Monte-Carlo Comparison of Confidence Interval Procedures for Estimating Survival in a Release-Recapture Study, with Applications to Snake River Salmonids
Prepared by:
Alan B. Lowther
John R. Skalski
University of Washington
Seattle, Washington
June 1996
ABSTRACT
Objectives
Confidence intervals for survival probabilities between hydroelectric facilities of migrating juvenile salmonids can be computed from the output of the SURPH software developed at the Centerfor Quantitative Science at the University of Washington. These intervals have been constructedusing the estimate of the survival probability, its associated standard error, and assuming the estimate is normally distributed. In order to test the validity and performance of this procedure, two additional confidence interval procedures for estimating survival probabilities were tested and compared using simulated mark-recapture data. Intervals were constructed using normal probability theory, using a percentile-based empirical bootstrap algorithm, and using the profile likelihood concept. Performance of each method was assessed for a variety of initial conditions (release sizes, survival probabilities, detection probabilities). These initial conditions were chosen to encompass the range of parameter values seen in the 1993 and 1994 Snake River juvenile salmonid survival studies. The comparisons among the three estimation methods included average interval width, interval symmetry, and interval coverage.
Results
We found that the three methods produced nearly identical results in cases where a large number of fish were detected after the initial release, whether this was due to a large release size, a high detection probability, or a high survival probability. In simulations with fewer fish detected after release, the normal theory intervals typically provided nominal coverage and the most narrow width but with a high degree of asymmetry, indicating that the intervals tended to underestimate the survival probability more often than overestimating it. In these cases, the bootstrap percentile and profile likelihood methods also produced intervals with nominal coverage, but with much better symmetry at the expense of slightly wider intervals.
Recommendations
In the simulations, the bootstrap intervals and profile likelihood intervals both provided nominal coverage and had the additional property of symmetry. Due to the high computational cost of the bootstrap procedure it is recommended that only the profile likelihood procedure be additionally implemented into the SURPH survival analysis software. The choice between normal theory intervals and profile likelihood intervals becomes a choice between the narrower, asymmetric intervals resulting from the normal theory, and the wider, symmetric intervals based on the profile likelihood. If there is equal concern about overestimation and underestimation of parameters, symmetric intervals would be desirable and the profile likelihood method should be used. Thus, our recommendation is that profile likelihood methods be incorporated into SURPH and that the profile likelihood should be the method for constructing confidence intervals for survival probabilities for juvenile salmonids on the Columbia and Snake River systems. For most river conditions, the resulting intervals will be similar to the normal theory intervals providing added assurance of reliable estimates.
Final Publication: Lowther, A.B. and J.R. Skalski. 1996. Design and Analysis of Salmonid Tagging Studies in the Columbia Basin, Volume VII: Monte-Carlo Comparison of Confidence Interval Procedures for Estimating Survival in a Release-Recapture Study, with Applications to Snake River Salmonids. Technical Report DOE/BP-02341-5. Portland, OR : Bonneville Power Administration.