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The use of correlation coefficients in epidemiologic analysis
0021.9681184
J Chron Dis Vol. 37, No. 6, p. 503, 1984 Printed in Great Britain
$3.00 + 0.00
Pergamon Press Ltd
Letter to the Editors THE USE OF CORRELATION COEFFICIENTS EPIDEMIOLOGIC ANALYSIS
IN
To the Editors: To THE excellent paper by Peduzzi et al. [I] I would like to give a more general support as to why the correlation coefficient should be used cautiously or rather should not be used in some types of epidemiologic analysis. When analyzing the dependency of the incidence of a particular disease on a number of explanatory variables, epidemiologists make use of stochastic models. A well-known example is the logistic model, where the probability rc, of a subject i developing a particular disease is a logistic function of a number of explanatory variables. Such a model does not explain the binary disease outcome, but it explains the probability of developing the disease. Suppose that one could completely explain the probabilities TC,.Then the fact that a subject i does or does not develop the disease still remains a purely random Bernouilly outcome with probability level rc,. This implies that the relative amount of variance explained in the binary disease outcome by the explanatory variables cannot reach unity. Also note that it is impossible for a logistic function for whatever values of explanatory variables to become 1 for all subjects developing the disease and 0 for all subjects not developing the disease. The essence thus is in the fact that a logistic model is a stochastic model quantifying the probability level of a purely random event. Adopting stochastic models necessarily implies the adoptation of pure randomness. PAUL G. H. MULDER Rotterdam The Netherlands REFERENCE 1. Peduzzi PN, Detre KM, Chan YK: Upper and lower bounds for correlations in 2 x 2 tables-revisited. J Chron Dis 36: 491-496, 1983
Response WE APPRECIATE the thoughtful comments of Paul Mulder on our recently published article. His arguments based on the logistic model provide further evidence of why the correlation coefficient should be used cautiously with binary data. West Haven, CT 06515 U.S.A.
PETER N. PEDUZZI KATHERINE M. DETRE YICK-KWONG CHAN
503
J Chron Dis Vol. 37, No. 6, p. 503, 1984 Printed in Great Britain
$3.00 + 0.00
Pergamon Press Ltd
Letter to the Editors THE USE OF CORRELATION COEFFICIENTS EPIDEMIOLOGIC ANALYSIS
IN
To the Editors: To THE excellent paper by Peduzzi et al. [I] I would like to give a more general support as to why the correlation coefficient should be used cautiously or rather should not be used in some types of epidemiologic analysis. When analyzing the dependency of the incidence of a particular disease on a number of explanatory variables, epidemiologists make use of stochastic models. A well-known example is the logistic model, where the probability rc, of a subject i developing a particular disease is a logistic function of a number of explanatory variables. Such a model does not explain the binary disease outcome, but it explains the probability of developing the disease. Suppose that one could completely explain the probabilities TC,.Then the fact that a subject i does or does not develop the disease still remains a purely random Bernouilly outcome with probability level rc,. This implies that the relative amount of variance explained in the binary disease outcome by the explanatory variables cannot reach unity. Also note that it is impossible for a logistic function for whatever values of explanatory variables to become 1 for all subjects developing the disease and 0 for all subjects not developing the disease. The essence thus is in the fact that a logistic model is a stochastic model quantifying the probability level of a purely random event. Adopting stochastic models necessarily implies the adoptation of pure randomness. PAUL G. H. MULDER Rotterdam The Netherlands REFERENCE 1. Peduzzi PN, Detre KM, Chan YK: Upper and lower bounds for correlations in 2 x 2 tables-revisited. J Chron Dis 36: 491-496, 1983
Response WE APPRECIATE the thoughtful comments of Paul Mulder on our recently published article. His arguments based on the logistic model provide further evidence of why the correlation coefficient should be used cautiously with binary data. West Haven, CT 06515 U.S.A.
PETER N. PEDUZZI KATHERINE M. DETRE YICK-KWONG CHAN
503