A Robust Computational Workflow Utilizing Generalized Least Squares (GLS) and Generalized Estimating Equations...

Routinely used statistical hypothesis tests are often inadequate for longitudinal flow cytometry data, necessitating more sophisticated modeling approaches. Analyzing dynamic biomarker expression across hematopoietic maturation presents several analytical challenges, notably nonlinearity, serial correlation between subsequent stages, and varying total cell counts. This study addresses these issues by comparing traditional stage-by-stage hypothesis tests with two marginal modeling approaches: Generalized least squares (GLS) and a generalized linear model fitted with generalized estimating equations (GEE-GLM). We analyzed cell fractions expressing the dynamic biomarkers Bcl-2 (anti-apoptotic marker) and Ki-67 (proliferation marker), as well as the Bcl-2:Ki-67 ratio, across 20 stages of erythropoietic maturation in bone marrow aspirates from 25 patients with myelodysplastic syndromes (MDS), 25 patients with acute myeloid leukemia (AML), and 50 nonmalignant controls. The GLS modeling approach accounts for nonlinearity and correlation between subsequent maturation stages, while GEE-GLM additionally accounts for varying total cell counts by assigning greater weight to observations with larger cell counts. Instead of repeated stage-by-stage testing, GLS and GEE-GLM model the average maturation profile across different sub-populations, enabling visualization and robust population-level statistical inference. We demonstrate that variations in the total number of cells influence the estimated population mean profiles and their confidence intervals. This effect is particularly pronounced during early maturation stages, where low Ki-67+ cell counts can lead to substantially different estimates and conclusions when using the GEE-GLM approach. Conversely, the GLS approach offers the flexibility to model the unbounded Bcl-2:Ki-67 ratio, revealing differences between AML and nonmalignant patients across all 20 stages. The computational workflow and scripts are provided to facilitate reproducibility and application to similar time-dependent flow cytometry datasets.