Abstract: This study focuses on a nonlinear mixed effects model
for repeated measures data to describe longitudinal changes in carcinoembryonic
antigen (CEA) levels of colorectal cancer patients over time. The CEA level of
colorectal cancer patients is regarded as the marker choice for monitoring.
Following surgery, if the CEA levels begin to rise, then there will be a
recurrence of disease. The fixed effects parameter of the proposed model represents the
recurrent time which is between the flat and rapid increase in an exponential
phase. Parameters of the proposed model are estimated by using Lindstrom and
Bates (LB) and the stochastic approximation version of the standard expectation
and maximization step (SAEM) algorithms. The results show that the estimates of
the recurrent time by using LB and SAEM algorithms are
equal to 17.4 and 22.8 months, respectively. Further, the residual sum of
squares of a proposed model by using the SAEM algorithm is equal to 25.14 which
is less than the residual sum of squares using the LB algorithm (88.04). Hence,
the predicted curve of the proposed model with parameters estimated by the SAEM
algorithm is outperforms the LB algorithm for the CEA level of colorectal cancer
patients.
Keywords and phrases: carcinoembryonic antigen, nonlinear mixed effects model, recurrent time, repeated measures.
