Why Dynamic Strategies Need Explicit Rules
Some treatment questions are not about assigning one treatment at baseline and leaving it unchanged. A clinician may begin with one option, reassess the patient’s response, and change treatment if a specified condition is met. To compare such approaches causally, the protocol must describe how treatment responds to evolving patient history. “Adjust treatment as needed” is not a complete strategy: different clinicians could interpret it differently, and the resulting treatment paths would not represent one clearly defined intervention.
The earlier material on specifying treatment strategies establishes the need to define treatment options and actions precisely. Here the focus is the extra structure required when the action at a later decision depends on information collected after treatment begins. A complete rule states when reassessment occurs, what information is used, what actions are available, and what action follows each relevant history—including a history with a missing measurement.
The history \(H_t\) can include baseline characteristics, earlier treatment, and measurements obtained before decision time \(t\). It must not include information that occurs after the action being assigned. The strategy also specifies the calendar or event-based decision times; a rule based on a week-four measurement is not the same intervention as one based on a measurement taken whenever a clinician happens to request it.
What a Protocol Must Specify
A usable dynamic protocol should make each branch of its decision rule interpretable and implementable. At a minimum, it identifies:
- Decision times: when treatment is initiated, reassessed, or changed.
- Information used: the measurement, its timing, and how it is calculated or classified.
- Available actions: the treatment options at each decision time, including whether a current treatment can be maintained, increased, reduced, held, or stopped.
- Decision conditions: thresholds, inequalities, and any other conditions that select an action.
- Exceptions and missing data: an explicit action when a measurement is missing, invalid, delayed, or outside the rule’s defined range.
When a patient’s history has more than one relevant feature, the branches must also resolve conflicts. For example, a rule that says “increase the dose if symptoms persist” does not say what to do if symptoms persist but a safety measurement is abnormal. The protocol needs a priority rule or a separate branch for that combination.
Worked Example: A Blood-Pressure Titration Rule
Suppose a hypothetical trial enrolls adults whose systolic blood pressure is above a stated eligibility threshold at baseline. At time zero, every participant starts the same named medication at 10 mg once daily. Reassessment occurs at weeks 4 and 8. The measured value is the mean of the last three valid home systolic readings recorded during the seven days before each visit. At each reassessment, the permitted doses are 10 mg, 20 mg, and 30 mg once daily.
The protocol’s rule is: if the mean is below 140 mmHg, maintain the current dose; if it is 140 mmHg or higher, increase by 10 mg, up to 30 mg. If the measurement is missing or invalid, maintain the current dose until the next scheduled reassessment. No other dose changes are part of this hypothetical strategy.
For a participant taking 10 mg at week 4 with valid readings of 146, 138, and 142 mmHg, the specified mean is
Because \(142\geq 140\), the week-four action is to increase to 20 mg once daily. If the week-eight measurement is 136 mmHg, the action is to maintain 20 mg. If instead the week-eight measurement is missing, the missing-data branch also prescribes maintaining the current 20 mg until the next scheduled reassessment. Thus the strategy defines an action for both observed and missing measurements.
This example is complete only within the scope stated: it defines the scheduled actions and the response to a missing measurement at those decisions. A protocol must separately specify other clinically relevant events if they are within its target question—for example, a safety event that requires stopping treatment. It must not silently assume that such events have no effect on the treatment path.
From a Rule to a Causal Contrast
A strategy determines a treatment path recursively. At baseline, the rule assigns an action using baseline history. The resulting treatment and subsequent measurements become part of the history used at the next decision. For each strategy \(g\), define \(Y^g\) as the outcome that would be observed if, at every decision time, treatment followed \(g\). A protocol can compare the mean outcome under two strategies, such as \(E[Y^g]\) and \(E[Y^{g'}]\), or their difference \(E[Y^g]-E[Y^{g'}]\). The outcome, follow-up horizon, target population, and direction of the contrast must be specified as part of the protocol.
The contrast is causal only under appropriate conditions. In particular, the strategy must describe well-defined interventions; patients’ treatment histories and outcomes must be defined consistently; and one patient’s assigned strategy must not alter another patient’s outcome. For observational emulation, additional identification conditions are needed:
- Sequential exchangeability: at each decision time, conditional on the measured history \(H_t\), the observed treatment action is independent of the counterfactual outcomes under the strategies being compared. This rules out unmeasured causes of both the treatment decision and those outcomes, after conditioning on the recorded history.
- Positivity: for histories that occur in the target population and are relevant to a strategy, there is a positive probability of observing the action that the strategy prescribes. If, for example, no patients with a particular history receive a specified dose, observational data cannot directly support that strategy for that history.
- Consistency: when a patient’s observed treatment path follows strategy \(g\), the patient’s observed outcome equals \(Y^g\). This requires sufficiently precise definitions of treatment and its timing; different versions of a nominally identical action can undermine the interpretation.
These assumptions explain why a strategy cannot be left vague. If “high blood pressure” is not operationalized, or the protocol does not say what happens when the reading is absent, it is unclear which path counts as following the intervention. In turn, the counterfactual outcome under that intervention is not well-defined for those histories.
Justification: Why Branches Define the Intervention
The logic can be seen by tracing a patient’s history forward. Suppose the decision times are \(t=0,1,2\). The baseline rule assigns \(A_0=g_0(H_0)\). After that action, the patient’s measured history at time 1 is observed, and the next action is \(A_1=g_1(H_1)\). The same process continues at time 2. Therefore a strategy defines a path through the sequence of actions for each history that can arise.
If \(g_1\) has no instruction for a missing value in \(H_1\), then \(A_1\) cannot be obtained from the stated rule for that history. There is no unique prescribed path for that patient, so “follow strategy \(g\)” does not identify a complete intervention on the full target population. Adding a fallback action (or explicitly restricting the target population to histories where the measurement is available) completes the definition. It does not by itself guarantee that the causal effect is identifiable; exchangeability and positivity, among other conditions, still need consideration.
Worked Example: A Response-and-Toxicity Rule
Consider a second hypothetical protocol for a treatment given at the beginning of each two-week cycle. At the end of cycles 2 and 4, clinicians assess a prespecified symptom score and a laboratory toxicity grade. The score is classified as controlled if it is below 6 points. The toxicity grade is classified as high if it is grade 3 or higher. Available actions are to continue the current dose or hold the next cycle.
The protocol states: if toxicity is high, hold the next cycle regardless of the symptom score. Otherwise, if the symptom score is 6 or higher, continue the current dose; if the score is below 6, also continue the current dose. In this particular strategy, the score determines classification but does not change the action unless a separately specified treatment option is added. If either assessment is missing, hold the next cycle until the assessment is available; if it remains unavailable at the next scheduled decision, continue holding.
For a patient with a symptom score of 8 and toxicity grade 3 at the cycle-2 assessment, the priority rule applies first: grade 3 is high toxicity, so the next cycle is held. For a patient with a score of 4 and grade 1, toxicity is not high and the score is below 6, so the next cycle is continued at the current dose. If the grade is missing, the specified fallback is to hold, rather than infer that toxicity is low. The example illustrates why the order of conditions and the action for missing information belong in the written protocol.
The score branches in this example do not distinguish actions, so they add no treatment adaptation. A protocol intended to compare symptom-guided treatment would need to define distinct actions for the score categories—for example, a specified dose change in one category—before it could be described as a response-adaptive strategy.
Diagnostics, Alternatives, and Limitations
Before emulation or analysis, check the protocol as if it were an executable decision algorithm. A reviewer should be able to take any allowed history at a decision time and determine one action without guessing. Common warning signs include an undefined threshold boundary, a measurement window that overlaps the treatment decision, mutually conflicting branches without a priority rule, or a missing-data branch that says only to “use clinical judgment.”
Data feasibility is also a design issue. If the protocol calls for weekly readings but the data source records them only at irregular visits, the strategy may not be reproducible from those records. If the measurement is recorded after treatment has already changed, it cannot straightforwardly serve as the pre-decision information that triggered that change. If some actions are never observed for certain histories, positivity may fail. These are not repaired merely by writing a more detailed rule; they may require a different target question or data source.
A dynamic strategy differs from a fixed-treatment strategy, which assigns the same treatment action regardless of later history. It also differs from a description of treatment as actually received: “patients who escalated” groups people according to a post-baseline event and does not itself define an intervention. A well-specified dynamic strategy can be compared with another dynamic strategy or with a fixed strategy, provided each is defined on the same relevant population and the causal assumptions are plausible.
Dynamic rules have practical limits. They may require measurements that are burdensome or unavailable, and their effects can depend on how faithfully the measurements and decisions are implemented. A highly detailed rule can still be clinically inappropriate or unsupported by data. Conversely, a rule so broad that it allows substantial discretion may fail to define a single intervention. The protocol should balance operational clarity with a realistic description of the intended care.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A protocol says, “At week 6, increase treatment if symptoms remain severe.” Name two details needed to make this a complete dynamic rule.
- At a decision time, the rule increases a dose when a measurement is at least 10 units and maintains it otherwise. What action is prescribed for a value of exactly 10?
- A rule uses a laboratory result but says nothing about a missing result. Why is the strategy incomplete for that history, and give one way to complete it.
- State the positivity condition in words for an observational comparison of dynamic strategies.
- At two decision times, a patient’s measurement is first 12 units and then 8 units. The rule increases treatment at values of 10 or more and otherwise maintains the current treatment. Starting at dose level 1, what path is prescribed if an increase adds one dose level?
Solutions. (1) Define “severe” using a specified measure and threshold, and state the treatment options and action for each category; the measurement window and a missing-measurement action are also needed. (2) Increase, because the condition is “at least 10,” which includes equality. (3) The rule does not assign a unique action when the result is missing, so the prescribed path is undefined for that history. It could specify, for example, maintaining the current treatment until the next scheduled measurement. (4) For histories relevant to the target population and strategy, the prescribed action must have positive probability of being observed, so the data contain support for following the rule at those histories. (5) At the first decision, \(12\geq10\), so dose level 1 increases to level 2. At the second, \(8<10\), so the current level is maintained. The path is therefore level 1, then level 2, then level 2.