On the estimation of hypoxic ventilatory response

The shape parameter, A, has been used to assess hypoxic sensitivity (ventilatory response, VE, to lowered alveolar oxygen tension, PAO2) in the model of the form VE = VEO + A/(PAO2 - C) where C is held constant at 32. In this paper we examine the consequence of holding C constant versus estimating both A and C from the data. Using computer-simulated data from 59 subjects whose A and C values had been previously determined, we indicate that when the actual C value is substantially different from 32, the model with C = 32 does not fit the data. In this case, the estimated A value with C = 32 is highly dependent upon the lowest value of PAO2 obtained in the experimental protocol and can be markedly different from the actual A value. In contrast, when C is also estimated from the subject's data the model fits the data and the estimate of A is unbiased but the precision may be diminished when the actual value of C is low. To improve this precision, we propose a Bayesian estimation scheme that adds a "soft" constraint on C.