Joint modeling of Longitudinal and Time-To-Event data
Typ
Examensarbete för masterexamen
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2022
Författare
Axillus, Sophia
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Joint modeling is a technique used for parameter estimation in linked models of
longitudinal and Time-To-Event (TTE) data. The goal of this is to reduce bias typically
found when sequentially estimating related parameters by considering errors
caused by both the models, the data, as well as between individuals (inter-individualvariability)
simultaneously. The aim of this thesis was to distinguish scenarios when
the joint model is suitable for use in the case of high frequent sampling.
To represent the longitudinal data, we apply a K-PD model to describe the effect
of an inhibition of a measurable biomarker (response) with added random effects.
This response is then linked to the TTE by using a parametric hazard equation for a
given set of parameters. The set of parameters for these models are estimated with
Maximum Likelihood Estimation for two approaches; a sequential and joint method.
The sequential approach firstly estimates the parameters related to the K-PD model
and then considers the individual simulated response as a covariate in the estimation
of the TTE related parameters. In contrast, the joint model considers two contributions
to the likelihood by including the TTE in order to get the full set of parameters.
The result of this is two algorithms based on the FOCE method. These algorithms
are compared for several datasets with fixed parameter values during different conditions.
By comparing metrics such as Relative Estimation Error and Relative
Standard Error, we are able to show that the joint estimation approach provides
less biased estimates for several different sampling frequencies. This is the case for
most parameters but the difference is the largest for the parameters related to the
TTE model. It is therefore concluded that for joint model frameworks using a joint
parameter estimation should be considered. Moreover, we also show that the joint
approach improves estimations when using a linked parametric hazard, especially in
the case of high frequent sampling.
Beskrivning
Ämne/nyckelord
joint model, NLME, survival analysis, FOCE, K-PD model