Abstract

Background: Circulating tumour cell counts are being used increasingly often in oncology for prognosis, stratification and the assessment of response to treatment in phase II trials. Cell counts have typically been based on visual or computer assisted counting of abnormal cells in blood samples drawn at the point of recruitment to a study. The number of cells in a given sample is subject to sampling variation and the recorded number of tumour cells in the sample is subject to measurement error.
Methods: A complete data likelihood was developed for a proportional hazards regression model which recognizes these sources of variation in the observed circulating tumour cell count when it is used as a prognostic covariate.
Results: The performance of the expectation-maximization algorithm was assessed in simulation studies and found to yield estimators with good frequency properties. The asymptotic bias of estimators based on the observed circulating tumour cell count was also examined.
Conclusions: In the situations examined, the proposed estimator was consistent and had considerably smaller empirical bias than estimators arising from analyses based on the observed cell count. The estimated standard error gave confidence intervals with coverage probabilities compatible with the nominal level.
Keywords: Circulating tumour cells, cox regression, measurement error, sampling variation