Genotype-Guided Dose Titration As A Dynamic Regimen

Why Titration Is a Dynamic Regimen

A genotype can inform an initial dose, but treatment often does not stop at that first decision. A clinician may revise the prescription after reviewing a measured drug concentration, clinical response, adverse effects, or adherence. The treatment being studied is therefore a sequence of decisions, not a single dose assigned at baseline. The central statistical task is to represent that sequence clearly enough to distinguish the contribution of genotype from the contribution of later dose changes and the information used to make them.

A dynamic regimen specifies what dose to prescribe at each decision time as a function of information available at that time. This differs from a fixed regimen, such as “prescribe 4 mg throughout follow-up.” It also differs from a statement such as “the dose was adjusted,” which does not say what information triggered a change or what dose rule was followed.

Definition: Let \(G\) denote baseline genotype. At decision time \(t\), let \(H_t\) denote the recorded history available before the decision, including relevant earlier prescriptions, adherence, clinical measurements, and adverse effects. A dynamic dose regimen is a sequence of rules \(d=(d_0,d_1,\ldots,d_{K-1})\), where the prescribed dose at time \(t\) is \(A_t=d_t(G,H_t)\). The history must contain only information available before that decision.

Several quantities that are often collapsed into “dose” should be distinguished. \(A_t\) is the dose prescribed. Adherence describes whether, and to what extent, the patient takes it. The dose received may therefore differ from the prescribed dose. A measured concentration or response is further downstream: it can reflect the dose received, pharmacokinetics, clinical condition, measurement error, and other factors. The earlier material on pharmacokinetic and pharmacodynamic response models provides ways to represent some of these relationships; here the emphasis is on how they enter a changing treatment rule.

The regimen can include genotype in its initial rule, in its later rules, or both. For example, it may prescribe different starting doses by genotype, then apply the same concentration-based adjustment rule to all patients. Alternatively, it may use genotype-specific adjustment thresholds. These are distinct policies and should be described separately.

Worked Example: Following a Hypothetical Titration Rule

Consider a purely hypothetical drug and a simplified policy. At baseline, the policy prescribes 5 mg per day for \(G=0\) and 3 mg per day for \(G=1\). At each monitoring visit, a trough concentration below 8 units prompts an increase of 1 mg per day; a concentration from 8 through 12 units prompts no change. These values illustrate the logic of a rule and are not clinical recommendations.

A hypothetical patient has \(G=1\), so the initial prescribed dose is \(A_0=3\) mg per day. Suppose the patient takes 80% of the prescribed dose on average during the first interval. Under the simplified assumption that average dose received is prescribed dose multiplied by adherence, the average dose received is \(3(0.80)=2.4\) mg per day. Suppose, for illustration, the steady-state concentration is \(2.5\) units per mg per day of dose received. The predicted concentration is \(2.5(2.4)=6.0\) units.

Because 6.0 is below the policy threshold of 8, the rule increases the next prescription by 1 mg per day, to \(A_1=4\) mg per day. If adherence in the next interval is 75%, the average dose received is \(4(0.75)=3.0\) mg per day and the simplified predicted concentration is \(2.5(3.0)=7.5\) units. That value is still below 8, so the next decision under this rule is another 1 mg per day increase, to 5 mg per day.

The example separates the rule from its implementation. Genotype determines the initial prescription; the measured concentration triggers subsequent changes; adherence helps explain why the measured concentration may not match what the prescription alone would suggest. A real application would require an appropriate pharmacologic model, clinically defined safety rules, and reliable measurements.

Which Effect Is Being Described?

The phrase “genotype effect” can refer to different comparisons. A genotype contrast at a common prescribed or received dose asks whether outcomes differ between genotype groups when dose is held fixed in the model or design. A policy contrast asks how outcomes differ under two specified dosing rules. A contrast between genotype groups receiving their usual genotype-guided care combines genotype differences with the different doses and monitoring histories that care produces. These quantities need not agree.

For example, a regression coefficient for genotype in a model that also includes dose is a conditional association under that model. It is not automatically a causal, intrinsic biological effect of genotype. A causal interpretation of a comparison at fixed dose requires a well-defined intervention on dose and adequate control of factors that affect both dose and outcome. In genetic comparisons, population structure and related sources of genotype-outcome association also require attention. The treatment-by-genotype material distinguishes effect modification; here the additional issue is that dose itself changes over time in response to prior history.

Key distinction: A genotype contrast at a common dose is not the same estimand as the contrast between outcomes under genotype-guided care. Under a policy, genotype can affect the initial prescription, later prescriptions, and the clinical information that triggers adjustment. A policy comparison concerns the whole decision sequence.

Worked Example: A Common-Dose Contrast Versus a Policy Contrast

Suppose a hypothetical analysis uses the model \(Y=10+2G+1.5(D-4)\), where \(Y\) is a response measured in points, \(G\) is 0 or 1, and \(D\) is average dose received in mg per day during the relevant interval. Assume for this illustration that the model is correctly specified and its coefficients have a causal interpretation under a suitable design and adjustment set.

At the same dose \(D=4\), the predicted response for \(G=0\) is \(10+2(0)+1.5(4-4)=10\) points. For \(G=1\), it is \(10+2(1)+1.5(4-4)=12\) points. Thus the model’s genotype contrast at this common dose is \(12-10=2\) points.

Now compare two dose levels within \(G=1\). At \(D=3\), the predicted response is \(10+2+1.5(3-4)=10.5\) points. At \(D=4\), it is 12 points. The model’s dose contrast over this one-unit increase is \(12-10.5=1.5\) points.

Finally, suppose the two genotype groups receive different doses under a hypothetical policy: \(D=4\) for \(G=0\) and \(D=3\) for \(G=1\). Their predicted responses are 10 and 10.5 points, respectively, so the between-group contrast under that policy is \(0.5\) points, not 2 points. The difference arises because the groups are being compared at different doses. Even in this simple model, the result under a policy cannot be read as the genotype contrast at a common dose.

History, Feedback, and Assumptions

Titration creates treatment-confounder feedback. A prior dose can affect a later concentration or symptom measure; that measure can influence the next dose; and both the measure and the next dose can be related to the final outcome. A standard regression that adjusts for the latest measurement may answer a different question from one that does not adjust for it. The measurement may be a confounder of the next dose-outcome relationship while also being affected by earlier treatment.

For causal evaluation of a regimen from observational data, the main assumptions should be stated relative to the decision times and the target population. Consistency means that a person who follows the specified rule has the outcome defined for that rule. Sequential exchangeability means that, conditional on the recorded history before each decision, the observed dose decision is independent of the relevant potential outcomes under the candidate regimens. Positivity means that, for histories occurring in the target population, there is a positive probability of receiving the dose required by the regimen. No interference means one person’s regimen does not change another person’s outcome.

These assumptions are substantive, not guaranteed by including genotype in a model. Sequential exchangeability can fail if clinicians use unrecorded information, such as an unmeasured symptom, when changing a dose. Positivity can fail if, for a particular history, clinicians always choose one dose and never choose the dose required by the policy being evaluated. Poor adherence and missing monitoring measurements also complicate the definition and evaluation of the regimen. If the policy is intended to describe prescribing, adherence should be reported separately; if it is intended to describe treatment actually received, adherence is part of implementation and must be incorporated explicitly.

Interpretation checklist: State the target population, the genotype information used, the dose rule at each decision, the history available to that rule, whether the target is prescribed or received dose, and the outcome under comparison. For observational evaluation, also state the assumptions about measurement, confounding, and treatment availability.

Estimating Outcomes Under a Dynamic Regimen

When treatment changes in response to history, simply comparing people who did and did not receive a dose increase can be misleading: the histories prompting the increase may themselves predict the outcome. One general approach is inverse-probability weighting. It gives greater weight to observed treatment paths that were relatively unlikely given their histories, so the weighted data can represent a population following a specified rule. This approach depends on correctly estimated treatment probabilities and the assumptions just stated.

For a one-time decision, let \(A\) be the observed action, \(H\) the measured pre-decision history, and \(d(H)\) the action required by a rule. If \(Y\) is the outcome, the contribution from people receiving the rule’s action is weighted by the inverse probability of receiving that action given their history. The basic identity follows by conditioning on \(H\).

E\left[\frac{I\{A=d(H)\}Y}{P\{A=d(H)\mid H\}}\middle|H\right] = E[Y\mid A=d(H),H] = E[Y^{d}\mid H].

Here \(I\{\cdot\}\) equals 1 when the condition is true and 0 otherwise, and \(Y^d\) is the outcome that would occur under the rule. The first equality follows because only people receiving \(d(H)\) contribute, and their probability of doing so cancels the denominator. The second equality uses consistency and conditional exchangeability: among people with the same measured history, the observed outcome under the rule’s action represents the corresponding potential outcome. For several decision times, the weight is the product of inverse probabilities of receiving the rule-required action at each time, conditional on the history before that decision. Positivity is needed so these probabilities are not zero.

Worked Example: Weighting Observed Paths That Follow a Rule

Suppose a hypothetical two-visit policy increases the dose when the measured concentration is below target and maintains it otherwise. Four patients follow the policy-required action at both visits. For each patient, the conditional probabilities of following the required action at visit 1 and visit 2, given the recorded histories, are listed below. Their final outcomes are measured in points.

Patient	Visit 1 probability	Visit 2 probability	Outcome (points)
1	0.80	0.75	12
2	0.50	0.80	10
3	0.40	0.50	8
4	0.90	0.60	11

The probability of following the required path is the product of the two conditional probabilities. The corresponding weight is its inverse. For patient 1, for instance, the path probability is \(0.80(0.75)=0.60\), so the weight is \(1/0.60=1.667\). The four weights are \(1.667,\ 2.500,\ 5.000,\) and \(1/(0.90(0.60))=1.852\), respectively.

The normalized weighted mean is

\frac{(1.667)(12)+(2.500)(10)+(5.000)(8)+(1.852)(11)} {1.667+2.500+5.000+1.852} \approx \frac{105.37}{11.019} =9.563\text{ points}.

Thus, in this deliberately small illustration, the weighted estimate of the mean outcome under the rule is about 9.563 points. The calculation does not establish that the rule is beneficial, nor does it provide a useful precision estimate from four people. In a real analysis, treatment probabilities would need to be estimated or justified, uncertainty would need to be quantified, and the assumptions about histories and treatment choices would need substantive support.

Why the Distinction Matters

A genotype-guided regimen is a clinical decision strategy, not merely a genotype coefficient or an initial dose comparison. Reporting only the starting dose can conceal later differences in monitoring, dose changes, and adherence. Conversely, reporting a genotype association after adjustment for the final dose can obscure part of the treatment pathway if genotype influenced that dose. The analysis should therefore align its estimand with the question: a common-dose genotype contrast, a dose effect under stated assumptions, or an outcome under a complete dynamic policy.

A useful description makes the decision sequence auditable. It specifies what is measured, when it is measured, how each result changes the prescription, and what happens when adherence is uncertain or a safety threshold is crossed. It also distinguishes the intended rule from what clinicians and patients actually did. This precision is essential for interpreting results and for considering whether the policy could be implemented in another setting.

Common Pitfalls

Calling the starting dose the regimen. A starting dose does not describe later decisions. State the rule at every decision time.
Equating prescribed dose with received dose. Nonadherence can make them differ. Record and analyze adherence when the question concerns exposure actually received.
Interpreting an adjusted genotype coefficient as the policy effect. A coefficient conditional on dose is not generally the contrast between outcomes under genotype-guided policies.
Ignoring why the dose changed. A response or concentration may influence later dose and predict the outcome. This treatment-confounder feedback requires an appropriate design or method.
Assuming every policy can be evaluated from observed data. If some relevant histories never receive the policy-required action, positivity fails and the data do not support that comparison without additional assumptions.

Check Your Understanding

Use the definitions and distinctions in this tutorial to answer the following questions.

What information can a dynamic dose rule use at decision time \(t\), and why must that information be available before the decision?
Explain why a genotype contrast at a common dose may differ from a comparison between genotype groups receiving genotype-guided care.
A patient is prescribed 6 mg per day and takes an average of 50% of the prescribed dose. What is the average dose received under the simple multiplication convention used in the example?
Name two assumptions required for inverse-probability weighting to evaluate a dynamic regimen from observational data, and describe one way each could fail.
Why can adjusting for a measurement that triggers a dose change alter the interpretation of a treatment-effect analysis?