Applications of Riemann Integration in Biostatistics

Music City Center 

Riemann integration is a mathematical approach that offers distinct advantages over single point for analyses making it a preferable endpoint under certain conditions. A prominent application is the estimation of the area under the curve (AUC), utilized in pharmacokinetic and pharmacodynamic analyses. Since these measurements are continuous and collected at discrete timepoints, Riemann integration becomes the most easily applied method for estimating integrals.

As an example, summed pain intensity (SPI) is calculated using the trapezoidal rule version of Riemann integration derived from Numeric Pain Rating Scale (NPRS) measurements. Simulations on this endpoint show reductions in coefficient of variation compared to single point analysis when there is variance between timepoints, and thus as a result increased statistical effect size.

This methodology can be utilized in additional endpoints to enhance endpoint robustness through aggregation of continuous data across multiple time points.

Endpoint

Power

Pharmacodynamics

Pharmacokinetics 

Biopharmaceutical Section