Time-to-event analysis as a framework for quantifying fish passage performance

Fish passage is the result of a sequence of processes, whereby fish must approach, enter, and pass a structure. Each of these processes takes time, and fishway performance is best quantified in terms of the rates at which each process is completed. Optimal performance is achieved by maximizing the rates of approach, entry, and passage through safe and desirable routes. Sometimes, however, it is necessary to reduce rates of passage through less desirable routes in order to increase proportions passing through the preferred route. Effectiveness of operational or structural modifications for achieving either of these goals is best quantified by applying time-to-event analysis, commonly known as survival analysis methods, to telemetry data. This set of techniques allows for accurate estimation of passage rates and covariate effects on those rates. Importantly, it allows researchers to quantify rates that vary over time, as well as the effects of covariates that also vary over time. Finally, these methods are able to control for competing risks, i.e., the presence of alternate passage routes, failure to pass, or other fates that remove fish from the pool of candidates available to pass through a particular route. In this chapter, we present a model simulation of telemetered fish passing a hydroelectric dam, and provide step-by-step guidance and rationales for performing time-to-event analysis on the resulting data. We demonstrate how this approach removes bias from performance estimates that can result from using methods that focus only on proportions passing each route. Time-to-event analysis, coupled with multinomial models for measuring survival, provides a comprehensive set of techniques for quantifying fish passage, and a framework from which performance among different sites can be better understood.