<p>This thesis consists of four papers about the assumption of proportional hazards for the Cox model in survival analysis. </p><p>The <b>first paper </b>compares the hazard ratio estimated from the Cox model to an exact calculation of the geometric average of the hazard ratio when the underlying assumption of proportional hazards is false, i.e. when the hazards are not proportional. The estimates are evaluated in a simulation study.</p><p>The <b>second paper</b> describes and compares six of the most common numerical procedures to check the assumption of proportional hazards for the Cox model. The tests are evaluated in a simulation study.</p><p>Six graphical procedures to check the same assumption of proportional hazards for the Cox model are described and compared in the <b>third paper</b>. A criterion for rejection is derived for each procedure, to make it possible to compare the results of the different methods. The procedures are evaluated in a simulation study.</p><p>In the <b>fourth paper </b>the effects of covariate measurement error on testing the assumption of proportional hazards is investigated. Three of the most common numerical procedures to check the assumption of proportional hazards for the Cox model are evaluated in a simulation study. </p>

This thesis consists of four papers about the assumption of proportional hazards for the Cox model in survival analysis. The <b>first paper </b>compares the hazard ratio estimated from the Cox model to an exact calculation of the geometric average of the hazard ratio when the underlying assumption of proportional hazards is false, i.e. when the hazards are not proportional. The estimates are evaluated in a simulation study. The <b>second paper</b> describes and compares six of the most common numerical procedures to check the assumption of proportional hazards for the Cox model. The tests are evaluated in a simulation study. Six graphical procedures to check the same assumption of proportional hazards for the Cox model are described and compared in the <b>third paper</b>. A criterion for rejection is derived for each procedure, to make it possible to compare the results of the different methods. The procedures are evaluated in a simulation study. In the <b>fourth paper </b>the effects of covariate measurement error on testing the assumption of proportional hazards is investigated. Three of the most common numerical procedures to check the assumption of proportional hazards for the Cox model are evaluated in a simulation study.

A general time-to-event data analysis known as event history analysis is considered. The focus is on the analysis of time-to-event data using Cox's regression model when the time to the event may be measured from different origins giving several observable time scales and when longitudinal measurements are involved. For the multiple time scales problem, procedures to choose a basic time scale in Cox's regression model are proposed. The connections between piecewise constant hazards, time-dependent covariates and time-dependent strata in the dual time scales are discussed. For the longitudinal measurements problem, four methods known in the literature together with two proposed methods are compared. All quantitative comparisons are performed by means of simulations. Applications to the analysis of infant mortality, morbidity, and growth are provided.

This thesis proposes a simplification of the model for dependent Bernoulli variables presented in Cox and Snell (1989). The simplified model, referred to as the simplified Cox model, is developed for identically distributed and dependent Bernoulli variables. Properties of the model are presented, including expressions for the loglikelihood function and the Fisher information. The special case of a bivariate symmetric model is studied in detail. For this particular model, it is found that the number of design points in a locally D-optimal design is determined by the log-odds ratio between the variables. Under mutual independence, both a general expression for the restrictions of the parameters and an analytical expression for locally D-optimal designs are derived. Focusing on the bivariate case, score tests and likelihood ratio tests are derived to test for independence. Numerical illustrations of these test statistics are presented in three examples. In connection to testing for independence, an E-optimal design for maximizing the local asymptotic power of the score test is proposed. The simplified Cox model is applied to a dental data. Based on the estimates of the model, optimal designs are derived. The analysis shows that these optimal designs yield considerably more precise parameter estimates compared to the original design. The original design is also compared against the E-optimal design with respect to the power of the score test. For most alternative hypotheses the E-optimal design provides a larger power compared to the original design.

Mouse models of human disease are valuable tools for studying pathogenesis and for evaluating novel therapies. T-cell lymphoma is a relatively rare disease in humans, affecting 100-150 persons yearly in Sweden. It exists in both aggressive and more indolent forms. We have established a mouse model for an aggressive T-cell lymphoma, the T-cell lymphoma/leukemia (TLL) mouse. In the present thesis, the TLL mouse model was characterized and used for experimental therapeutic and primary prevention studies. The TLL mouse was established unintentionally in our laboratory during work on VH-gene replacement in a “knock-in” mouse experimental setting. The generated chimeras all developed aggressive T-cell lymphomas affecting the lymphoid organs, lungs, kidneys and liver. The lymphoma phenotype segregated from the targeted locus and we could demonstrate the presence of Moloney murine leukemia virus (MMLV) in the germline of the affected mice. MMLV is a retrovirus known to induce T-cell lymphomas when inoculated in newborn mice.  We further characterized two TLL substrains; TLL-2 and TLL-14 carrying the proviral integrations on chromosomes 2 and 14 respectively. Significant differences were found between the substrains regarding lymphoma frequency and immunophenotype, the TLL-14 substrain developing tumors with higher frequency than TLL-2 and with a more mature immunophenotype. A transfer model was developed in which TLL cells could be readily transferred intravenously to syngenic recipients causing aggressive lymphomas. The transfer model was used in a therapeutic study where the selective COX-2 inhibitor celecoxib was evaluated as a single agent and in combination with the established anti-tumor agent cyclophosphamide. The study was based on results from other tumor types that have indicated celecoxib, originally an anti-inflammatory and analgetic drug, to have possible anti-tumor effects. In our TLL model, however, we could not demonstrate any benefit of celecoxib monotherapy or any additive effect to cyclophosphamide. Dietary fatty acids, in particular omega-3 fatty acids, have been a focus of public and scientific interest due to observed effects on the prevention of cardiovascular disease, cancer and inflammatory conditions. In addition, omega-3 fatty acids inhibit T-cell proliferation in vitro. We supplemented the diet of TLL mice with omega-3 and omega-6 fatty acids respectively and could demonstrate a significant delay in lymphoma onset between 5-8 months of age in the group receiving an omega-3 rich diet.

Chronic wasting disease (CWD) has infected wild deer of Saskatchewan for at least the past 10 years. Disease management plans have evolved over the years, but without information on mule deer (<i>Odocoileus hemionus</i>) habits and movements in the grasslands of southern Saskatchewan. We radio-collared and monitored the survival and movements of 206 mule deer from 2006 to 2009. Long distance movements by deer have potential to transfer disease to previously naïve areas. Survival rates had not yet been evaluated in this area; baseline data will provide a useful measure for population-level impacts of the disease in the future.<p> Juvenile dispersals and adult migrations were contrasted from 4 study areas along the South Saskatchewan River. Dispersal distance (median = 22.8 km, n = 14) was similar to migration distance (median = 16.0 km, n = 49). Median migration distance was similar between males (15.7 km, n = 51) and females (19.7 km, n = 65). Obligatory migrants were more likely to be female. Deer from an area of extensive grassland were more likely to be migratory than their counterparts in fragmented grassland of an agricultural landscape. Maximum migration and dispersal distances were 113 km and 195 km, respectively. Movement paths of 33 GPS-collared deer were best explained by high terrain ruggedness values and proximity to grassland.<p> Seasonal survival rates showed that deer had lowest survival in autumn months during hunting season. Juveniles had lower survival than adults in all seasons. Harvest regime changes in 2008 improved the autumn survival of adult females but adult males had lower survival than in 2007. Body condition of captured deer was evaluated from residuals of mass-length regression. Cox regression analyses suggested that deer in good body condition (75th percentile) were half as likely to die and that those in very poor body condition (10th percentile) were twice as likely to die. Radio collars that weighed > 2% of body mass negatively affected survival and we recommend future researchers take this into consideration. <p> Survival, dispersal, and migration rates and patterns are crucial parameters in modeling CWD in local mule deer populations. Saskatchewan wildlife managers aim to prevent CWD spread into new areas, and can use mule deer movement orientations to target surveillance accordingly. White-tailed deer (<i>Odocoileus virginianus</i>) movements are briefly discussed; further knowledge of their movements is required for CWD management in all of Saskatchewan.

Studien undersöker utvecklingen av afrikansk-amerikansk religion i början på 1800-talet i USA. Materialet som studien är konstruerad på består av en undersökning gjord på sex olika slavar som blev predikanter och pastorer. Undersökningen i Studien svarar om dessa individers yrkesroll och socialisering var av betydelse för det religiösa engagemanget och dess utveckling. Slavarnas yrkens betydelse undersöks med hjälp av Etzionis teori om tvångsorganisationer och med Durkheims arbetsfördelningsteori. Studien avser att bidra med information om hur afrikansk-amerikansk religion utformades i början av 1800-talet.

Chronic wasting disease (CWD) has infected wild deer of Saskatchewan for at least the past 10 years. Disease management plans have evolved over the years, but without information on mule deer (<i>Odocoileus hemionus</i>) habits and movements in the grasslands of southern Saskatchewan. We radio-collared and monitored the survival and movements of 206 mule deer from 2006 to 2009. Long distance movements by deer have potential to transfer disease to previously naïve areas. Survival rates had not yet been evaluated in this area; baseline data will provide a useful measure for population-level impacts of the disease in the future.<p> Juvenile dispersals and adult migrations were contrasted from 4 study areas along the South Saskatchewan River. Dispersal distance (median = 22.8 km, n = 14) was similar to migration distance (median = 16.0 km, n = 49). Median migration distance was similar between males (15.7 km, n = 51) and females (19.7 km, n = 65). Obligatory migrants were more likely to be female. Deer from an area of extensive grassland were more likely to be migratory than their counterparts in fragmented grassland of an agricultural landscape. Maximum migration and dispersal distances were 113 km and 195 km, respectively. Movement paths of 33 GPS-collared deer were best explained by high terrain ruggedness values and proximity to grassland.<p> Seasonal survival rates showed that deer had lowest survival in autumn months during hunting season. Juveniles had lower survival than adults in all seasons. Harvest regime changes in 2008 improved the autumn survival of adult females but adult males had lower survival than in 2007. Body condition of captured deer was evaluated from residuals of mass-length regression. Cox regression analyses suggested that deer in good body condition (75th percentile) were half as likely to die and that those in very poor body condition (10th percentile) were twice as likely to die. Radio collars that weighed > 2% of body mass negatively affected survival and we recommend future researchers take this into consideration. <p> Survival, dispersal, and migration rates and patterns are crucial parameters in modeling CWD in local mule deer populations. Saskatchewan wildlife managers aim to prevent CWD spread into new areas, and can use mule deer movement orientations to target surveillance accordingly. White-tailed deer (<i>Odocoileus virginianus</i>) movements are briefly discussed; further knowledge of their movements is required for CWD management in all of Saskatchewan.

The objective of the present study is to investigate various problems associate with breast cancer and lung cancer patients. In this study, we compare the effectiveness of breast cancer treatments using decision tree analysis and come to the conclusion that although certain treatment shows overall effectiveness over the others, physicians or doctors should discretionally give different treatment to breast cancer patients based on their characteristics. Reoccurrence time of breast caner patients who receive different treatments are compared in an overall sense, histology type is also taken into consideration. To further understand the relation between relapse time and other variables, statistical models are applied to identify the attribute variables and predict the relapse time. Of equal importance, the transition between different breast cancer stages are analyzed through Markov Chain which not only gives the transition probability between stages for specific treatment but also provide guidance on breast cancer treatment based on stating information. Sensitivity analysis is conducted on breast cancer doubling time which involves two commonly used assumptions: spherical tumor and exponential growth of tumor and the analysis reveals that variation from those assumptions could cause very different statistical behavior of breast cancer doubling time. In lung cancer study, we investigate the mortality time of lung cancer patients from several different perspectives: gender, cigarettes per day and duration of smoking. Statistical model is also used to predict the mortality time of lung cancer patients.

Σκοπός της μελέτης ήταν η ανάδειξη της νεοαγγειογένεσης και ο προσδιορισμός της έκφρασης των VEGF-A, FGF-2, COX-2, AR και BCL-2 στην καλοήθη υπερπλασία και το αδενοκαρκίνωμα του προστάτη. Το υλικό αφορούσε σε δείγματα προστατικού ιστού μονιμοποιημένα και εγκλεισμένα σε παραφίνη, από 24 περιστατικά καλοήθους υπερπλασίας και 139 περιστατικά προστατικού αδενοκαρκινώματος. Τα τελευταία χωρίστηκαν περαιτέρω σε 3 υποομάδες (Grade I, II και ΙΙΙ) ανάλογα με το βαθμό διαφοροποίησης του νεοπλάσματος κατά Gleason (2-4, 5-7 και 8-10 αντίστοιχα). Χρησιμοποιήθηκε ανοσοϊστοχημική μέθοδος Βιοτίνης-Στρεπταβιδίνης-Υπεροξειδάσης, και εφαρμόστηκε ημιποσοτική μέθοδος για την εκτίμηση της ανοσοϊστοχημικής χρώσης. Τα ευρήματά μας ανέδειξαν σαφή αύξηση της νεοαγγείωσης (MVD) στο αδενοκαρκίνωμα του προστάτη σε σχέση με την καλοήθη υπερπλασία, η οποία εμφάνισε στατιστικώς σημαντική θετική σχέση με το βαθμό κακοήθειας των προστατικών νεοπλασμάτων (ANOVA p<0.001) και με την έκφραση των VEGF-A και COX-2 (ANOVA p<0.001). Αναδείχθηκε αντίστροφη συσχέτιση της πυρηνικής έκφρασης του ανδρογονικού υποδοχέα (AR) με το βαθμό διαφοροποίησης των νεοπλασμάτων (p<0.0001) και την έκφραση του VEGF-A στο προστατικό στρώμα (p<0.001 Spearman r = -0.312). Η έκφραση της BCL-2 παρουσιάστηκε αυξημένη στα προστατικά αδενοκαρκινώματα και σχετίστηκε με το βαθμό διαφοροποίησης των νεοπλασμάτων (p<0.001) και την έκφραση των VEGF-A και COX-2 (p<0.001). Η έκφραση του VEGF-A σε όλα τα περιστατικά αδενοκαρκινώματος του προστάτη εμφάνισε στατιστικώς σημαντική σχέση με το βαθμό διαφοροποίησης των νεοπλασμάτων (p<0.0001). Ωστόσο στα πτωχής διαφοροποίησης αδενοκαρκινώματα η μέση τιμή της έκφρασης του VEGF-A παρουσίασε πτώση. Αντίθετα, η σημασία της COX-2 στον προστατικό καρκίνο αναδείχθηκε με την έκφρασή της τόσο στην καλοήθη υπερπλασία όσο και στα αδενοκαρκινώματα του προστάτη. Η έκφραση παρουσίασε σημαντική σχέση με το βαθμό διαφοροποίησης των νεοπλασμάτων (p<0.01). Η σαφώς αυξημένη έκφραση της COX-2 σε σχέση με τη μείωση της έκφρασης του VEGF-A στα πτωχής διαφοροποίησης νεοπλάσματα πιθανόν υποδηλώνει την ύπαρξη ενός αγγειογενετικού διακόπτη στα νεοπλάσματα αυτά όπου η COX-2 φαίνεται να παίζει σημαντικότερο ρόλο από τον VEGF-A. Η σημαντική αυτή πληροφορία θα μπορούσε να βρει πιθανή θεραπευτική εφαρμογή, καθώς σε πτωχής διαφοροποίησης αδενοκαρκινώματα του προστάτη ίσως η θεραπεία με COX-2 εκλεκτικούς αναστολείς να είχε πολύ καλύτερα αποτελέσματα από τις αντι-αγγειογενετικές θεραπείες με αναστολείς του VEGF. / The aim of this study was to immunohistochemically evaluate the expression of VEGF-A, FGF-2, COX-2, AR and BCL-2 in benign prostatic hyperplasia (BPH) and prostate carcinoma in relation to microvessel density (MVD) and the Gleason grade of the neoplasms. A total of 139 cases of primary prostate carcinoma and 24 cases of benign hyperplasia were included in the study. Tumors were graded according to the Gleason grading system and further divided into 3 subgroups (GRADE I, II and III). The immunostaining was performed according to the Streptavidin-Biotin Complex Peroxidase method, in formalin fixed paraffin-embedded tissue. Mean micro vessel density (MVD) was strongly related to tumor grade, VEGF-A and COX-2 histoscore (ANOVA, p<0.001). The androgen receptor was localized in the nuclei of prostate epithelial cells in 97% of cases. The comparison of AR staining with tumor grade revealed an inverse relationship between these two parameters (ANOVA, p<0,0001). An interesting finding was the inverse relationship of stromal AR expression in relation to VEGF-A immunoreactivity. BCL-2 expression was correlated with tumor grade in prostate carcinoma cases (p<0.001) and was strongly correlated with COX-2 and VEGF-A expression (p<0.001). These findings suggest that BCL-2 may play a dual role in tumorigenesis, possibly through an angiogenetic axis. VEGF-A expression was detected in only 17% of BPH cases but all prostate cancer specimens demonstrated some degree of immunoreactivity. COX-2 immunopositivity was present in 54% of BPH specimens and in 99% of primary prostate carcinomas. The increased COX-2 expression correlated significantly with Gleason grade. In our study, high-grade neoplasms presented low to moderate VEGF staining intensity compared to COX-2 expression. These results suggest the activation of an angiogenic switch in poorly differentiated neoplasms, where COX-2 may play a crucial role compared to VEGF and the possible key role of COX-2 in poorly differentiated cancers. According to our findings, anti-VEGF therapy could prove to be more beneficial in patients with low-grade disease, while patients with high-grade prostate carcinoma are more likely to respond to selective COX-2 inhibitors. Immunohistochemical determination of VEGF-A and COX-2 content might prove a useful tool in the design of patient-tailored, anti-angiogenic treatments.