Methods of competing risks analysis of end-stage renal disease and mortality among people with diabetes

<p>Abstract</p> <p>Background</p> <p>When a patient experiences an event other than the one of interest in the study, usually the probability of experiencing the event of interest is altered. By contrast, disease-free survival time analysis by standard methods, such as the Kaplan-Meier method and the standard Cox model, does not distinguish different causes in the presence of competing risks. Alternative approaches use the cumulative incidence estimator by the Cox models on cause-specific and on subdistribution hazards models. We applied cause-specific and subdistribution hazards models to a diabetes dataset with two competing risks (end-stage renal disease (ESRD) or death without ESRD) to measure the relative effects of covariates and cumulative incidence functions.</p> <p>Results</p> <p>In this study, the cumulative incidence curve of the risk of ESRD by the cause-specific hazards model was revealed to be higher than the curves generated by the subdistribution hazards model. However, the cumulative incidence curves of risk of death without ESRD based on those three models were very similar.</p> <p>Conclusions</p> <p>In analysis of competing risk data, it is important to present both the results of the event of interest and the results of competing risks. We recommend using either the cause-specific hazards model or the subdistribution hazards model for a dominant risk. However, for a minor risk, we do not recommend the subdistribution hazards model and a cause-specific hazards model is more appropriate. Focusing the interpretation on one or a few causes and ignoring the other causes is always associated with a risk of overlooking important features which may influence our interpretation.</p

Evaluating hospital performance based on excess cause-specific incidence

Formal evaluation of hospital performance in specific types of care is becoming an indispensable tool for quality assurance in the health care system. When the prime concern lies in reducing the risk of a cause-specific event, we propose to evaluate performance in terms of an average excess cumulative incidence, referring to the center's observed patient mix. Its intuitive interpretation helps give meaning to the evaluation results and facilitates the determination of important benchmarks for hospital performance. We apply it to the evaluation of cerebrovascular deaths after stroke in Swedish stroke centers, using data from Riksstroke, the Swedish stroke registry

The role of survival functions in competing risks

Competing risks data usually arises in studies in which the failure of an individual may be classified into one of k (k > 1) mutually exclusive causes of failure. When competing risks are present, there are two main differences with classical survival analysis: (i) survival functions are not mainly used to describe cause-specific failures and, (ii) classical estimation techniques may provide biased results. The main goal of this paper is to review, clarify and present the formulation of a competing risks model and the basic nonparametric estimation methods. We show why the use of survival functions in the competing risks framework may mislead the user, and we illustrate the presented methodologies by developing two examples from real data. The methods presented here can be implemented with several statistical packages, including R, SPSS and SAS: we give some highlights on how to perform a competing risks analysis with these software packages

Survival analysis for AdVerse events with VarYing follow-up times (SAVVY): summary of findings and a roadmap for the future of safety analyses in clinical trials

The SAVVY project aims to improve the analyses of adverse events (AEs) in clinical trials through the use of survival techniques appropriately dealing with varying follow-up times and competing events (CEs). This paper summarizes key features and conclusions from the various SAVVY papers. Through theoretical investigations using simulations and in an empirical study including randomized clinical trials from several sponsor organisations, biases from ignoring varying follow-up times or CEs are investigated. The bias of commonly used estimators of the absolute and relative AE risk is quantified. Furthermore, we provide a cursory assessment of how pertinent guidelines for the analysis of safety data deal with the features of varying follow-up time and CEs. SAVVY finds that for both, avoiding bias and categorization of evidence with respect to treatment effect on AE risk into categories, the choice of the estimator is key and more important than features of the underlying data such as percentage of censoring, CEs, amount of follow-up, or value of the gold-standard. The choice of the estimator of the cumulative AE probability and the definition of CEs are crucial. SAVVY recommends using the Aalen-Johansen estimator (AJE) with an appropriate definition of CEs whenever the risk for AEs is to be quantified. There is an urgent need to improve the guidelines of reporting AEs so that incidence proportions or one minus Kaplan-Meier estimators are finally replaced by the AJE with appropriate definition of CEs.Comment: 17 pages, 1 Figure, 4 Tables. arXiv admin note: text overlap with arXiv:2008.0788

Summary of survival analysis with SAS procedures.

The research conducted for this thesis was performed to summarize some of the most commonly used survival analysis techniques as well as to create one macro that will provide the solutions for these techniques. Some of the techniques that this thesis focuses on are survival and hazard functions, mean and median survival times, life table, log rank test, proportional hazards/model building, and competing risk. To further analyze these survival analysis techniques I will use the Bone Marrow Transplantation for Leukemia dataset. This trial consists of either acute myelocytic leukemia (AML 99 patients) or acute lymphoblastic leukemia (ALL 38 patients). There are two risk level for AML, low risk first readmission (54 patients) and high risk second readmission or untreated first relapse (15 patients) or second or greater relapse or never in remission (30 patients). Any further details of this study can be found in (Copelan, 1991)

Additive and Multiplicative Hazards Regression Models In Competing Risks Analysis: Application To The Canadian Heart Health Survey

Background: In survival analysis, an event whose occurrence influences the occurrence of another event is termed a competing risk event. The Cox hazards model is applicable in standard survival analysis with a single event. To correctly assess covariate effects in competing risks analysis, the Fine & Gray (F-G) subdistribution hazards and the Cox cause-specific hazards models are appropriate. Equally, additive hazards models can be used to examine the covariate effects in a competing risks framework. Objectives: (i) To examine the additive and multiplicative hazards models in the competing risks setting by applying the said models to the Canadian Heart Health Survey data; (ii) To determine the risk factors for cardiovascular disease using the competing risks approach; (iii) To compare the risk factors identified by the additive and multiplicative hazards models in the context of competing risks. Methods: The observational Canadian Heart Health Survey database collected between 1986 and 1995 is the baseline data used in this study. Two competing outcomes, cardiovascular disease (CVD) and non-CVD-related deaths, are analyzed with the Cox cause-specific and the F-G multiplicative hazards models. Similarly, the additive hazards models of Aalen and that of Lin & Ying (L-Y) are modeled for the outcomes using the competing risks approach. Results: There were 13,996 eligible subjects in my data, and 7,071 (50.5%) of them were women. After a median follow-up time of 15 years (interquartile range = 5.52 years), a total of 1,536 deaths were observed, and 549 (35.7%) of these were CVD related deaths. Factors like male gender, old age, and alcohol abstinence significantly increased the risk of CVD mortality in the additive and multiplicative hazards models. Former alcohol users compared to current alcohol users have a 53% (P-value= 0.002) and a 55% (P-value= 0.001) increased risk of CVD mortality in the Cox cause-specific and the F-G models, respectively. In the L-Y additive model, former alcohol users compared to current users increased CVD mortality by adding 16 new cases per 10,000 person-years (P-value = 0.008). Conclusion: The results from my study suggest that covariate effects in the Cox cause-specific and the F-G subdistribution hazards models may be identical in terms of magnitude and direction. The numerical results from the multiplicative and the additive hazards models give different interpretation of the covariate effects, and using both the additive and multiplicative models together would boost understanding of the data

Population Attributable Fraction (PAF) in epidemiologic follow-up studies

Tieto kuolleisuuteen tai erilaisten sairauksien ilmaantumiseen vaikuttavien riskitekijöiden suhteellisesta merkityksestä väestötasolla on tärkeää muun muassa terveysvalistusta tai sairauksien ehkäisyyn tarkoitettuja interventioita suunniteltaessa. Riskitekijän suhteellisen merkityksen arvioinnissa olennaista on paitsi se, miten voimakkaasti kyseinen tekijä vaikuttaa kuolleisuuteen tai sairastuvuuteen, myös se, miten yleinen kyseinen tekijä on väestössä. Väestösyyosuus (Population Attributable Fraction, PAF) on tilastollinen tunnusluku, joka huomioi nämä molemmat näkökulmat ja jolla siis voidaan arvioida eri riskitekijöiden selittämää osuutta kuolleisuudesta tai sairastuvuudesta. Väestösyysosuus kuvaa, miten suuri osuus tapahtumista voitaisiin välttää, jos yksi tai useampi riskitekijä voitaisiin poistaa tai sen arvoja parantaa. Menetelmiä väestösyyosuuden arviointiin on tähän asti pääasiassa kehitetty ja sovellettu epidemiologisista tutkimusasetelmista tapaus-verrokki- ja poikkileikkaustutkimuksissa. Menetelmiä väestösyyosuuden arviointiin kohorttitutkimuksissa, joissa seurataan tutkitun väestöryhmän kuolleisuutta tai sairastuvuutta tietyn ajan, on puolestaan ryhdytty kehittämään vasta viime vuosina. Tässä väitöskirjatyössä kehitetään tilastollisia menetelmiä riskitekijöiden sekä kokonaiskuolleisuudesta että sairastuvuudesta selittämän väestösyyosuuden arviointiin kohorttitutkimuksissa, joissa huomioidaan näille tutkimuksille tyypillinen aikaulottuvuus sekä näihin erityyppisiin vastetapahtumiin liittyvät ominaisuudet. Riskitekijöiden selittämä väestösyyosuus määriteltiin osuudeksi kokonaiskuolleisuudesta tai sairastuvuudesta, joka voitaisiin välttää tietyllä seuranta-aikavälillä, jos niiden riskitekijöitä kyettäisiin muuttamaan. Kuolleisuuden ja sairauden ilmaantuvuuden oletettiin noudattavan parametrista suhteellisten hasardien mallia. Potentiaaliset riskitekijän ja tutkittavan tapahtuman välistä yhteyttä sekoittavat tekijät vakioitiin ja potentiaaliset riskitekijän vaikutusta tutkittavan tapahtuman ilmaantumiseen muokkaavat tekijät huomioitiin mallituksessa. Riskitekijöiden kokonaiskuolleisuudesta selittämän väestösyyosuuden estimoinnissa huomioitiin seurannan päättymisestä johtuva havaintojen sensuroituminen, kun taas niiden selittämää väestösyyosuutta sairastuvuudesta estimoitaessa huomioitiin myös kuolleisuudesta johtuva sensuroituminen. Tässä väitöskirjatyössä kehitettiin myös uusi, kuvattuihin tilastollisiin menetelmiin pohjautuva, yleiskäyttöinen SAS-ohjelma sekä riskitekijöiden kokonaiskuolleisuudesta että sairastuvuudesta selittämän väestösyyosuuden estimointiin. Uutta tilastollista menetelmää ja ohjelmaa sovellettiin tyypin 2 diabeteksen elämäntapaan liittyvien riskitekijöiden suhteellisen merkityksen arviointiin väestötasolla kyseisen sairauden aiheuttajina kahdessa suomalaista väestöä edustavassa aineistossa (Mini-Suomi -aineisto ja Terveys 2000 -aineisto). Tämä sovellus toi lisää näyttöä painonhallinnan merkityksestä tyypin 2 diabeteksen tärkeimpänä ehkäisykeinona. Lisäksi selvitettiin näiden riskitekijöiden mahdollisesti eri tyyppistä vaikutusta tyypin 2 diabetekseen matalan ja korkean riskin ryhmissä, jotka määriteltiin tyypin 2 diabeteksen esivaiheen, niin sanotun metabolisen oireyhtymän olemassaolon perusteella. Tämä tutkimus tuotti uutta tietoa elintapatekijöiden muutosten ilmeisestä merkityksestä tyypin 2 diabeteksen ehkäisyssä matalamman riskin ryhmissä. Väestösyyosuus on hyödyllinen mittari, jolla voidaan tuottaa väestötasoista tietoa erilaisten tekijöiden vaikutuksesta kiinnostuksen kohteena oleviin tapahtumiin ja jolla on laajoja käyttömahdollisuuksia monilla eri tutkimusalueilla.Quantification of the impact of exposure to different risk factors on mortality or morbidity at the population level is a fundamental issue in epidemiologic research. Population Attributable Fraction (PAF) is a statistical concept that can be used to quantify this impact. PAF assesses the proportion of outcome that could be avoided if the current exposure distribution was replaced by a hypothetical, presumably preferable exposure distribution. So far, the methods for the estimation of PAF have mostly been developed for and applied in case-control and cross-sectional studies. The development of methods for the estimation of PAF from cohort studies, which properly take into account the time perspective, has started only recently. In the estimation of PAF for a certain follow-up time interval, the type of outcome (mortality vs. morbidity) of interest has not, however, been taken into account. In this study, the statistical methodology for the estimation of PAF in cohort studies will be extended to cover both the estimation of PAF for total mortality and disease incidence. The PAF for total mortality or disease incidence was defined as the proportion of mortality or disease incidence, respectively, that could be avoided during a follow-up time interval (0, t] if their risk factors were modified. A parametric proportional hazards model, with a piecewise constant baseline hazard function for death and disease occurrences, was assumed. Potential confounding factors were adjusted for and potential effect modifying factors accounted for in the model. The estimation of PAF and its asymptotic variance based on the delta method was demonstrated. The complementary logarithmic transformation in the calculation of the confidence interval of PAF was used. In the estimation of PAF for total mortality, censoring due to loss to follow-up was taken into account, whereas in the estimation of PAF for disease incidence censoring due to death was also considered. Furthermore, the meta-analysis techniques developed for pooling of relative risks were extended for the pooling of PAF estimates. In the data examples of this study, the PAF estimates for total mortality and disease incidence were demonstrated to decrease as the follow-up time increased. In the simulated data sets, taking censoring due to death into account in the estimation of PAF for disease incidence was shown to decrease the point estimates of PAF significantly in comparison to when censoring due to death was ignored. Ignoring censoring due to death increased the overestimation of PAF, especially when the impact of risk factors on mortality was strong and the follow-up time long. A new program for the estimation of PAF both for total mortality and disease incidence, implementing the new methods, was developed using SAS/IML language. This program was shown to be flexible and fast. An application of PAF to evaluate the relative importance of the risk factors of type 2 diabetes and the potential effect-modifying role of metabolic syndrome or its components in a meta-analysis of two representative Finnish cohorts was carried out using this program. As a result, the use of PAF provided further evidence of weight control being the primary diabetes prevention method. The pooling of the PAF estimates increased the power to detect associations in smaller subpopulations defined by the metabolic syndrome or its components, establishing new evidence on the importance of early lifestyle changes in the prevention of type 2 diabetes. In conclusion, it is essential to take time perspective into account in the estimation of PAF. Different estimators of PAF for a certain time interval, taking into account different sources of censoring, are needed, depending on the outcome of interest. PAF is a useful measure in cohort studies for providing population-level information on the effects of predictor modifications on the outcome in time and has wide applications in many different fields of research

Interval-censored semi-competing risks data: a novel approach for modelling bladder cancer

Aquesta tesi tracta sobre tècniques d'anàlisi de supervivència en situacions amb múltiples esdeveniments i patrons complexes de censura. Proposem una nova metodologia per tractar la situació de riscos semi-competitius quan les dades estan censurades en un interval. La motivació del treball neix de la nostra col·laboració amb l'Estudi Espanyol del Càncer de Bufeta (SBC/EPICURO), el més gran estudi sobre càncer de bufeta realitzat fins ara a l'Estat Espanyol. La nostra contribució en el projecte es centra en la modelització i identificació de factors pronòstics de l'evolució de la malaltia.L'evolució de malalties complexes, com el càncer o la infecció VIH, es caracteritza per la ocurrència de múltiples esdeveniments en el mateix pacient: per exemple, la recaiguda de la malaltia o la mort. Aquests esdeveniments poden ser finals, quan el seguiment del pacient s'atura després de l'esdeveniment, o bé intermedis, quan l'individu continua sota observació. La presència d'esdeveniments finals complica l'anàlisi dels intermedis ja que n'impedeix la seva completa observació, induint una possible censura depenent.En aquest context, es requereixen metodologies apropiades. Els següents mètodes són emprats: riscos competitius, models multiestat i riscos semi-competitius. A resultes de l'aplicació de mètodes per riscos competitius i models multi-estat, proposem dues aportacions rellevants al coneixement de la malaltia: (1) la caracterització dels pacients amb un alt risc de progressió com a primer esdeveniment després de la diagnosi, i (2) la construcció d'un model pronòstic dinàmic per al risc de progressió.La situació de riscos competitius es dóna quan volem descriure el temps fins al primer entre K possibles esdeveniments, juntament amb un indicador del tipus d'esdeveniment observat. En l'estudi EPICURO, és rellevant estudiar el temps fins al primer entre recidiva, progressió o mort. La caracterització d'aquest primer esdeveniment permetria seleccionar el millor tractament d'acord amb el perfil de risc basal del pacient.Els models multi-estat descriuen les diferents evolucions que la malaltia pot seguir, establint relacions entre els esdeveniments d'interès: per exemple, un pacient pot experimentar una recidiva del tumor primari, i després morir, o bé pot morir sense haver tingut cap recaiguda de la malaltia. Una característica interessant d'aquests models és que permeten fer prediccions del risc de futurs esdeveniments per a un pacient, d'acord amb la història que hagi pogut tenir fins aquell moment. En el cas de càncer de bufeta podrem avaluar la influència que té en el risc de progressar haver patit o no una recidiva prèvia.Un cas especial de model multi-estat és aquell que conté un esdeveniment intermedi E1, i un esdeveniment final, E2. Siguin T1 i T2 els temps fins aquests esdeveniments, respectivament. Ni l'anàlisi de riscos competitius ni els models multi-estat permeten adreçar l'estudi de la distribució marginal de T1. En efecte, l'anàlisi de riscos competitius tracta amb la distribució del mínim entre els dostemps, T=min(T1,T2), mentre que els models multi-estat es centren en la distribució condicional de T2|T1, és a dir, en com la ocurrència de E1 modifica el risc de E2. En aquest cas, la distribució de T1 no és identificable a partir de les dades observades. La situació abans descrita, on la ocurrència d'un esdeveniment final impedeix l'observació de l'esdeveniment intermedi és coneguda com a riscos semi-competitius (Fine et al., 2001). L'estratègia d'aquests autors passà per assumir un model per a la distribució conjunta (T1, T2), i aleshores recuperar la distribució marginal de T1 derivada d'aquest model.Proposem una nova metodologia per tractar amb riscos semi-competitius quan el temps fins l'esdeveniment intermedi, T1, està censurat en un interval. En molts estudis mèdics longitudinals, la ocurrència de l'esdeveniment d'interès s'avalua en visites periòdiques del pacient, i per tant, T1 és desconegut, però es sap que pertany al interval comprès entre els temps de dues visites consecutives. Els mètodes per riscos semi-competitius en el context usual de censura per la dreta no són vàlids en aquest cas i és necessària una nova aproximació. En aquest treball ampliem la metodología semi-paramètrica proposada per Fine et al. (2001), que assumeix un model de còpula de Clayton (1978) per a descriure la dependència entre T1 i T2. Assumint el mateix model, desenvolupem un algoritme iteratiu que estima conjuntament el paràmetre d'associació del model de còpula, així com la funció de supervivència del temps intermedi T1.Fine, J. P.; Jiang, H. & Chappell, R. (2001), 'On Semi-Competing Risks Data', Biometrika 88(4), 907--919.Clayton, D. G. (1978), 'A Model for Association in Bivariate Life Tables and Its Application in Epidemiological Studies of Familial. Tendency in Chronic Disease Incidence', Biometrika 65(1), 141--151.La presente tesis trata sobre técnicas de análisis de supervivencia en situaciones con múltiples eventos y patrones complejos de censura. Proponemos una nueva metodología para tratar el problema de riesgos semi-competitivos cuando los datos están censurados en un intervalo. La motivación de este trabajo nace de nuestra colaboración con el estudio Español de Cáncer de Vejiga (SBC/EPICURO), el más grande estudio sobre cáncer de vejiga realizado en España hasta el momento. Nuestra participación en el mismo se centra en la modelización e identificación de factores pronósticos en el curso de la enfermedad.El curso de enfermedades complejas tales como el cáncer o la infección por VIH, se caracteriza por la ocurrencia de múltiples eventos en el mismo paciente, como por ejemplo la recaída o la muerte. Estos eventos pueden ser finales, cuando el seguimiento del paciente termina con el evento, o bien intermedios, cuando el individuo sigue bajo observación. La presencia de eventos finales complica el análisis de los eventos intermedios, ya que impiden su completa observación, induciendo una posible censura dependiente.En este contexto, se requieren metodologías apropiadas. Se utilizan los siguientes métodos: riesgos competitivos, modelos multiestado y riesgos semi-competitivos. De la aplicación de métodos para riesgos competitivos y modelos multi-estado resultan dos aportaciones relevantes sobre el conocimiento de la enfermedad: (1) la caracterización de los pacientes con un alto riesgo de progresión como primer evento después del diagnóstico, y (2) la construcción de un modelo pronóstico y dinámico para el riesgo de progresión.El problema de riesgos competitivos aparece cuando queremos describir el tiempo hasta el primero de K posibles eventos, junto con un indicador del tipo de evento observado. En el estudio SBC/EPICURO es relevante estudiar el tiempo hasta el primero entre recidiva, progresión o muerte. La caracterización de este primer evento permitiría seleccionar el tratamiento más adecuado de acuerdo con el perfil de riesgo basal del paciente.Los modelos multi-estado describen las diferentes tipologías que el curso de la enfermedad puede seguir, estableciendo relaciones entre los eventos de interés. Por ejemplo, un paciente puede experimentar una recidiva y después morir, o bien puede morir sin haber tenido recaída alguna. El potencial interesante de los modelos multi-estado es que permiten realizar predicciones sobre el riesgo de futuros eventos dada la historia del paciente hasta ese momento. En el caso del cáncer de vejiga, podremos evaluar la influencia que tiene en el riesgo de progresar el haber tenido o no una recidiva previa.Un caso especial de modelo multi-estado es el que contiene un evento intermedio E1 y uno final, E2. Sean T1 y T2 los tiempos hasta tales eventos, respectivamente. Ni el análisis de riesgos competitivos ni los modelos multi-estado permiten estudiar la distribución marginal de T1. En efecto, el análisis de riesgos competitivos trata con la distribución del mínimo entre los dos tiempos, T=min(T1,T2), mientras que los modelos multi-estado se centran en la distribución condicional de T2 dado T1, T2|T1, en cómo la ocurrencia de E1 modifica el riesgo de E2. En ambos casos, la distribución de T1 no es identificable a partir de los datos observados.La situación anteriormente descrita donde un evento final impide la observación de un evento intermedio se conoce como riesgos semi-competitivos (Fine et al. 2001). La estrategia de estos autores asume un modelo para la distribución conjunta (T1,T2) para así recuperar la distribución de T1 derivada de ese modelo.Proponemos una nueva metodología para tratar con riesgos semi-competitivos cuando el tiempo hasta el evento intermedio, T1, esta censurado en un intervalo. En muchos estudios médicos longitudinales, la ocurrencia del evento de interés se evalúa en visitas periódicas al paciente, por lo que T1 es desconocido, aunque se conoce que pertenece al intervalo comprendido entre los tiempos de dos visitas consecutivas. Los métodos para riesgos semi-competitivos en el contexto usual de censura por la derecha no son válidos en este caso y se requiere una nueva aproximación. En este trabajo ampliamos la metodología semi-paramétrica propuesta por Fine et al. (2001), que asume una cópula de Clayton (1978) para describir la dependencia entre T1 y T2. Bajo el mismo modelo de asociación, desarrollamos un algoritmo iterativo que estima conjuntamente el parámetro de asociación del modelo de cópula, así como la función de supervivencia del tiempo al evento intermedio T1.Fine, J. P.; Jiang, H. & Chappell, R. (2001), 'On Semi-Competing Risks Data', Biometrika 88(4), 907--919. Clayton, D. G. (1978), 'A Model for Association in Bivariate Life Tables and Its Application in Epidemiological Studies of Familial. Tendency in Chronic Disease Incidence', Biometrika 65(1), 141--151