Comparing corrosion control treatments using a robust Bayesian generalized additive model

Pipe loop studies are used routinely to evaluate corrosion control treatment, and updated regulatory guidance will ensure that they remain an important tool for water quality management. But they are inherently complex and the data they generate are difficult to analyze: non-linear time-trends, non-detects, extreme values, and autocorrelation are common features, the latter due to repeatedly measuring the effluent from test pipes. Popular statistical tests, such as the Student t or rank-sum tests, are often inadequate descriptions of the data. Here, we propose an approach to statistical analysis of pipe loop data that accommodates many of these difficult-to-model characteristics: a robust Bayesian generalized additive model with continuous-time autoregressive errors. Our model facilitates corrosion control treatment comparisons without the need for imputing non-detects or special handling of outliers. It is well-suited to describing nonlinear trends without overfitting, and it accounts for reduced information content due to autocorrelation. We demonstrate the model using an example pipe loop study comprising four years of data, multiple pipe configurations, and multiple orthophosphate dosing protocols. We compare the experimental treatments, finding that an initially high dose of orthophosphate (2 mg P L-1) that is subsequently lowered (0.75 mg P L-1) can yield lower lead release than an intermediate dose (1 mg P L-1) in the long term. We also find that—consistent with previous work—galvanic corrosion yields relatively high particulate lead release, especially at higher orthophosphate doses. An advantage of the Bayesian approach we adopt here is that it yields the full posterior distribution of all parameters and all quantities derived from those parameters, including the model predictions. This means that analysts can construct any comparison that is relevant to the study goals, without the need to rely on a particular statistical test.