This descriptive study was done 1) to explore and describe the proportional distribution of breast, cervical and colorectal cancers by stage (a proxy measure of availability, access, and utilization of secondary prevention strategies) in northern Saskatchewan First Nations and non-First Nations in comparison to southern Saskatchewan First Nations and non-First Nations; 2) to assess the impact of stage and age on the survival patterns for these cancers in northerners and First Nations whose survival patterns have been shown by previous research to be equal or poorer in comparison to southerners. Univariate and multivariate survival analyses were carried out to ascertain the impact of the different proportions of stage for each study group on survival. Stage at time of diagnosis is a proxy assessment of secondary prevention services, which include formal screening programs.<p> Data for this study was obtained from the Saskatchewan Cancer Registry, which has been maintaining cancer data since 1932. Cancer stage at time of diagnosis information is complete in the registry for different years for each cancer site. Hence data for breast cancer was for the years 1970 to 1995; cervical cancer data for the years 1980 to 1995; colorectal cancer data for the years 1990 to 1995. <p> The proportion of cancer cases for each site by TNM stage and age were compared among the four study groups. First Nation and northern populations were found to have a larger proportion of diagnoses at a later stage in comparison to the southern non-First Nation group. <p> Using Cox's proportional hazards model, both stage and age at time of diagnosis were found to be significant predictors of survival for all study groups. Age and stage adjusted relative risks were calculated and found to be significant in comparison to the southern non-First Nation group for cancer of the breast (RR =1.81 P=0.013). For cervical cancer the relative risk of dying of cervical cancer for southern First Nations in comparison to southern non­-First Nations was found to be 1.38 but this was not statistically significant (p = 0.097). For colorectal cancer, the relative risk of dying of colorectal cancer was found to be better for northern First Nations in comparison to southern non-First Nations (RR = 0.59), however this was not statistically significant (p = 0.45).<p> This study showed that despite adjusting for stage and age at time of diagnosis, there were still some unexplained differences in the survival pattern of northern First Nations, northern non-First Nations and southern First Nations in comparison to southern non-First Nations. Hypotheses as to what these unexplained differences are have been offered. These include differences in socio-economic status as well as availability, accessibility, attitudes towards and knowledge of secondary prevention strategies. Further study into these unexplained differences should be carried out.

This descriptive study was done 1) to explore and describe the proportional distribution of breast, cervical and colorectal cancers by stage (a proxy measure of availability, access, and utilization of secondary prevention strategies) in northern Saskatchewan First Nations and non-First Nations in comparison to southern Saskatchewan First Nations and non-First Nations; 2) to assess the impact of stage and age on the survival patterns for these cancers in northerners and First Nations whose survival patterns have been shown by previous research to be equal or poorer in comparison to southerners. Univariate and multivariate survival analyses were carried out to ascertain the impact of the different proportions of stage for each study group on survival. Stage at time of diagnosis is a proxy assessment of secondary prevention services, which include formal screening programs.<p> Data for this study was obtained from the Saskatchewan Cancer Registry, which has been maintaining cancer data since 1932. Cancer stage at time of diagnosis information is complete in the registry for different years for each cancer site. Hence data for breast cancer was for the years 1970 to 1995; cervical cancer data for the years 1980 to 1995; colorectal cancer data for the years 1990 to 1995. <p> The proportion of cancer cases for each site by TNM stage and age were compared among the four study groups. First Nation and northern populations were found to have a larger proportion of diagnoses at a later stage in comparison to the southern non-First Nation group. <p> Using Cox's proportional hazards model, both stage and age at time of diagnosis were found to be significant predictors of survival for all study groups. Age and stage adjusted relative risks were calculated and found to be significant in comparison to the southern non-First Nation group for cancer of the breast (RR =1.81 P=0.013). For cervical cancer the relative risk of dying of cervical cancer for southern First Nations in comparison to southern non­-First Nations was found to be 1.38 but this was not statistically significant (p = 0.097). For colorectal cancer, the relative risk of dying of colorectal cancer was found to be better for northern First Nations in comparison to southern non-First Nations (RR = 0.59), however this was not statistically significant (p = 0.45).<p> This study showed that despite adjusting for stage and age at time of diagnosis, there were still some unexplained differences in the survival pattern of northern First Nations, northern non-First Nations and southern First Nations in comparison to southern non-First Nations. Hypotheses as to what these unexplained differences are have been offered. These include differences in socio-economic status as well as availability, accessibility, attitudes towards and knowledge of secondary prevention strategies. Further study into these unexplained differences should be carried out.

Survival analysis is an essential statistics and machine learning field in various critical applications like medical research and predictive maintenance. In these domains understanding models' predictions is paramount. While machine learning techniques are increasingly applied to enhance the predictive performance of survival models, they simultaneously sacrifice transparency and explainability.  Survival models, in contrast to regular machine learning models, predict functions rather than point estimates like regression and classification models. This creates a challenge regarding explaining such models using the known off-the-shelf machine learning explanation techniques, like Shapley Values, Counterfactual examples, and others.    Censoring is also a major issue in survival analysis where the target time variable is not fully observed for all subjects. Moreover, in predictive maintenance settings, recorded events do not always map to actual failures, where some components could be replaced because it is considered faulty or about to fail in the future based on an expert's opinion. Censoring and noisy labels create problems in terms of modeling and evaluation that require to be addressed during the development and evaluation of the survival models. Considering the challenges in survival modeling and the differences from regular machine learning models, this thesis aims to bridge this gap by facilitating the use of machine learning explanation methods to produce plausible and actionable explanations for survival models. It also aims to enhance survival modeling and evaluation revealing a better insight into the differences among the compared survival models. In this thesis, we propose two methods for explaining survival models which rely on discovering survival patterns in the model's predictions that group the studied subjects into significantly different survival groups. Each pattern reflects a specific survival behavior common to all the subjects in their respective group. We utilize these patterns to explain the predictions of the studied model in two ways. In the first, we employ a classification proxy model that can capture the relationship between the descriptive features of subjects and the learned survival patterns. Explaining such a proxy model using Shapley Values provides insights into the feature attribution of belonging to a specific survival pattern. In the second method, we addressed the "what if?" question by generating plausible and actionable counterfactual examples that would change the predicted pattern of the studied subject. Such counterfactual examples provide insights into actionable changes required to enhance the survivability of subjects. We also propose a variational-inference-based generative model for estimating the time-to-event distribution. The model relies on a regression-based loss function with the ability to handle censored cases. It also relies on sampling for estimating the conditional probability of event times. Moreover, we propose a decomposition of the C-index into a weighted harmonic average of two quantities, the concordance among the observed events and the concordance between observed and censored cases. These two quantities, weighted by a factor representing the balance between the two, can reveal differences between survival models previously unseen using only the total Concordance index. This can give insight into the performances of different models and their relation to the characteristics of the studied data. Finally, as part of enhancing survival modeling, we propose an algorithm that can correct erroneous event labels in predictive maintenance time-to-event data. we adopt an expectation-maximization-like approach utilizing a genetic algorithm to find better labels that would maximize the survival model's performance. Over iteration, the algorithm builds confidence about events' assignments which improves the search in the following iterations until convergence. We performed experiments on real and synthetic data showing that our proposed methods enhance the performance in survival modeling and can reveal the underlying factors contributing to the explainability of survival models' behavior and performance.

We studied the dynamic of nine populations of Alpine ibex ( Capra ibex ibex ) in five protected areas. We showed a strong effect of age on demographic parameters, with a marked decrease of survival after 10-12 years of age. We also found a high variability of old females' reproduction between populations. Contrary to what is expected for a highly dimorphic species like ibex, males survived as well as females except for old individuals. Winter harshness had a negative impact on survival of old individuals but not on reproduction and survival of young. We conclude that ibex have evolved a highly conservative life-history tactic compared to other ungulates studied to now. From a management viewpoint we also showed that under some circumstances ground counts might provide reliable estimates of ibex population trends.