The Trigonometric Responder Approach: A New Method for Detecting Responders to Pharmacological or Experimental Challenges

The paper presents a newly developed response measure that is particularly suitable for the evaluation of pharmacokinetic data. This method is based on trigonometric considerations, defining a hormone response as the difference between the angle of the slope of the curve before and after drug intake. In addition, the size of this difference is compared to the difference obtained in placebo conditions. In this way, the trigonometric response measure overcomes one of the most problematic shortcomings of the ‘area under the curve’ (AUC) approach, the problem of the initial value. We will present the mathematical background of the trigonometric method and demonstrate its usefulness by evaluating empirical data (a pharmacological challenge test using the dopamine agonist lisuride) and comparing it to classical AUC measures. This has been achieved by contrasting both approaches with responder definitions according to binary time series analysis and the peak value of the curve.

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Appendix

*** SPSS syntax for the calculation of the trigonometric response measure. ***

COMPUTE tanmed_p = (p.y3 + p.y2 - (2 * p.y1))/(t3 + t2 - 2 * t1).

VARIABLE LABELS tanmed_p ‘Tangent Drug Placebo’ .

EXECUTE .

COMPUTE tanphy_p = (p.y1 - p.y0)/(t1 - t0) .

VARIABLE LABELS tanphy_p ‘Tangent Physiol Placebo’ .

EXECUTE .

COMPUTE tanrsp_p = (tanphy_p - tanmed_p)/(1 + (tanphy_p * tanmed_p)) .

VARIABLE LABELS tanrsp_p ‘Tangent Response Placebo’ .

EXECUTE .

COMPUTE ARCTAN_p = ARTAN(tanrsp_p) .

VARIABLE LABELS ARCTAN_p ‘Arc Tangent Placebo’ .

EXECUTE .

COMPUTE Angle_p = arctan_p * 57.29578 .

*** 180 Grad/PI = 57,29578 ***

VARIABLE LABELS Angle_p ‘Angle Placebo’ .

EXECUTE .

COMPUTE tanmed_l = (p.l3 + l.y2 - (2 * l.y1))/(t3 + t2 - 2 * t1) .

VARIABLE LABELS tanmed_l ‘Tangent Drug Lisuride’ .

EXECUTE .

COMPUTE tanphy_l = (l.y1 - l.y0)/(t1 - t0) .

VARIABLE LABELS tanphy_l ‘Tangent Physiol Lisuride’ .

EXECUTE .

COMPUTE tanrsp_l = (tanphy_l - tanmed_l)/(1 + (tanphy_l * tanmed_l)) .

VARIABLE LABELS tanrsp_l ‘Tangent Response Lisuride’ .

EXECUTE .

COMPUTE ARCTAN_l = ARTAN(tanrsp_l) .

VARIABLE LABELS ARCTAN_l ‘Arc Tangent Lisuride’ .

EXECUTE .

COMPUTE Angle_l = arctan_l * 57.29578 .

*** 180 Grad/PI = 57,29578 ***

VARIABLE LABELS Angle_l ‘Angle Lisuride’ .

EXECUTE .

COMPUTE A_dif_lp = Angle_l - Angle_p .

VARIABLE LABELS A_dif_lp ‘Angle Difference Lisuride - Placebo’ .

EXECUTE .

IF (A_dif_lp > 0) Ang_l_re = 1 .

VARIABLE LABELS Ang_l_re ‘Angle Lisuride Responder’ .

EXECUTE .

IF (A_dif_lp < 0) Ang_l_re = 0 .

VARIABLE LABELS Ang_l_re ‘Angle Lisuride Responder’ .

EXECUTE .