The Effects of Measurement Error on Previously Reported Mathematical Relationships between Indicator Organism Density and Swimming-Associated Illness: A Quantitative Estimate of the Resulting Bias

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Abstract
Several recent epidemiological studies seeking associations between swimming in recreational waters contaminated with domestic sewage and increased illness among such swimmers have reported mathematical relationships relating indicator organism densities to illness among swimmers. Common to the design of all of these studies is the failure to adequately control for large amounts of measurement error contained in estimates of exposure, i.e. estimated indicator organism densities. The limited precision of current methods of indicator organism enumeration, coupled with temporal and spacial variation in indicator organism densities at the locations studied, are responsible for a substantial portion of this measurement error. The failure to control adequately for these sources of measurement error has resulted in a significant amount of bias being present in the mathematical relationships reported by these previously published epidemiological studies. In order to explore the magnitude and direction of this bias, computer simulations were conducted using data in which estimation of indicator organism density was obtained by the two most widely used techniques of enumeration: the Multiple Tube Fermentation Technique and the Membrane Filtration Technique. The results of the computer simulations show that the bias caused by this measurement error is non-differential causing the mathematical relationships between indicator organism density and swimming-associated illness reported in previous epidemiological studies to underestimate true risk by a minimum of approximately 14%, and that this underestimate could range as high as approximately 30 to 57%. This study also demonstrates that substantial reduction of this bias can be easily accomplished by incorporating a formal water quality sampling strategy, based on statistical principles of experimental design and analysis, into the design of future epidemiological studies seeking mathematical relationships between indicator organism density and swimming-associated illness.

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