BMJ No 7119 Volume 315
Letters Saturday 22 November 1997
New method for expressing survival in cancer
Relation between survival times and patients' age at diagnosis must be taken into account
EditorThe idea of expressing survival in patients with cancer as the observed number of years that the patient survives after diagnosis divided by the actuarially expected years of life remaining, as in the real life expectancy method proposed by Vaidya and Mittra,(1) looks appealing. A similar approach - using the "longevity quotient" - was proposed by Palmore(2,3) but to our knowledge it has not been widely used. We have two reasons for concern, however.
Our first concern is that the life expectancy is calculated by assuming that the age specific mortality does not change in the future. If this assumption does not hold, due to possible time trends in mortality, the real life expectancy method might yield biased results. Secondly, when first reading the paper we wondered whether it was appropriate to extrapolate the curves computed for each category of patients defined by nodal status to patients of different age, as Vaidya and Mittra did in their examples.
To verify this aspect, we analysed, according to the real life expectancy method, a case series of 2,396 women with primary breast cancer treated with breast conservation surgery at our institute (R Zucali et al, unpublished findings). In particular, age and nodal status were entered as covariates into a Cox regression model, after the proportional hazard assumption had been checked. Nodal status was categorised as node negative, 1-4 nodes positive, or >4 nodes positive, whereas age was flexibly modelled as a continuous covariate. A highly significant effect was detected for nodal status and age, with no evidence of a possible interaction between the two. The figure shows the estimated survival curves obtained for node negative women of different ages (70, 50, and 30 years). The three curves are quite different. The estimated probability of achieving a full normal remaining life was 61%, 48%, and 13%, respectively. Similar findings were obtained for node positive women.
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It is thus evident that a relation exists between rescaled survival times and patients' age at the time of diagnosis and that such a relation must be taken into account for prediction purposes. The extent to which the above results apply in contexts other than breast cancer needs to be investigated. In conclusion, we do not challenge the idea of using the real life expectancy method, provided that age is regarded as a possibly important predictor. |  | |
| Estimated survival curves for node negative women of different ages |
Ettore Marubini
Director
Luigi Mariani
Assistant
Istituto Nazionale per lo Studio e la Cura dei Tumori,
Division of Medical Statistics and Biometry,
Via G Venezian 1,
I-20133
Milan,
Italy
Reference
1 Vaidya J S, Mittra I. Fraction of normal remaining life span:
a new method for expressing survival in cancer. BMJ 1997;
314:1682-4. (7 June.)
2 Palmore E. Predicting longevity: a new method. In: Palmore E,
ed. Normal ageing II. Reports from the Duke longitudinal
studies, 1970-1973. Durham, NC: Duke University Press,
1974:281-5.
3 Palmore E. Predictors of longevity difference. In: Palmore E,
Bussee E W, Maddox G L, Nowlin J B, Siegler I C, eds. Normal ageing
III. Reports from the Duke longitudinal studies, 1974-1975.
Durham, NC: Duke University Press, 1985:19-29.
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