A Time-varying Covariate Approach for Survival Analysis of Paediatric Outcomes

Conventional survival analysis is commonly applied in the analysis of time-to-event data in paediatric studies, where the exposure variables of interest are often treated as time-fixed. However, the values of these exposure variables can vary over time and time-fixed analysis may introduce time-dependent bias.

Time-dependent bias is illustrated graphically considering two scenarios in longitudinal study settings for paediatric time-to-event outcomes. As an illustrative example, the time-varying covariate approach was applied to survival analysis of breast-feeding data (n = 695) collected in China between 2010 and 2011, with an emphasis on the effects of covariates 'solid foods introduction' and 'maternal return to work' on breast-feeding duration up to 12 months postpartum.

Time-varying exposures could occur before or after the occurrence of an event of interest so that time-fixed analysis can lead to biased and imprecise parameter estimates. In the illustrative example, the reduced risk of 'solid foods introduction' (hazard ratio (HR) 0.61, 95% confidence interval (CI) 0.50, 0.75) on breast-feeding cessation and an absence of an association with 'maternal return to work' (HR 0.99, 95% CI 0.73, 1.36) from the time-fixed analysis reversed (HR 1.50, 95% CI 1.17, 1.93) and became significant (HR 1.45, 95% CI 1.06, 2.00), respectively, based on the time-varying covariate model.

The time-varying covariate approach is preferable for survival analysis of time-to-event data in the presence of time-varying exposures.