Master of Science (MS)

<p>Community-based human services have traditionally been provided by autonomous service agencies. They have their own funding source and independent process. Integration has been advocated as a key strategy to integrate different agencies together to provide multiple services for a targeted community. The Children’s Treatment Network (CTN) of Simcoe York is a network of agencies and organizations providing services to children with multiple needs and their families in Simcoe County and York Region. This study was designed to evaluate the different levels of integrated service approaches for children on outcomes. The study consisted of two parts: phase I and phase II measurement.</p> <p>Our project covered phase I measurement with the following objectives. Clinically, we aimed to evaluate agencies’ integration in the network, promote discussion, and determine any interrelationship between a network’s integration and its functioning. The statistical objectives were to quantify the network integration for agency, to represent the overall integration, to quantify the association between network’s integration and functioning and to assess the sensitivity of results.</p> <p>We measured agencies’ integration through measuring its agreement in collaboration with other agencies in the network. The higher agreement in collaboration indicates a better services integration. We defined four different agreement measures from different perspectives. The agreement based on group’s perception was defined to be the primary measure. We used mean difference, percentage and the Kappa statistic to measure the agreement for each agency. Correlation and regression analyses were applied in investigating the association between network’s integration and its functioning. The sensitivity of the results was analyzed by examining the re-sampling bias of bootstrapping regression models.</p> <p>Agreement measures were consistent for each agency. In Simcoe, agencies had an average agreement 0.874 (S.D. 0.213) in mean difference, 46.63 (S.D. 12.91) in percentage and 0.258 (S.D. 0.143) in Kappa. Agencies of York had average agreements of 0.662 (S.D. 0.204), 49.36 (S.D. 13.06) and 0.282 (S.D. 0.121), respectively. Agency 10 and 33 in Simcoe and Agency 14 in York were found to have the highest agreement. Agency 3 and 21 in Simcoe and Agency 8 and 9 in York, on the other hand, were found to have the lowest agreement. Different graphical displays illustrated that the overall agreement in collaboration was low and the agencies in York generally had a higher agreement. Correlation analysis showed that synergy and agencies’ perception of pros and cons were significantly correlated with the primary percentage agreement. In regression analysis, we did not find any significant functioning component. However, synergy was found to be much more associated with agreement than the other components. The estimates were 11.48% (-1.03%, 24.00%) and 11.21% (-2.48%, 24.90%) in un-weighted and weighted models respectively. Bootstrapping regression analysis showed that the results were robust to a change of sample.</p> <p>We concluded that the level of integration of CTN was low because the agencies generally had poor agreement in collaboration. Synergy was the most important component associated with the network’s integration. Other functioning components detected were also associated with the integrating process but were less clinically important. We discussed the statistical approaches used in other contexts and some of their strength and weaknesses. We also considered some key limitations of the study. This study was a baseline measurement of CTN of Simcoe York for further analysis. The results provided a basis for future enhancement of integration of the network. Our experiences also provided ideas for improving design and analysis in integrated network measurement.</p> / Master of Science (MS)

<p>A new sampling method was developed for use in areas where standard methods for sampling from a population may be difficult or impossible to use. The new method uses Global Positioning System (GPS) points and satellite photos to identify datapoints (locations) within selected towns. A circle (of a specified radius) is drawn around each datapoint, which may include several buildings or sometimes none. A single household is sampled from each circle and then one adult (aged 18 years or older) is interviewed from the household, based on who had the most recent birthday. Two issues arise with this new sampling method: first, the probability of sampling any household may vary, depending on the datapoint its chosen from; and second, circles surrounding the chosen datapoints may overlap. The thesis used simulations to see whether the first issue affected the point estimates of two population parameters. The second issue was too complex to investigate so it was ignored when sampling households. Simulations were run to test the sampling method on two different hypothetical towns, one with denser population than the other. Results from the simulations showed that estimates did not always match what was expected, but the observed differences were not substantial. It was presumed that the reason for differences was due to the issue of multiple probabilities for selection as well as overlapping circles (which had been ignored during sampling), since both issues were inherent in this sampling method. Although some differences were observed from true values, they appeared not to be very different from the population values, so I conclude that this sampling method is a useful one. Future work may look more closely at understanding the issue of overlapping circles and how it affects the point estimates.</p> / Master of Science (MSc)

<p>The money put into health care has been increasing dramatically. Comparison of different programs is important in helping government to make decision as to what health care services to be provided. The cost-effectiveness of different health care programs can be compared based on the improvement of a person's health states and the cost it incurred. To measure the health states of a person, health utility scores can be used. But health utility data exhibit features such as non-normality, heteroscedasticity of variances, and the majority of observations attaining values close to or at the maximum of the measurement scale. This brings challenges to analyzing health utility data. For example, linear regression with the assumption of normality might not be valid since non-normality is present in health utility data. To address these problems, other methods are used. In this study, we investigate the performance of generalized additive models (GAMs) in handling health utility data. In GAMs, the relationship between the response and the predictor variables can be non-linearly defined. So GAM methods give more options in the assumption of the relationship between the response and the predictors. For comparison, we also use ordinary least squares. To evaluate the performance of generalized additive models, simulation is used. Data are generated from the simulation model, and GAMs will be used to fit the simulated data. Bias and coverage probability will be used to assess the performance of the GAM method. A comparison between OLS and GAM will be also be done in the study. And, as an illustration, GAM will be applied to a real data set called Diabetes Hamilton which "vas collected from some diabetic patients who participated in a community program based in Hamilton, Ontario.</p> <p>When GAM is applied to the real data set, similar results to the OLS method in terms of the estimates of the parameters is observed. Both methods give similar coefficient values for each parameter. From the simulation results, the estimate given by the GAM method is closer to the true value than the OLS method in general. The bias produced by the GAM is smaller than the OLS method. So overall, GAM method seems to be valid in analyzing the data set such as those used in this study and also the general health utility data.</p> / Master of Science (MSc)

<p>In the analysis of lifetime data, heterogeneity may be present in many situations. This heterogeneity is also referred to as frailty. Analysis that ignore frailty when it is present leads to incorrect inferences. In lifetime analysis, Cox proportional hazards model is commonly used to measure the effects of covariates. The covariates may fail to fully account for the true differences in risk. This may be due to an existence of another variable that is ignored in the model but can be explained by random frailty. Including frailty in the model can avoid underestimation and overestimation of parameters and also correctly measure the effects of the covariates on the response variable. This thesis presents an extension of Cox model to parametric frailty model in which the exponential and Weibull distributions are used as the distributions of baseline hazard, and the gamma and Weibull distributions are used as frailty distributions. We examine the maximum likelihood estimation procedures and propose the use of Monte Carlo integration method or quadrature method in complicated cases where explicit solutions to the likelihood functions can not be obtained. The gamma distribution is one of the most commonly used distributions for frailty. It has a closed form likelihood function that can be readily maximized. In this thesis, we study the performance of the Weibull distribution as a frailty distribution and compare with the gamma frailty model. Through simulation studies, the performance of the parameter estimates are evaluated. The effects of increasing the sample size and cluster size separately are also studied through Monte Carlo simulations. The Akaike Information Criteria (AIC) is used to compare the performance of the gamma and Weibull frailty models. The developed methods are then illustrated with numerical examples.</p> / Master of Science (MSc)

This ethnicity-based research based on Canadian Community Health Survey (CCHS) 2.2 demonstrates that majority people of all ethnic groups in Canada do not consume adequate times/servings of fruit and vegetables per day which might pose a potential risk factor for long-term diseases. The term 'ethnicity' is defined in this analysis with 'common cultural traits' instead of 'common gene pool'. Hence, Canadian diverse population has been decomposed into 14 explicit cultural/racial groups in CCHS 2.2. Significant differences in the consumption of 5 or more times/servings of fruit and vegetables per day exist among Canadian ethnic groups. Southeast Asian, Aboriginal people of North America, West Asian, Korean, Japanese and Chinese ethnic groups tend to exhibit the lowest intake of 5 or more times/servings of fruit and vegetables per day. As CCHS 2.2 is a complex survey, logistic regressions with bootstrap weights have been run to delineate the association between fruit & vegetables, race/ethnicity, and long-term diseases. Ethnic people with lower intake of total fruit and vegetables, fruit, and green salad have reported themselves to be more susceptible to long-term health conditions and chronic conditions. Low consumption of carrot and other vegetables are found to be responsible for bowel disorder and intestinal ulcers along with the long-term and chronic health conditions. Aboriginal people of North America has the highest propensity to contract most of the long-term diseases among all ethnic groups as opposed to the While ethnic group which may have an strong association with their lowest Fruit and vegetables intake. / Master of Science (MSc)

<p>Children with acute lymphoblastic leukemia (ALL) are at high risk for getting thromboembolism (TE), which is a serious complication leading to morbidity and mortality. As treatment protocols have been developed achieving the cure rates as high as 80% [39], study efforts need to turning to evaluating the risk and management of associated TE. Published studies in this field have been mostly exploratory and have had different results in terms of screening TE risk factors predisposing to TE.</p> <p>Based on the records of 150 ALL children treated with central venous line (CVL) from 1995 to 2005 at McMaster Children's Hospital, this study was conducted to evaluate the prevalence ofTE, to explore the association between TE and infection, and to screen TE and Infection risk factors disposing children with ALL for TE and for Infection. The prevalence ofTE was estimated as 15 .07% (9.27%, 20.87%). Logistic regressions, Bayesian approaches, in combination with multiple imputation techniques, were employed to estimate predictors' odds ratios and their 95% confidence (credibility) intervals. The study suggested two significant factors, CVL functionality and ANC category for infection, and no significant factors for TE.</p> <p>As a comparative and supplementary tool to the traditional parametric analyses, we conducted Classification and Regression Trees (CART) modeling, by using three software packages, with intention to visualize predictors of TE and Infection by level of importance. SAS EM 5.0, SPSS 14.0 and S-Plus 6.1 were compared in their tree misclassifications based on our data and their features of tree growth algorithms, validation techniques, missing data handling, model pruning / recovering, output setting, tool tabs transparency, and advantages. SPSS 14.0 and SAS EM 5.0 are recommended based on our experience, though the strengths and weaknesses of each package should be weighted according to the users and the problem natures.</p> <p>The limitations of this exploratory study such as small sample size, missing values, imbalance between data categories, the lack of information about the timing of treatment and the lack of cross-validation techniques in some CART modeling packages led biases to our results. Large prospective cohort studies with few missing values are critical to achieve more accurate results.</p> / Master of Science (MSc)

<p>One of the fundamental assumptions of measurement theory is that a set of its items forming a test is unidimensional. The purposes of this dissertation were (1) to review various methods for determining unidimensionality and to assess the rationale of those methods; (2) to attempt to clarify the term unidimensionality, and to show how it differs from other terms often used interchangeably; and (3) to assess the effectiveness of various indices proposed to determine unidimensionality.</p> <p>Indices based on answer patterns, reliability, component and factor analysis, and latent traits were reviewed and it was shown that many of these lacked a rationale, that for many the sampling distributions were not known, and that many were adjustments to an established index to take into account some criticism of it. Altogether 87 indices were reviewed.</p> <p>It was demonstrated that unidimensionality often is used interchangeably with reliability, internal consistency, and homogeneity. Reliability was defined as the ratio of the true score variance to obsesrved score variance. Internal consistency has been used often as a synonym for unidimensionality, and it also denotes a group of methods that are intended to estimate reliability. Internal consistency methods are based on the variances and covariances of test-items, and depend on only one administration of a test. Homogeneity seems to refer more specifically to the similarity of the item correlations, but the term is often used as a synonym for unidimensionality. Unidimensionality was defined as the existence of one latent trait underlying the data. The usefulness of the terms internal consistency and homogeneity was questioned.</p> <p>A Monte Carlo simulation was conducted to assess the 87 indices under known conditions. A three-parameter, multivariate, logistic latent-trait model was used to generate item responses. Difficulty, guessing, discrimination, and the number of factors underlying the data were varied.</p> <p>Many of the indices were highly correlated, some resulted in estimates outside their theoretical bounds, and most were particularly sensitive to the intercorrelations between the factors. Indices based on answer patterns, reliability, component analysis, linear factor analysis, and one the one-parameter latent trait model were ineffective. The sums of absolute residuals from a nonlinear factor analysis (specifying one factor with cubic terms) and from two-parameter latent trait models (Christoffersson, 1975; McDonald, 1980; Muthen, 1978) were able to discriminate between cases with one latent trait and cases with more than one latent trait.</p> / Doctor of Philosophy (PhD)

The contemporary risk management practice emphasizes the interplay of multilevel risks, of which the systematic and systemic risks are considered the main culprits of catastrophic losses. With this in mind, this thesis investigates three important topics in quantitative risk management, in which the systematic and systemic risks play a devastating role. First of all, we center on the design of reinsurance policies that accommodate the joint interests of the insurer and reinsurer by drawing upon the celebrated notion of Pareto optimality in the context of a distortion-risk-measure-based model. Such a topic is of considerable practical interest in the current post financial crisis era when people have witnessed the significant systemic risk posed by the insurance industry and the vulnerability of insurance companies to systemic events. Specifically, we characterize the set of Pareto-optimal reinsurance policies analytically and introduce the Pareto frontier to visualize the insurer-reinsurer trade-off structure geometrically. Another enormous merit of developing the Pareto frontier is the considerable ease with which Pareto-optimal reinsurance policies can be constructed even in the presence of the insurer's and reinsurer's individual risk constraints. A strikingly simple graphical search of these constrained policies is performed in the special cases of value-at-risk and tail value-at-risk. Secondly, we propose probabilistic and structural characterizations for insurance indemnities that are universally marketable in the sense that they appeal to both policyholders and insurers irrespective of their risk preferences and risk profiles. We begin with the univariate case where there is a single risk facing the policyholder, then extend our results to the case where multiple possibly dependent risks co-exist according to a mixture structure capturing policyholder's exposure to systematic and systemic risks. Next, we study the asymptotic behavior of the loss from defaults of a large credit portfolio. We consider a static structural model in which latent variables governing individual defaults follow a mixture structure incorporating idiosyncratic, systematic, and systemic risks. The portfolio effect, namely the decrease in overall risk due to the portfolio size increase, is taken into account. We derive sharp asymptotics for the tail probability of the portfolio loss as the portfolio size becomes large and our main finding is that the occurrence of large losses can be attributed to either the common shock variable or systematic risk factor, whichever has a heavier tail. Finally, we extend the asymptotic study of loss from defaults of a large credit portfolio under an amalgamated model. Aiming at investigating the dependence among the risk components of each obligor, we propose a static structural model in which each obligor's default indicator, loss given default, and exposure at default are respectively governed by three dependent latent variables with exposure to idiosyncratic, systematic, and systemic risks. The asymptotic distribution as well as the asymptotic value-at-risk and expected shortfall of the portfolio loss are obtained. The results are further refined when a specific mixture structure is employed for latent variables.

In this thesis, we look into two important issues that involve the interplay between insurance and finance, namely the pricing of insurance-linked securities (ILS) and the liquidation risk in insurance under contemporary regulatory frameworks. First, we employ the utility indifference and risk-neutral pricing approaches to price ILS. For the former, we extend the utility indifference pricing approach widely used in one-period models to a multi-period case with intermediate payments by working with time-$0$ equivalent values and solving, through backward induction, a multi-period optimization problem. We offer insights into the issues regarding coherence and time consistency of the ask and bid indifference prices obtained. For the latter, we focus on three desirable properties of a pricing measure in an arbitrage free and incomplete market, namely, equivalence, structure preserving, and amplifying unfavorable events. We also propose a downside risk process which enables us to quantify the riskiness of an ILS and to characterize the property of amplifying unfavorable events under our framework. Second, we quantify the rehabilitation proceeding in insurance, which is akin to Chapter 11 reorganization of the U.S. Bankruptcy Code, and we conduct a probabilistic analysis of the liquidation risk of an insurance company having the option of rehabilitation. In doing so, we construct a three-barrier model to describe the solvent and insolvent states in which the surplus process follows either different time-homogeneous diffusions or different double exponential jump-diffusions. We derive analytical expressions for the liquidation probability and the moment generating function of the liquidation time with a fixed or an independent exponentially distributed grace period.