Degree Type


Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Alicia L. Carriquiry

Second Advisor

Wayne A. Fuller


Monitoring vitamin D status in sub-populations is important to reduce the risk of negative heath outcomes associated with low vitamin D such as increased risk of bone fractures, rickets, and osteoporosis. Information about the nutritional status of groups is critical in the development of nutritional guidelines for a healthy diet. Measuring nutrient intake precisely is challenging, and biomarkers may be more closely associated with the health endpoint of interest. Thus, biomarkers are likely to provide less noisy measurements to estimate the association between diet and health. Serum 25-hydroxy vitamin D (25(OH)D) has been suggested as a biomarker to monitor vitamin D status (IOM (2011)). It is well established that 25(OH)D has a negative association with serum intact parathyroid hormone (iPTH) (IOM (2011); WHO & FAO (2004)). The relationship between iPTH and 25(OH)D is of interest to nutrition epidemiologists, because iPTH has a better understood relationship with bone health than 25(OH)D. More specifically, excessive production of iPTH is linked to poor bone health.

Measurements of iPTH and 25(OH)D are not only subject to between-person variability, but also within-person variability. The long-run average of repeated measurements of iPTH is called usual iPTH. Similarly, usual 25(OH)D is the long-run average of repeated measurements of 25(OH)D. The usual quantities are a better measure of an individual's habitual level of iPTH or 25(OH)D, than the error-prone repeated measurements. The usual quantities are not observable in practice. Therefore, the observed measurements are error-prone measurement of the usual quantities. We propose an estimation method for nonlinear regression models describing the association between usual iPTH and usual 25(OH)D when both variables are subject to measurement error. Rather than making standard assumptions on the distribution of the covariate, we propose a semi-parametric likelihood approach that allows us to approximate the distribution of the unobservable covariate with few assumptions on the shape of the distribution. We also investigate approaches to estimation of the value of usual 25(OH)D, above which, usual iPTH no longer decreases. This is known as the threshold value of usual 25(OH)D.

Copyright Owner

Maria LaVonne Joseph



File Format


File Size

145 pages