Repeated-Measures & Longitudinal Analysis

Methods for data where measurements are not independent — because the same patient is measured repeatedly over time, or because patients are clustered (within wards, hospitals, clinicians). Two readings from one patient are more alike than two readings from different patients; that within-subject correlation violates the core assumption of ordinary t-tests, χ² and standard regression. Mixed-effects (multilevel) models and generalised estimating equations (GEE) explicitly model this correlation, and use partial / unbalanced data efficiently rather than discarding it.

One patient at the top produces several serial readings, then two ways to analyse them. The wrong path pours every reading into a test that assumes independence, manufacturing a large sample out of a small one. The correct path keeps track of which readings belong to which patient and models the correlation, so the precision it reports reflects the number of patients, not the number of measurements.

Ask: where did each data point come from? If many points share a source — same patient over time, same cluster — they carry less independent information than their count suggests. A mixed model splits the variation into a between-patient part (random effects / random intercepts) and a within-patient part, and widens the confidence interval accordingly. GEE targets the population-average effect with a robust handling of the correlation. Either way, the reported precision should fall once correlation is respected.

EM data is saturated with repetition: serial observations, repeated bloods, readings clustered within departments. Analysing them as if independent — pseudoreplication — inflates the effective sample size, narrows confidence intervals and produces falsely small p-values, so noise gets reported as a real effect. Spotting clustered or longitudinal data and demanding the right model is a recurring critical-appraisal mark.

• Repeated / clustered readings are correlated, not independent
• Mixed-effects model = fixed effects + random effects for patient/cluster
• GEE = population-average effect, correlation handled robustly
• Ignoring correlation = pseudoreplication → CIs too narrow

Serial lactates and repeated pain scores — a common EM example: a sepsis study tracks lactate clearance with measurements at 0, 2, 4 and 6 hours per patient, or an analgesia trial records a pain score every 30 minutes. With, say, 20 patients and five readings each, a naïve analysis sees “100 data points” — but they are 20 correlated trajectories, not 100 independent observations. A mixed-effects model with a random intercept per patient (and often a random slope for time) gives the honest answer; a t-test on the pooled readings does not. Beware dropout too: patients who improve or deteriorate may stop being measured, so missing readings are rarely missing at random — handle the dropout, don’t just delete it.

• Ignoring within-subject correlation — pseudoreplication inflates effective n and shrinks CIs.
• Mishandling dropout — informative missingness over time biases the trajectory if treated as missing-at-random.
• Treating clustered data as independent — readings within a ward/hospital are correlated and need a multilevel model.