On the estimation of hypoxic ventilatory response

The shape parameter, A, has been used to assess hypoxic sensitivity (ventilatory response, V ̇_E, to lowered alveolar oxygen tension, P_AO₂) in the model of the form V ̇_E = V ̇_EO + A (P_AO₂ - 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 P_AO₂ 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.