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Paul C. Lambert - One of the best experts on this subject based on the ideXlab platform.
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Understanding disparities in cancer prognosis: An extension of mediation analysis to the Relative Survival framework.
Biometrical journal. Biometrische Zeitschrift, 2020Co-Authors: Elisavet Syriopoulou, Mark J Rutherford, Paul C. LambertAbstract:Mediation analysis can be applied to investigate the effect of a third variable on the pathway between an exposure and the outcome. Such applications include investigating the determinants that drive differences in cancer Survival across subgroups. However, cancer disparities may be the result of complex mechanisms that involve both cancer-related and other-cause mortality differences making it difficult to identify the causing factors. Relative Survival, a commonly used measure in cancer epidemiology, can be used to focus on cancer-related differences. We extended mediation analysis to the Relative Survival framework for exploring cancer inequalities. The marginal effects were obtained using regression standardization, after fitting a Relative Survival model. Contrasts of interests included both marginal Relative Survival and marginal all-cause Survival differences between exposure groups. Such contrasts include the indirect effect due to a mediator that is identifiable under certain assumptions. A separate model was fitted for the mediator and uncertainty was estimated using parametric bootstrapping. The avoidable deaths under interventions can also be estimated to quantify the impact of eliminating differences. The methods are illustrated using data for individuals diagnosed with colon cancer. Mediation analysis within Relative Survival allows focus on factors that account for cancer-related differences instead of all-cause differences and helps improve our understanding on cancer inequalities.
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Marginal measures and causal effects using the Relative Survival framework.
International journal of epidemiology, 2020Co-Authors: Elisavet Syriopoulou, Mark J Rutherford, Paul C. LambertAbstract:Background In population-based cancer Survival studies, the event of interest is usually death due to cancer. However, other competing events may be present. Relative Survival is a commonly used measure in cancer studies that circumvents problems caused by the inaccuracy of the cause of death information. A summary of the prognosis of the cancer population and potential differences between subgroups can be obtained using marginal estimates of Relative Survival. Methods We utilize regression standardization to obtain marginal estimates of interest in a Relative Survival framework. Such measures include the standardized Relative Survival, standardized all-cause Survival and standardized crude probabilities of death. Contrasts of these can be formed to explore differences between exposure groups and under certain assumptions are interpreted as causal effects. The difference in standardized all-cause Survival can also provide an estimate for the impact of eliminating cancer-related differences between exposure groups. The potential avoidable deaths after such hypothetical scenarios can also be estimated. To illustrate the methods we use the example of Survival differences across socio-economic groups for colon cancer. Results Using Relative Survival, a range of marginal measures and contrasts were estimated. For these measures we either focused on cancer-related differences only or chose to incorporate both cancer and other cause differences. The impact of eliminating differences between groups was also estimated. Another useful way for quantifying that impact is the avoidable deaths under hypothetical scenarios. Conclusions Marginal estimates within the Relative Survival framework provide useful summary measures and can be applied to better understand differences across exposure groups.
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A flexible parametric approach to examining spatial variation in Relative Survival
Statistics in medicine, 2016Co-Authors: Susanna M. Cramb, Paul C. Lambert, Kerrie Mengersen, Louise Ryan, Peter D. BaadeAbstract:Most of the few published models used to obtain small-area estimates of Relative Survival are based on a generalized linear model with piecewise constant hazards under a Bayesian formulation. Limitations of these models include the need to artificially split the time scale, restricted ability to include continuous covariates, and limited predictive capacity. Here, an alternative Bayesian approach is proposed: a spatial flexible parametric Relative Survival model. This overcomes previous limitations by combining the benefits of flexible parametric models: the smooth, well-fitting baseline hazard functions and predictive ability, with the Bayesian benefits of robust and reliable small-area estimates. Both spatially structured and unstructured frailty components are included. Spatial smoothing is conducted using the intrinsic conditional autoregressive prior. The model was applied to breast, colorectal, and lung cancer data from the Queensland Cancer Registry across 478 geographical areas. Advantages of this approach include the ease of including more realistic complexity, the feasibility of using individual-level input data, and the capacity to conduct overall, cause-specific, and Relative Survival analysis within the same framework. Spatial flexible parametric Survival models have great potential for exploring small-area Survival inequalities, and we hope to stimulate further use of these models within wider contexts. Copyright © 2016 John Wiley & Sons, Ltd.
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Should Relative Survival be used with lung cancer data
British journal of cancer, 2012Co-Authors: Sally R. Hinchliffe, Mark J Rutherford, Christopher P. Nelson, Michael J. Crowther, Paul C. LambertAbstract:Lung cancer is commonly known to be a disease that has strong associations with smoking (Doll and Hill, 1956; Korhonen et al, 2008; Papadopoulos et al, 2011). A report published by Peto et al, 2006 showed that, in Finland in the year 2000, 86% of lung cancer deaths in males and 60% of lung cancer deaths in females were deemed to be attributed to smoking. In addition to this, they showed that 12% of cardiovascular deaths in males and 3.6% of cardiovascular deaths in females were also deemed to be attributed to smoking. Figures were also reported for other types of cancer and other causes of death. Not only does smoking put you at a high risk of developing lung cancer and consequently dying from lung cancer (Doll and Hill, 1956; Papadopoulos et al, 2011), it also increases your chances of dying from many other diseases (Wolf et al, 1988), such as cardiovascular disease (Willett et al, 1987) and other less common forms of cancer (Moore, 1971; Fuchs et al, 1996). This has led to heavy debate as to whether Relative Survival should be used as a method to analyse lung cancer data (Dickman and Adami, 2006; Sarfati et al, 2010). Relative Survival is a method that compares the Survival experience of a group of patients to the Survival experience of the general population. The method is particularly advantageous, as it does not require an accurate cause-of-death information. Mortality estimates for the general population are usually taken from national life tables that are broken down by age, sex and calendar year. One of the key assumptions of Relative Survival is comparability – if the patient did not have cancer, then it is assumed that they would have the same Survival experience as the general population. It is argued, as most lung cancer patients are smokers and therefore carry a higher risk of many other diseases, that they are not comparable to a population where the majority are likely to be non-smokers (Phillips et al, 2002). However, despite these potential problems, Relative Survival is still the usual method of analysis in population-based cancer studies. This paper assesses the impact that the non-comparability has on the Relative Survival estimates through the use of a sensitivity analysis. Similar studies have been carried out previously to assess the impact that specific cancer deaths in the population mortality figures can have on the estimate of Relative Survival (Hinchliffe et al, 2011; Talback and Dickman, 2011).
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choosing the Relative Survival method for cancer Survival estimation
European Journal of Cancer, 2011Co-Authors: Timo Hakulinen, Karri Seppä, Paul C. LambertAbstract:Abstract Background A new net Survival method has been introduced by Pohar Perme et al. (2012 [4]) and recommended to substitute the Relative Survival methods in current use for evaluating population-based cancer Survival. Methods The new method is based on the use of continuous follow-up time, and is unbiased only under non-informative censoring of the observed Survival. However, the population-based cancer Survival is often evaluated based on annually or monthly tabulated follow-up intervals. An empirical investigation based on data from the Finnish Cancer Registry was made into the practical importance of the censoring and the level of data tabulation. A systematic comparison was made against the earlier recommended Ederer II method of Relative Survival using the two currently available computer programs (Pohar Perme (2013) [10] and Dickman et al. (2013) [11]). Results With exact or monthly tabulated data, the Pohar-Perme and the Ederer II methods give, on average, results that are at five years of follow-up less than 0.5% units and at 10 and 14 years 1–2% units apart from each other. The Pohar-Perme net Survival estimator is prone to random variation and may result in biased estimates when exact follow-up times are not available or follow-up is incomplete. With annually tabulated follow-up times, estimates can deviate substantially from those based on more accurate observations, if the actuarial approach is not used. Conclusion At 5 years, both the methods perform well. In longer follow-up, the Pohar-Perme estimates should be interpreted with caution using error margins. The actuarial approach should be preferred, if data are annually tabulated.
Timo Hakulinen - One of the best experts on this subject based on the ideXlab platform.
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Standard errors of non-standardised and age-standardised Relative Survival of cancer patients.
British Journal of Cancer, 2011Co-Authors: Lina Jansen, Timo Hakulinen, Hermann BrennerAbstract:Standard errors of non-standardised and age-standardised Relative Survival of cancer patients
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choosing the Relative Survival method for cancer Survival estimation
European Journal of Cancer, 2011Co-Authors: Timo Hakulinen, Karri Seppä, Paul C. LambertAbstract:Abstract Background A new net Survival method has been introduced by Pohar Perme et al. (2012 [4]) and recommended to substitute the Relative Survival methods in current use for evaluating population-based cancer Survival. Methods The new method is based on the use of continuous follow-up time, and is unbiased only under non-informative censoring of the observed Survival. However, the population-based cancer Survival is often evaluated based on annually or monthly tabulated follow-up intervals. An empirical investigation based on data from the Finnish Cancer Registry was made into the practical importance of the censoring and the level of data tabulation. A systematic comparison was made against the earlier recommended Ederer II method of Relative Survival using the two currently available computer programs (Pohar Perme (2013) [10] and Dickman et al. (2013) [11]). Results With exact or monthly tabulated data, the Pohar-Perme and the Ederer II methods give, on average, results that are at five years of follow-up less than 0.5% units and at 10 and 14 years 1–2% units apart from each other. The Pohar-Perme net Survival estimator is prone to random variation and may result in biased estimates when exact follow-up times are not available or follow-up is incomplete. With annually tabulated follow-up times, estimates can deviate substantially from those based on more accurate observations, if the actuarial approach is not used. Conclusion At 5 years, both the methods perform well. In longer follow-up, the Pohar-Perme estimates should be interpreted with caution using error margins. The actuarial approach should be preferred, if data are annually tabulated.
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Has equity in Relative Survival improved over time in Finland - a methodological exercise
Acta oncologica (Stockholm Sweden), 2011Co-Authors: Maja Pohar Perme, Timo Hakulinen, Manca Jesenko, Risto Sankila, Janez StareAbstract:AbstractBackground. Population-based Relative Survival is widely used as a method of monitoring the success of cancer control. This success may not be relevant only for an entire country but also regional developments over time are of interest. It would not only be important that the Relative Survival improved but also that the differences between regions decreased over time. Methods. In this paper the authors show how Relative Survival methods can be used to study such differences. In addition to standard methods, some more recently introduced approaches are used, most notably a method for checking the goodness of fit of the Relative Survival model. This gives confidence in the obtained results and provides additional insight when assumptions are not met. Results. An analysis of cancers of the colon and ovary by cancer control region in Finland in 1953–2003 shows an overall improvement in Relative Survival, accompanied in colon cancer also by a decrease of differences in Relative Survival between the reg...
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Choosing the Relative Survival method for cancer Survival estimation.
European journal of cancer (Oxford England : 1990), 2011Co-Authors: Timo Hakulinen, Karri Seppä, Paul Christopher LambertAbstract:The methods on how to calculate cumulative Relative Survival have been ambiguous and have given differences in empirical results. The gold standard for the cumulative Relative Survival ratio is the weighted average of age-specific cumulative Relative Survival ratios, with weights proportional to numbers of patients at diagnosis. Mathematics and representative empirical materials from the population-based Finnish Cancer Registry were studied for the different Relative Survival methods and compared with the gold standard. The theoretical and empirical results show a good agreement between the method suggested in 1959 by Ederer and Heise (the so-called Ederer II method) and the gold standard. This result is in part due the fact that as follow-up time increases the conditional (annual) Relative Survival ratios become increasingly more independent of age. Moreover, the dependence between the excess mortality due to cancer and the baseline general mortality does not introduce an important enough selection in practice to cause a notable bias. The use of the method by Ederer and Heise, multiplication of the annual Relative Survival ratios, instead of direct standardisation, should be considered in future applications. This would be particularly important for the long-term follow-up when age-specific Relative Survival is not available in the oldest age categories. Copyright © 2011 Elsevier Ltd. All rights reserved.
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Age-standardisation of Relative Survival ratios of cancer patients in a comparison between countries, genders and time periods.
European journal of cancer (Oxford England : 1990), 2008Co-Authors: Arun Pokhrel, Timo HakulinenAbstract:A recent method of age-standardisation of Relative Survival ratios for cancer patients does not require calculation of age-specific Relative Survival ratios, as ratios of age-specific proportions between the standard population and study group at the beginning of the follow-up are used to substitute the original individual observations. This method, however, leads to direct age-standardisation with weights that are different for each patient group if the general population mortality patterns for the groups are different. This is the case in international comparisons, and in comparisons between genders and time periods. The magnitude of the bias caused by the differences in general population mortality is investigated for comparisons involving European countries and the USA. Patients in each country are assumed to have exactly the same age-specific Relative Survival ratios as those diagnosed in Finland in 1985-2004. An application of a properly functioning age-standardisation method should then give exactly equal age-standardised Relative Survival ratios for each country. However, the recent method shows substantial differences between countries, with highest Relative Survival for populations, where the general population mortality in the oldest ages is the highest. This source of error can thus be a serious limitation for the use of the method, and other methods that are available should then be employed.
Roch Giorgi - One of the best experts on this subject based on the ideXlab platform.
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Analysis of time-dependent covariates in a regressive Relative Survival model.
Statistics in medicine, 2005Co-Authors: Roch Giorgi, Joanny GouvernetAbstract:Relative Survival is a method for assessing prognostic factors for disease-specific mortality. However, most Relative Survival models assume that the effect of covariate on disease-specific mortality is fixed-in-time, which may not hold in some studies and requires adapted modelling. We propose an extension of the Esteve et al. regressive Relative Survival model that uses the counting process approach to accommodate time-dependent effect of a predictor's on disease-specific mortality. This approach had shown its robustness, and the properties of the counting process give a simple and attractive computational solution to model time-dependent covariates. Our approach is illustrated with the data from the Stanford Heart Transplant Study and with data from a hospital-based study on invasive breast cancer. Advantages of modelling time-dependent covariates in Relative Survival analysis are discussed.
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A Metropolis within Gibbs sampling in Relative Survival
2005Co-Authors: Roch Giorgi, Ariane Sahel, Jean-pierre Daures, Joanny GouvernetAbstract:Relative Survival analysis is a method which provides an estimate of the effect on Survival corrected for the effect of other independent causes of death, using the natural mortality in the underlying general population as the reference. This method is frequently used when the specifics causes of deaths are uncertain or unavailable as in some population or hospital-based registries. We proposed a Markov Chain Monte Carlo (MCMC) approach to perform Relative Survival analysis using a proportional hazards regression model. We used gamma and normal prior distributions, respectively, for the baseline mortality hazard function and the regression parameters and we established the likelihood function. Conditional posterior distributions cannot be reduced analytically to well known distributions and we used a Metropolis within Gibbs sampling to obtain samples from the conditional posterior distributions. The accuracy of the estimates obtained by this MCMC approach were evaluated in simulations studies. Data from a population-based of pharyngeal cancer were used to illustrate our approach.
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RSURV: a function to perform Relative Survival analysis with S-PLUS or R.
Computer methods and programs in biomedicine, 2005Co-Authors: Roch Giorgi, Julie Payan, Joanny GouvernetAbstract:Relative Survival is a method used to estimate net Survival using the expected mortality in the general population. This method is frequently used in cancer registries, more particularly with the Esteve et al. regressive proportional hazards model. Recently, extensions of this model have been developed to account for time-dependent covariate and for time-dependent hazards using B-spline functions. We propose a function, RSurv, to take into account these extensions. Written in the R/S language this function has the same structure of the standard Cox function coxph of R and S-PLUS software with the goal to homogenise Survival functions and to take advantages of the power of R and S-PLUS software. We also propose a function, plot.RSurv, for plotting Relative Survival curves and time-dependent hazards ratio. The usage of these functions is exemplified by a study of a breast cancer hospital-based data set.
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A Relative Survival regression model using B‐spline functions to model non‐proportional hazards
Statistics in medicine, 2003Co-Authors: Roch Giorgi, Michal Abrahamowicz, Catherine Quantin, Joanny Gouvernet, Philippe Bolard, Jacques Estève, Jean FaivreAbstract:Relative Survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most Relative Survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new Relative Survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.
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a Relative Survival regression model using b spline functions to model non proportional hazards
Statistics in Medicine, 2003Co-Authors: Roch Giorgi, Michal Abrahamowicz, Catherine Quantin, Joanny Gouvernet, Philippe Bolard, J Esteve, J FaivreAbstract:Relative Survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most Relative Survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new Relative Survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.
Joanny Gouvernet - One of the best experts on this subject based on the ideXlab platform.
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Analysis of time-dependent covariates in a regressive Relative Survival model.
Statistics in medicine, 2005Co-Authors: Roch Giorgi, Joanny GouvernetAbstract:Relative Survival is a method for assessing prognostic factors for disease-specific mortality. However, most Relative Survival models assume that the effect of covariate on disease-specific mortality is fixed-in-time, which may not hold in some studies and requires adapted modelling. We propose an extension of the Esteve et al. regressive Relative Survival model that uses the counting process approach to accommodate time-dependent effect of a predictor's on disease-specific mortality. This approach had shown its robustness, and the properties of the counting process give a simple and attractive computational solution to model time-dependent covariates. Our approach is illustrated with the data from the Stanford Heart Transplant Study and with data from a hospital-based study on invasive breast cancer. Advantages of modelling time-dependent covariates in Relative Survival analysis are discussed.
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A Metropolis within Gibbs sampling in Relative Survival
2005Co-Authors: Roch Giorgi, Ariane Sahel, Jean-pierre Daures, Joanny GouvernetAbstract:Relative Survival analysis is a method which provides an estimate of the effect on Survival corrected for the effect of other independent causes of death, using the natural mortality in the underlying general population as the reference. This method is frequently used when the specifics causes of deaths are uncertain or unavailable as in some population or hospital-based registries. We proposed a Markov Chain Monte Carlo (MCMC) approach to perform Relative Survival analysis using a proportional hazards regression model. We used gamma and normal prior distributions, respectively, for the baseline mortality hazard function and the regression parameters and we established the likelihood function. Conditional posterior distributions cannot be reduced analytically to well known distributions and we used a Metropolis within Gibbs sampling to obtain samples from the conditional posterior distributions. The accuracy of the estimates obtained by this MCMC approach were evaluated in simulations studies. Data from a population-based of pharyngeal cancer were used to illustrate our approach.
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RSURV: a function to perform Relative Survival analysis with S-PLUS or R.
Computer methods and programs in biomedicine, 2005Co-Authors: Roch Giorgi, Julie Payan, Joanny GouvernetAbstract:Relative Survival is a method used to estimate net Survival using the expected mortality in the general population. This method is frequently used in cancer registries, more particularly with the Esteve et al. regressive proportional hazards model. Recently, extensions of this model have been developed to account for time-dependent covariate and for time-dependent hazards using B-spline functions. We propose a function, RSurv, to take into account these extensions. Written in the R/S language this function has the same structure of the standard Cox function coxph of R and S-PLUS software with the goal to homogenise Survival functions and to take advantages of the power of R and S-PLUS software. We also propose a function, plot.RSurv, for plotting Relative Survival curves and time-dependent hazards ratio. The usage of these functions is exemplified by a study of a breast cancer hospital-based data set.
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A Relative Survival regression model using B‐spline functions to model non‐proportional hazards
Statistics in medicine, 2003Co-Authors: Roch Giorgi, Michal Abrahamowicz, Catherine Quantin, Joanny Gouvernet, Philippe Bolard, Jacques Estève, Jean FaivreAbstract:Relative Survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most Relative Survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new Relative Survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.
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a Relative Survival regression model using b spline functions to model non proportional hazards
Statistics in Medicine, 2003Co-Authors: Roch Giorgi, Michal Abrahamowicz, Catherine Quantin, Joanny Gouvernet, Philippe Bolard, J Esteve, J FaivreAbstract:Relative Survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most Relative Survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new Relative Survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.
Michal Abrahamowicz - One of the best experts on this subject based on the ideXlab platform.
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Relative Survival multistate Markov model
Statistics in medicine, 2011Co-Authors: Ella Huszti, Michal Abrahamowicz, Ahmadou Alioum, Christine Binquet, Catherine QuantinAbstract:Prognostic studies often have to deal with two important challenges: (i) separating effects of predictions on different ‘competing’ events and (ii) uncertainty about cause of death. Multistate Markov models permit multivariable analyses of competing risks of, for example, mortality versus disease recurrence. On the other hand, Relative Survival methods help estimate disease-specific mortality risks even in the absence of data on causes of death. In this paper, we propose a new Markov Relative Survival (MRS) model that attempts to combine these two methodologies. Our MRS model extends the existing multistate Markov piecewise constant intensities model to Relative Survival modeling. The intensity of transitions leading to death in the MRS model is modeled as the sum of an estimable excess hazard of mortality from the disease of interest and an ‘offset’ defined as the expected hazard of all-cause ‘natural’ mortality obtained from relevant life-tables. We evaluate the new MRS model through simulations, with a design based on registry-based prognostic studies of colon cancer. Simulation results show almost unbiased estimates of prognostic factor effects for the MRS model. We also applied the new MRS model to reassess the role of prognostic factors for mortality in a study of colorectal cancer. The MRS model considerably reduces the bias observed with the conventional Markov model that does not permit accounting for unknown causes of death, especially if the ‘true’ effects of a prognostic factor on the two types of mortality differ substantially. Copyright © 2011 John Wiley & Sons, Ltd.
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A Relative Survival regression model using B‐spline functions to model non‐proportional hazards
Statistics in medicine, 2003Co-Authors: Roch Giorgi, Michal Abrahamowicz, Catherine Quantin, Joanny Gouvernet, Philippe Bolard, Jacques Estève, Jean FaivreAbstract:Relative Survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most Relative Survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new Relative Survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.
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a Relative Survival regression model using b spline functions to model non proportional hazards
Statistics in Medicine, 2003Co-Authors: Roch Giorgi, Michal Abrahamowicz, Catherine Quantin, Joanny Gouvernet, Philippe Bolard, J Esteve, J FaivreAbstract:Relative Survival, a method for assessing prognostic factors for disease-specific mortality in unselected populations, is frequently used in population-based studies. However, most Relative Survival models assume that the effects of covariates on disease-specific mortality conform with the proportional hazards hypothesis, which may not hold in some long-term studies. To accommodate variation over time of a predictor's effect on disease-specific mortality, we developed a new Relative Survival regression model using B-splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease-specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population-based study of colon cancer.
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Assessing time-by-covariate interactions in Relative Survival models using restrictive cubic spline functions.
Journal of cancer epidemiology and prevention, 2002Co-Authors: Philippe Bolard, Michal Abrahamowicz, Christine Binquet, Catherine Quantin, Roch Giorgi, Jacques Estève, Chadha-boreham H, Jean FaivreAbstract:BACKGROUND The Cox model is widely used in the evaluation of prognostic factors in clinical research. However, in population-based studies, which assess long-term Survival of unselected populations, Relative-Survival models are often considered more appropriate. In both approaches, the validity of proportional hazards hypothesis should be evaluated. METHODS We propose a new method in which restricted cubic spline functions are employed to model time-by-covariate interactions in Relative Survival analyses. The method allows investigation of the shape of possible dependence of the covariate effect on time without having to specify a particular functional form. Restricted cubic spline functions allow graphing of such time-by-covariate interactions, to test formally the proportional hazards assumption, and also to test the linearity of the time-by-covariate interaction. RESULTS Application of our new method to assess mortality in colon cancer provides strong evidence against the proportional hazards hypothesis, which is rejected for all prognostic factors. The results corroborate previous analyses of similar data-sets, suggesting the importance of both modelling of non-proportional hazards and Relative Survival approach. We also demonstrate the advantages of using restricted cubic spline functions for modelling non-proportional hazards in Relative-Survival analysis. The results provide new insights in the estimated impact of older age and of period of diagnosis. DISCUSSION Using restricted cubic splines in a Relative Survival model allows the representation of both simple and complex patterns of changes in Relative risks over time, with a single parsimonious model without a priori assumptions about the functional form of these changes.
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Modelling time-dependent hazard ratios in Relative Survival: application to colon cancer.
Journal of clinical epidemiology, 2001Co-Authors: Philippe Bolard, Catherine Quantin, Jacques Estève, Jean Faivre, Michal AbrahamowiczAbstract:The Cox model is widely used in the evaluation of prognostic factors in clinical research. In population-based studies, however, which assess long-term Survival of unselected populations, Relative Survival models are often considered more appropriate. In both approaches, the validity of proportional hazard hypothesis should be evaluated. To explore the validity of the proportional hazard assumption in a population-based study of colon cancer, to propose non-proportional hazard Relative Survival models and to evaluate their utility. The use of a piecewise proportional hazard Relative Survival model in colon cancer has shown that the effects of most clinical prognostic factors such as age, period of diagnosis and stage are non-proportional. The non-proportional hazard Relative Survival models developed in this article have been found to be efficient tools for better understanding the time-dependent aspect of prognostic factors.
