Encoding Irregular Visit Histories

Why Encoding Matters

In longitudinal follow-up, patients are not always measured at the same scheduled times. One patient may have visits on days 4, 15, and 39; another may have visits on days 10 and 41. A representation that stores only a sequence of outcome values loses the timing information that distinguishes these histories. Conversely, a list of visit times without the measurements and observed history available at those times is incomplete for many analyses.

The aim here is to construct a patient-level record that preserves four things: the follow-up window, each visit’s exact time, the outcome measured at that visit, and the time spans between visits. A separate history record can preserve observed covariates and prior measurements as they were known over time. This is a data-organization task, not a model for why visits occurred.

A Patient-Level Representation

A useful representation has a patient-level record plus linked visit-level and interval-level records. The patient-level record stores the patient identifier, the start and end of the follow-up window, the time unit, and the available information about whether that window is fully covered by the data. The visit-level record has one row per visit, with at least the patient identifier, visit index, visit time, and measured outcome. It can also include observed covariates measured at that visit.

The interval-level record makes the time between visits explicit. For \(m_i>0\), define the first segment as \([a_i,t_{i1}]\), the segment ending at visit \(j\) as \((t_{i,j-1},t_{ij}]\) for \(j=2,\ldots,m_i\), and the final segment as \((t_{im_i},b_i]\). For \(m_i=0\), the observed interval is \([a_i,b_i]\), with its coverage status recorded. This zero-visit case must be represented directly: there is no last visit time from which to define a final segment. The closed start endpoint is a bookkeeping convention; another endpoint convention is possible, but it must be used consistently.

These segments partition the recorded follow-up window under the stated convention. Each segment ending in a visit has no other recorded visit in its interior, and the final segment has no later recorded visit in the window. The segment ending at a visit includes that endpoint; it does not mean that a visit-free interval includes its endpoint. It is often helpful to store the segment start, segment end, elapsed duration, and whether the window is known to be covered through that end.

The durations are elapsed calendar time in the chosen units, such as days. When \(m_i=0\), the sole interval has duration \(b_i-a_i\). The time units and the meaning of the window endpoints should be stated in the data definition; otherwise a recorded gap such as “12” is ambiguous.

For observed history, a useful notation is \(H_i(t-)\): the recorded information for patient \(i\) available strictly before time \(t\). It may include baseline covariates, earlier measured outcomes, and time-stamped treatment history, provided those records genuinely precede \(t\). Store the original timestamped records, or an auditable summary linked to them, rather than attaching later information to an earlier visit. If two records share a timestamp and their order is unknown, retain that fact rather than imposing an invented sequence.

Worked Representations and Edge Cases

Why the Interval Construction Works

The interval representation is useful partly because it gives a simple consistency check. For \(m_i>0\), add the durations of the initial segment, all between-visit segments, and the final segment:

Every intermediate visit time appears once with a positive sign and once with a negative sign, so those terms cancel. Only \(b_i-a_i\) remains. If \(m_i=0\), the total interval duration is \(b_i-a_i\) by direct definition. This identity justifies checking that the interval records cover exactly the stated window, without an unexplained gap or overlap in elapsed time.

Choosing and Checking a Data Layout

A long visit table is usually a clear primary representation: one row per patient-visit pair, with exact times and outcomes. It accommodates unequal numbers of visits naturally and can be linked to a patient table and to time-stamped history records. A wide table, with columns such as “visit 1 outcome” and “visit 2 outcome,” can be convenient for a small fixed schedule, but irregular numbers and times of visits create many empty columns or risk hiding when measurements occurred. A compact patient-level vector of visit times and a matching vector of outcomes is also possible, provided their positions stay aligned and the interval information is recoverable.

Whichever layout is used, run basic diagnostics before analysis:

• Check that each patient has one defined window and that every recorded visit lies within it.
• Check that visit times are ordered and that visit indices agree with that order.
• Check that every outcome is linked to the intended patient and visit, rather than matched by row position after sorting.
• Recalculate all interval durations and verify that they sum to \(b_i-a_i\), including the \(m_i=0\) case.
• Check whether equal timestamps represent duplicate records, multiple measurements at one encounter, or records whose order is unresolved; do not silently sort ties into a false sequence.
• Record coverage limitations explicitly. A span with no recorded visit is not automatically evidence that data collection continued throughout that span.

A common mistake is to treat visit number as elapsed time—for example, to regard every “visit 2” as occurring at the same time for every patient. The correction is to retain actual timestamps and calculate gaps from them. Another mistake is to assume that an interval without recorded visits contains a known outcome trajectory. It contains no recorded visit in the represented span; the outcome between measurements is not supplied by this encoding.

This representation does not explain why observation schedules differ, and it does not resolve what unrecorded outcomes mean. It is a foundation for later analyses, not a substitute for specifying their assumptions. The introductory material on informative visit timing motivates why those differences can matter; the practical task here is to preserve enough detail that they are not erased by data processing.