Estimating Concentration Response Function and Change-Point using Time-Course and Calibration Data

In this paper the problem of determining the functional relationship between time and the concentration of a chemical substance is studied. An intervention drug is administered on the experimental unit from which the chemical substance (specimen) is measured. This drug is hypothesized to cause a change in the concentration level of the chemical substance a certain lag-time after the intervention. However, the concentration value could not be directly measured, but rather a surrogate response can be measured. In the time-course study, this surrogate response is measured using different electrodes which possess varied behaviors. To utilize these surrogate measurements arising from the different electrodes (sensors), a calibration study is undertaken which measures the surrogate response for the different electrodes at known concentration levels. Based on the time-course and calibration data sets, a statistical procedure to estimate the signal function and the lag-time is proposed. Simulation studies indicate that the proposed procedure is able to reasonably recover the signal function and the lag-time. The procedure is then applied to the real data sets obtained during an analytical chemistry experiment.