Correlation Coefficient Inference on Censored Bioassay Data

ABSTRACT

In vaccine clinical trials, immunologic responses sometimes can not be accurately measured by bioassays. For example, a serial dilution assay usually reports the range of the response instead of the exact value. In some other assays, the measurement is not available if the response is lower than the assay's detection limit. In both cases, the measurements are censored. We are interested in computing the confidence interval for the correlation coefficient of two assay measurements that are subject to censoring. We propose using the maximum likelihood method to estimate the correlation coefficient, and constructing its confidence interval based on the second-order Taylor's expansion of the Fisher Z transformation. The method can be viewed as an extension of the Fisher Z transformation to the case of censored data. Extensive simulations show that the proposed method provides satisfactory coverage probabilities under finite sample sizes. The proposed method performs well compared with existing methods, but it is computationally much simpler. In addition, the proposed method works with many types of censored data in a similar way. Furthermore, we proposed an Monte Carlo exact test to assess the goodness-of-fit of the model.

Key Words:

• Coarse data
• Confidence interval
• Exact test
• Fisher Z transformation
• Goodness-of-fit
• Multivariate normality.

ACKNOWLEDGMENTS

Liang Li's work was partially supported by grant CA53786 from the National Cancer Institute and grant HL62252 from the National Heart Lung and Blood Institute. Most of the work was done during the first author's summer internship at Merck Research Laboratories.

Notes

There are 10% and 60% left- and right-censoring with X, and 10% left-censoring with Y. Left right error rate is the robability that ρ is to the left right of the CI. Result is based on 6000 simulation runs. Coverage probabilities between 94.43% and 95.53% are considered as not significantly different from 95% at the 0.05 level. Wald and proposed method use the same MLE of ρ.

The percentages of left- and right-censoring of X are both 10%. Result is based on 6000 simulation runs. Coverage probabilities between 94.43% and 95.53% are considered as not significantly different from 95% at the 0.05 level.

There are 10% left- and right-censoring with X, and 30% left-censoring with Y. Left right error rate is the probability that ρ is to the left right of the CI. Result is based on 1000 simulation runs.

The Wald, proposed, and profile likelihood methods all use MLE as their parameter estimates. The numbers in brackets are SE estimates for the MLEs.