This report deals with an analysis of data from a collaborative health survey of 6691 individuals identified by occupation and census in the West of Scotland [1]. The method employed in the survey was to ask each individual to complete a cardio-respiratory questionnaire before attending a temporary examination centre where each was given a multiphasic screening examination. This examination provided the data for the medical record accompanying the questionnaire. A copy of the questionnaire and medical report is included in Appendix I. Since the survey was carried out between 1965 and 1969, 131 deaths have been recorded (until June 1975) - 53 from coronary heart disease (C.H.D.) [2]. The questions which arose now were 1) Can the C.H.D. decedants' data be used to predict which individuals in the remainder of the population are at most risk of death from C.H.D.? 2) Can some measure of this risk be found? 3) Can this measure be used to rank the population in order of increasing risk? The first requirement is to decide which of the many variables on tape are of most interest and value in answering these questions. We will call these variables features. On medical advice, it was decided to consider the following 9 features: On the questionnaire, the E.C.G. summary is coded as 1, 2, 3, 9 where 9 is the value for a normal person. The value 9 has been transformed to 4 in this report for convenience in the calculations later on. Note: Pages 52 and 53 constitute the medical record. It turned out that, of the 53 deaths from C.H.D. only 2 were female (of the 6691 individuals only 1100 were female). This is not really surprising since it is well known that C.H.D. mainly affects males in the middle-age group. Because of the lack of data on female deaths, it was decided to look at C.H.D. for males only for the time being and to try to find some measure of risk for males only. Thus, feature 9 will be omitted from now on. Now we have to decide what measure of risk we will adopt. There are various possibilities. One method is to assign to each individual a risk score which is a fixed linear function of the features. Such a function is quoted in the paper by Greaves et al [3] and the work behind its derivation is given by Truett et al [4]. Their risk score is defined by R = 0.7 Age + 0.01 Chol. + 0.02 S.B.P. + 1.5 Phlegm + 0.5 P.I. +0.5 Dyspnoea + 1.5 Ang. + a variable amount for E.C.G. and F.L.V. (Note: F.L.V. - forced expiratory volume.) An individual is classified as being at high risk if his R-value is > 10. However, this method is open to criticism since it does not take into account any interactions between the variables, and it could be that such interactions are of critical importance. This method will be referred to later for comparison. Thus it was decided to look for a method which did take into account all interactions between the features. It was also decided to use some of the theory of methods of statistical diagnosis and to proceed as follows. There are two groups of individuals in the population in which we are primarily interested. They are CATEGORY 1 - those who have died from C.H.D. CATEGORY 2 - those who are alive at the present time. There are also individuals in the population who have died from reasons other than C.H.D. but they will be excluded from the analysis. Also, any individual in category 1 or 2 whose feature vector was incomplete (e.g. no Chol, value available) was excluded from the analysis. This left 48 individuals in category 1 and approximately 5100 in category 2. Now we must choose a set of basic individuals on which to base our 'diagnostic system'. It was decided to include in our basic set all 48 individuals from category 1 along with a random sample of 100 individuals from category 2. So, if we now choose an individual at random from the remainder of the population, we can, in some way, compare his feature vector with those in the basic set and arrive at some measure of 'the likelihood of his belonging to category 1'. Of course, to talk literally of an individual from the rest of the population as belonging to category 1 is meaningless since he is known to be alive while those in category 1 are known to be dead. However, this method should give us some indication of the risk of death from C.H.D. for each individual. The actual choice of the measure to be used, along with the theory behind the calculation of it is given in the following section.