From Sustained Strategies to Follow-Up Records
A comparison of sustained strategies asks what would happen under continued adherence to each of two treatment rules, not merely what happens to people classified by their treatment at baseline. To represent that comparison, the protocol must say what treatment is required at each decision point, when a deviation occurs, and which outcome interval belongs to each decision.
This tutorial works through a simple comparison: sustained use versus sustained nonuse. The same record-building logic applies to other explicitly defined strategies, but the rule must be precise enough to determine whether a participant’s observed treatment history remains compatible with each strategy.
The decision point at \(k\) is followed by an outcome interval \(k\). Thus treatment status is assessed before that interval’s outcome is counted. Set time zero at the first decision point, after eligibility has been assessed and before follow-up outcomes accrue. This ordering avoids assigning a person-time interval to a strategy based on information that occurs later in that interval.
For clarity, suppose the outcome is a first event. Once the event occurs, that participant contributes no later at-risk intervals. Loss to follow-up similarly ends observed records. Administrative end of follow-up occurs after the final interval. These are distinct from a treatment deviation: a deviation makes a particular strategy-specific record incompatible with its assigned rule, but does not remove the participant’s record under another strategy if it remains compatible there.
Worked Example: Writing the Protocol Rules
Worked Example: Writing the Protocol Rules
Suppose a study compares a daily preventive medication with no use of that medication over three monthly intervals. Eligible participants may be using or not using the medication at baseline. Treatment status is recorded at the start of each month, and a first hospitalization is ascertained during that month.
The time zero is the start of month 1, after eligibility and baseline covariates have been recorded. There are three decisions, \(k=0,1,2\), and three corresponding outcome intervals. Under sustained use, the required sequence is \((1,1,1)\). Under sustained nonuse, it is \((0,0,0)\).
A participant with observed sequence \((1,1,0)\) follows the use strategy for the first two intervals, then deviates at the third decision. A participant with sequence \((0,1,0)\) deviates from the nonuse strategy at the second decision; the later return to nonuse does not erase that earlier deviation. Stating the sequence makes the rule auditable: “usually takes the medication” would not.
The protocol must also define what counts as treatment during a month: for example, a dispensing record, a medication reconciliation, or a prespecified coverage threshold. Here the example treats \(A_{ik}\) as a correctly measured binary status at the start of each month. A real study needs to specify its measurement rule and how it handles uncertain or missing status.
Clone Participants and Mark Deviations
At time zero, create one strategy-specific record, or clone, for each eligible participant under each strategy. Both clones begin at the same time and share the participant’s measured baseline information. The participant’s observed treatment history is then checked against each clone’s assigned rule. A clone stops contributing at the first decision point where the observed treatment differs from the required treatment. This is often called artificial censoring: it is a record-level rule imposed to represent adherence to the assigned strategy, not a claim that the person disappeared from the study.
Worked Example: Finding the First Deviation
Consider three participants followed for three intervals. Each treatment value is observed at the start of the interval, and there is no loss to follow-up.
| Participant | Observed treatment sequence | First event |
|---|---|---|
| P1 | (1, 1, 1) | Interval 3 |
| P2 | (1, 0, 0) | None |
| P3 | (0, 0, 0) | Interval 2 |
For P1, the sustained-use clone matches all three decisions. It contributes intervals 1 and 2 and the event in interval 3. The sustained-nonuse clone mismatches at decision 1, so it contributes no outcome interval.
For P2, the sustained-use clone matches decision 1 and contributes interval 1, then mismatches at decision 2 and contributes no later interval. Its sustained-nonuse clone mismatches at decision 1 and contributes none. P2’s later nonuse does not restore compatibility with the sustained-use strategy.
For P3, the sustained-nonuse clone matches both decisions preceding the event and contributes the event in interval 2. The sustained-use clone mismatches at decision 1 and contributes no interval. The event is counted for the compatible clone because treatment at the start of interval 2 matches nonuse; it would be incorrect to censor that clone merely because an event occurs during the interval.
The resulting records are therefore: P1 contributes to sustained use through the event in interval 3; P2 contributes to sustained use in interval 1 only; and P3 contributes to sustained nonuse through the event in interval 2. No participant contributes an outcome interval to both clones under these particular histories, but the two records were both created at baseline.
Participant-Period Record Construction
A practical data set usually has one row per participant, strategy, and interval in which that strategy-specific record remains at risk and compatible. Useful fields include the original participant identifier, strategy identifier, interval, observed treatment, outcome indicator, and indicators for deviation, event, and loss to follow-up. Keep the original identifier: two clones from one participant are not two independent people.
The following rule makes the record definition explicit. Let \(Y_{ik}=1\) indicate that participant \(i\) has the event during interval \(k\), and let \(L_{ik}=1\) indicate loss to follow-up before interval \(k\) is observed. A row for interval \(k\) under strategy \(g\) is present only if the participant was eligible, had no earlier event or loss, and matched the required treatment at decisions \(0,\ldots,k\). In particular, treatment mismatch at decision \(k\) prevents an outcome row for interval \(k\).
To verify the rule, begin with interval 0. The participant contributes only if eligible, observed and at risk, and the treatment at decision 0 equals \(g_0\); these are exactly the factors in \(R_{ig0}\). Now suppose the rule identifies rows correctly through interval \(k-1\). For an interval-\(k\) row, the participant must additionally remain event-free and observed through the start of \(k\), and must match \(g_k\) at the current decision. Multiplying the prior conditions by these requirements gives the product through \(s=k\). Conversely, if any factor is zero, at least one required condition fails and there is no row. This proves the rule for each interval by induction. \(\square\)
Worked Example: Building Rows for One Participant
A participant is eligible, has treatment sequence \((1,1,0)\), experiences no event or loss, and is followed for three intervals. Construct the rows under both sustained strategies.
Under sustained use, the participant matches at decisions 0 and 1, so the use clone contributes intervals 0 and 1. At decision 2, \(A_{i2}=0\ne g^1_2=1\), so the clone is censored before interval 2. Its treatment-match products are \(1\), \(1\), and \(0\) for \(k=0,1,2\), respectively.
Under sustained nonuse, the clone mismatches at decision 0 because \(A_{i0}=1\ne g^0_0=0\). Its treatment-match products are \(0\), \(0\), and \(0\); it contributes no outcome interval. The participant therefore generates two rows total, both in the sustained-use clone, with no event recorded in either row.
If an event had occurred in interval 1, it would be entered on the interval-1 use row and the clone would have no interval-2 row. It would not be reclassified as a treatment deviation: the interval-1 treatment matched the use strategy.
What the Records Do—and Do Not—Establish
Cloning gives each strategy the same eligible baseline population. Formally, if there are \(N\) eligible participants, each strategy has \(N\) baseline clones, one per participant. This follows directly from the construction: for every eligible identifier \(i\), create exactly one clone labelled \(g^1\) and exactly one labelled \(g^0\). No treatment history after time zero is needed to determine baseline membership. Therefore both strategy records start from the same empirical distribution of eligible participants, although they contain paired records from the same people. \(\square\)
That baseline symmetry is a design feature, not a causal estimate. After follow-up begins, clones are censored at different times according to observed treatment. A simple comparison among the remaining rows can be biased if the factors that predict deviation also predict the outcome. Consistency, exchangeability for treatment adherence and censoring, positivity, and suitable outcome and censoring adjustment are among the conditions needed for a causal interpretation. Cloning alone does not establish them.
A useful comparison is with classifying participants once by baseline treatment. Baseline classification does not represent sustained adherence if treatment changes later. Another alternative is to restrict analysis to people who remained adherent throughout follow-up. That restriction uses future information to determine who is included and can select a non-comparable subset. Strategy-specific cloning instead begins with the eligible participants at time zero and records when each strategy becomes incompatible with observed care. The resulting artificial censoring still requires appropriate handling for causal estimation.
As a basic diagnostic, tabulate treatment sequences and the number of retained records by strategy and interval. Check that each row’s treatment agrees with its strategy, that no row follows a first event or loss, and that a mismatching decision removes the clone before that interval’s outcome. Also confirm that the number of baseline clones equals the eligible-participant count in each strategy. Sparse or absent compatible histories in later intervals signal that the observed data provide limited support for the sustained strategy; this is not repaired by duplicating records.
Common Mistakes and Limitations
- Using a vague strategy label. “Stay on treatment” is incomplete if dose, treatment window, or allowable interruptions are unspecified. State the decision times and exactly what counts as adherence.
- Censoring after, rather than before, a mismatching interval. If treatment is assessed at the interval’s start, a mismatch at that decision means the clone does not contribute that interval. A different measurement schedule requires a correspondingly different ordering rule.
- Removing a participant from both strategies after one deviation. Compatibility is strategy-specific. A deviation from one clone does not by itself remove the other clone.
- Treating clones as independent participants. They share the same original person and baseline data. Inference must account for this dependence.
- Calling the unweighted retained-record contrast causal. Strategy-specific censoring can select participants over time. The record construction defines the emulation; it is not a substitute for identification assumptions or adjustment.
The method is also limited by the treatment data. If exposure status is only measured intermittently, a recorded sequence may not reveal what happened between decisions. If strategies permit grace periods or exceptions, those rules must be built into the protocol and record algorithm rather than improvised after seeing outcomes.
Check Your Understanding
Answer each question, then compare with the solutions below.
- Under the two sustained strategies, what treatment sequence is required over four decision points for each strategy?
- A participant’s sequence is \((0,1,1)\). At which decision does the sustained-nonuse clone stop contributing? Does the later treatment history restore that clone?
- Why should an event in an interval be recorded if treatment matched the strategy at the start of that interval?
- There are 80 eligible participants. How many baseline clones should be created for each of two strategies, and why are the 160 clones not 160 independent participants?
- Name two checks that can detect errors in the participant-period records.
Solutions. (1) Sustained use requires \((1,1,1,1)\); sustained nonuse requires \((0,0,0,0)\). (2) The nonuse clone first deviates at decision 2, where treatment is 1; later nonuse does not undo the deviation. (3) Treatment is assessed before the interval’s outcome, so a compatible clone remains at risk for that interval and its event belongs in the record. (4) Create 80 clones per strategy, or 160 records at baseline; each pair shares one original participant, so the clones are dependent. (5) For example, verify that each row’s treatment matches its strategy and that no row occurs after the first event; one may also check baseline clone counts and whether mismatches censor before the corresponding outcome interval.