Writing The Causal Contrast Into The Protocol

Why the Contrast Belongs in the Protocol

A protocol can specify who is eligible, what treatment options are compared, and how outcomes are measured, yet still leave the causal question ambiguous. “Does treatment work?” does not say whose outcomes are being compared, what “treatment” means over time, or whether the question concerns being assigned a strategy or following it. Those choices define the causal contrast: the particular comparison between potential outcomes that the study is intended to estimate.

Writing the contrast explicitly prevents a mismatch between the scientific question and the number eventually reported. For example, the effect of assignment to an offer of treatment is not automatically the effect of taking treatment continuously. Both can be reasonable questions, but they compare different interventions and generally have different answers.

Writing a Population Contrast

Let \(P\) denote the population defined by the protocol’s eligibility criteria at time zero. Let \(g_1\) and \(g_0\) denote two clearly specified treatment strategies. For individual \(i\), \(Y_i^{g}(\tau)\) is the outcome that would be observed by follow-up horizon \(\tau\) if that individual followed strategy \(g\). The outcome must itself be defined: it might be a measurement at \(\tau\), an event by \(\tau\), or a summary over the period from time zero through \(\tau\).

For a quantitative outcome, a common population-average contrast is the difference in mean potential outcomes. The population and horizon are part of the definition, not optional context:

The first mean is the average outcome in the target population under \(g_1\); the second is the average under \(g_0\). The difference is expressed in the outcome’s units. A ratio of these means is another possible contrast, but it answers a different question and requires an interpretable ratio scale.

For a binary outcome, define \(Y^{g}(\tau)=1\) if the event occurs by \(\tau\), and 0 otherwise. Then \(E[Y^{g}(\tau)\mid P]\) is the event risk in the target population under \(g\). A risk difference is measured in percentage points when risks are reported as percentages; a risk ratio is unitless. The protocol should name the intended scale rather than leaving readers to guess which comparison matters.

Assignment-Based and Adherence-Based Questions

An assignment-based contrast compares potential outcomes under strategies that assign or offer treatment. Each strategy must specify what is assigned—for example, an offer of a program versus usual care—and may specify other features of the intervention. The outcome is attributed to the assigned strategy regardless of whether each person follows it exactly. In a randomized trial, this is commonly described as an intention-to-treat question. In an observational emulation, the protocol must still state the corresponding assignment strategies; the label does not make assignment randomized.

An adherence-based contrast instead compares potential outcomes under strategies for actual treatment use, such as initiating a medication and continuing it as directed throughout a stated period versus not initiating it. That is a different intervention from being assigned an offer. It asks what outcomes would be under adherence to each specified regimen, not what would follow from assignment when adherence may vary.

The two questions can differ even when they use the same population, outcome, and horizon. Assignment to an offer can affect outcomes through participation and other consequences of the offer. An adherence strategy concerns treatment receipt over time. To define the latter, the protocol must be precise about what counts as following the regimen and about the relevant period. This tutorial distinguishes the estimands; details for operationalizing adherence and protocol deviations belong in the protocol’s treatment-strategy specification.

A Short Justification for Making Every Element Explicit

The contrast follows directly from the definition of a population-average comparison. Once the two strategies and outcome are fixed, the mean under each strategy is a separate quantity. Subtracting them defines the difference:

Changing the population changes the conditional means; changing either strategy changes the potential outcomes; changing the outcome definition or horizon changes what \(Y^g(\tau)\) represents. Therefore the contrast is not fully specified if any of those elements is missing. This is a definitional point, not a claim that the contrast is identified by observed data. Identification requires additional conditions and information, which should not be confused with defining the question.

Protocol Checks, Comparisons, and Limitations

Before moving from a research question to an analysis, write the contrast in one sentence and check each component. A useful sentence form is: “Among [target population], compare [strategy 1] with [strategy 0] on [outcome] through [horizon], using [contrast scale].” This makes omissions visible and separates the causal question from the data or estimator later used to address it.

The most common alternative is not a competing causal method but a different target question. Assignment-based effects answer what follows from assigning or offering strategies; adherence-based effects answer what follows under treatment-use strategies. Neither is universally preferable. The appropriate choice depends on the decision the study is meant to inform. A risk difference may communicate an absolute change in event frequency, whereas a risk ratio communicates a relative comparison; reporting one does not make it interchangeable with the other.

Several warning signs indicate an under-specified or mismatched contrast:

• The population is only implied. “Patients with the condition” may not identify which stage, setting, or eligibility group is intended.
• The strategy is a label rather than an intervention. “Medication users versus nonusers” does not say whether the target is assignment, initiation, or a defined pattern of use.
• The horizon is missing. Risks “after treatment” cannot be interpreted without a time window.
• The outcome or scale shifts between groups. A contrast requires the same outcome definition under both strategies, and its scale should be named.
• The conclusion overstates the target. A contrast defined for an eligible population does not automatically describe all patients, and an assignment contrast does not automatically describe adherence.

A fully defined contrast is necessary for a coherent causal study, but it is not sufficient for a credible estimate. It does not guarantee that the interventions are well-defined in practice, that required data are available, or that the contrast is identifiable from the observed design. Those are separate questions. Likewise, the contrast alone does not prescribe a statistical estimator. Keeping the estimand distinct from the estimation procedure makes it possible to assess whether a proposed analysis actually targets the protocol question.