Aligning Covariate Values With Event and Censoring Times

Why Time Alignment Matters

In survival data, a covariate value is useful for an event-time analysis only if it represents information available during the risk period being modelled. A measurement taken at one visit does not automatically describe every later interval. Likewise, a value recorded at the same time as an event may have been measured after the event. The data records must preserve these distinctions before missing covariate values are imputed.

This tutorial focuses on aligning observed covariate measurement times with each person's event or censoring time. It uses the start-stop representation introduced in the earlier material on start-stop data and interval splitting. The central rule is simple: an interval may use a covariate value only for the times during which that value is known, or justifiably assumed, to apply. An event or censoring time ends the observed risk history; it is not a reason to extend a value beyond that endpoint.

State the Timing Assumptions First

A reliable alignment depends on knowing what the timestamps mean. Before constructing records, establish a common time origin, the units of time, the event and censoring times, and the times at which covariates were measured. Also establish what a measurement represents: a value at an instant, a value intended to remain valid until the next measurement, or a value known to apply over a stated validity period. These are different data-generating and recording conventions.

In particular, periodic measurement does not by itself prove that a covariate stayed constant between visits. Treating the value at one visit as applying until the next is a piecewise-constant representation and requires substantive justification, such as a treatment record showing no change in that period or a protocol that defines the covariate that way. If no such justification exists, the unmeasured portion is not made observed merely by carrying the last value forward. The earlier material on avoiding future-information leakage motivates using only information available at the relevant time; here, the additional task is to map that information onto the correct intervals.

Use one tie convention consistently. A useful convention is that a measurement at time \(t\) becomes available for intervals after \(t\). An event at time \(t\) is evaluated using covariate history available just before the event, often denoted \(X_i(t-)\). Thus, a measurement timestamped exactly at the event time is not used to predict that event unless the measurement process establishes that it was obtained before the event. If the actual ordering is known, record that ordering; if not, the conservative choice is not to use the tied measurement for the event.

With start-stop intervals written as \((a,b]\), the value assigned to a row is the value valid over that risk interval. A measurement at \(a\) can supply information for times after \(a\); it does not automatically describe time before \(a\). The interval must also end no later than \(T_i\). If a covariate's documented validity ends before the interval does, split the interval at that validity boundary or mark the later part as unknown.

A Construction Rule

Worked Examples

Why the Endpoint and Covariate History Must Agree

The risk-set logic explains the alignment rule. A person contributes to an event-time analysis only while under observation and at risk. For an ordinary right-censored record with time origin 0, the at-risk indicator is \(Y_i(t)=1\) for \(0<t\leq T_i\), and is 0 after \(T_i\). A time-varying predictor for an event at time \(t\) must represent information available immediately before \(t\), not information recorded later.

This gives a direct check on a constructed record. If a row ends at \(b\), it can describe risk only through \(b\), and the assigned covariate must be supported for the interval up to \(b\). If \(b=T_i\) and \(\Delta_i=1\), the event is at that endpoint; a measurement available only at or after \(b\) cannot be assumed to describe the pre-event history. If \(b=T_i\) and \(\Delta_i=0\), the record ends at censoring, with no observed event at that time.

This justification does not assert that a covariate is truly constant between measurements. It shows why the analysis record must not claim more temporal information than the measurement process supports. A piecewise-constant covariate history is a modelling representation; its intervals and values must be justified by how the variable was recorded or by an explicit assumption.

Checks, Alternatives, and Limitations

After aligning the records, check them as a timeline rather than treating the rows as an ordinary independent data table. Useful checks include:

• Every interval has positive length: stop time is greater than start time.
• Intervals follow chronological order, do not overlap, and cover only the intended observed follow-up.
• The last stop time for each person equals \(T_i\), not a later measurement time.
• There is one terminal event indicator for an observed event, on the row ending at the event time; censored histories have no event indicator of 1.
• Values change at the recorded measurement or validity boundary, not at an unrelated row boundary.
• Measurements tied with an event have an explicit ordering rule; unexplained ties are not automatically treated as pre-event values.
• Unknown intervals remain visible as unknown. A complete-looking covariate column is not evidence that all values were observed or valid.

The alternatives differ in what they assume. Baseline-only analysis uses a baseline value throughout follow-up and does not represent later covariate changes. Carrying the last value forward can provide a piecewise-constant history, but only when continued validity is defensible; otherwise it fills gaps with unsupported information. Time-updated intervals represent observed changes more directly, while leaving periods without supported values as missing. These choices are not interchangeable data-cleaning details: they define different covariate histories for the analysis.

In MICE, alignment is a preparation and data-definition issue as well as an imputation issue. An imputation procedure can draw plausible values for missing covariates under its assumptions; it cannot determine whether a timestamp was recorded before an event, establish an undocumented validity period, or justify extending follow-up. When one person contributes multiple interval rows, those rows also remain parts of that person's history, not separate people. The imputation setup must preserve the repeated-measure structure rather than treating duplicated person records as independent observations.

Common Mistakes

• Wrong: “The last value is the best available value, so it should fill every later row.” Correction: Use it later only if the variable's definition or measurement protocol supports that period; otherwise retain an unknown interval.
• Wrong: “The measurement and event share a timestamp, so the measurement predicts the event.” Correction: Establish the order. Without evidence that measurement preceded the event, do not use it for the event-time covariate history.
• Wrong: “A measurement after censoring can fill the end of follow-up.” Correction: A later measurement does not extend the observed risk period or show what the covariate was before censoring.
• Wrong: “Splitting at a visit makes the value valid up to the next visit.” Correction: Splitting creates rows, not evidence of persistence. The validity assumption must come from the variable's meaning or a defensible model.