Improving Mixture Cure Modelling of Multiple Molecular Factors in Cancer Prognosis
In analysis of time-to-event data in which the study sample includes long-term survivors, the mixture cure (MC) model is more appropriate than a conventional proportional hazards model. In samples with few events, standard maximum likelihood (ML) estimates can be biased and Wald-type confidence intervals may not be valid. This problem can be exacerbated when multiple imputation is used to deal with missing covariate values. Motivated by a cohort study of breast cancer prognosis with incomplete prognostic biomarkers, I i) extend Firth-type penalized likelihood (FT-PL) developed for bias reduction in the exponential family to the Weibull-logistic MC, using the Jeffreys invariant prior; ii) develop profile ikelihood confidence interval (PLCI) methods with likelihood ratio tests (LRT) for MC model inference, iii) extend their application to pooled estimates of multiple-imputed data, via a combined likelihood profile (CLIP); and iv) improve the specification of imputation model to refine estimation efficiency with FT-PL and CLIP. In data-based simulation studies of samples with low event numbers, we find that: i) compared to ML, FT-PL exhibits smaller mean bias and mean squared error, as well as higher statistical power by LRT; ii) the PLCI for FT-PL shows better coverage than Wald CI, and exceeds that of PLCI for ML; iii) FT-PL with CLIP-CI has good coverage of underlying parameter values and narrower width than the common Rubin’s Rule approach; and iv) an imputation model that follows the exact conditional distribution of the missing covariate values under the MC framework demonstrates overall smaller estimation bias and better coverage compared to other commonly used imputation models, and can be well approximated in some practical cases. Finally, we illustrate the practicality and strength of FT-PL with profile likelihood based inference for MC analysis in a cohort study of breast cancer prognosis with long-term followup for disease free survival, where we apply the refined imputation strategy to incompletely measured prognostic factors.
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