Abstract
A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature.
Highlights
The usual approach in models for time-to-event data is built on the assumption that all subjects will experience the event of interest if the follow-up time is long enough
From the seminal contributions in [1,2] and the approach based on competing risks for cure rate models in [3], we find many papers in recent years on this research area
A cure rate model is proposed under the competing risks setup
Summary
In a sample of size n, the observed variables are Ti = min(Yi , Ci ) and δi = I (Yi ≤ Ci ), where δi = 1 and δi = 0 denote either if a failure or a censored time was observed for the i-th subject, respectively, i = 1, . Direct maximization is not computationally simple because some terms in (6) involve both β and λ For this reason and taking advantage of the EM algorithm developed for the power series family of cure rate models in [14], ML estimates in the Bellcr model are computed using this algorithm. We might be interested in the cure rate for subjects who survived up to a certain time t0 , denoted by pt0.
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