Confidence intervals for the mean of diagnostic test charge data containing zeros

In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero va lues, and the nonzero values can often be modeled by a log-normal distribut ion. Under such a model, a-e propose three different interval estimation pr ocedures: a percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are on ly first-order accurate and that the bootstrap-based one-sided confidence i nterval is second-order accurate. For two-sided confidence intervals, all t hree proposed methods are second-order accurate. A simulation study in fini te-sample sizes suggests all three proposed intervals outperform a widely u sed minimum variance unbiased estimator (MVUE)-based interval except for th e case of one-sided lower end-point intervals when the skewness is very sma ll. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size i s small, the bootstrap method still yields the best coverage accuracy unles s the skewness is very small, in which case the bias-corrected ML method ha s the best accuracy. When the sample size is large, all three proposed inte rvals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adu lts with depression.