Why a Common Time Zero Matters
A causal comparison needs a clear starting point. At that point, the people in the comparison must be eligible for the strategies being compared, the strategies must be assigned or initiated according to the protocol, and outcome follow-up must begin. When these events are placed at different times for different groups, the comparison may no longer answer one well-defined causal question.
The issue is not that every date in a study must be identical. It is that the protocol needs a coherent common reference point for eligibility, assignment, and follow-up. In an observational emulation, the corresponding dates must be defined in the data in a way that preserves this ordering.
Let \(t_0\) denote time zero, \(S(t_0)=1\) indicate that a person meets the prespecified eligibility criteria at that time, and \(A\) denote the assigned treatment strategy. Let \(Y^a\) be the outcome that would be observed under strategy \(a\), with follow-up beginning at \(t_0\). A basic target contrast is then defined among people eligible at the common time zero, for example \(E[Y^1-Y^0\mid S(t_0)=1]\). The particular outcome and follow-up horizon must also be specified in a protocol; the point here is that both strategies use the same starting point.
The Required Ordering
Eligibility must be determined using information available at or before \(t_0\), before the strategy is assigned. Assignment identifies which strategy applies from \(t_0\); follow-up for outcomes begins at that same point. A timeline makes it easier to detect a violation than a list of variables does.
The arrows indicate the logical order, not necessarily three separated clock times. A single clinical decision can embody all three events. The design must nevertheless say what counts as the eligibility assessment, the assignment, and the beginning of observation. Eligibility criteria should not depend on events that occur after assignment, such as surviving long enough to start a treatment, because that would select participants using future information.
For a causal interpretation, alignment is necessary but not sufficient. The strategies and outcome must be well defined, the observed outcome must correspond to the strategy actually received (consistency), and the assignment mechanism must support a valid comparison. In a randomized trial, assignment is randomized among those eligible at \(t_0\). In an observational emulation, identification typically also requires conditional exchangeability given measured pre-assignment covariates and positivity: within relevant covariate strata, each strategy has a positive probability of being followed. Alignment does not establish these conditions; it makes the intended comparison coherent.
Worked Example: Drawing the Same Starting Point for Both Strategies
Suppose a hypothetical clinic is planning a comparison of two medication strategies for adults whose blood pressure exceeds a prespecified threshold. The protocol defines eligibility using a blood-pressure measurement recorded at a visit, and compares starting medication A with starting medication B at that visit.
Step 1: Set the reference time. Define \(t_0\) as the date and time of the qualifying visit, before either medication is started. Eligibility is determined from the measurement at that visit and other criteria known by then.
Step 2: Define assignment. At \(t_0\), each eligible person is assigned to the strategy of starting A or starting B. In a hypothetical randomized version, randomization occurs at the visit. In an observational emulation, the records must support a clear classification of which strategy begins at that visit.
Step 3: Start follow-up. The outcome record begins at \(t_0\) in both groups. Thus the comparison concerns outcomes after the same defined starting point in people eligible at the same kind of decision point.
This protocol has the required temporal structure: eligibility information is not taken from after treatment starts, and the outcome period does not begin earlier for one strategy than the other. Whether the comparison identifies a causal effect still depends on the assignment mechanism and other assumptions; the timeline alone cannot guarantee that.
What Misalignment Changes
Two kinds of timing differences should be kept distinct. Suppose strategy 1 is defined using eligibility at time \(e_1\), while strategy 0 uses eligibility at time \(e_0\). Write the resulting eligible sets as \(S_1=1\) and \(S_0=1\). If \(S_1\ne S_0\), the contrast changes the population. Separately, let \(L_1\) and \(L_0\) denote the respective follow-up start times. If \(L_1\ne L_0\), the contrast changes the observation period. If both differ, it changes both. Neither difference alone implies that the other also differs.
This distinction matters because a difference between group averages may then combine the effect of treatment with a difference in who entered the comparison, a difference in when outcomes began to count, or both. Statistical adjustment for measured covariates does not automatically turn distinct eligibility populations into the same target population, nor does it make unequal outcome observation periods equivalent.
Worked Example: Eligibility Dates Define Different Populations
Consider a hypothetical emulation with 100 patients seen on day 0. All 100 meet a broad screening criterion on day 0. By day 7, 12 have developed a condition that makes them ineligible under the protocol. Suppose one strategy group is assembled using day-0 eligibility, while the other is assembled using eligibility on day 7.
The day-0 group has 100 eligible patients. The day-7 group has \(100-12=88\) eligible patients. The two groups therefore do not represent the same eligibility population: the later eligibility rule excludes the 12 people whose status changed during the week.
The relevant arithmetic is \(12/100=0.12\), so 12% of the day-0 screened population is removed by the later rule. That percentage describes the difference in eligibility under this hypothetical example; it is not an estimate of a treatment effect.
The design correction is to define eligibility for both strategies at the same decision point, before assignment. If day 7 is the clinically relevant decision point, assess both strategies at day 7 and define the target population as those eligible then. If day 0 is the decision point, use day-0 eligibility for both. Which time is appropriate depends on the clinical question, but mixing the dates makes the target population differ by strategy.
Worked Example: Different Follow-Up Starts Change the Observation Period
In a hypothetical study, both strategy groups are selected from the same 80 people who are eligible on day 0. For the first group, outcomes are counted starting on day 0. For the second, outcomes are counted starting on day 5. Suppose the protocol intends to compare outcomes over 30 days from the decision to use a strategy.
The first group's observation begins on day 0 and covers days 0 through 29. If the second group's 30-day clock begins on day 5, it covers days 5 through 34. The groups thus have different observation periods even though their eligibility population is the same. An outcome occurring on day 3 is counted for the first group but falls before follow-up for the second.
Here \(S_1=S_0\), but \(L_1\ne L_0\). Therefore, this mismatch changes the observation period, not necessarily the population. To align the design, define follow-up from the common day-0 assignment point in both groups. If day 5 is actually the intended decision point, both strategies instead need eligibility, assignment, and follow-up anchored there.
Why Waiting to Classify Treatment Can Create Bias
A particularly consequential misalignment occurs when people are classified according to treatment they receive later, but follow-up begins earlier. To enter the “treated” group, a person may have to remain alive and outcome-free until treatment initiation. The time before initiation is then guaranteed to be event-free for those classified as treated, even though the comparison may count it as treated follow-up. This is the core structure of immortal-time bias.
Worked Example: A Future Treatment Requirement Selects Survivors
Suppose 100 hypothetical people are eligible and untreated on day 0. Researchers classify as “treated” anyone who begins a medication by day 10, but count outcomes from day 0. During days 0–9, 15 people experience the outcome or die before they could start the medication. The remaining 85 begin it by day 10.
Under this rule, a person in the treated group must have remained eligible to start treatment through the start date. The 15 early events cannot appear among the 85 people ultimately classified as treated, even though the treated group’s outcome clock was said to start on day 0. The pre-initiation interval is therefore guaranteed event-free by the group definition, not by a protective effect of medication.
The arithmetic shows the selection: \(100-15=85\) people are available to be classified as treated by day 10. The count of 15 early events is not evidence that treatment prevented events; treatment had not yet begun for those individuals. A coherent design must assign strategies at a common time zero, or use a method explicitly designed for a treatment-initiation window. That latter design issue requires additional protocol rules and is not solved by simply labeling future initiators as treated at baseline.
A Practical Timeline Audit
Before analysis, write one timeline per strategy and verify that eligibility, assignment, and follow-up have the same reference time. The audit should be based on actual operational definitions: for example, the date of a qualifying examination, the timestamp of a prescription, and the first date an outcome could be recorded.
State the clinical moment at which a person could be assigned to either strategy. Label this common instant \(t_0\).
Confirm that every criterion is assessed by \(t_0\), and that the same criteria and reference time apply to both strategies.
Specify which strategy is assigned at \(t_0\), using no future treatment or outcome information to define baseline group membership.
Confirm that outcome observation begins at \(t_0\) for both strategies. If not, state whether eligibility populations, observation periods, or both have changed.
Diagnostics include counting how many people become eligible or ineligible between candidate index dates, tabulating the time from eligibility to assignment by strategy, and checking whether any outcomes occur in a period counted for one group but excluded for another. A substantial delay or a cluster of early events warrants investigation. These checks reveal design inconsistencies; they do not, by themselves, quantify or remove resulting bias.
Common Mistakes and Limits
- Using treatment initiation as time zero for one group and an earlier enrollment date for another. This can create unequal observation periods. Define one decision point and anchor both groups there.
- Defining eligibility with future information. A rule such as “eligible if the person survives until treatment” selects on post-baseline events. Apply the protocol’s eligibility rules at the common time zero.
- Assuming any mismatch changes everything. If \(S_1\ne S_0\), the contrast changes the population; if \(L_1\ne L_0\), it changes the observation period. If both differ, it changes both. One mismatch does not establish the other.
- Thinking adjustment repairs an incoherent timeline. Covariate adjustment can address confounding under appropriate assumptions, but it cannot make two different eligibility definitions or follow-up clocks identical by itself.
- Treating a good timeline as proof of causality. Alignment is a design requirement, not a substitute for a defensible assignment mechanism, adequate confounder measurement where needed, or a clearly defined outcome.
The main alternatives are to redesign the comparison around a common decision point, or to use an analysis method specifically built for the timing structure at issue. The first is usually clearest when the clinical question permits it. Specialized methods may be needed when treatment can begin over a window or eligibility recurs, but they require additional protocol decisions. Neither option should be replaced by silently comparing groups with different starting dates.
Check Your Understanding
Answer each question, then compare with the solutions below.
- A study applies the same eligibility criteria to both groups, but starts outcome counting on day 0 for one group and day 4 for the other. What is misaligned?
- One group is eligible if a laboratory value is below a threshold on day 0; the other must meet that threshold on day 7. What can be concluded about the target population?
- Why can classifying people as treated based on medication initiation by day 10 create immortal-time bias if outcomes are counted from day 0?
- Name two conditions, beyond time-zero alignment, that are needed for a causal interpretation in an observational emulation.
Solutions. (1) The follow-up start differs, so the observation periods differ; this fact alone does not imply that the eligibility populations differ. (2) The eligibility dates define potentially different eligible sets, so the target population may differ; determine the size and composition of that difference from the data. (3) Treated-group members must remain able to initiate treatment through their initiation date, so the pre-initiation period is guaranteed event-free by classification even if counted as treated follow-up. (4) Examples are consistency, conditional exchangeability given measured pre-assignment covariates, and positivity. Alignment alone does not establish any of these conditions.