Analysis of linear and mildly nonlinear relationships using pooled subject data.

The detection of mild nonlinearities and/or state-dependent variability in otherwise linear physiological relationships is generally difficult in the presence of significant measurement errors. Conventional approaches using pooled subject data to increase the degree of freedom for statistical inference are enervated by the resultant introduction of intersubject variability. This paper proposes a new, simple method of pooling multiple subject data for linearity analysis. With the use of a special standardization procedure for the individual response curves, this method allows sensitive detection of occult nonlinearities as well as any state-dependent variability in the underlying relationship. Application of this analytic approach to reported hypercapnic exercise-response data in eight healthy subjects showed that 1) the hypercapnic ventilation-CO2 output relationship is nonlinear with a downward concavity; and 2) the ventilation-tidal volume relationship, which is linear at low tidal volume values, is similar in hypercapnic exercise as in resting hypercapnia or eucapnic exercise.