Defense Date


Document Type


Degree Name

Master of Science



First Advisor

Jessica Ketchum


In the pharmaceutical setting, it is often necessary to establish the shelf life of a drug product and sometimes suitable to assess the risk of product failure at the desired expiry period. The current statistical methodology use confidence intervals for the predicted mean to establish the expiry period and prediction intervals for a predicted new assay value or a tolerance interval for a proportion of the population for use in a risk assessment. A major concern is that most methodology treat a homogeneous subpopulation, say batch, either as a fixed effect and therefore uses a fixed-effects regression model (Graybill, 1976) or as a mixed-effects model limited to balanced data structures (Jonsson, 2003). However, batch is definitely a random effect as this fact has been reflected by some recent methodology [Altan, Cabrera and Shoung (2005), Hoffman and Kringle (2005)]. Thus, to assess the risk of product failure at expiry, it is necessary to use tolerance intervals since they provide an estimate of the proportion of assay values and/or batches failing at the expiry period. In this thesis, we illustrate the methodology described by Jonsson (2003) to construct β-expectation tolerance limits for longitudinal data in a random-effects setting. We underline the limitations of Jonsson’s approach to constructing tolerance intervals and highlight the need for a better methodology.


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Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

December 2008

Included in

Biostatistics Commons