Modeling Microbial Density Trend in Pharmaceutical Water with Irregular Intervals using CART Regression

Abstract

Monitoring and controlling the microbiological quality of water in the pharmaceutical and biopharmaceutical industries is paramount to ensure the safety and quality of intermediate and final medicinal products. An integral task of the quality system is to trend, interpret, and investigate this crucial inspection characteristic. Analyzing time series data with irregular sampling intervals presents a significant challenge, particularly when standard methods like ARIMA, which assume fixed-frequency observations, are desired but achieving consistent sample spacing is unattainable. This study investigated the applicability of Classification and Regression Tree (CART) regression as a practical alternative, using Minitab® Statistical Software, to model microbial density collected at irregular intervals. Three response variables were studied with respect to Elapsed Time: a sequential counter, cumulative untransformed microbial density, and cumulative log-transformed microbial density. CART could not model the sequential counter but succeeded with both cumulative variables. The log-transformed cumulative model achieved a test R-squared of 97.88% and a Mean Absolute Percent Error (MAPE) of 0.1610%. The cumulative untransformed model also performed well, with a test R-squared of 95.40% and MAPE of 0.5477 %. The transformed data yielded slightly better results. These findings show that CART regression with Elapsed Time robustly models cumulative trends in irregularly sampled data and is a valuable alternative when fixed-frequency model assumptions cannot be met.