Modelling multiple time-scales with flexible parametric survival models : with applications to myeloproliferative neoplasms

Survival models are often based on only one time-scale for the analysis. However, when analysing time-to-event data, it may be important to model multiple time-scales. The objectives of this thesis are to assess bias from modelling only one time-scale, and to describe and apply a novel method for modelling multiple time-scales in time-to-event data within the framework of flexible parametric survival models (FPM).

Study I investigates the bias in estimates when only one time-scale is used. Using simulated data with two time-scales and a binary covariate, we fitted FPM on the log-hazard scale with one time-scale. Our findings indicate slight bias in survival proportions for most scenarios and large bias in log hazard ratios when non-proportional hazards existed on the second time-scale. This highlights the importance of considering multiple time-scales and exploring non-proportional hazards in the model.

Study II presents a novel FPM approach that incorporates multiple time-scales without time-splitting the data. This method's flexibility arises from using a linear relationship between time-scales, simplifying the modelling process. We demonstrated this with two case studies, comparing it to the Poisson rate model and showcasing various graphical representations of survival and hazard rates.

Study III applies FPM on the log-hazard scale to estimate thrombosis rates in patients with myeloproliferative neoplasms (MPN) over both attained age and time since diagnosis. Results show the highest thrombosis rates within the first two years post-diagnosis, with subsequent rates more influenced by attained age. Hazard ratios for thrombosis remained consistently above one when comparing MPN patients with matched population controls Study IV estimates hazard rates and cumulative incidence functions (CIF) for transformation to acute myeloid leukaemia or myeloidisplastic syndromes in MPN patients over both attained age and time since diagnosis. Transformation rates and CIF showed a stronger dependence on time since diagnosis, though this dependence varied greatly across attained ages by subtype and outcome.

In conclusion, this thesis demonstrates the effectiveness of FPM in modelling multiple time-scales, providing a robust tool for complex time-to-event data analysis, particularly in the context of myeloproliferative neoplasms.

List of scientific papers

I. Batyrbekova N, Bower H, Dickman PW, Szulkin R, Lambert PC, Andersson TML. Potential bias introduced by not including multiple time-scales in survival analysis: a simulation study. Communications in Statistics - Simulation and Computation. 2022;0(0):1-14. https://doi.org/10.1080/03610918.2022.2038626

II. Batyrbekova N, Bower H, Dickman PW, Ravn-Landtblom A, Hultcrantz M, Szulkin R, Lambert PC, Andersson TML. Modelling multiple time-scales with flexible parametric survival models. BMC Medical Research Methodology. 2022;22(1):290. https://doi.org/10.1186/s12874-022-01773-9

III. Batyrbekova N, Hultcrantz M, Ravn-Landtblom A, Szulkin R, Dickman P, Andersson TML, Syriopoulou E. Do thrombosis rates for MPN patients increase with both age and time since diagnosis? A nationwide register-based matched-cohort study. [Submitted]

IV. Batyrbekova N, Ravn-Landtblom A, Hultcrantz M, Szulkin R, Dickman P, Andersson TML. Risk of transformation to acute myeloid leukemia and myelodysplastic syndromes in patients with myeloproliferative neoplasms over attained age and time since diagnosis: a nationwide cohort study. [Manuscript]