Generalized P-Values and Confidence Intervals: A Novel Approach for Analyzing Lognormally Distributed Exposure Data

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA.
Journal of Occupational and Environmental Hygiene (Impact Factor: 1.17). 12/2006; 3(11):642-50. DOI: 10.1080/15459620600961196
Source: PubMed


The problem of assessing occupational exposure using the mean of a lognormal distribution is addressed. The novel concepts of generalized p-values and generalized confidence intervals are applied for testing hypotheses and computing confidence intervals for a lognormal mean. The proposed methods perform well, they are applicable to small sample sizes, and they are easy to implement. Power studies and sample size calculation are also discussed. Computational details and a source for the computer program are given. The procedures are also extended to compare two lognormal means and to make inference about a lognormal variance. In fact, our approach based on generalized p-values and generalized confidence intervals is easily adapted to deal with any parametric function involving one or two lognormal distributions. Several examples involving industrial exposure data are used to illustrate the methods. An added advantage of the generalized variables approach is the ease of computation and implementation. In fact, the procedures can be easily coded in a programming language for implementation. Furthermore, extensive numerical computations by the authors show that the results based on the generalized p-value approach are essentially equivalent to those based on the Land's method. We want to draw the attention of the industrial hygiene community to this accurate and unified methodology to deal with any parameter associated with the lognormal distribution.

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    • "Generalized procedures have been successfully applied to several problems of practical importance. The areas of applications include comparison of means, testing and estimation of functions of parameters of normal and related distributions (Weerahandi, [2] [3] [4] [5], Krishnamoorthy and Mathew [6], Johnson and Weerahandi [7], Gamage, Mathew and Weerahandi [8]); testing fixed effects and variance components in repeated measures and mixed effects ANOVA models (Zhou and Mathew [9], Gamage and Weerahandi [10], Chiang [11], Krishnamoorthy and Mathew [6], Weerahandi [5], Mathew and Webb [12], Arendacka [13]); interlaboratory testing (Iyer, Wang and Mathew [14]); bioequivalence (McNally, Iyer and Mathew [15]); growth curve modeling (Weerahandi and Berger [16], Lin and Lee [17]); reliability and system engineering (Roy and Mathew [18], Tian and Cappelleri [19], Mathew, Kurian and Sebastian [20]); process control (Burdick, Borror and Montgomery [21], Mathew, Kurian and Sebastian [22]); environmental health (Krishnamoorthy, Mathew and Ramachandran [23]) and many others. The simulation studies in Johnson and Weerahandi [7], Weerahandi [4] [5] Zhou and Mathew [9], Gamage and Weerahandi [10], among others have demonstrated the success of the generalized procedure in many problems where the classical approach fails to yield adequate confidence intervals. "
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