# Omitting patients with no follow-up leads to bias when using inverse-intensity weighted GEEs to handle irregular and informative assessment times

## TL;DR

Excluding patients with no follow-up data in longitudinal studies can bias results when using inverse-intensity weighted GEEs.

## Contribution

The paper shows mathematically and through simulations that omitting patients with no follow-up leads to biased estimates in inverse-intensity weighted GEEs.

## Key findings

- Bias increases with lower visit frequency and shorter follow-up duration in simulations.
- Omitting patients with no follow-up visits over-estimates improvement in depressive symptoms in the STAR*D trial.
- Study design recommendations include ensuring inclusion of patients with no follow-up data.

## Abstract

Longitudinal data can be used to study disease progression and are often collected at irregular intervals. When the assessment times are informative about the severity of the disease, regression analyses of the outcome trajectory over time based on Generalized Estimating Equations (GEEs) result in biased estimates of regression coefficients. Inverse-intensity weighted GEEs (IIW-GEEs) are a popular approach to account for informative assessment times and yield unbiased estimates of outcome model coefficients when the assessment times and outcomes are conditionally independent given previously observed data. However, a consequence of irregular assessment times is that some patients may have no follow-up assessments at all, and it is common practice to omit these patients from analyses when studying the outcome trajectory over time.

We show mathematically that IIW-GEEs yield biased estimates of regression coefficients when patients with no follow-up assessments are excluded from analyses. We design a simulation study to evaluate how the bias varies with sample size, assessment frequency, follow-up time, and the informativeness of the assessment time process. Using the STAR*D trial of treatments for major depressive disorder, we examine the extent of bias in practice.

Our simulation results showed the bias incurred by omitting patients with no follow-up visits increased as visit frequency decreased and as the duration of follow-up decreased. In the STAR*D trial, omitting patients with no follow-up visits led to over-estimation of the rate of improvement in depressive symptoms.

Studies should be designed to ensure patients with no follow-up are included in the data. This can be achieved by a) creating inception cohorts; b) when taking sub-samples of existing cohorts, ensuring that patients without follow-up assessments are included; c) dropping exclusion criteria based on availability of follow-up visits.

The online version contains supplementary material available at 10.1186/s12874-025-02721-z.