Estimation of response slopes in respiratory control

Abstract

The ventilatory response to changes in alveolar (arterial) CO2 is widely used as an index of respiratory control behavior. Methods for estimating these response slopes should incorporate the possibility that there may be errors in both the independent (PCO2) and dependent (ventilation) variables. In a recent paper, Daubenspeck and Ogden have suggested problems inherent in the traditional technique of reduced major axis and have suggested a more contemporary technique of directional statistics. Both techniques were previously analyzed and a method was developed to overcome the problems of reduced major axis and problems inherent in the use of directional statistics. Under the assumption of a bivariate normal distribution, the slope estimate is similar to the maximum likelihood estimate proposed by Mardia et al. (1983) for this problem. A bootstrap statistical approach is indicated when the distributions are not normally distributed. These concepts are illustrated using O2-CO2 interaction data.