Sequential Sampling Data Set Analysis.

For the sequential sampling analysis, the effects of two explanatory variables on concentrations of Pb in drinking water were considered: the presence of LSLs and CCT status. To estimate drinking water Pb concentrations at the tap under each scenario, available sequential tap water sampling data were solicited and obtained from utilities, EPA branch offices, and authors of published journal articles. These data represented 18 039 samples from 3,102 sequential sampling events from 1690 sites in 15 cities across the U.S. and Canada (Tables S1–S3). The number of sequential samples per sampling event varied from 1 to 26. Data included Pb concentrations and information regarding LSL status, location, and date of sample collected between 1998 and 2016. The data set contained samples from eight cities in the northern Midwest, midAtlantic, and northeastern U.S. and seven cities in southern Canada; most cities sampled had populations between 100 000 and one million (Table S1). Most data sources contained a series of samples, or profiles, taken after periods of stagnation of varying length, with identifiers for sampling volume and position in series (“profile liter”). Corrosion control status was defined using records of CCT practices and implementation dates, as well as data obtained from water quality samples (Tables S2 and S3). Because these measurements were collected for different purposes and obtained using several sampling designs over many years, a statistical model was developed to account for this variation.

Multiple, nested, mixed-effects models were used (Supporting Information Eqs 1–5 and Table S5) to log-transform the measured Pb concentration with predictor variables for LSL presence or absence, CCT, and profile liter, the cumulative volume interval a sample represented within a sampling series and included nested random effects of the city, site, and sampling event. Using the fitted model and the original data, the data set was simulated, then the geometric mean and standard deviation of simulated Pb concentrations in water after their respective stagnation intervals obtained at a point analogous to the fifth liter taken from the tap were calculated. This was based on the fitted regression and bootstrapped 95% confidence intervals that showed the highest Pb concentrations after the last stagnation period occurring roughly 5 liters from the sampling tap in homes with LSLs (Figure S1). We fitted models and produced simulated data sets using R statistical software (R Core Team 2016) with the lme4 package.⁴⁷ Details of this analysis are in the Supporting Information.

Seven combinations of LSL and CCT scenarios produced statistically distinct predictions (see the Supporting Information) of drinking water concentrations for use in SHEDS-IEUBK modeling. Table 1 shows the seven scenarios and corresponding estimated geometric mean and geometric standard deviation drinking water Pb concentrations used as inputs in SHEDS-IEUBK. For LSL scenarios, “yes” indicates Pb service lines; “partial” indicates some presence of Pb in service lines (some portion of the LSL remains after a section of the line was removed); and “no” indicates no Pb in service lines. For CCT scenarios, no indicates no CCT, “some” represents systems that have some CCT in place, but not optimized, and “representative” indicates a water chemistry that exemplifies the best CCT currently in use (which can include some combination of higher phosphate values and/or optimized pH levels). The simulated predictions overlapped completely for all CCT scenarios in homes with no LSL (see the Supporting Information), so “combined” indicates pooled CCT estimates representing all three states of CCT in these cases. This is not meant to imply that benefits would not be gained under actual circumstances with implementation of CCT in homes without LSLs.