Statistical modelling of the consistency of symptoms reported during hypoglycaemia for individual patients
Zulkaﬂi, Hani Syahida
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In this thesis, we use Bayesian methodology and Markov chain Monte Carlo tech- niques to construct logistic-type latent variable statistical models for estimating the consistency of hypoglycaemic symptoms experienced by individual diabetic patients. Consistency in reporting experienced symptoms of hypoglycaemia is related to early detection of symptoms and is therefore important for fast corrective action. Based on a model developed by Zammit et al. (2011) we classify symptoms into diﬀerent groups and consider between-groups variability. Our work also explores a number of possible symptom-experiencing thresholds that can be used in the consistency model. To evaluate the performance of each consistency model, we develop ideas based on Bayesian latent residuals (Streftaris and Gibson, 2012) to check on the models’ ﬁt and utilise posterior predictive checking methodology (Gelman et al., 1996 and Streftaris et al., 2013) to assess relevant performance. The impact of using data from hypo- glycaemic episodes occurring within 24 hours from an earlier episode is also explored using various approaches, as previous work claims that such episodes might lead to di- minished intensity of the episodes. Using generalised linear-type model methodology, we investigate how various factors such as age, gender, type and duration of diabetes, body mass index, retinopathy and others, or their interaction, can aﬀect patients’ consistency. Additionally, we develop a hierarchical model that is able to estimate consistency and identify factors aﬀecting it in a single setting. Finally, we work on determining the best sets of variables for a predictive model. For this purpose, we use Gibbs variable selection and a stepwise regression procedure. Due to model un- certainty, we apply Bayesian model averaging to a number of selected models given by Gibbs variable selection.