To extend the polynomial method for evaluating linearity in 2 ways. First, we developed a screen to ascertain whether the data were precise enough to permit a reliable evaluation of linearity and therefore eliminate findings of linearity due to low statistical power. Second, we assessed whether the degree of nonlinearity detected by the polynomial method was clinically relevant using a statistically rigorous method.
Because we assessed linearity relative to a clinically determined level of importance instead of the default value of zero, we used sampling theory based on the noncentral chi(2) distribution. Using statistical power calculations, we incorporated a screen for imprecision that guarantees that the probability of correctly identifying nonlinear methods is at least 80%.
With the described methods, we achieved a sensitivity of at least 80% and a specificity of at least 95%. When the data were too imprecise to achieve a sensitivity of 80%, no determination of linearity was made. This procedure mimics the practice in manual inspection of flagging data that appear imprecise by visual inspection and halting the evaluation.
Formal statistical tests for precision and amount of nonlinearity are advantageous because they allow us to quantify and limit classification errors. By formalizing these various aspects of linearity assessment, we maintain some of the complex features of manual methods while making the linearity assessment feasible to apply to a high volume of assessments and removing the between-analyst variability.