Inaug. Diss.--Zürich. / Vita. Includes bibliographical references.

This research study had shown various probable rational methods of quantifying subjective information in a probability distribution with particular reference to the evaluation of economic projects by computer simulation. Computer simulation to give all the possible outcomes of a capital project using the Monte Carlo technique (method of statistical trials) provides a strong practical appeal for the evaluation of a risky project. However, a practical problem in the application of computer simulation to the evaluation of capital expenditures is the numerical quantification of uncertainty in the input variables in a probability distribution. One serious shortcoming in the use of subjective probabilities is that subjective probability distributions are not in a reproducible or mathematical form. They do not, therefore, allow for validation of their general suitability in particular cases to characterize input variables by independent means. At the same time the practical derivation of subjective probability distributions is by no means considered an easy or exact task. The present study was an attempt to suggest a simplification to the problem of deriving a probability distribution by the usual method of direct listing of subjective probabilities. The study examined the possible applicability of four theoretical probability distributions (lognormal, Weibull, normal and triangular) to the evaluation of capital projects by computer simulation. Both theory and procedures were developed for employing the four theoretical probability distributions to quantify the probability of occurrence of input variables in a simulation model. The procedure established for fitting the lognormal probability function to three-level estimates of probabilistic information was the principal contribution from this study to research in the search for improved techniques for the analysis of risky projects. A priori considerations for studying the lognormal function were discussed. Procedures were also shown on how to apply the triangular probability function and the normal approximation to simulate the outcomes of a capital project. The technique of fitting the Weibull probability function to three-level estimates of forecasts was adopted from a paper by William D. Lamb. The four theoretical probability functions wore applied to a case problem which was analyzed using subjective probabilities by David B. Hertz and reported in the Harvard Business Review. The proposal considered was a $10/-million extension to a chemical processing plant for a medium-sized industrial chemical producer. The investigations of the present study disclosed that the log-normal function showed considerable promise as a suitable probability distribution to quantify the uncertainties surrounding project variables. The normal distribution was also found to hold promise of being an appropriate distribution to use in simulation studies. The Weibull probability function did not show up too favourably by the results obtained when it was applied to the case problem under study. The triangular probability function was found to be either an inexact or unsuitable approximation to use in simulation studies as shown by the results obtained on this case problem. Secondary investigations were conducted to test the sensitivity of Monte Carlo simulation outputs to (l) number of statistical trials; (2) assumptions made on tail probabilities and (3) errors in the three-level estimates. / Business, Sauder School of / Graduate

<p>Cancer can be an extremely aggressive disease, with a poor survival rate among the patients that are in the advanced stages of the disease. Early intervention can significantly affect the outcome of the disease. The requirement of early intervention necessitates a reliable cancer screening. Regular use of screening, followed by timely treatment when cancer is diagnosed, can help decrease the chances of occurrence of death due to cancer. There are several tests available for the early detection and diagnosis of cancer. When multiple diagnostic tests are performed on an individual or multiple disease markers are available it may be possible to combine the information to diagnose disease. By combining multiple tests we can optimize diagnostic accuracy. The combination of ultrasound and mammography as markers for cancer diagnosis could be useful for early intervention. Selecting a statistical tool capable of assessing the performance of a combination of different diagnostic tests is important in selecting the most suitable diagnostic standard. One way of determining the performance of any combination of diagnostic tests is through the use of the receiver operating characteristic (ROC) curve. Baker (2000) proposed three ranking algorithms that optimize the ROC curve. The objective of this study was to develop and select the ranking algorithm which provides the optimal area under the ROC curve to differentiate cancer from benign. Statistically, unordered algorithms proved to be the best among the three algorithms giving average AUCs of 0.96510, followed by Jagged Ordered Algorithm and Rectangular Ordered Algorithm giving average AUCs of 0.96396 and 0.94314 respectively. Clinically, ordered algorithms seem to be the better choice due to their convenience.</p> / Master of Science (MS)

<p>Meta-analysis is a statistical technique for combining findings from independent studies. A meta-analysis was performed to evaluate the effectiveness of integrated treatment programs for women with substance use issues and their children. Primary outcomes included substance use, maternal and child well-being, length of treatment, and parenting. A total of 9 randomized controlled trials (RCTs) and 84 observational studies were included in the final analysis. The <em>p</em>-value and capture re-capture method, were used to combine studies using different measures of treatment effect and evaluate the completeness of the literature search, respectively. Modified weights incorporating study quality were used to assess the impact of study quality on treatment effects. We also conducted a sensitivity analysis of correlation coefficients on combined estimates as a method for handling missing data.</p> <p>Study quality adjusted weighting and traditional inverse variance weights provided different results for combined estimates of birth weight outcomes measured by standardized mean difference. The results from weighting by study quality provided a statistically significant result with a combined estimate of 0.2644 (95% CI: 0.0860, 0.4428), while the traditional method gave a non-significant combined estimate of 0.3032 with (95% CI: -0.0725,0.6788). The sensitivity analysis of correlation coefficients (r) on combined estimates of maternal depression effects were similar, with confidence intervals that narrowed as r increased. Values ofr = 0.2, 0.5, 0.65, 0.75, and 0.85 gave corresponding results (with 95% CI) of 0.67 (-0.10, 1.45), 0.67 (0.04, 1.3), 0.67 (0.12, 1.2),0.67 (0.18, 1.15), and 0.66 (0.25, 1.07). Robustness of the sensitivity analysis for study quality weighting and choice of correlation coefficient on combined estimates revealed benefits of integrated treatment programs for birth weight outcomes and maternal depression.</p> <p>Evidence of benefit for at least some of the clients was apparent for parenting attitude measured by the Adult-Adolescent Parenting Inventory (AAPI). Results for each subscale of the AAPI were reported by timing of assessments (=< 4,5-8, => 9 months). Combined <em>p</em>-values were 0.0006, <0.0001, <<0.0001 for Inappropriate Expectations, 0.1938, 0.1656, <<0.0001 for Lack of Empathy, 0.0007, <0.0001 <<0.0001 for Corporal Punishment, 0.0352, 0.0002, <<0.0001 for Role Reversal, and 0.5178 (5-8 months) for Power Independence. There was insufficient evidence for concluding a significant effect of treatment on neonatal behavioural assessments measured by Apgar scores. Combined <em>p</em>-values of 0.6980 and 0.3294 were obtained for the 1-minute and 5-minute Apgar, respectively.</p> <p>The number of missing articles estimated by the capture recapture method was 8 (95% CI: 2,24), which suggests a 90% capture rate of all relevant world literature. This result indicates that a sufficient amount of studies were retrieved to avoid bias in the results of the meta-analysis.</p> <p>Conclusions regarding the effectiveness of integrated treatment programs were limited by poor quality evidence from individual studies. We suggest the use of statistical methods such as the <em>p</em>-value, capture re-capture, study quality weighting, and sensitivity analysis of correlation coefficients to handle missing data to address meta-analytic research questions and direct higher quality research in the future.</p> / Master of Science (MS)

<p>In the statistical analysis of a health research study, it is quite common to have some missing data after data collection. Typically in a clinical trial, the treatment variable is completely recorded most of the time, but the associated covariates may not be. The multi-variable analysis is often conducted by including all the important medically relevant covariates with the expectation that a valid estimate of the treatment effect could be obtained by properly adjusting for these covariates . In this scenario, if the data of the covariates are Missing Not at Random (MNAR) , the situation becomes complicated. The estimate of the treatment effect obtained will be invalid. The situation when the data are Missing Completely at Random (MCAR) is interesting since a dilemma exists: if you include the covariates with a high missing proportion, the analysis loses power although the validity might be good. If the covariates with a high missing proportion are excluded, the validity might be of question but the precision is good. Although the literature suggests that the validity is more important, there might be cases where the precision would improve substantially with a little sacrifice on validity by omitting the covariate from the analysis. In this t hesis, this dilemma will be evaluated in the context of multivariable logistic regression with the hope that some of the results from this work would shed light on the understanding of the situation. This work is significant in that it could potentially change the data collection process. For example, in the research design stage, if we expect that a covariate would have a high rate of missingness, there might be little to gain by collecting this information. Furthermore, the results from this work may guide decisions about data collection. If we decide that a covariate does not need to be collected, then the relevant resources could be released to apply to other important aspects of a study.</p> / Master of Science (MS)

<p>The problem of estimation when the data are interval censored has been investigated by several authors. Lindsey and Ryan (1998) considered the application of conventional methods to interval mid (or end) points and showed that they tended to underestimate the standard errors of the estimated parameters and give potentially misleading results. MacKenzie (1999) and Blagojevic (2002) conjectured that the estimator of the parameter was artificially precise when analyzing inspection times as if they were exact when the "time to event" data followed an exponential distribution. In this thesis, we derive formulae for pseudo and true (or exact) likelihoods in the exponential regression model in order to examine the consequences for inference on parameters when the pseudo-likelihood is used in place of the true likelihood. We pay particular attention to the approximate bias of the maximum likelihood estimates in the case of the true likelihood. In particular we present analytical work which proves that the conjectures of Lindsey and Ryan (1998), MacKenzie (1999) and Blagojevic (2002) hold, at least for the exponential distribution with categorical or continuous covariates.<br /><br />We undertake a simulation study in order to quantify and analyze the relative performances of maximum likelihood estimation from both likelihoods. The numerical evidence suggests that the estimates from true likelihood are more accurate. We apply the proposed method to a set of real interval-censored data collected in a Medical Research Council (MRC, UK) multi-centre randomized controlled trial of teletherapy in the age-related macular disease (the ARMD) study.</p> / Master of Science (MS)

<p>This project aims to identify the single nucleotide polymorphisms(SNPs), which are associated with the muscle size and strength in Caucasian. Two methods sparse partial least squares (SPLS) and sparse Hilbert-Schmidt independence criterion (HSIC) were applied for dimension reduction and variables selection in the Functional SNPs Associated with Muscle Size and Strength(FAMuss) Study. The selection ability of two methods was compared by simulations. The genetic determinants of skeletal muscle size and strength before and after exercise training in Caucasian were selected by using these two methods.</p> / Master of Science (MS)

<p>In this project, an application of the Cox proportional hazard model is being considered. Cox proportional hazard model is fitted to estimate the effect of the covariates, age and drugs, on the survival of the HIV positive patients. These estimates also agree with the estimates obtained by using the numerical method. Likelihood ratio, Wald test and Score test are applied to test the significance of these estimates. Power for these test are performed by Monte Carlo simulation method. Simulated powers for sample size n = 10, 20 and 30, β = 0.1, 0.2, 0.4 and 1%, 5% and 10% are tabulated.</p> / Master of Science (MS)

<p>Manufacturers and consumers often use acceptance sampling to determine the acceptability of a lot from an outgoing production or incoming shipment base on a sample. Multilevel acceptance sampling for attributes is applied when the product has multiple levels of product quality or multiple types of (mutually exclusive) possible defects.</p> <p>The aim of this project is to develop an <strong>R</strong> package <strong>MFSAS</strong> which provides the tools to create, evaluate, plot, and display multilevel acceptance sampling plans for attributes for both fixed and sequential sampling. The Dirichlet recursive functions are used to calculate cumulative probabilities for several common multivariate distributions which are needed in the package.</p> / Master of Science (MS)

<p>Mixture distributions are typically used to model data in which each observation belongs to one of some number of different groups. They also provide a convenient and flexible class of models for density estimation. When the number of components <em>k</em> is assumed known, the Gibbs sampler can be used for Bayesian estimation of the component parameters. We present the implementation of the Gibbs sampler for mixtures of Normal distributions and show that, spurious modes can be avoided by introducing a Gamma prior in the Kiefer-Wolfowitz example.</p> <p>Adopting a Bayesian approach for mixture models has certain advantages; it is not without its problems. One typical problem associated with mixtures is nonidentifiability of the Gomponent parameters. This causes label switching in the Gibbs sampler output and makes inference for the individual components meaningless. We show that the usual approach to this problem by imposing simple identifiability constraints on the mixture parameters is sometimes inadequate, and present an alternative approach by arranging the mixture components in order of non-decreasing means whilst choosing priors that are slightly more informative. We illustrate the success of our approach on the fishery example.</p> <p>When the number of components <em>k</em> is considered unknown, more sophisticated methods are required to perform the Bayesian analysis. One method is the Reversible Jump MCMC algorithm described by Richardson and Green (1997), which they applied to univariate Normal mixtures. Alternatively, selection of <em>k</em> can be based on a comparison of models fitted with different numbers of components by some joint measures of model fit and model complexity. We review these methods and illustrate how to use them to compare competing mixture models using the acidity data.</p> <p><br />We conclude with some suggestions for further research.</p> / Master of Science (MS)