Comparison of Failure Time Analysis and Abbott's Formula for Estimating Survival of Organisms Entrained at Power Stations

Abstract During the 1970s and 1980s, numerous studies were conducted to estimate the survival of ichthyoplankton following passage through power plant cooling systems. These studies generally used Abbott's formula to adjust the observed survival of organisms collected at the discharge for sampling mortality, as measured at the intake. The U.S. Environmental Protection Agency (USEPA) criticized these past studies for methodological faults (including the data analysis methods) on the basis that Abbott's formula may introduce a bias if sample sizes are small or unequal at the intake and discharge locations, sampling mortality is high, the samples contain organisms that were already dead, or the organisms are heterogeneous with respect to their probability of surviving entrainment. The effects of these issues on the bias and precision of entrainment survival estimates calculated using Abbott's formula and using failure time analysis were determined from simulated samples. Failure time analysis produced estimates that were minimally biased in terms of the issues raised by the USEPA and often more accurate and precise than Abbott's formula estimates. The failure time models were applied to experimental data used to estimate sampling stress at the Indian Point Generating Station in 1980 and supported the equality of sampling stress at the intake and discharge samplers, a critical requirement for obtaining unbiased survival estimates.