Why Timing Is Part of the Research Question
A regression question is not fully specified by naming a predictor and an outcome. It also matters when each is measured. A question about whether baseline activity is associated with blood pressure six months later targets something different from a question about activity and blood pressure measured on the same day. Likewise, predicting an outcome one week ahead is not the same task as predicting it one year ahead.
A clear time plan identifies the study's time anchor, the period used to measure each predictor, the outcome measurement or observation window, and the follow-up period. These choices help make the intended target interpretable and show whether the recorded data are aligned with the question.
For example, let \(t_0\) be an index time. A predictor could summarize activity in the month ending at \(t_0\), while an outcome could be a measurement taken six months after \(t_0\). The calendar windows may be defined as intervals before and after the index time, but the important point is to specify them in words and apply the definitions consistently.
Specify the Time Windows Before Collecting Data
A useful plan answers four questions: What is the index time for each observational unit? When, or over what period, is each predictor measured? When or over what period is the outcome measured? How long is follow-up? State time units and the rule for assigning observations to a window. “Later blood pressure” is vague; “blood pressure measured at the six-month visit, scheduled within a stated visit window” is more precise.
The target can be represented simply as a conditional mean for a defined population and time plan. If \(X\) is a predictor defined using its stated window and \(Y_h\) is an outcome measured at a specified horizon \(h\), then a descriptive target might be \(E(Y_h\mid X=x)\): the mean outcome at that horizon among units with predictor value \(x\). Changing \(h\), or changing how \(X\) is summarized, changes the target. This notation describes what quantity is of interest; it does not by itself establish that a regression model is appropriate or that an association is causal.
The timing should follow the kind of question. A descriptive question may ask how two measurements vary together at a particular visit. An explanatory association question may use a predictor measured before a later outcome, while still recognizing that observational timing alone does not establish causation. A prediction question must define what information is available at the time a prediction is made and the horizon over which the future outcome is predicted.
Worked Example: Baseline Activity and Six-Month Blood Pressure
Suppose a hypothetical clinic wants to describe the association between adults' recent activity and their later systolic blood pressure. For each adult, staff record average daily walking minutes during the 30 days before enrollment and measure systolic blood pressure at the six-month visit. The planned follow-up is six months after enrollment.
Index time: the enrollment date, \(t_0\). Predictor: average daily walking minutes over the 30-day period ending at \(t_0\). Outcome: systolic blood pressure, in mmHg, measured at the six-month visit. Follow-up: from enrollment to that visit.
For a hypothetical participant who walked 20, 30, and 40 minutes per day over three example days, the mean for those days is \( (20+30+40)/3=30 \) minutes per day. If that participant's six-month systolic blood pressure is 124 mmHg, the paired record is \(X=30\) minutes per day and \(Y_6=124\) mmHg. In an actual study, the predictor average must use the pre-specified full 30-day window, not just three selected days unless those are the available measurements by design.
The timing fits a question about baseline activity and six-month blood pressure because the predictor window ends by enrollment and the outcome is measured afterward. It does not show that walking caused any blood-pressure difference. If the question instead concerned blood pressure on the enrollment date, this six-month outcome would not answer it.
Changing the Outcome Window Changes the Target
An outcome may be measured at a single visit or summarized over a period. A single measurement at six months asks about status at that horizon. A count of events during the first six months asks about events accumulated over that interval. Those are distinct outcomes, even when both are called “the six-month outcome.” Longer follow-up can capture more events or changes that a shorter period misses, so a result for one horizon should not automatically be described as a result for another.
Follow-up needs a clear start and end. If some participants are observed for shorter periods, a raw event count may not represent the same observation opportunity for everyone. The design should specify what outcome is recorded and how the observation period is defined; the chosen outcome window must match the research question.
Worked Example: Two Horizons for a Recovery Question
Imagine a hypothetical study asking whether a home exercise plan is associated with recovery after a minor injury. Recovery is recorded as a functional score from 0 to 100, with higher scores indicating better function. The study measures scores at four weeks and at twelve weeks after enrollment.
For illustration, suppose three participants have four-week scores of 60, 70, and 80. Their mean score is \( (60+70+80)/3=70 \). Suppose their twelve-week scores are 75, 85, and 95; the mean at twelve weeks is \( (75+85+95)/3=85 \).
The value 70 describes the mean score at the four-week horizon in this hypothetical group; 85 describes the mean at twelve weeks. They are not competing estimates of one identical target. A question about early recovery calls for the four-week outcome, while a question about later recovery calls for the twelve-week outcome. If exercise-plan participation is measured at enrollment, it can be related to either horizon, but the two analyses answer different time-specific questions.
These arithmetic summaries do not establish what caused the scores to change. Nor do they imply that the average increase of 15 points would occur in another population. The example's purpose is to show that defining the horizon is part of defining the outcome.
Prediction Requires an Information Cutoff
For a prediction question, specify the moment when the prediction would be made. Predictors must be available by that cutoff if the intended use is to forecast a future outcome. A predictor recorded after the outcome, or one that incorporates information from the outcome period, cannot be treated as information available at the earlier prediction time. This timing mismatch makes the apparent prediction unrealistic.
A prediction plan should name both the predictor information available at the cutoff and the horizon for the future outcome. For instance, “use measurements available at discharge to predict an unplanned return to the clinic within 30 days” states a cutoff and a future observation window. “Predict return visits” leaves both unclear.
Worked Example: Predicting a Return Visit
A hypothetical clinic wants to predict whether a patient will return for an unplanned visit within 30 days after discharge. It proposes to use age and the number of clinic visits in the 90 days before discharge.
Index time and prediction cutoff: the discharge date. Predictors: age known at discharge and prior visits counted in the 90 days ending on or before discharge. Outcome: whether an unplanned return occurs in the 30 days after discharge. Follow-up: those 30 days.
For one hypothetical patient aged 42 with two prior visits, the predictor record is age 42 years and prior-visit count 2. If that patient makes one unplanned return during the next 30 days, the outcome is “Yes”; if none occurs, it is “No.” The rule is explicit about which visits count: a visit on day 20 after discharge belongs to the outcome period, not the predictor count.
If the clinic instead counts visits during the 30 days after discharge as a predictor, that information is not available at discharge and overlaps the outcome window. It therefore does not match the stated real-time prediction task. Moving the prediction cutoff to day 30 would define a different task, because the prediction would then be made later and could not forecast events that had already occurred in that period.
A Practical Timing Plan
Before data collection, write the proposed time plan in a compact form. The sequence below is useful for descriptive, explanatory-association, and prediction questions, though the interpretation differs by question type.
State what outcome is of interest, for whom, and whether the question is descriptive, explanatory, or predictive.
Define the same kind of reference event or date for each observational unit, such as enrollment or discharge.
For every predictor, state whether it is a point measurement or a summary over a specified period, and when that period ends.
State what is measured, its units or categories, and the exact horizon or observation period.
Confirm that the resulting measurements answer the stated question and, for prediction, that the predictors are available by the prediction cutoff.
Common Timing Pitfalls
- Using a vague horizon. “Later outcome” does not identify whether follow-up is a week, a year, or a visit chosen differently for each person. Specify a common horizon or a clear rule for determining it.
- Mixing time windows without saying so. A predictor based on the previous month and another based on the previous year summarize different periods. Name each window so the quantities can be interpreted.
- Using future information for an earlier prediction. A variable collected after the prediction cutoff cannot be presented as information available at that cutoff.
- Treating temporal order as proof of causation. Measuring a predictor before an outcome helps clarify sequence, but the order alone does not rule out other explanations for an association.
- Changing the horizon but keeping the same verbal conclusion. An association with an outcome at four weeks is a result for four weeks, not automatically for twelve months or for recovery in general.
A well-specified time plan makes the target concrete: it identifies what is known at the relevant time and what is measured afterward. This precision is essential for deciding whether a data set can answer the research question at all.
Check Your Understanding
For each question, identify the timing detail that must be specified.
- A study relates sleep to exam performance. Give one suitable index time, a predictor window, and an outcome time that would support a question about performance on a future exam.
- Why do blood-pressure measurements at four weeks and twelve weeks define different time-specific outcomes?
- A model predicts a 30-day return visit using the number of visits in the 90 days before discharge. Identify the prediction cutoff and explain why visits after discharge should not be included in that predictor for this task.
- Does measuring a predictor before an outcome, by itself, establish that the predictor caused the outcome? Explain briefly.
- A researcher records the number of events each person experiences but allows follow-up to vary without stating its duration. Why is the outcome definition incomplete?