### Quantile Regression: Reference range of Thyroid function test in pregnancy

#### Kevin Brosnan, Dr. Kevin Hayes & Dr. Norma Bargary

##### Final Year Project 2014

Thyroid disease is the commonest endocrine condition in women of childbearing age and complicates approximately 1-2% of pregnancies. The hyper-metabolic state of normal pregnancy makes clinical assessment of thyroid function more difficult and therefore thyroid function often needs to be checked biochemically. However physiological changes of pregnancy, including 50% plasma volume expansion, increased thyroid binding globulin production and a relative iodine defficiency, mean that thyroid hormone reference ranges for non-pregnant women may not be appropriate in pregnancy.

One acceptable approach for establishing legitimate reference ranges requires that a Box-Cox transformation be applied to the data, and prediction ranges calculated using using classical polynomial regression. Alternatively, non-parametric smoothing such as quantile can be used to estimate the 2.5% and 97.5% percentiles. Although this approach provides an estimate of the reference range, it does not routinely quantify the precision of the end points of this reference range. This is the aim of the project.

### Thyroid Data - Select a column for Validation

### User Inputs

### Model Fit

### Descriptive Statistics

### Results

### Research Team

Kevin Brosnan is a passionate developer of statistical techniques to address real life problems. He completed a B.Sc in Mathematical Sciences at the University of Limerick, with a major in Statistics in August 2014. Kevin is currently pursuing a Ph.D. at the University of Limerick with a thesis titled “Statistical Modelling with Application to Flow Cytometry & Sports Science”. Flow Cytometry is used across industries such as medical diagnostics and dairy sciences, however the current statistical methods do not compliment the technology used. Developing these improved statistical methods is the aim of the research. The fair and impartial refereeing of elite athletics is the research area of sports science which Kevin is currently working on. Kevin also has vast industry experience in Management Consultancy (Accenture), Banking (AIB) and developing analytic tools for multinational companies (Accenture).

Dr. Kevin Hayes holds the position of senior lecturer (statistics) in the department of mathematics and statistics and is co-PI (with Professors Stephen O'Brien, and Eugene Benilov) of the applied mathematics and statistics SFI funded research group MACSI. Dr. Hayes' main research area concerns the statistical analysis of curve data as applied to the area of human biomechanics, in collaboration with Doctors Drew Harrison (PESS) and Norma Bargary (MACSI). Kevin's current research is concerned with developing mathematical and statistical models to help understand the relationship and interaction between biomechanical function and muscular stimulus. He also has considerable experience analysing large epidemiological / population based data sets and data from biomedical applications.

Dr. Norma Bargary graduated in 2005 from the University of Limerick with a BSc. in Mathematical Sciences and Computing (majoring in Statistics). Norma subsequently began a PhD at UL in 2005 with Dr. Kevin Hayes, examining the use of the linear mixed effects model in functional data analysis. She graduated in 2008 and then spent a year lecturing statistics in UL. In 2009 Dr. Bargary began a postdoctoral position with Professor John Hinde at NUI Galway, developing models to cluster time-course microarray data. In 2011, she was appointed as lecturer in statistics at UCD and began the position in January 2012. This was a joint appointment between the School of Mathematical Sciences and Systems Biology Ireland. In September 2013 she took up her current lecturing position at the University of Limerick. Norma's main area of interest is in the statistical modelling of time-course/functional data using the mixed effects model. Previously, she has applied these methods to analyse biological data, e.g. RNA-seq, ChIP-seq, mass-spectometry, microarray data and biomechanics data.

### Source Code

Full source code is available from the quantileregression github repository.

### References

- shiny: Chang, W., Cheng J., Allaire, J.J., Xie, Y. & McPherson, J. (2013). shiny: Web Application Framework for R. R package version 0.11.1
- shinydashboard:Chang, W. (2015). shinydashboard: Create Dashboards with Shiny. R package version 0.5.1
- quantreg: Koenker, R. et al. (2016). quantreg: Quantile Regression. R package version 5.26
- DT: Xie, Y. (2015). DT: A Wrapper of the JavaScript Library 'DataTables'. R package version 0.1.57
- bayesQR: Benoit, D.F., Al-Hamzawi, R., Yu, K. & Van den Poel, D.. (2014). bayesQR: Bayesian quantile regression. R package version 2.2
- lqmm: Geraci, M. (2016). lqmm: Linear Quantile Mixed Models. R package version 1.5.3