The occurrence of Simpson's paradox if site-level effect was ignored in the TREAT Asia HIV Observational Database

Abstract

Objectives: In multisite human immunodeficiency virus (HIV) observational cohorts, clustering of observations often occurs within sites. Ignoring clustering may lead to "Simpson's paradox" (SP) where the trend observed in the aggregated data is reversed when the groups are separated. This study aimed to investigate the SP in an Asian HIV cohort and the effects of site-level adjustment through various Cox regression models.

Study design and setting: Survival time from combination antiretroviral therapy (cART) initiation was analyzed using four Cox models: (1) no site adjustment; (2) site as a fixed effect; (3) stratification through site; and (4) shared frailty on site.

Results: A total of 6,454 patients were included from 23 sites in Asia. SP was evident in the year of cART initiation variable. Model (1) shows the hazard ratio (HR) for years 2010-2014 was higher than the HR for 2006-2009, compared to 2003-2005 (HR = 0.68 vs. 0.61). Models (2)-(4) consistently implied greater improvement in survival for those who initiated in 2010-2014 than 2006-2009 contrasting findings from model (1). The effects of other significant covariates on survival were similar across four models.

Conclusions: Ignoring site can lead to SP causing reversal of treatment effects. Greater emphasis should be made to include site in survival models when possible.

Keywords: Clustering; Cohort; Cox; Human immunodeficiency virus; Simpson's paradox; Yule-Simpson.