On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Application of signal detection methods to fisheries management

The abundance of many commercially important fish stocks are declining and this has led to widespread concern on the performance of traditional approach in fisheries management. Quantitative models are used for obtaining estimates of population abundance and the management advice is based on annual harvest levels (TAC), where only a certain amount of catch is allowed from specific fish stocks. However, these models are data intensive and less useful when stocks have limited historical information. This study examined whether empirical stock indicators can be used to manage fisheries. The relationship between indicators and the underlying stock abundance is not direct and hence can be affected by disturbances that may account for both transient and persistent effects. Methods from Statistical Process Control (SPC) theory such as the Cumulative Sum (CUSUM) control charts are useful in classifying these effects and hence they can be used to trigger management response only when a significant impact occurs to the stock biomass. This thesis explores how empirical indicators along with CUSUM can be used for monitoring, assessment and management of fish stocks. I begin my thesis by exploring various age based catch indicators, to identify those which are potentially useful in tracking the state of fish stocks. The sensitivity and response of these indicators towards changes in Spawning Stock Biomass (SSB) showed that indicators based on age groups that are fully selected to the fishing gear or Large Fish Indicators (LFIs) are most useful and robust across the range of scenarios considered. The Decision-Interval (DI-CUSUM) and Self-Starting (SS-CUSUM) forms are the two types of control charts used in this study. In contrast to the DI-CUSUM, the SS-CUSUM can be initiated without specifying a target reference point (‘control mean’) to detect out-of-control (significant impact) situations. The sensitivity and specificity of SS-CUSUM showed that the performances are robust when LFIs are used. Once an out-of-control situation is detected, the next step is to determine how much shift has occurred in the underlying stock biomass. If an estimate of this shift is available, they can be used to update TAC by incorporation into Harvest Control Rules (HCRs). Various methods from Engineering Process Control (EPC) theory were tested to determine which method can measure the shift size in stock biomass with the highest accuracy. Results showed that methods based on Grubb’s harmonic rule gave reliable shift size estimates. The accuracy of these estimates can be improved by monitoring a combined indicator metric of stock-recruitment and LFI because this may account for impacts independent of fishing. The procedure of integrating both SPC and EPC is known as Statistical Process Adjustment (SPA). A HCR based on SPA was designed for DI-CUSUM and the scheme was successful in bringing out-of-control fish stocks back to its in-control state. The HCR was also tested using SS-CUSUM in the context of data poor fish stocks. Results showed that the scheme will be useful for sustaining the initial in-control state of the fish stock until more observations become available for quantitative assessments.

Lower extremity amputation in people with diabetes: Trends and determinants

Introduction: The prevalence of diabetes is rising rapidly. Assessing quality of diabetes care is difficult. Lower Extremity Amputation (LEA) is recognised as a marker of the quality of diabetes care. The focus of this thesis was first to describe the trends in LEA rates in people with and without diabetes in the Republic of Ireland (RoI) in recent years and then, to explore the determinants of LEA in people with diabetes. While clinical and socio-demographic determinants have been well-established, the role of service-related factors has been less well-explored. Methods: Using hospital discharge data, trends in LEA rates in people with and without diabetes were described and compared to other countries. Background work included concordance studies exploring the reliability of hospital discharge data for recording LEA and diabetes and estimation of diabetes prevalence rates in the RoI from a nationally representative study (SLAN 2007). To explore determinants, a systematic review and meta-analysis assessed the effect of contact with a podiatrist on the outcome of LEA in people with diabetes. Finally, a case-control study using hospital discharge data explored determinants of LEA in people with diabetes with a particular focus on the timing of access to secondary healthcare services as a risk factor. Results: There are high levels of agreement between hospital discharge data and medical records for LEA and diabetes. Thus, hospital discharge data was deemed sufficiently reliable for use in this PhD thesis. A decrease in major diabetes-related LEA rates in people with diabetes was observed in the RoI from 2005-2012. In 2012, the relative risk of a person with diabetes undergoing a major LEA was 6.2 times (95% CI 4.8-8.1) that of a person without diabetes. Based on the systematic review and meta-analysis, contact with a podiatrist did not significantly affect the relative risk (RR) of LEA in people with diabetes. Results from the case-control study identified being single, documented CKD and documented hypertension as significant risk factors for LEA in people with diabetes whilst documented retinopathy was protective. Within the seven year time window included in the study, no association was detected between LEA in patients with diabetes and timing of patient access to secondary healthcare for diabetes management. Discussion: Many countries have reported reduced major LEA rates in people with diabetes coinciding with improved organisation of healthcare systems. Reassuringly, these first national estimates in people with diabetes in the RoI from 2005 to 2012 demonstrated reducing trends in major LEA rates. This may be attributable to changes in diabetes care and also, secular trends in smoking, dyslipidaemia and hypertension. Consistent with international practice, LEA trends data in Ireland can be used to monitor quality of care. Quantifying this improvement precisely, though, is problematic without robust denominator data on the prevalence of diabetes. However, a reduction in major diabetes-related LEA rates suggests improved quality of diabetes care. Much controversy exists around the reliability of hospital discharge data in the RoI. This thesis includes the first multi-site study to explore this issue and found hospital discharge data reliable for the reporting of the procedure of LEA and diagnosis of diabetes. This project did not detect protective effects of access to services including podiatry and secondary healthcare for LEA in people with diabetes. A major limitation of the systematic review and meta-analysis was the design and quality of the included studies. The data available in the area of effect of contact with a podiatrist on LEA risk are too sparse to say anything definitive about the efficacy of podiatry on LEA. Limitations of the case-control study include lack of a diabetes register in Ireland, restricted information from secondary healthcare and lack of data available from primary healthcare. Due to these issues, duration of disease could not be accounted for in the study which limits the conclusions that can be drawn from the results. The model of diabetes care in the RoI is currently undergoing a re-configuration with plans to introduce integrated care. In the future, trends in LEA rates should be continuously monitored to evaluate the effectiveness of changes to the healthcare system. Efforts are already underway to improve the availability of routine data from primary healthcare with the recent development of the iPCRN (Irish Primary Care Research Network). Linkage of primary and secondary healthcare records with a unique patient identifier should be the goal for the future.

Insertion of metal oxides into block copolymer nanopatterns as robust etch masks for nanolithography

Directed self-assembly (DSA) of block copolymers (BCPs) is a prime candidate to further extend dimensional scaling of silicon integrated circuit features for the nanoelectronic industry. Top-down optical techniques employed for photoresist patterning are predicted to reach an endpoint due to diffraction limits. Additionally, the prohibitive costs for “fabs” and high volume manufacturing tools are issues that have led the search for alternative complementary patterning processes. This thesis reports the fabrication of semiconductor features from nanoscale on-chip etch masks using “high χ” BCP materials. Fabrication of silicon and germanium nanofins via metal-oxide enhanced BCP on-chip etch masks that might be of importance for future Fin-field effect transistor (FinFETs) application are detailed.