Evaluation of two methods of interpolating quarterly trihalomethane levels between sampling dates

Abstract

Epidemiological studies of the relationship between disinfection byproducts (DBPs) and adverse birth outcomes often use a single quarterly sample result to characterize an exposure period during a pregnancy. Concentrations of trihalomethanes (THMs), a frequently studied class of DBPs, can fluctuate considerably between sampling periods so that a single point measurement in time may not adequately characterize levels over an exposure period. In addition to obtaining compliance samples that are required quarterly at a limited number of sampling sites, the New York City water supply system takes monthly THM samples at a large number of sites. We used these monthly data to investigate two methods for interpolating between quarterly measurements: cubic splines and linear interpolation. We based interpolations on 1 month in each calendar quarter and checked the interpolated values against the actual data values from the other 2 months of the quarter. Both methods produced generally acceptable fits: 90% of the observed discrepancies between fitted and actual values were less than 14 mg/l and over half were less than 5 mg/l for total trihalomethanes (THM4). These numbers are about half the change in THM4 level from one quarter to the next and compare favorably with the range of 0-80 mg/l or more used in many studies. Comparable results were obtained for chloroform and bromodichloromethane, the two THMs with levels high enough to analyze. Linear interpolation generally performed better than the spline fit, producing lower average discrepancies and fewer large discrepancies. Linear interpolation can be a useful and easily applied method for developing improved exposure estimates using quarterly sampling data.

Association of Brominated Trihalomethane and Haloacetic Acid Exposure With Fetal Growth and Preterm Delivery in Massachusetts

“…Recent studies have helped advances in DBP exposure assessment methods by interpolating missing data, 47 developing dose estimates on the basis of individual water-use data, 7,10 and through the use of exposure biomarkers. 27,30,48 Nonetheless, given the potential number of DBPs present in drinking water, the delineation of which surrogate DBP mixture to target remains elusive.…”

Flow‐covariate prediction of stream pesticide concentrations

“…Previously [5] we showed that use of a seasonal covariate based on the deterministic model PRZM did not lead to improved predictions. In contrast, in the present study we found that seasonality, as modeled by linear and quadratic terms of time (in days), can lead to improved prediction.…”

“…Other parameters of the semivariogram model include the partial sill (i.e., s 2 ) and range (i.e., lag distance beyond which little or no temporal correlation exists). In Richter et al [5] we investigated a variety of semivariogram models, finding a piecewise linear semivariogram model with nugget ¼ 0.0025, range ¼ K, and sill (i.e., nugget plus partial sill) equal to the semivariogram estimate at lag K, K ¼ 7 or 14 depending on sample design, to be best predicting. Use of this semivariogram model resulted in ordinary kriging predictions that were almost identical to log-linear interpolations.…”

“…In practice, time series predictions of atrazine concentrations in surface waters are often obtained by linearly interpolating the gap days on the original scale [3][4][5], a method that corresponds to fitting a piecewise linear spline to data with knots at sample data points. For the prediction of the target quantities of maximum m-day (m ¼ 1, 7, 14, 30) rolling averages, it was demonstrated that for right-skewed data with an approximately log-normal distribution, linear interpolation on the original (linear) scale performed poorly relative to linear interpolation on the logarithmic scale (hereafter referred to as log-linear interpolation); and therefore, linear interpolation should be avoided [1].…”

Community Drinking Water Quality Monitoring Data

“…Quarterly or annual measurements may miss seasonal trends that could be identified by more frequent monitoring, such as the case with the Atrazine Monitoring Program. 18,23 Estimates of drinking water quality in the interim between measurements could be obtained through interpolation, 12,33 imputation, 34,35 or hierarchical modeling 24 techniques. Frequent measurements are particularly important in the context of fetal development and birth outcomes, where linkage should be to critical periods of susceptibility in utero.…”