Statistical modelling of time to relapse or onset of metastatic disease following treatment for cancer: relationship to residual/resistant disease and re-growth

Response to treatment for some cancers may result in a proportion of the patients being permanently cured of the disease, while the rest remain at risk of a relapse or progression. Standard survival analysis approaches assume that all patients will eventually experience the event of interest and so are not appropriate in these situations. The residual disease and tumour re-growth rate following treatment are two of the important predictors of outcomes among cancer patients following treatment. However, in most cases, data on these measures is not always available. Using data from multiple myeloma and chronic lymphocytic leukaemia trials conducted at the Leeds Institute of Clinical Trials Research, we investigated the role of the residual disease and other important factors associated with time to relapse and overall survival, as well as the probability of being cured of the malignancy following treatment. As the multiple myeloma trial also collected data on bio-markers for tumour growth rate, we used the structural equation modelling approach to investigate the role of growth rate on the survival outcomes using available statistical software. We then extended these models to also investigate the association of growth and the probability of being cured after treatment in a Bayesian framework including in situations where not all patients will relapse or die after treatment. This work demonstrates that it is feasible to use structural equation modelling within survival analysis to investigate the role of latent variables on time to event outcomes even in situations where not all patients will relapse or die after treatment.