Sheffield investigators attribute these benefits to reductions in cholesterol, which is a class effect of the statins. The choice of threshold is based on costeffectiveness, and the justification for the 3% level reasoned on the historical costs of the drugs used in 4S and WOSCOPS. In clinical practice less expensive statins, which produce similar effects on cholesterol to those seen in the clinical trials, are being prescribed and should alter the economic threshold. The Sheffield table1 is claimed to identify those with an annual CHD risk of 3%. The Framingham equation, on which the table is based, uses the ratio of total to high-density lipoprotein (HDL) cholesterol. The Sheffield group have had to use assumed values for HDL in their calculations, and their figures can be reproduced with values of 1·15 mmol/L for men and 1·40 mmol/L for women. These concentrations are inappropriate for certain patients such as those with diabetes mellitus. The table therefore incorrectly suggests that few male diabetics, and no females, achieve a 3% risk, whereas gender has no effect on CHD risk in diabetes, which on average for type II diabetes is 2% per year.5 Furthermore, variations in HDL within the normal range have a large effect on the calculated CHD risk. The cholesterol value cited in the table may, depending on the actual HDL, be too high or low by 22%, or indeed more if the HDL is abnormal. For primary prevention, it may be preferable to calculate, rather than guess, the risk of CHD by measuring both cholesterol and HDL. It is theoretically possible for the laboratory computer to report a calculated CHD risk from the lipids and clinical information, and there is an established example of such risk calculations in biochemical screening programmes for Down’s syndrome. The investment would be fairly small and allow more accurate targeting of drugs. A F Jones Department of Clinical Biochemistry, Birmingham Heartlands Hospital, Birmingham B9 5SS, UK 1
Ramsay LE, Haq IU, Jackson PR, et al. Targeting lipid-lowering drug therapy for primary prevention of coronary heart disease: an updated Sheffield table. Lancet 1996; 348: 387–88. Scandinavian Simvastatin Survival Study Group. Randomised trial of cholesterol lowering in 4444 patients with heart disease: the Scandinavian Simvastatin Survival Study (4S). Lancet 1994; 344: 1383–89. Sacks FM, Pfeffer MA, Moye LA, et al. The effect of parvastatin on coronary events after myocardial infarction in patients with average cholesterol levels. N Engl J Med 1996; 335: 1001–09.
Vol 350 • October 18, 1997
Shepherd J, Cobbe SM, Ford I, et al. Prevention of coronary heart disease with parvastatin in men with hypercholesterolaemia. N Engl J Med 1995; 333: 1301–07. UK Prospective Diabetes Study Group. UK Prospective Diabetes Study 16. Overview of 6 years’ therapy of type II diabetes: a progressive disease. Diabetes 1995; 44: 1249–58.
Cox DR. Regression models and life tables. J R Stat Soc 1972; 34: 187–220. Faraggi D, Simon R. A neural network model for survival data. Stat Med 1989; 14: 73–82. Liestol K, Andersen PK, Andersen U. Survival analysis and neural nets. Stat Med 1989; 13: 1189–200.
Artificial neural networks SIR—The report on neural networks by Leonard Bottaci and co-workers (Aug 16, p 469)1 demands comment. One cannot share their enthusiasm for a method presented as being able to predict the outcome of individual patients. They claim that traditional statistical analyses fail to predict when the individual patient will die. But so will neural networks. Predictions at the individual level are not merely outside our present research, they are fundamentally impossible. Irrespective of the statistical models used, the unexplained variability of individual outcomes will remain large, a fact that should not preclude us from finding better ways of predicting average outcomes for well defined groups of patients. How do neural networks perform in this respect? Bottaci and colleagues do not provide a convincing answer, because they have not made the relevant comparison. Instead of debunking traditional statistical methods based on linear models, they should have presented the predictive value of these models (for example, based on Cox’s proportional hazard regression2), instead of that of physicians presented with “data in tabular form”. Perhaps their most remarkable observation is that physicians who had not seen the patients did not do so badly without recourse to any mathematical model at all. We wish it were true that with neural networks clinicians “may well find the answers that they seek”, but we doubt it. Other authors who have used neural networks have come to less extravagant conclusions.3,4 Whilst advanced statistical tools may be useful, new treatments and a better understanding of the biology of colorectal cancer remain, as ever, the cornerstone of future progress. Marc Buyse, *Pascal Piedbois Limburgs Universitair Centrum, Department of Biostatistics, Diepenbeek, Belgium; and *Hôpital Henri Mondor, Department of Oncology, 94010 Créteil, France 1
Bottaci L, Drew PJ, Hartley JE, et al. Artifical neural networks applied to outcome prediction for colorectal cancer patients in separate institutions. Lancet 1997; 350: 469–72.
SIR—It is obvious that no measurement can be so precise as to permit the design of a model to predict the behaviour of any system with complete accuracy. Therefore, it is theoretically impossible to produce “individual” predictions. But our use of neural networks for the prediction of outcome is a more pragmatic approach. When one considers assumptions about the statistical distribution and independent nature of the predictors required for regression analysis, its mathematical handicaps become clear.1 Traditional statistics can often provide a reliable answer only for groups of patients defined by a small number of linearly separable rules.2 Artificial neural networks allow the addition of further datasets to allow a more personalised prediction than our methods. This means that, whilst in the purest sense the prediction remains for groups of patients, neural networks are able to provide an individual prediction, especially when compared with clinicopathological methods. We agree that the “cornerstone of future” involves the elucidation of the biology of colorectal cancer and much of the work in our own unit is directed towards this aim. However, this research has continued for at least 50 years and, though advances have been made, we are still unable to provide many of our patients with an accurate prediction of their chance of survival. Use of neural networks to analyse data that are already available may well provide further insights into the nature of colorectal cancer and other tumours, with the advantage of individualised prediction of outcome rather than crude general estimates taken from the patient’s particular peer group. There is already a move towards a more connectionist approach to modelling the behaviour of biological systems, including cancer, which reflects the recognition of non-linear causal relations within complex systems.3 The design of neural networks makes them ideally suited for the analysis of these models, many of which are beyond the reach of traditional statistical methods. It is a fallacy to suggest that the clinicians had no recourse to a mathematical model. Even the most junior trainee is aware of the important