This dissertation serves as a unifying document for three related articles developed during my dissertation research. The projects involve the development of single-subject transcriptome (i.e. gene expression data) methodology for precision medicine and related applications. Traditional statistical approaches are largely unavailable in this setting due to prohibitive sample size and lack of independent replication. This leads one to rely on informatic devices including knowledgebase integration (e.g., gene set annotations) and external data sources (e.g., estimation of inter-gene correlation). Common statistical themes include multivariate statistics (such as Mahalanobis distance and copulas) and large-scale significance testing. Briefly, the first work describes the development of clinically relevant single-subject metrics of gene set (pathway) differential expression, N-of-1-pathways Mahalanobis distance (MD) scores. Next, the second article describes a method which overcomes a major shortcoming of the MD framework by accounting for inter-gene correlation. Lastly, the statistics developed in the previous works are re-purposed to analyze single-cell RNA-sequencing data derived from rare cells. Importantly, these works represent an interdisciplinary effort and show that creative solutions for pressing issues become possible at the intersection of statistics, biology, medicine, and computer science.

The currently available distribution-free confidence interval for a difference of medians in a within-subjects design requires an unrealistic assumption of identical distribution shapes. A confidence interval for a general linear function of medians is proposed for within-subjects designs that do not assume identical distribution shapes. The proposed method can be combined with a method for linear functions of independent medians to provide a confidence interval for a linear function of medians in mixed designs. Simulation results show that the proposed methods have good small-sample properties under a wide range of conditions. The proposed methods are illustrated with examples, and R functions that implement the new methods are provided.

Introduktion: Att påverka de sensoriska egenskaperna hos kyckling genom att anpassa fodret kycklingarna får vid uppfödningen, är ett intressant koncept som kan leda till många möjligheter. På Bosarps gård utanför Blentarp i Skåne har man arbetat med ett sådant koncept genom att tillföra morötter och grönkål som ett komplement till basfodret.Syfte: Syftet med denna studie är att undersöka om morot och grönkål, som ett komplement till basfodret, påverkar kycklingköttets sensoriska egenskaper.Material och metod: För att ta reda på detta har två olika sensoriska skillnadstester använts, först ett duo-triotest och sedan ett partest.Resultat: Det fanns inga skillnader beträffande egenskaperna utseende och smak mellan kött från kycklingar som fötts upp med eller utan tillsats av morötter och grönkål i fodret, dock fanns det en signifikant skillnad avseende texturen. Morotskyckligen hade en fastare fibertextur.Slutsats: Det fanns en skillnad i texturen, som antingen kan förklaras av/bero på fodret, tillagningen, åldern på kycklingarna eller hanteringen av kycklingköttet efter slakt. / Introduction: Being able to influence the sensory properties of chicken by affecting the feed during breeding, is an interesting concept that can lead to many possibilities. At Bosarp's farm just outside of Blentarp in Skåne they have tried to execute this concept by adding carrots and kale as a complement to the chicken’s basic diet.Aim: The aim of this study is to investigate whether carrot and kale, as a complement to the basal diet, affect the sensory characteristics of the chicken meat.Material and method: To achieve the aim of this study two different sensory differences tests have been applied, first a duo trio test and then a two paired sample test.Results: There were no differences regarding the appearance and taste characteristics between the samples of meat from chickens bred with or without the addition of carrots and kale in the feed, but there was a significant difference regarding the texture.Conclusion: There was a difference in texture, which was either due to the feeding, the cooking, the age of the chicken or handling of the chicken meat after slaughter.

The prediction of a company's financial health is of critical importance to a variety of stakeholders ranging from auditors, creditors, customers, employees, financial institutions and investors through to management. There has been considerable research in this field, ranging from the univariate dichotomous approach of Beaver (1966) to the multivariate multi-state approaches of Lau (1987) and Ward (1994). All of the South African studies namely, Strebel and Andrews (1977), Daya (1977), De La Rey (1981), Clarke et al (1991) and Court et al (1999), and even, Lukhwareni's (2005) four separate models, were dichotomous in nature providing either a "Healthy" or a "Failed" state; or a "Winner" or "Loser" as in the latter case. Notwithstanding, all of these models would be classified as first stage, initial screening models. This study has focused on following a two stage approach to identifying (first stage) and analysing (second stage) the States of Health in a company. It has not adopted the rigid "Healthy" or "Failed" dichotomous methodology. For the first stage, three-state models were developed classifying a company as Healthy, Intermittent or Distressed. Both three year and five year Profit after Tax (PAT) averages for Real Earnings Growth (REG) calculations were used to determine the superior definition for the Intermittent state; with the latter coming out as superior. Models were developed for the current year (Yn), one (Yn-1), two (Yn-2) and three years (Yn-3) forward using a Test sample of twenty companies and their predictive accuracy determined by using a Holdout sample of twenty-two companies and all their data points or years of information. The statistical methods employed were a Naïve model using the simple Shareholder Value Added (SVA) ratio, CHAID and MDA, with the latter providing very disappointing results - for the Yn year (five year average), the Test sample results were 100%, 95% and 95%, respectively; with the Holdout sample results being 81.3%, 83.8% and 52.5%, respectively. The Yn-1 to Yn-3 models produced very good results for the Test sample but somewhat disappointing Holdout sample results. The best two Yn models namely, the Naïve and the CHAID models, were modified so as to enable a comparison with the notable, dichotomous De La Rey (1981) model. As such, three different approaches were adopted and in all cases, both the modified Naïve (100%, 81.3%, 100%) and the modified CHAID (100%, 85.9%, 98%) produced superior results to the De La Rey model (84.8%, 62.6%, 75.3%). For the second stage, a Financial Risk Analysis Model (FRAM) using ratios in the categories of Growth, Performance Analysis, Investment Analysis and Financial Status were used to provide underlying information or clues, independent of the first stage model, so as to enable the stakeholder to establish a more meaningful picture of the company. This would pave the way for the appropriate strategy and course of action to be followed, to take the company to the next level; whether it be taking the company out of a Distressed State (D) or further improving on its Healthy status (H). / Business Management / D. BL.

The prediction of a company's financial health is of critical importance to a variety of stakeholders ranging from auditors, creditors, customers, employees, financial institutions and investors through to management. There has been considerable research in this field, ranging from the univariate dichotomous approach of Beaver (1966) to the multivariate multi-state approaches of Lau (1987) and Ward (1994). All of the South African studies namely, Strebel and Andrews (1977), Daya (1977), De La Rey (1981), Clarke et al (1991) and Court et al (1999), and even, Lukhwareni's (2005) four separate models, were dichotomous in nature providing either a "Healthy" or a "Failed" state; or a "Winner" or "Loser" as in the latter case. Notwithstanding, all of these models would be classified as first stage, initial screening models. This study has focused on following a two stage approach to identifying (first stage) and analysing (second stage) the States of Health in a company. It has not adopted the rigid "Healthy" or "Failed" dichotomous methodology. For the first stage, three-state models were developed classifying a company as Healthy, Intermittent or Distressed. Both three year and five year Profit after Tax (PAT) averages for Real Earnings Growth (REG) calculations were used to determine the superior definition for the Intermittent state; with the latter coming out as superior. Models were developed for the current year (Yn), one (Yn-1), two (Yn-2) and three years (Yn-3) forward using a Test sample of twenty companies and their predictive accuracy determined by using a Holdout sample of twenty-two companies and all their data points or years of information. The statistical methods employed were a Naïve model using the simple Shareholder Value Added (SVA) ratio, CHAID and MDA, with the latter providing very disappointing results - for the Yn year (five year average), the Test sample results were 100%, 95% and 95%, respectively; with the Holdout sample results being 81.3%, 83.8% and 52.5%, respectively. The Yn-1 to Yn-3 models produced very good results for the Test sample but somewhat disappointing Holdout sample results. The best two Yn models namely, the Naïve and the CHAID models, were modified so as to enable a comparison with the notable, dichotomous De La Rey (1981) model. As such, three different approaches were adopted and in all cases, both the modified Naïve (100%, 81.3%, 100%) and the modified CHAID (100%, 85.9%, 98%) produced superior results to the De La Rey model (84.8%, 62.6%, 75.3%). For the second stage, a Financial Risk Analysis Model (FRAM) using ratios in the categories of Growth, Performance Analysis, Investment Analysis and Financial Status were used to provide underlying information or clues, independent of the first stage model, so as to enable the stakeholder to establish a more meaningful picture of the company. This would pave the way for the appropriate strategy and course of action to be followed, to take the company to the next level; whether it be taking the company out of a Distressed State (D) or further improving on its Healthy status (H). / Business Management / D. BL.