Markov processes have been widely studied and used for modeling problems. A Markov process has two main components (i.e., an evolution law and an initial distribution). Markov processes are not suitable for modeling some problems, for example, the problem of predicting a trajectory with a known destination. Such a problem has three main components: an origin, an evolution law, and a destination. The conditionally Markov (CM) process is a powerful mathematical tool for generalizing the Markov process. One class of CM processes, called $CM_L$, fits the above components of trajectories with a destination. The CM process combines the Markov property and conditioning. The CM process has various classes that are more general and powerful than the Markov process, are useful for modeling various problems, and possess many Markov-like attractive properties. Reciprocal processes were introduced in connection to a problem in quantum mechanics and have been studied for years. But the existing viewpoint for studying reciprocal processes is not revealing and may lead to complicated results which are not necessarily easy to apply. We define and study various classes of Gaussian CM sequences, obtain their models and characterizations, study their relationships, demonstrate their applications, and provide general guidelines for applying Gaussian CM sequences. We develop various results about Gaussian CM sequences to provide a foundation and tools for general application of Gaussian CM sequences including trajectory modeling and prediction. We initiate the CM viewpoint to study reciprocal processes, demonstrate its significance, obtain simple and easy to apply results for Gaussian reciprocal sequences, and recommend studying reciprocal processes from the CM viewpoint. For example, we present a relationship between CM and reciprocal processes that provides a foundation for studying reciprocal processes from the CM viewpoint. Then, we obtain a model for nonsingular Gaussian reciprocal sequences with white dynamic noise, which is easy to apply. Also, this model is extended to the case of singular sequences and its application is demonstrated. A model for singular sequences has not been possible for years based on the existing viewpoint for studying reciprocal processes. This demonstrates the significance of studying reciprocal processes from the CM viewpoint.

Background: Childhood excess weight and family food insecurity are food-system related public health problems that exist in Canada. Since both relate to issues of food accessibility and availability, which have elements of “place”, they may share common risk factors in the local environment that are amenable to intervention. In this area of research, the literature derives mostly from a US context, and there is a dearth of high quality evidence, specifically from longitudinal studies. Objectives: The main objectives of this thesis were to examine the adjusted associations between the place factors: material deprivation, social deprivation, social cohesion, disorder, and living location, with change in child BMI Z-score and with change in family food insecurity status in a Canadian cohort of children. Methods: The Québec Longitudinal Study of Child Development was used to meet the main objectives of this thesis. Response data from six collection cycles (4 – 10 years of age) were used in three main analyses. The first analysis examined change in child BMI Z-score as a function of the place factors using mixed models regression. The second analysis examined change in child BMI Z-score as a function of place factors using group-based trajectory modeling. The third and final analysis examined change in family food insecurity status as a function of the place factors using generalized estimating equations. Results: Social deprivation, social cohesion and disorder were strongly and positively associated with family food insecurity, increasing the odds by 45-76%. These place factors, on the other hand, were not consistently associated with child weight status. Material deprivation was not important for either outcome, except for a slight positive association in the mixed models analysis of child weight status. Living location was not important in explaining family food insecurity. On the other hand, it was associated with child weight status in both analyses, but the nature of the relationship is still unclear. Conclusions: Results do not suggest that addressing similar place factors may alleviate both child excess weight and family food insecurity. More high quality longitudinal and experimental studies are needed to clarify relationships between the local environment and child weight status and family food insecurity.

Ovarian cancer (OC) is the fifth most common cancer among women and has the highest mortality of any cancer of the female reproductive system. The majority (61%) of OC cases are diagnosed at a distant stage. Because diagnoses occur most commonly at a late-stage and prognosis for advanced disease is poor, research focusing on the development of effective OC screening methods to facilitate early detection in high-risk, asymptomatic women is fundamental in reducing OC-specific mortality. Presently, there is no screening modality proven efficacious in reducing OC-mortality. However, transvaginal ultrasonography (TVS) has shown value in early detection of OC. TVS presents with the possibility of false positive results which occur when a women receives an abnormal TVS screening test result that is deemed benign following repeat testing (about 7% of the time). The purpose of this dissertation was to evaluate the impact of false positive TVS screening test results on a variety of psychological and behavioral outcomes using mixed and trajectory statistical modeling. The three specific aims of this dissertation were to 1) compare psychological and behavioral outcomes between women receiving normal and false positive results, 2) identify characteristics of women receiving false positive results associated with increased OC-specific distress and 3) characterize distress trajectories following receipt of false positive results. Analyses included a subset of women participating in an experimental study conducted through the University of Kentucky Ovarian Cancer Screening Program. 750 women completed longitudinal assessments: 375 false positive and 375 normal results. Mixed and group-based trajectory modeling were used to evaluate the specific aims. Results suggest women receiving false positive TVS result experience increased OC-specific distress compared to women receiving normal results. Among those receiving false positives, less education, no history of an abnormal screening test result, less optimism and more social constraint were associated with increased OC-specific distress. Family history was associated with increased distress among women with monitoring informational coping styles. Three distinct trajectories characterize the trajectory of distress over a four-month study period. Although decreasing over time, a notable proportion of women experience sustained high levels of OC-specific distress.

Background: Childhood excess weight and family food insecurity are food-system related public health problems that exist in Canada. Since both relate to issues of food accessibility and availability, which have elements of “place”, they may share common risk factors in the local environment that are amenable to intervention. In this area of research, the literature derives mostly from a US context, and there is a dearth of high quality evidence, specifically from longitudinal studies. Objectives: The main objectives of this thesis were to examine the adjusted associations between the place factors: material deprivation, social deprivation, social cohesion, disorder, and living location, with change in child BMI Z-score and with change in family food insecurity status in a Canadian cohort of children. Methods: The Québec Longitudinal Study of Child Development was used to meet the main objectives of this thesis. Response data from six collection cycles (4 – 10 years of age) were used in three main analyses. The first analysis examined change in child BMI Z-score as a function of the place factors using mixed models regression. The second analysis examined change in child BMI Z-score as a function of place factors using group-based trajectory modeling. The third and final analysis examined change in family food insecurity status as a function of the place factors using generalized estimating equations. Results: Social deprivation, social cohesion and disorder were strongly and positively associated with family food insecurity, increasing the odds by 45-76%. These place factors, on the other hand, were not consistently associated with child weight status. Material deprivation was not important for either outcome, except for a slight positive association in the mixed models analysis of child weight status. Living location was not important in explaining family food insecurity. On the other hand, it was associated with child weight status in both analyses, but the nature of the relationship is still unclear. Conclusions: Results do not suggest that addressing similar place factors may alleviate both child excess weight and family food insecurity. More high quality longitudinal and experimental studies are needed to clarify relationships between the local environment and child weight status and family food insecurity.

Background: Childhood excess weight and family food insecurity are food-system related public health problems that exist in Canada. Since both relate to issues of food accessibility and availability, which have elements of “place”, they may share common risk factors in the local environment that are amenable to intervention. In this area of research, the literature derives mostly from a US context, and there is a dearth of high quality evidence, specifically from longitudinal studies. Objectives: The main objectives of this thesis were to examine the adjusted associations between the place factors: material deprivation, social deprivation, social cohesion, disorder, and living location, with change in child BMI Z-score and with change in family food insecurity status in a Canadian cohort of children. Methods: The Québec Longitudinal Study of Child Development was used to meet the main objectives of this thesis. Response data from six collection cycles (4 – 10 years of age) were used in three main analyses. The first analysis examined change in child BMI Z-score as a function of the place factors using mixed models regression. The second analysis examined change in child BMI Z-score as a function of place factors using group-based trajectory modeling. The third and final analysis examined change in family food insecurity status as a function of the place factors using generalized estimating equations. Results: Social deprivation, social cohesion and disorder were strongly and positively associated with family food insecurity, increasing the odds by 45-76%. These place factors, on the other hand, were not consistently associated with child weight status. Material deprivation was not important for either outcome, except for a slight positive association in the mixed models analysis of child weight status. Living location was not important in explaining family food insecurity. On the other hand, it was associated with child weight status in both analyses, but the nature of the relationship is still unclear. Conclusions: Results do not suggest that addressing similar place factors may alleviate both child excess weight and family food insecurity. More high quality longitudinal and experimental studies are needed to clarify relationships between the local environment and child weight status and family food insecurity.

Ce travail est principalement axé sur la modélisation par approche de groupe de trajectoires développementales de la consommation d'alcool des adolescents au Quebec. / Contexte: L’impulsion à cette étude est le fait que la consommation d'alcool chez les adolescents a augmenté au cours des dernières années et que la consommation excessive d'alcool épisodique est de plus en plus fréquente chez les jeunes adultes. La prévention des problèmes de la consommation d’alcool chez les jeunes doit commencer par l'identification appropriée des sous-groupes d'adolescents à risque élevé. Objectifs: Cette étude avait trois objectifs: (i) identifier les trajectoires de développement de la consommation d'alcool chez les adolescents; (ii) d'examiner l'influence du sexe sur les trajectoires et (iii) d'examiner la relation entre les trajectoires de consommation d'alcool à l'adolescence et la consommation d'alcool excessive épisodique à l'âge jeune adulte. Méthode: Nous avons utilisé des données de l'étude longitudinale (n = 1294, 1999 - 2012) des adolescents âgés de 12 à 13 ans au début de l'étude de NDIT (Dépendance de la nicotine chez les adolescents). Les 1245 participants qui ont complété au moins trois des 22 cycles de NDIT ont été stratifiés selon leur statut alcoolique. C’est à dire ceux qui avaient consommé de l'alcool au début de l’étude, les buveurs (n = 497) et ceux qui n'avaient jamais consommé d'alcool au début de l’étude, les abstinents (n=748). Nous avons identifié les trajectoires de développement de la fréquence de la consommation d'alcool sur la base de 19 vagues de collecte de données après le début de l’étude de la 7e année (de 12 à 13 ans) à la 11e année (17-18 ans) en utilisant la modélisation semi-paramétrique basée sur l’approche des trajectoires par groupe (GBTM). Nous avons conduit des séries de régression logistique afin d'étudier l'association entre les trajectoires de développement de la consommation d'alcool et la consommation excessive épisodique à l'âge jeune adulte chez les buveurs d’alcool au début de l’étude et les abstinents au début de l’étude. Résultats: Pour l’ensemble de l’échantillon global (abstinents et buveurs) cinq groupes de trajectoires ont été identifiés. Ensuite, quatre groupes de trajectoires ont été identifiés parmi les abstinents au début de l’étude (‘faible’ consommateurs (28.3%, n=215), consommateurs tardifs croissants (21.5%, n=161), consommateurs modérés (29.9%, n=224) et consommateurs réguliers (20.3%, n=152). Parmi les consommateurs d’alcool (buveurs) au début de l’étude, les groupes de trajectoires comprenaient des consommateurs d’alcool peu fréquents (rares) (15.4%, n=76), des consommateurs en hausse (34.1%, n=170), des consommateurs réguliers (41.7%, n=207) et des consommateurs en baisse (8.8%, n=44). Les adolescents des groupes de trajectoires de fréquence de consommation d’alcool les plus élevées étaient plus susceptibles de pratiquer la consommation d’alcool excessive épisodique à l’âge jeune adulte. Conclusion: Cette étude montre la variabilité des trajectoires de développement de la consommation d'alcool des adolescents. Les données suggèrent que des approches multiples peuvent être nécessaires pour prévenir la consommation problématique d'alcool chez les adolescents et que ces approches devraient être nécessairement adaptées au sexe. / Background: The impetus for this study is that alcohol use among adolescents has increased in recent years and that heavy episodic or binge drinking is increasingly common in young adults. Prevention of problem drinking must begin with appropriate identification of sub-groups of adolescents at higher risk. Objective: This study had three objectives: (i) to identify the developmental trajectories of alcohol consumption among teens; (ii) to examine the influence of sex on trajectories and (iii) to examine the relationship between alcohol consumption trajectories in adolescence and binge drinking in young adulthood. Method: We used data from the NDIT (Nicotine Dependence In Teens) longitudinal study (n=1294; 1999 – 2012) of adolescents ages 12-13 years at inception. The 1245 participants who completed at least three of 22 NDIT cycles were stratified into those who had consumed alcohol at baseline, baseline drinkers (n=497) and those who had never consumed alcohol, baseline nondrinkers (n=748). We identified the developmental trajectories of the frequency of alcohol consumption based on 19 data collection waves after baseline from grade 7 (age 12-13) to grade 11 (age 17-18), using semi-parametric group-based trajectory modeling. Logistic regression was conducted to investigate the association between the alcohol consumption developmental trajectories and binge drinking in young adulthood among baseline drinkers and baseline nondrinkers. Results: Five trajectory were identified for the whole sample (baseline nondrinkers and baseline drinkers, n=1245). Then, four trajectory groups were identified among baseline nondrinkers (low consumers (28.3%, n=211), increasing late consumers (21.5%, n=161), moderate drinkers (29.9%, n=224), and regular users (20.3%, n=152). Among baseline drinkers, trajectory groups included experimenters (15.4%, n=76), increasing (34.1%, n=170), regular (41.7%, n=207) and decreasing consumers (8.8%, n=44). Participants in the higher trajectory groups were more likely to binge drink in young adulthood. Conclusion: This study shows variability among adolescents in alcohol consumption developmental trajectories. The data suggest that multiple approaches may be necessary to prevent problem alcohol consumption among adolescents and that these approaches may need to be sex-sensitive.

Introduction : Seulement 7% des Canadiens de 17 ans et moins pratiquent 60 minutes d’activité physique modérée à vigoureuse quotidiennement. La majorité dépasse le temps d’écran quotidien recommandé de deux heures. Plusieurs études transversales indiquent que les deux comportements évoluent indépendamment et ne seraient que faiblement corrélés. Objectifs et hypothèses : Les objectifs de ce mémoire est d’identifier des trajectoires d’activité physique et des trajectoires de temps devant l’écran durant l’adolescence, par sexe, et de décrire la distribution des individus selon l’appartenance simultanée aux deux trajectoires. Nos hypothèses stipulent que des trajectoires différentes seront observées pour les deux sexes et que les deux comportements ne s’influenceront pas. Méthodes : Les données proviennent d’une étude prospective de 1294 adolescents de la région de Montréal, recrutés en 1999 à l’âge de 12-13 ans. Des questionnaires ont été remplis en classe à chaque 3 mois, de la première à la cinquième année du secondaire. Des modélisations de trajectoires de groupe ont identifié des trajectoires d’activité physique et de temps devant l’écran. Une modélisation de trajectoires jointes a rapporté des probabilités d’appartenance aux trajectoires des deux variables. Résultats : Cinq groupes ont été identifiés pour les trajectoires d’activité physique pour les deux sexes. Quatre groupes ont été identifiés pour les garçons et 5 pour les filles concernant le temps passé devant l’écran. 57% des garçons et 46% des filles ont fait des activités physiques pendant 6-7 jours par semaine, durant toute l’adolescence. Toutes les trajectoires de temps devant l’écran accumulent plus de deux heures d’écran quotidiennement. Les probabilités conditionnelles suggèrent une relation entre l’activité physique et le temps devant l’écran. Conclusion : Le développement de l’activité physique et du temps devant l’écran est hétérogène durant l’adolescence. Leur coévolution doit être prise en compte par les professionnels en santé publique. / Introduction: Only 7% of Canadians age ≤ 17 years engage in the recommended 60 minutes or more of moderate-to-vigorous physical activity (PA) daily. Further, most youth surpass the recommended screen time maximum of 2-hours daily. Many cross-sectional studies suggest that PA and screen time are only weakly correlated and that they evolve independently. Objectives and hypotheses: The first objective of this MSc thesis was to model PA and screen time trajectories during adolescence, in boys and girls. The second objective was to describe the distribution of participants according to concurrent membership in the two sets of trajectories. Our hypotheses were that trajectories differ by sex and that PA trajectories are independent of screen time trajectories. Methods: Data were drawn from an ongoing longitudinal study of 1294 adolescents age 12-13 years recruited in 1999-2000 in 10 Montreal-area high schools. Self-report questionnaires were completed during class time, every 3 months from grade 7 to 11. Group-based trajectory modeling identified PA and screen time trajectories. Joint trajectory models provided membership probabilities in both PA and screen time trajectories. Results: Five groups of PA trajectories were identified in both sexes. Four and five screen time trajectory groups were identified in boys and girls, respectively. Half (57%) of boys and 46% of girls engaged in PA 6-7 days weekly during the entire 5-year follow-up. All screen time trajectories were above the recommended 2-hours daily. Conditional probabilities suggested weak associations between PA and screen time. Conclusion: Patterns of PA and screen time are heterogeneous during adolescence. Their co- evolution may need to be considered by public health practitioners.

Introduction: Malgré un progrès considérable durant les dernières années, beaucoup de jeunes Canadiens fument la cigarette. La plupart des fumeurs rapportent avoir initié le tabagisme à l’adolescence ou au début de l’âge adulte. Les trajectoires développementales du tabagisme présentent une description des changements du niveau de consommation de cigarettes durant de longues périodes. Celles-ci peuvent être modélisées à l’aide de programmes statistiques qui groupent les individus démontrant le même type de changement(s) à travers le temps en sous-groupes de trajectoires. L’analyse des trajectoires pourrait potentiellement être utile à la santé publique quant à ses efforts pour contrer le tabagisme. En effet, celles-ci pourraient permettre l’identification de sous-groupes qui diffèrent selon leur consommation tabagique à travers le temps. Des facteurs de risque pour et des conséquences de ces trajectoires pourraient donc être identifiés qui pourraient s’avérer utiles pour l’intervention pour réduire ou prévenir le tabagisme chez les jeunes. Les objectifs de cette thèse étaient de: (1) résumer la littérature portant sur les modèles de trajectoires de consommation de cigarette chez les adolescents; (2) au sein d’une cohorte de 1293 participants âgés de 12 et 13 ans au début de l’étude, de modéliser les trajectoires incidentes de consommation de cigarettes et de comparer celles-ci avec les trajectoires mixtes (c’est-à-dire qui combinent les fumeurs incidents et prévalents); (3) dans la même cohorte d’adolescents, d’étudier l’initiation de la cigarette et du cannabis en relation l’une à l’autre, ainsi que leur lien(s) potentiel(s) avec les trajectoires de consommation de la cigarette. Méthodes: Nous avons effectué une revue systématique de la littérature portant sur les études présentant des modèles de trajectoires tabagiques chez les adolescents. Ces recherches ont fait usage de PubMed et EMBASE de 1980 à 2018 et 43 articles ont été retenus. Les données extraites de chaque article portaient sur la population à l’étude, le contexte et plan d’étude, les analyses statistiques et les résultats. Afin de déterminer si certains aspects du plan des études auraient pu avoir influencé le nombre ou la forme des trajectoires identifiées, nous avons groupé les études en catégories. Celles-ci étaient basées sur la taille de l’échantillon, le type de variable tabagique utilisée lors de la modélisation des trajectoires, l’axe du temps et le nombre de points de données utilisés pour estimer les trajectoires. Nous avons alors examiné les distributions ainsi que le nombre et les formes des trajectoires identifiés selon ces caractéristiques. Dans le deuxième manuscrit nous avons modélisé et comparé deux ensembles de trajectoires tabagiques. Le premier modélisait uniquement les fumeurs incidents alors que le second modélisait à la fois les fumeurs incidents et prévalents. Nos données proviennent d’une cohorte de 1293 étudiants en septième année au début de l’étude. Proc Traj et le logiciel SAS ont été utilisés afin de modéliser les trajectoires de consommation de cigarettes chez ces adolescents. L’analyse des trajectoires incidentes incluait 307 fumeurs incidents, alors que l’analyse des trajectoires dites «mixtes» incluait 307 fumeurs incidents et 338 fumeurs prévalents qui rapportaient avoir déjà essayé de fumer la cigarette au début de l’étude. Nous avons par la suite étudié plusieurs facteurs de risque potentiels pouvant être associés avec ces trajectoires dans les sphères socio-démographique, de la cigarette, psychosociale et du mode de vie. Le statut tabagique et la dépendance à la nicotine ont été étudiées comme conséquences potentielles à l’âge de 24 ans. À l’aide des mêmes données, nous avons comparé les participants à travers les trajectoires de tabagiques obtenues lors du manuscrit 2, ainsi qu’avec les individus n’ayant jamais fumé durant l’adolescence, les participants qui avaient déjà tenté de fumer la cigarette lors de leur entrée dans l’étude et les fumeurs incidents qui ont cessé peu après l’initiation. À l’aide de méthodes descriptives, nous avons effectué une comparaison entre ces groupes de la séquence d’initiation pour la cigarette et le cannabis, ainsi que de l’âge au premier usage de cannabis. Avec des modèles de régression, nous avons identifié des prédicteurs du temps écoulé entre l’initiation de la cigarette et du cannabis. Résultats: Les résultats de notre revue de la littérature ont révélé une hétérogénéité considérable entre les études, qui pourrait être le résultat de variations réelles de la consommation tabagique. Cependant celle-ci pourrait aussi avoir résulté de variations quant au plan d’études et des décisions quant à la modélisation des données. Un résultat clé était que seulement deux études avaient modélisé le tabagisme incident et ainsi représenté le cours naturel du tabagisme. Cinq trajectoires furent identifiées dans nos analyses chez les fumeurs incidents: les fumeurs au tabagisme léger et stable, léger et décroissant, augmentant lentement, augmentant moyennement et augmentant de façon précoce et importante. Quatre trajectoires furent identifiées pour le modèle combinant les fumeurs incidents et prévalents. La vitesse de changement était généralement moins importante pour les trajectoires tabagiques obtenues à partir du modèle mixte. Dans les deux modèles, les trajectoires où le tabagisme allait en augmentant étaient associées à de plus hauts niveaux de consommation de cigarettes et de dépendance à la nicotine à l’âge (jeune) adulte. Nous avons comparé les cinq groupes obtenus du modèle de trajectoires de fumeurs incidents avec les individus n’ayant jamais fumé durant l’adolescence, ainsi qu’avec les fumeurs prévalents et les fumeurs incidents qui ont cessé peu après l’initiation. Malgré le fait que l’initiation à la cigarette semble généralement avoir lieu avant l’initiation au cannabis, plusieurs des groupes avaient une proportion de participants qui avaient initié le cannabis avant la cigarette. L’initiation au cannabis avait généralement lieu à un âge moins élevé chez les participants ayant une consommation plus importante de cigarettes. L’âge à l’entrée dans l’étude était le seul facteur associé de façon statistiquement significative avec le temps écoulé entre l’initiation à la cigarette et l’initiation au cannabis chez les participants ayant initié la cigarette avant le cannabis. Aucun facteur n’était associé au temps écoulé entre l’initiation au cannabis et la première bouffée de cigarette chez les individus ayant initié le cannabis avant la cigarette. La proportion de participants rapportant avoir jamais consommé du cannabis était plus élevée dans les groupes tabagiques ayant une consommation plus importante de cigarettes. Discussion: Les études publiées jusqu’à présent n’ont pas établi l’utilité de la modélisation des trajectoires tabagiques pour la santé publique: il s’agit d’une méthode utile quand il s’agit de résumer et de décrire la consommation tabagique à travers le temps. Cependant il n’est présentement pas clair que ce genre d’analyse puisse offrir des informations additionnelles au-delà des approches plus traditionnelles. Modéliser un mélange de fumeurs incidents et prévalents peut servir à camoufler le cours naturel du développement de l’habitude tabagique ainsi que des facteurs de risque y qui sont associés. Nous recommandons donc que les études futures dans ce domaine modélisent les trajectoires incidentes de consommation tabagique. Nos résultats présentent aussi de nouvelles informations sur l’initiation de la cigarette et du cannabis qui devraient mener à une meilleure compréhension de l’interaction entre ces deux substances. L’usage de cannabis et le fait du fumer la cigarette sont liés l’un à l’autre de façon complexe: nos résultats suggèrent qu’il est important de considérer l’usage d’une substance dans son contexte, soit en présence d’autre(s) substances. / Introduction: Despite undeniable progress, far too many Canadian youth still smoke cigarettes. Most smokers report initiation in adolescence or young adulthood. Developmental trajectories of cigarette smoking are descriptions of change in smoking over relatively long time-periods which can be modeled using software platforms which group individuals with similar developmental patterns into subgroups of trajectories. Trajectory analysis may be useful to public health efforts to curb smoking because it permits identification of subgroups that differ according to the pattern of growth in cigarette smoking. Risk factors for, and outcomes of these trajectories can be identified, which may be amenable to intervention to effect positive change in youth smoking. The objectives of this thesis were: (1) to synthesize the literature on studies of adolescent cigarette smoking trajectories; (2) in an adolescent cohort of 1293 participants age 12-13 years at inception, to model trajectories of incident cigarette smoking and compare incident trajectories with mixed (i.e. incident and prevalent smokers combined) trajectories; (3) in the same adolescent cohort, to study cannabis and cigarette initiation in relation to each other and to cigarette smoking trajectories. Methods: We carried out a systematic review of studies of cigarette smoking trajectories in adolescents. PubMed and EMBASE were searched 1980–2018 and 43 articles retained. Data were extracted from each article relating to study population, setting and design, statistical analyses, and results. In order to assess whether study design features might have influenced the number or shapes of trajectories identified, we collapsed studies into categories based on study sample size, type of cigarette smoking indicator used, time axis, and number of data points used to estimate trajectories. We examined the distributions of number and shapes of trajectories identified according to these characteristics. In Manuscript 2 we modeled and compared two sets of cigarette smoking trajectories. The first included incident cigarette smokers alone while the second included both incident and prevalent cigarette smokers. Data were from a cohort of 1293 grade 7 students at baseline. We used SAS Proc Traj to model trajectories of cigarette smoking in adolescence. Analysis of incident trajectories included 307 incident smokers; analysis of “mixed” trajectories included 307 incident and 338 prevalent smokers who reported having ever smoked at baseline. We studied various potential sociodemographic, smoking-related, psychosocial, and lifestyle risk factors in relation to trajectory group. Smoking status and nicotine dependence outcomes were assessed at age 24. Using these data, we compared participants across the cigarette smoking trajectories obtained in Manuscript 2, as well as never smokers during adolescence, baseline ever smokers, and incident smokers who stopped. Using descriptive methods, we compared these groups according to age at first cannabis use and determined the order of initiation of tobacco and cannabis among participants. Using regression, we identified predictors of elapsed time between tobacco and cannabis initiation. Results: The findings of our review revealed considerable heterogeneity between studies which may have reflected real variations in cigarette smoking but which may also have resulted from variation in study design features and modelling decisions. A key finding was that only two studies modeled incident smoking and depicted the natural course of smoking. Five trajectories were identified in incident smokers: stable-low consumers, low-level decreasers, slow escalators, moderate escalators, and early-rapid escalators. Four trajectories were identified in the mix of incident and prevalent smokers. The rate of change was generally attenuated across curves in the mixed trajectory analysis. Escalating trajectories in both analyses were associated with higher levels of cigarette consumption and nicotine dependence in early adulthood. When comparing these five incident trajectory groups with never smokers, prevalent smokers at baseline, and incident smokers who stopped, we report that while first puff on a cigarette usually preceded cannabis use, several groups had a number of participants who initiated cannabis before cigarettes. Age at first cannabis use was generally lower in participants with heavier cigarette consumption. Age at baseline was the only significant risk factor for time to first cannabis use among ever smokers; no factors were associated with time to first cigarette use among ever cannabis users. Ever use of cannabis was higher in trajectory groups with heavier cigarette consumption. Discussion: The literature published thus far has not established the usefulness of this methodology to public health: it is useful for summarizing and describing cigarette smoking patterns, yet it is not clear whether trajectory analyses offer additional information useful to public health. Modeling a mix of incident and prevalent adolescent smokers obscures depiction of the natural course of smoking onset and identification of factors associated with the natural course of cigarette smoking: we therefore recommend that future studies in this area model incident trajectories of cigarette smoking. Our findings also present new information on the initiation of cigarettes and cannabis which should lead to a greater understanding of the interplay between these substances. Cannabis use and cigarette smoking relate to each other in complex ways: our results suggest that it is important to consider use of any one substance in the context of use with other substances.

Football trajectory modeling is a powerful tool for predicting and evaluating the movement of a football and its dynamics. Masked autoencoders are scalable self-supervised learners used for representation learning of partially observable data. Masked autoencoders have been shown to provide successful results in pre-training for computer vision and natural language processing tasks. Using masked autoencoders in the multivariate time-series data field has not been researched to the same extent. This thesis aims to investigate the potential of using masked autoencoders for multivariate time-series modeling for football trajectory data in collaboration with Tracab. Two versions of the masked autoencoder network with alterations are tested, which are implemented to be used with multivariate time-series data. The resulting models are used to detect anomalies in the football trajectory and propose corrections based on the reconstruction. The results are evaluated, discussed, and compared against the tracked and manually corrected value of the ball trajectory. The performance of the different frameworks is compared and the overall anomaly detection capabilities are discussed. The result suggested that even though the regular autoencoder version had a smaller average reconstruction error during training and testing, using masked autoencoders improved the anomaly detection performance. The result suggested that neither the regular autoencoder nor the masked autoencoder managed to propose plausible trajectories to correct anomalies in the data. This thesis promotes further research to be done in the field of using masked autoencoders for time series and trajectory modeling. / Modellering av en fotbolls bollbana är ett kraftfullt verktyg för att förutse och utvärdera rörelsen och dynamiken hos en fotboll. Maskerade autoencoders är skalbara självövervakande inlärare som används för representationsinlärning av delvis synlig data. Maskerade autoencoders har visat sig ge framgångsrika resultat vid förträning inom datorseende och naturlig språkbearbetning. Användningen av maskerade autoencoders för multivariat tidsserie-data har det inte forskats om i samma omfattning. Syftet med detta examensarbete är att undersöka potentialen för maskerade autoencoders inom tidsseriemodellering av bollbanor för fotboll i samarbete med Tracab. Två versioner av maskerade autoencoders anpassade för tidsserier testas. De tränade modellerna används för att upptäcka avvikelser i detekterade fotbollsbanor och föreslå korrigeringar baserat på rekonstruktionen. Resultaten utvärderas, diskuteras och jämförs med det detekterade och manuellt korrigerade värdet för fotbollens bollbana. De olika ramverken jämförs och deras förmåga för detektion och korrigering av avvikelser diskuteras. Resultatet visade att även om den vanliga autoencoder-versionen hade ett mindre genomsnittligt rekonstruktionsfel efter träning, så bidrog användningen av maskerade autoencoders till en förbättring inom detektering av avvikelser. Resultatet visade att varken den vanliga autoencodern eller den maskerade autoencodern lyckades föreslå trovärdiga bollbanor för att korrigera de funna avvikelserna i datan. Detta examensarbete främjar ytterligare forskning inom användningen av maskerade autoencoders för tidsserier och banmodellering.