Proportion cured and mean log survival time as functions of tumour size

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Abstract
We obtained maximum likelihood estimates (MLEs) of the proportion cured πcand mean log survival time μtfor a sample of 4355 patients with intraocular melanoma whose survival times subsequent to treatment were assumed to follow a log‐normal distribution. Following stratification by tumour size, MLEs of πcand μtderived for each stratum correlate inversely with tumour size. We then expressed πcand μtas continuous functions of tumour size and calculated MLEs for the parameters of these functions from the entire sample. This investigation documents for ocular melanoma a significant relationship of tumour size to both cured fraction and mean log survival time.