Log or not log

Log or not log, that is the question

May 19, 2018

In 2014 I taught a special topics class on statistical issues associated with the measurement of the concentration of cyanobacterial toxin microcystins (MC) in Toledo's drinking water. That class led to a paper documenting the high level of uncertainty in the measured MC. An idea from that paper was to develop a better curve-fitting method to reduce the measurement uncertainty. The Ohio EPA and other regulatory agencies expressed no interest in my proposals. In following two summers, I directed two REU students to learn the measurement process. We designed an experiment using two ELISA kits to measure samples with known MC concentrations. These samples were obtained by diluting the standard solutions. Using the result tested to fit the standard curve fit on the MC concentration scale to the curve fit on the log-concentration scale. Both curves fit the data well. However, the curve fit to the log-concentrations leads to a far smaller predictive uncertainty. Based on this simple result, my students wrote a paper. After the paper was published, I learned that the current ELISA test kits come with three quality control samples with known MC concentrations. We are now searching for raw data from various sources to replicate our study. This replication is important because our study was done using a single test kit and many argued that the kit-to-kit variation is often more important, although we believe that such variation is largely due to the small sample size used for fitting the curve.