Specify a Target Population and Time Zero

Why the Study Clock Matters

An observational question can sound clear while leaving crucial details unsettled. “Does starting a medication reduce hospitalization?” does not say which patients are being studied, when they qualify, what counts as starting, or how long hospitalization is monitored. Different answers define different studies—and can define different causal questions.

The key is to set a common time zero: the point when eligibility is assessed, the exposure strategy is assigned or recorded, and outcome follow-up begins. Eligibility, exposure, and follow-up must be aligned to that point. Otherwise, the compared groups may not represent the same population at the same stage of their health history.

Specify the Population Before Comparing Exposures

Eligibility criteria should describe who could enter the study at time zero, using information available by that time. They might specify age, diagnosis, clinical setting, and whether a person has previously used a treatment. The criteria should also make clear the relevant calendar period and, when needed, the source population from which eligible people are drawn.

This is not merely administrative detail. If one study includes all adults with a condition and another includes only people newly diagnosed and not previously treated, the two studies concern different target populations. Even if they compare the same exposure strategies, their average causal effects need not be identical: the people and their risks may differ.

Eligibility should not depend on future information that would only become known after time zero. For example, requiring that a person remain alive for 30 days after enrollment selects people based on what happens during follow-up. Such a rule changes the population in a way that can distort the intended comparison. State eligibility using facts that are established at the common start.

Set Exposure Status and Follow-Up at the Same Point

In an observational study, exposure is not randomly assigned. Nevertheless, the question needs a clearly specified exposure contrast: which strategies or exposure states are being compared, and when is each person classified? For a treatment question, a contrast might be “initiate treatment at today’s eligible visit” versus “do not initiate at that visit.” The exposure rule should be precise enough that two people applying it to the same record would classify the person the same way.

Follow-up begins at time zero, not at a later date chosen separately for each exposure group. The outcome definition should state what event counts, how it is identified, and the time period over which it is counted. For example, “hospitalization” might mean any unplanned admission, and the window might be the 90 days after the eligible visit. A count at 30 days and a count at one year answer different questions.

The causal estimand also needs a population. Let \(Y^1\) and \(Y^0\) denote the potential outcomes under two specified exposure strategies for a person in the target population. For a binary outcome by a fixed horizon, a population-average risk difference can be written as:

This expression is meaningful only after the eligible population, the strategies, the outcome, and the horizon have been specified. It describes a contrast in potential outcomes for that population; it is not automatically equal to the observed difference between exposed and unexposed people. A causal interpretation from observational data also requires assumptions about how exposure and outcomes relate to measured and unmeasured factors. Defining time zero is necessary for a coherent question, but it does not by itself establish those assumptions.

Why Misaligned Timing Can Mislead

A common timing error is to start follow-up at an initial visit but define the exposed group by whether a person receives treatment later. People classified as exposed must remain alive and observable long enough to receive it. If events during that waiting period are counted for the unexposed group but cannot occur for the future-treated group before treatment, the groups have been given unequal opportunities for the outcome. This is one form of immortal time bias.

The problem is not solved by calling the future-treated people “exposed.” Their exposure classification uses information from after follow-up began. One remedy, when it matches the question, is to define the comparison at a common decision point and classify the strategies using information available then. Other designs may require more careful methods; the central lesson here is to specify the question and timeline before choosing an analysis.

How Choices Change the Causal Contrast

Changing eligibility or timing changes what effect is being asked about, not just which rows appear in a data set. Consider two plausible questions about the same medication: its effect among newly diagnosed, treatment-naive adults at their first eligible visit, and its effect among all adults with the condition, including people who have used the medication before. The second population includes different treatment histories and may have different baseline risks. The two population-average contrasts are not interchangeable.

Likewise, an outcome horizon is part of the estimand. A treatment could affect short-term risk differently from longer-term risk. “Risk by 30 days” and “risk by 365 days” refer to different potential outcomes and different contrasts, even when eligibility and exposure strategies are otherwise the same. State the horizon explicitly rather than relying on a vague phrase such as “during follow-up.”

A Practical Specification

Before analyzing observational data, write the study question in a form that makes the timeline inspectable. A compact specification should answer each of the following:

• Target population: Who is eligible, where and when could they enter, and which eligibility facts are known at time zero?
• Exposure strategies: What exactly distinguishes the groups, and at what point is exposure assigned or recorded?
• Time zero: What single event or date starts eligibility assessment and outcome follow-up?
• Outcome: What event or measurement counts, and how will it be determined?
• Horizon: How long after time zero is the outcome assessed?
• Contrast: Which population-level quantity is of interest, such as a risk difference by the stated horizon?

Then check that the timeline is coherent: eligibility is established by time zero, exposure classification does not quietly depend on later events, and outcomes are counted over the same stated period. This check will not settle every causal question, but it prevents an avoidable mismatch between the question and the data.

Common Mistakes

• Using future survival as an eligibility rule. Requiring people to remain alive or event-free after entry can select the study population using post-entry information. Define eligibility from facts available at time zero.
• Classifying exposure by later treatment receipt. If follow-up starts before exposure classification, the groups may have unequal time at risk. State the exposure strategy at a common time zero.
• Leaving the outcome window vague. “Later readmission” does not define an estimand. Specify the event and the horizon, such as unplanned readmission within 90 days.
• Assuming alignment proves causality. A clear target population and timeline make a causal question interpretable; they do not guarantee that exposed and unexposed people are comparable.
• Reporting an effect without naming the population. A population-average effect always refers to a specified group. Avoid generalizing beyond the eligibility criteria without justification.