rule, so stopping on day 20 does not violate the definition given. (2) The untreated status on day 4 is still compatible with the deadline. Starting prohibited drug E on day 5 is the first deviation, so censoring for this strategy would occur then if the per-protocol plan uses artificial censoring. (3) The probability of remaining adherent through both intervals is \(0.90 \times 0.80=0.72\); the weight is \(1/0.72=1.389\) to three significant figures. (4) The treatment-policy contrast follows the initially assigned strategy regardless of later treatment, so switching does not itself terminate outcome follow-up. The per-protocol contrast concerns adherence to the specified strategy, so switching violates that strategy and may trigger artificial censoring, with adjustment needed if such censoring is informative.