Methodology to predict long-term cancer survival from short-term data using Tobacco Cancer Risk and Absolute Cancer Cure models

Abstract

Three parametric statistical models have been fully validated for cancer of the larynx for the prediction of long-term 15, 20 and 25 year cancer-specific survival fractions when short-term follow-up data was available for just 1–2 years after the end of treatment of the last patient. In all groups of cases the treatment period was only 5 years. Three disease stage groups were studied, T1N0, T2N0 and T3N0. The models are the Standard Lognormal (SLN) first proposed by Boag (1949 J. R. Stat. Soc. Series B 11 15–53) but only ever fully validated for cancer of the cervix, Mould and Boag (1975 Br. J. Cancer 32 529–50), and two new models which have been termed Tobacco Cancer Risk (TCR) and Absolute Cancer Cure (ACC). In each, the frequency distribution of survival times of defined groups of cancer deaths is lognormally distributed: larynx only (SLN), larynx and lung (TCR) and all cancers (ACC). All models each have three unknown parameters but it was possible to estimate a value for the lognormal parameter S a priori. By reduction to two unknown parameters the model stability has been improved. The material used to validate the methodology consisted of case histories of 965 patients, all treated during the period 1944–1968 by Dr Manuel Lederman of the Royal Marsden Hospital, London, with follow-up to 1988. This provided a follow-up range of 20– 44 years and enabled predicted long-term survival fractions to be compared with the actual survival fractions, calculated by the Kaplan and Meier (1958 J. Am. Stat. Assoc. 53 457–82) method. The TCR and ACC models are better than the SLN model and for a maximum short-term follow-up of 6 years, the 20 and 25 year survival fractions could be predicted. Therefore the numbers of follow-up years saved are respectively 14 years and 19 years. Clinical trial results using the TCR and ACC models can thus be analysed much earlier than currently possible. Absolute cure from cancer was also studied, using not only the prediction models which incorporate a parameter for a statistically cured fraction of patients CSLN, CTCR and CACC, but because of the long follow-up range of 20–44 years, also by complete life analysis. The survival experience of those who did not die of their original cancer of the larynx was compared to the expected survival experience of a population with the same age, birth cohort and sex structure. To date it has been generally assumed for early stage disease that although for some 5–10 years after treatment the survival experience of this patient subgroup might be no different from that expected in the matched group, thereafter the death rate of this subgroup becomes lower than that of the matched group. This implies that surviving cancer patients cured of their disease tend to die of other conditions at a higher than normal rate as they become older, and therefore cancer is never totally cured. Our conclusion is that at least for cancer of the glottic larynx, the answer to the question: ‘Can cancer totally be cured?’ is ‘Yes to at least 15-years post-treatment and also probably to 25 years.’