The Birnbaum-Saunders (BS) distribution is a positively skewed distribution and is a popular model for analyzing lifetime data. In this thesis, we first develop an improved method of estimation for the BS distribution and the corresponding inference. Compared to the maximum likelihood estimators (MLEs) and the modified moment estimators (MMEs), the proposed method results in estimators with smaller bias, but having the same mean squared errors (MSEs) as these two estimators. Next, the existence and uniqueness of the MLEs of the parameters of BS distribution are discussed based on Type-I, Type-II and hybrid censored samples. In the case of five-parameter bivariate Birnbaum-Saunders (BVBS) distribution, we use the distributional relationship between the bivariate normal and BVBS distributions to propose a simple and efficient method of estimation based on Type-II censored samples. Regression analysis is commonly used in the analysis of life-test data when some covariates are involved. For this reason, we consider the regression problem based on BS and BVBS distributions and develop the associated inferential methods. One may generalize the BS distribution by using Laplace kernel in place of the normal kernel, referred to as the Laplace BS (LBS) distribution, and it is one of the generalized Birnbaum-Saunders (GBS) distributions. Since the LBS distribution has a close relationship with the Laplace distribution, it becomes necessary to first carry out a detailed study of inference for the Laplace distribution before studying the LBS distribution. Several inferential results have been developed in the literature for the Laplace distribution based on complete samples. However, research on Type-II censored samples is somewhat scarce and in fact there is no work on Type-I censoring. For this reason, we first start with MLEs of the location and scale parameters of Laplace distribution based on Type-II and Type-I censored samples. In the case of Type-II censoring, we derive the exact joint and marginal moment generating functions (MGF) of the MLEs. Then, using these expressions, we derive the exact conditional marginal and joint density functions of the MLEs and utilize them to develop exact confidence intervals (CIs) for some life parameters of interest. In the case of Type-I censoring, we first derive explicit expressions for the MLEs of the parameters, and then derive the exact conditional joint and marginal MGFs and use them to derive the exact conditional marginal and joint density functions of the MLEs. These densities are used in turn to develop marginal and joint CIs for some quantities of interest. Finally, we consider the LBS distribution and formally show the different kinds of shapes of the probability density function (PDF) and the hazard function. We then derive the MLEs of the parameters and prove that they always exist and are unique. Next, we propose the MMEs, which can be used as initial values in the numerical computation of the MLEs. We also discuss the interval estimation of parameters. / Thesis / Doctor of Science (PhD)

Indiana University-Purdue University Indianapolis (IUPUI) / Introduction: The prevalence of diabetes mellitus (DM) is rapidly increasing among the aging United States population. This poses a challenge to dental providers since DM and multiple oral conditions have been identified as comorbidities. Hypertension (HTN) is associated with more poorly controlled DM and has been identified as contributing to RCT tooth loss in prior studies. Links have also been established between DM and the survival rate of root canal treated teeth, however, previous research has focused on institutional settings despite the majority of RCT being performed in private dental practices. This study will use data from private dental practices to evaluate the survival rate of RCT teeth in patients with DM and HTN. Materials and Methods: This retrospective study evaluated the survival rate of endodontic treated teeth among patients with DM and HTN using National Dental PBRN Practice data. Electronic dental records from 42 private dental practices in the United States over a period of 15 years with a minimum 2-year follow-up comprising 11,532 root canal treated teeth were analyzed. Kaplan-Meier survival curves were used to demonstrate the effects of HTN and DM on RCT tooth survival and Cox proportional hazards survival analysis was used to evaluate the DM and HTN effects after accounting for age, gender, insurance, year of treatment, tooth type, and crown and filling placement as covariates. Results: Patients with HTN only had significantly lower risk of failure than patients with both HTN and DM (p=0.003). Patients with neither HTN nor DM had significantly lower risk of failure than patients with both HTN and DM (p=0.020). Patients with DM only did not have significantly different risk of failure than patients with both HTN and DM (p=0.223). Patients with DM only did not have significantly different risk of failure than patients with HTN only (p=0.361). Patients with neither HTN nor DM did not have significantly different risk of failure than patients with HTN only (p=0.121) or patients with DM only (p=0.800). Conclusions: Patients with both DM and HTN have an increased chance of root canal treated tooth failure while patients with only DM or only HTN do not. Evaluation of severity of DM may be more important in determining RCT failure and studies utilizing laboratory values should be considered for future research.

對於生存時間的資料而言，通常我們所想要研究瞭解的是，至少存活到某特定時間點的機率，而這個機率亦即生存分析中的生存函數(survival function)。當有兩個不同的母體存在時，為了要知道這兩個母體的生存函數是否相同，在統計方法上，我們將進行一些檢定，常用的有Gehan-Wilcoxon和Cox-Mantel之兩樣本檢定，後來又有修飾型的Kolmogorov-Smirnov檢定。但是，前兩種檢定方法，只對此兩組生存函數呈現某特殊型式時，具有好的檢定力。因此，透過一些實證的研究，將上述檢定方法做有系統的整理，進而發展出一套簡單又有效率的檢定程序。再者，若檢定得此兩個母體之生存函數不相等時，如何利用Bootstrap方法，進一步對兩組生存函數之特定生存機率點或生存時間點所分別對應之生存時間或生存機率差距做推論與比較，本文將有詳細她說明；以提供研究人員更多有效的資訊，不再僅止於檢定虛無假設是否拒絕而已。最後，我們又藉由推廣上述Bootstrap方法，將其運用到檢定方法上，而另外發展出一種新的兩母體生存函數之檢定方法。 / When two different populations exist, we will take some tests by Cehan-Wilcoxon, Cox-Mantel or Modified Kolmogorov- Smirnov in satistical way. Therefore we develope a simple and efficient test process from arranging above test ways system- atically through some real study. How to use Bootstrap way to infer the difference of survival time or survival probability of specular point. We infer Bootstrap way on test work and then develope a new two populations survival function test way.

Made available in DSpace on 2014-07-22T13:16:48Z (GMT). No. of bitstreams: 2 Regina Elizabeth Müller.pdf: 4161979 bytes, checksum: 5df884fdb04b617145c35c1741e9b502 (MD5) license.txt: 1914 bytes, checksum: 7d48279ffeed55da8dfe2f8e81f3b81f (MD5) Previous issue date: 2011 / Fundação Oswaldo Cruz. Instituto Nacional de Saúde da Mulher, da Criança e do Adolescente Fernandes Figueira. Rio de Janeiro, RJ, Brasil. / Introdução: A cardiopatia reumática persiste como a principal doença cardiovascular adquirida em crianças e adultos jovens em todo o mundo, sendo responsável por altas taxas de morbimortalidade e evoluindo com frequência para a necessidade de cirurgia cardíaca valvar em pacientes na fase aguda ou crônica da doença. Objetivo: Estimar os fatores associados e o tempo desde o diagnóstico até a cirurgia cardíaca valvar em crianças e adolescentes portadores de cardiopatia reumática, em um centro cardiológico de referência terciária no Rio de Janeiro. Material e Métodos: estudo observacional longitudinal de base hospitalar, utilizando metodologia de análise de sobrevivência, para estimativa do tempo até a cirurgia, e modelo de regressão de Cox, para avaliar as razões de risco associadas segundo as covariáveis. A coorte foi composta por pacientes com 3 a 20 anos, cadastrados no Instituto Nacional de Cardiologia no Rio de Janeiro entre julho de 1986 e junho de 2006 e acompanhados até setembro de 2011. O diagnóstico da lesão valvar foi confirmado pelo exame Doppler-ecocardiográfico. As covariáveis, avaliadas no início do acompanhamento, foram reunidas em três dimensões: sociodemográfica (sexo, grupo etário, cor da pele, região de moradia e década do diagnóstico); clínica (apresentação clínica, classe funcional, número de surtos anteriores, profilaxia secundária, endocardite infecciosa e fibrilação atrial); e ecocardiográfica (lesão valvar por tipo e gravidade; diâmetro do átrio esquerdo, diâmetro sistólico do ventrículo esquerdo, função ventricular esquerda, hipertensão arterial pulmonar, e ruptura de cordoalha mitral). O banco de dados foi elaborado com o programa ACCESS 2000 e a análise estatística foi realizada pelo programa R versão 2.13.1. Foi considerado significativo o valor de - 0,05. Resultados: a coorte foi composta por 348 pacientes, 58% do sexo feminino, com idade mediana ao cadastro de 12,5 anos, e de 21,5 anos ao final do acompanhamento. O tempo médio de seguimento foi de 9,0 anos (2-21 anos). O evento cirurgia cardíaca ocorreu em 39% da amostra, com tempo mediano até a cirurgia de 22,3 anos. Na análise univariada todas as covariáveis das três dimensões (socioedemográfica, clínica e ecocardiográfica) apresentaram significância estatística e risco para realização de cirurgia cardíaca (hazard ratio>1), com exceção apenas da covariável região de moradia (p>0,5). Na análise multivariada, o modelo final incluiu as variáveis: década do diagnóstico, classe funcional, número de surtos anteriores, endocardite infecciosa, lesão valvar por tipo e gravidade, diâmetro do átrio esquerdo, diâmetro sistólico do ventrículo esquerdo e ruptura de cordoalha mitral. Conclusões: A realização da cirurgia cardíaca em pacientes com cardiopatia reumática está associada a fatores sociodemográficos, clínicos e ecocardiográficos. / Introduction: Rheumatic heart disease remains as the most common acquired heart disease in children and young adults all over the world, being responsible for high mortality and morbidity rates and often demanding valve surgery in the acute or chronic phase of the disease. Objective: To estimate the time from diagnosis until valve operation and the associated factors in children and young adults with rheumatic heart disease followed up in a tertiary center for cardiovascular care in Rio de Janeiro. Methods – It is a longitudinal observational study of a hospital based population, using survival analysis methodology for time estimation and Cox regression model for hazard risk evaluation of associated variables. Cohort was composed by 3 to 20 years old patients, registered in the National Institute of Cardiology (Instituto Nacional de Cardiologia), in Rio de Janeiro, between July 1986 and June 2006, and followed up until September 2011. Valve disease diagnosis was confirmed through Doppler echocardiography examination. Variables were evaluated at the patient´s first visit and separated in three dimensions: socio demographic (gender, age group, skin color, residence region, decade of diagnosis); clinic (disease status at presentation, functional class, number of previous rheumatic episodes, secondary prophylaxis, infectious endocarditis, atrial fibrillation); echocardiographic (valve lesion and severity, left atrium diameter, systolic left ventricle diameter, left ventricle function, pulmonary hypertension, rupture of mitral chordae). The database wasbased on the program ACCESS 2000 and statistical analysis was performed using the R Program version 2.13.1. For statistical analysis was considered as significant values for  value 0.05. Results – 348 patients were included in the cohort, 58% female. Median age at the register was 12.5 years, and 21.5 years at the end of follow up. Median follow-up time was 9.0 years (2 to 21 years). 39% underwent valve operation and the median time until surgery was 22.3 years. In the univariate analysis all the variables from the three dimensions (socio demographic, clinic and echocardiographic) presented statistical significance as hazard risk in predicting valve operation (hazard ratio>1), with only one exception, that was residence region (p>0.5). In the multivariate analysis the final model included the following variables: decade of diagnosis, functional class, number of anterior rheumatic episodes, infectious endocarditis, valve lesion and severity, left atrium diameter, systolic left ventricle diameter and rupture of mitral chordate. Conclusions: Valve surgery in patients with rheumatic heart disease is associated with socio demographic, clinic and echocardiographic factors.

Dans cette thèse, nous étudions des modèles définis par des équations de moments conditionnels. Une grande partie de modèles statistiques (régressions, régressions quantiles, modèles de transformations, modèles à variables instrumentales, etc.) peuvent se définir sous cette forme. Nous nous intéressons au cas des modèles avec un paramètre à estimer de dimension finie, ainsi qu’au cas des modèles semi paramétriques nécessitant l’estimation d’un paramètre de dimension finie et d’un paramètre de dimension infinie. Dans la classe des modèles semi paramétriques étudiés, nous nous concentrons sur les modèles à direction révélatrice unique qui réalisent un compromis entre une modélisation paramétrique simple et précise, mais trop rigide et donc exposée à une erreur de modèle, et l’estimation non paramétrique, très flexible mais souffrant du fléau de la dimension. En particulier, nous étudions ces modèles semi paramétriques en présence de censure aléatoire. Le fil conducteur de notre étude est un contraste sous la forme d’une U-statistique, qui permet d’estimer les paramètres inconnus dans des modèles généraux. / In this dissertation we study statistical models defined by condition estimating equations. Many statistical models could be stated under this form (mean regression, quantile regression, transformation models, instrumental variable models, etc.). We consider models with finite dimensional unknown parameter, as well as semiparametric models involving an additional infinite dimensional parameter. In the latter case, we focus on single-index models that realize an appealing compromise between parametric specifications, simple and leading to accurate estimates, but too restrictive and likely misspecified, and the nonparametric approaches, flexible but suffering from the curse of dimensionality. In particular, we study the single-index models in the presence of random censoring. The guiding line of our study is a U-statistics which allows to estimate the unknown parameters in a wide spectrum of models.

Le cancer du sein est actuellement dans les pays occidentaux le premier cancer chez la femme, en termes d’incidence et de mortalité (taux standardisés de 101,5 et 17.7 pour 100 000 personnes années en 2005 respectivement). De très nombreux facteurs de risque et facteurs pronostiques sont déjà connus et étudiés, plusieurs axes de recherche sont développés sur toutes les étapes de la maladie, mais l’influence des facteurs socio-économiques et géographiques, aux niveaux individuel et environnemental n’avait pas encore été étudiée en France sur le cancer du sein.L’objectif général de ce travail était d’explorer cette influence par différents moyens afin d’en tirer des connaissances et une application pratique dans la prévention du cancer du sein, qu’elle soit primaire, secondaire ou tertiaire.Dans notre première étude nous avons montré que les femmes d’un niveau socio-éducatif faible étaient moins à même d’avoir bénéficié d’au moins une mammographie dans les 6 ans ou d’au moins un suivi gynécologique dans les 3 ans précédant leur diagnostic de cancer du sein. Egalement elles ont un stade de diagnostic plus avancé que les femmes de niveau socio-éducatif plus élevé. Ces variables sont ensuite retrouvées comme facteurs pronostiques péjoratifs de la survie. Dans notre seconde étude nous avons montré que l’accès à un chirurgien spécialisé dans les interventions du cancer du sein, gage d’une meilleure survie, était influencé par le niveau socio-économique du lieu de résidence de la patiente, ainsi que par son éloignement géographique par rapport aux centres de traitement de référence du cancer, où travaillent les chirurgiens spécialisés. Dans notre troisième étude nous avons montré qu’à l’inverse de nombre de cancers, l’incidence du cancer du sein était plus élevée dans les zones socio-économiquement plus favorisées, et ce quelle que soit la classe d’âge de la patiente, phénomène pour lequel nous n’avons pas vraiment d’explication, surtout pour les femmes les plus jeunes. Enfin dans notre quatrième étude actuellement en cours, nous avons pour objectif d’étudier au niveau individuel, conjointement avec le nouvel indice de défavorisation européen adapté à la France, en quoi le degré de richesse économique et sociale et la proximité des services médicaux des patientes atteintes de cancer du sein joue sur le stade de la tumeur, l’accès et les modalités de traitement, et la survie. / In developed countries, breast cancer is currently the leading cancer in women in terms of incidence and mortality (standardized rate of 101.5 and 17.7 per 100,000 person-years in 2005, respectively). Many risk factors and prognostic factors have been studied and are well known. Research is under way with regard to every step in the development of breast cancer, but the impact of socio-economic and geographic factors, at the individual and environmental level with regard to the disease have never been studied in France.The general aim of this work was to explore the impact of these factors in different ways to build on our knowledge and to develop practical applications in the primary, secondary or tertiary prevention of breast cancer.In our first study, we showed that women with a low socio-educational level were less likely to have benefited from at least one mammography within the 6 years or at least one gynaecological consultation within the 3 years before the diagnosis of breast cancer. These women also had a more advanced tumour at diagnosis than did women with a higher socio-educational level. These variables also came to light as predictors of a poor prognosis in terms of survival. In our second study, we showed that access to a surgeon specialised in breast cancer surgery, which is associated with better survival, was influenced by the socio-economic level of the patient’s place of residence, as well as the distance between the patient’s home and reference centres for cancer treatment, where the specialised surgeons work. In our third study, we showed that in contrast to many cancers, the incidence of breast cancer was highest in the most socio-economically privileged areas, and this whatever the age of the patient. We have no explanation for this phenomenon, particularly with regard to the youngest age group of women. Finally, the aim of our fourth study, which is currently on-going, is to study at the individual level, using the new European deprivation index adapted to France, to what extent economic wealth and social standing, as well as the proximity of medical services for patients with breast cancer have an impact on tumour stage, access to treatment, treatment techniques and survival.

Le risque attribuable (RA) mesure la proportion de cas de maladie qui peuvent être attribués à une exposition au niveau de la population. Plusieurs définitions et méthodes d'estimation du RA ont été proposées pour des données de survie. En utilisant des simulations, nous comparons quatre méthodes d'estimation du RA dans le contexte de l'analyse de survie : deux méthodes non paramétriques basées sur l'estimateur de Kaplan-Meier, une méthode semi-paramétrique basée sur le modèle de Cox à risques proportionnels et une méthode paramétrique basée sur un modèle à risques proportionnels avec un risque de base constant par morceaux. Nos travaux suggèrent d'utiliser les approches semi-paramétrique et paramétrique pour l'estimation du RA lorsque l'hypothèse des risques proportionnels est vérifiée. Nous appliquons nos méthodes aux données de la cohorte E3N pour estimer la proportion de cas de cancer du sein invasif attribuables à l'utilisation de traitements hormonaux de la ménopause (THM). Nous estimons qu'environ 9 % des cas de cancer du sein sont attribuables à l'utilisation des THM à l'inclusion. Dans le cas d'une exposition protectrice, une alternative au RA est la fraction préventive (FP) qui mesure la proportion de cas de maladie évités. Cette mesure n'a pas été considérée dans le contexte de l'analyse de survie. Nous proposons une définition de la FP dans ce contexte et des méthodes d'estimation en utilisant des approches semi-paramétrique et paramétrique avec une extension permettant de prendre en compte les risques concurrents. L'application aux données de la cohorte des Trois Cités (3C) estime qu'environ 9 % de cas d'accident vasculaire cérébral peuvent être évités chez les personnes âgées par l'utilisation des hypolipémiants. Notre étude montre que la FP peut être utilisée pour évaluer l'impact des médicaments bénéfiques dans les études de cohorte tout en tenant compte des facteurs de confusion potentiels et des risques concurrents. / The attributable risk (AR) measures the proportion of disease cases that can be attributed to an exposure in the population. Several definitions and estimation methods have been proposed for survival data. Using simulations, we compared four methods for estimating AR defined in terms of survival functions: two nonparametric methods based on Kaplan-Meier's estimator, one semiparametric based on Cox's model, and one parametric based on the piecewise constant hazards model. Our results suggest to use the semiparametric or parametric approaches to estimate AR if the proportional hazards assumption appears appropriate. These methods were applied to the E3N women cohort data to estimate the AR of breast cancer due to menopausal hormone therapy (MHT). We showed that about 9% of cases of breast cancer were attributable to MHT use at baseline. In case of a protective exposure, an alternative to the AR is the prevented fraction (PF) which measures the proportion of disease cases that could be avoided in the presence of a protective exposure in the population. The definition and estimation of PF have never been considered for cohort studies in the survival analysis context. We defined the PF in cohort studies with survival data and proposed two estimation methods: a semiparametric method based on Cox’s proportional hazards model and a parametric method based on a piecewise constant hazards model with an extension to competing risks. Using data of the Three-City (3C) cohort study, we found that approximately 9% of cases of stroke could be avoided using lipid-lowering drugs (statins or fibrates) in the elderly population. Our study shows that the PF can be estimated to evaluate the impact of beneficial drugs in observational cohort studies while taking potential confounding factors and competing risks into account.

Today there exists two types of preventive surgical treatment procedures for Abdominal Aortic Aneurysm. In order to make an informed choice of treatment, the clinician needs to have a clear picture of how the choice will affect the patients chances of survival. In this master thesis, machine learning techniques are used to predict survival probabilities after respective treatment procedure and the performance is compared to the more conventional Kaplan-Meier estimator.  Using Danish patient data, different machine learning models for survival predictions were trained and evaluated by their performance. Administrative Brier Score was used as performance metric as the data was administratively censored. An Ensemble model consisting of one Random Survival Forest and one Neural Multi Task Logistic Regression model was shown to achieve the best performance and significantly outperformed the conventional Kaplan-Meier model. Furthermore, an approach to investigate the predicted effects of choice of treatment was introduced. It showed that on average the Ensemble model predicted the choice of treatment to have less effect on the long term survival than what the corresponding prediction using the Kaplan-Meier estimator suggested. This applies to the full patient group as well as for patients of age between 70 and 79 years. In the latter case this prediction was also shown to be more accurate. / Idag finns det två typer av förebyggande kirurgiska behandlingsmetoder för abdominal aortaaneurysm. För att göra ett välgrundat val av behandlingsmetod måste läkaren ha en tydlig bild av hur valet kommer att påverka patienternas överlevadschanser. I detta examensarbete används maskininlärningstekniker för att förutsäga överlevnadssannolikheten efter respektive behandlingsmetod och prestandan jämförs mot den mer konventionella Kaplan-Meier-estimatorn. Med hjälp av dansk patientdata tränades olika maskininlärningsmodeller avsedda för överlevnadanalys och utvärderades utifrån deras prestanda. Administrativt Brier Score användes som mätvärde då censureringen i datan skett administrativt. En Ensemble-modell bestående av en Random Survival Forest- och en Neural Multi-Task Logistic Regression-modell visade sig uppnå bäst prestanda och överträffade signifikant den konventionella Kaplan-Meier-estimatorn.  Dessutom introducerades ett tillvägagångssätt för att undersöka de predikterade effekterna av valet av behandling. Resultaten visade att Ensemble-modellen i genomsnitt förutspådde valet av behandling att ha mindre effekt på den långsiktiga överlevnaden än vad motsvarande förutsägelse med Kaplan-Meier-estimatorn föreslog. Detta både för alla patienter såväl som för patienter i åldern mellan 70 och 79 år. I det senare fallet visade sig denna förutsägelse också vara mer träffsäker.

Fire is the primary natural disturbance vital to the ecological integrity of Quetico Provincial Park, Ontario, Canada. A new provincial park planning process (i.e., Class Environmental Assessment) has required the review of Quetico’s Fire Management Plan. To support this review, large and severe (stand-replacing) Quetico fires were studied using 1966 Ontario Ministry of Natural Resources (OMNR) forest resource inventory (FRI) mapping. A Geographic Information Systems (GIS) database of the FRI was created and updated with the OMNR digital fire atlas. This database was used as a time-since-fire and fire interval dataset to estimate fire frequency. It also served to archive the 1966 FRI for the largest protected area in the transition between the Boreal and Great Lakes-St. Lawrence forest regions. Non-parametric (Kaplan-Meier) survival analysis was used to estimate survival functions and mean fire intervals (i.e., the expected time between two consecutive stand-replacing fires for any location within the Park). Previous studies that have used Kaplan-Meier survival analysis methods have based fire frequency estimates solely on time-since-fire data. However, time-since-fire data cannot be equated with fire interval data when using non-parametric methods. At least one fire interval is required to obtain reliable results. The mean fire interval for the entire 475,782 ha Park between the years 1668 and 2007 was 230 years. Performing the analysis on various geographic and temporal partitions revealed fire frequency spatial and temporal variability. A constant (independent of time-since-fire) probability of burning was not observed for Quetico which is contrary to accepted conjecture for northwestern Ontario boreal/mixed-wood forests. A current fire cycle was also estimated for the Park (342 years) using the digital fire atlas. The results suggested that use of historical static fire frequency estimates as fire management prescriptions may not be justified given considerable fire frequency temporal variability. The observed fire frequency spatial variability suggests that studies should be undertaken at coarser scales than is the norm to characterise the regions fire regime in support of landscape level fire management planning.

Fire is the primary natural disturbance vital to the ecological integrity of Quetico Provincial Park, Ontario, Canada. A new provincial park planning process (i.e., Class Environmental Assessment) has required the review of Quetico’s Fire Management Plan. To support this review, large and severe (stand-replacing) Quetico fires were studied using 1966 Ontario Ministry of Natural Resources (OMNR) forest resource inventory (FRI) mapping. A Geographic Information Systems (GIS) database of the FRI was created and updated with the OMNR digital fire atlas. This database was used as a time-since-fire and fire interval dataset to estimate fire frequency. It also served to archive the 1966 FRI for the largest protected area in the transition between the Boreal and Great Lakes-St. Lawrence forest regions. Non-parametric (Kaplan-Meier) survival analysis was used to estimate survival functions and mean fire intervals (i.e., the expected time between two consecutive stand-replacing fires for any location within the Park). Previous studies that have used Kaplan-Meier survival analysis methods have based fire frequency estimates solely on time-since-fire data. However, time-since-fire data cannot be equated with fire interval data when using non-parametric methods. At least one fire interval is required to obtain reliable results. The mean fire interval for the entire 475,782 ha Park between the years 1668 and 2007 was 230 years. Performing the analysis on various geographic and temporal partitions revealed fire frequency spatial and temporal variability. A constant (independent of time-since-fire) probability of burning was not observed for Quetico which is contrary to accepted conjecture for northwestern Ontario boreal/mixed-wood forests. A current fire cycle was also estimated for the Park (342 years) using the digital fire atlas. The results suggested that use of historical static fire frequency estimates as fire management prescriptions may not be justified given considerable fire frequency temporal variability. The observed fire frequency spatial variability suggests that studies should be undertaken at coarser scales than is the norm to characterise the regions fire regime in support of landscape level fire management planning.