On models for the estimation of the excess mortality hazard in case of insufficiently stratified life tables

Area-based social inequalities in adult mortality: construction of French deprivation-specific life tables for the period 2016-2018

Background

In order to tackle social inequalities in mortality, it is crucial to quantify them. We produced French deprivation-specific life tables for the period 2016-2018 to measure the social gradient in adult all-cause mortality.

Methods

Data from the Permanent Demographic Sample (EDP) were used to provide population and death counts by age, sex and deprivation quintile. The European Deprivation Index (EDI), applied at a sub-municipal geographical level, was used as an ecological measure of deprivation. Smoothed mortality rates were calculated using a one-dimensional Poisson counts smoothing method with P-Splines. We calculated life expectancies by age, sex and deprivation quintile as well as interquartile mortality rate ratios (MRR).

Results

At the age of 30, the difference in life expectancy between the most and least deprived groups amounted to 3.9 years in males and 2.2 years in females. In terms of relative mortality inequalities, the largest gaps between extreme deprivation groups were around age 55 for males (MRR = 2.22 [2.0; 2.46] at age 55), around age 50 in females (MRR = 1.77 [1.48; 2.1] at age 47), and there was a decrease or disappearance of the gaps in the very older adults.

Conclusions

There is a strong social gradient in all-cause mortality in France for males and females. The methodology for building these deprivation-specific life tables is reproducible and could be used to monitor its development. The tables produced should contribute to improving studies on net survival inequalities for specific diseases by taking into account the pre-existing social gradient in all-cause mortality.

Including uncertainty of the expected mortality rates in the prediction of loss in life expectancy

PURPOSE

This study introduces a novel method for estimating the variance of life expectancy since diagnosis (LEC) and loss in life expectancy (LLE) for cancer patients within a relative survival framework in situations where life tables based on the entire general population are not accessible. LEC and LLE are useful summary measures of survival in population-based cancer studies, but require information on the mortality in the general population. Our method addresses the challenge of incorporating the uncertainty of expected mortality rates when using a sample from the general population.

METHODS

To illustrate the approach, we estimated LEC and LLE for patients diagnosed with colon and breast cancer in Sweden. General population mortality rates were based on a random sample drawn from comparators of a matched cohort. Flexible parametric survival models were used to model the mortality among cancer patients and the mortality in the random sample from the general population. Based on the models, LEC and LLE together with their variances were estimated. The results were compared with those obtained using fixed expected mortality rates.

RESULTS

By accounting for the uncertainty of expected mortality rates, the proposed method ensures more accurate estimates of variances and, therefore, confidence intervals of LEC and LLE for cancer patients. This is particularly valuable for older patients and some cancer types, where underestimation of the variance can be substantial when the entire general population data are not accessible.

CONCLUSION

The method can be implemented using existing software, making it accessible for use in various cancer studies. The provided example of Stata code further facilitates its adoption.

On near-redundancy and identifiability of parametric hazard regression models under censoring

We study parametric inference on a rich class of hazard regression models in the presence of right-censoring. Previous literature has reported some inferential challenges, such as multimodal or flat likelihood surfaces, in this class of models for some particular data sets. We formalize the study of these inferential problems by linking them to the concepts of near-redundancy and practical nonidentifiability of parameters. We show that the maximum likelihood estimators of the parameters in this class of models are consistent and asymptotically normal. Thus, the inferential problems in this class of models are related to the finite-sample scenario, where it is difficult to distinguish between the fitted model and a nested nonidentifiable (i.e., parameter-redundant) model. We propose a method for detecting near-redundancy, based on distances between probability distributions. We also employ methods used in other areas for detecting practical nonidentifiability and near-redundancy, including the inspection of the profile likelihood function and the Hessian method. For cases where inferential problems are detected, we discuss alternatives such as using model selection tools to identify simpler models that do not exhibit these inferential problems, increasing the sample size, or extending the follow-up time. We illustrate the performance of the proposed methods through a simulation study. Our simulation study reveals a link between the presence of near-redundancy and practical nonidentifiability. Two illustrative applications using real data, with and without inferential problems, are presented.

What is relative survival and what is its role in haematology?

In many haematological diseases, the survival probability is the key outcome. However, when the population of patients is rather old and the follow-up long, a significant proportion of deaths cannot be attributed to the studied disease. This lessens the importance of common survival analysis measures like overall survival and shows the need for other outcome measures requiring more complex methodology. When disease-specific information is of interest but the cause of death is not available in the data, relative survival methodology becomes crucial. The idea of relative survival is to merge the observed data set with the mortality data in the general population and thus allow for an indirect estimation of the burden of the disease. In this work, an overview of different measures that can be of interest in the field of haematology is given. We introduce the crude mortality that reports the probability of dying due to the disease of interest; the net survival that focuses on excess hazard alone and presents the key measure in comparing the disease burden of patients from populations with different general population mortality; and the relative survival ratio which gives a simple comparison of the patients' and the general population survival. We explain the properties of each measure, and some brief notes are given on estimation. Furthermore, we describe how association with covariates can be studied. All the methods and their estimators are illustrated on a sub-cohort of older patients who received a first allogeneic hematopoietic stem cell transplantation for myelodysplastic syndromes or secondary acute myeloid leukemia, to show how different methods can provide different insights into the data.

Individual frailty excess hazard models in cancer epidemiology

Unobserved individual heterogeneity is a common challenge in population cancer survival studies. This heterogeneity is usually associated with the combination of model misspecification and the failure to record truly relevant variables. We investigate the effects of unobserved individual heterogeneity in the context of excess hazard models, one of the main tools in cancer epidemiology. We propose an individual excess hazard frailty model to account for individual heterogeneity. This represents an extension of frailty modeling to the relative survival framework. In order to facilitate the inference on the parameters of the proposed model, we select frailty distributions which produce closed-form expressions of the marginal hazard and survival functions. The resulting model allows for an intuitive interpretation, in which the frailties induce a selection of the healthier individuals among survivors. We model the excess hazard using a flexible parametric model with a general hazard structure which facilitates the inclusion of time-dependent effects. We illustrate the performance of the proposed methodology through a simulation study. We present a real-data example using data from lung cancer patients diagnosed in England, and discuss the impact of not accounting for unobserved heterogeneity on the estimation of net survival. The methodology is implemented in the R package IFNS.

A new cure model that corrects for increased risk of non-cancer death: analysis of reliability and robustness, and application to real-life data

BACKGROUND

Non-cancer mortality in cancer patients may be higher than overall mortality in the general population due to a combination of factors, such as long-term adverse effects of treatments, and genetic, environmental or lifestyle-related factors. If so, conventional indicators may underestimate net survival and cure fraction. Our aim was to propose and evaluate a mixture cure survival model that takes into account the increased risk of non-cancer death for cancer patients.

METHODS

We assessed the performance of a corrected mixture cure survival model derived from a conventional mixture cure model to estimate the cure fraction, the survival of uncured patients, and the increased risk of non-cancer death in two settings of net survival estimation, grouped life-table data and individual patients' data. We measured the model's performance in terms of bias, standard deviation of the estimates and coverage rate, using an extensive simulation study. This study included reliability assessments through violation of some of the model's assumptions. We also applied the models to colon cancer data from the FRANCIM network.

RESULTS

When the assumptions were satisfied, the corrected cure model provided unbiased estimates of parameters expressing the increased risk of non-cancer death, the cure fraction, and net survival in uncured patients. No major difference was found when the model was applied to individual or grouped data. The absolute bias was < 1% for all parameters, while coverage ranged from 89 to 97%. When some of the assumptions were violated, parameter estimates appeared more robust when obtained from grouped than from individual data. As expected, the uncorrected cure model performed poorly and underestimated net survival and cure fractions in the simulation study. When applied to colon cancer real-life data, cure fractions estimated using the proposed model were higher than those in the conventional model, e.g. 5% higher in males at age 60 (57% vs. 52%).

CONCLUSIONS

The present analysis supports the use of the corrected mixture cure model, with the inclusion of increased risk of non-cancer death for cancer patients to provide better estimates of indicators based on cancer survival. These are important to public health decision-making; they improve patients' awareness and facilitate their return to normal life.

Correcting for heterogeneity and non-comparability bias in multicenter clinical trials with a rescaled random-effect excess hazard model

In the presence of competing causes of event occurrence (e.g., death), the interest might not only be in the overall survival but also in the so-called net survival, that is, the hypothetical survival that would be observed if the disease under study were the only possible cause of death. Net survival estimation is commonly based on the excess hazard approach in which the hazard rate of individuals is assumed to be the sum of a disease-specific and expected hazard rate, supposed to be correctly approximated by the mortality rates obtained from general population life tables. However, this assumption might not be realistic if the study participants are not comparable with the general population. Also, the hierarchical structure of the data can induces a correlation between the outcomes of individuals coming from the same clusters (e.g., hospital, registry). We proposed an excess hazard model that corrects simultaneously for these two sources of bias, instead of dealing with them independently as before. We assessed the performance of this new model and compared it with three similar models, using extensive simulation study, as well as an application to breast cancer data from a multicenter clinical trial. The new model performed better than the others in terms of bias, root mean square error, and empirical coverage rate. The proposed approach might be useful to account simultaneously for the hierarchical structure of the data and the non-comparability bias in studies such as long-term multicenter clinical trials, when there is interest in the estimation of net survival.

Hidden variable models reveal the effects of infection from changes in host survival

The impacts of disease on host vital rates can be demonstrated using longitudinal studies, but these studies can be expensive and logistically challenging. We examined the utility of hidden variable models to infer the individual effects of infectious disease from population-level measurements of survival when longitudinal studies are not possible. Our approach seeks to explain temporal deviations in population-level survival after introducing a disease causative agent when disease prevalence cannot be directly measured by coupling survival and epidemiological models. We tested this approach using an experimental host system (Drosophila melanogaster) with multiple distinct pathogens to validate the ability of the hidden variable model to infer per-capita disease rates. We then applied the approach to a disease outbreak in harbor seals (Phoca vituline) that had data on observed strandings but no epidemiological data. We found that our hidden variable modeling approach could successfully detect the per-capita effects of disease from monitored survival rates in both the experimental and wild populations. Our approach may prove useful for detecting epidemics from public health data in regions where standard surveillance techniques are not available and in the study of epidemics in wildlife populations, where longitudinal studies can be especially difficult to implement.

Is the Social Gradient in Net Survival Observed in France the Result of Inequalities in Cancer-Specific Mortality or Inequalities in General Mortality?

BACKGROUND

In cancer net survival analyses, if life tables (LT) are not stratified based on socio-demographic characteristics, then the social gradient in mortality in the general population is ignored. Consequently, the social gradient estimated on cancer-related excess mortality might be inaccurate. We aimed to evaluate whether the social gradient in cancer net survival observed in France could be attributable to inaccurate LT.

METHODS

Deprivation-specific LT were simulated, applying the social gradient in the background mortality due to external sources to the original French LT. Cancer registries' data from a previous French study were re-analyzed using the simulated LT. Deprivation was assessed according to the European Deprivation Index (EDI). Net survival was estimated by the Pohar-Perme method and flexible excess mortality hazard models by using multidimensional penalized splines.

RESULTS

A reduction in net survival among patients living in the most-deprived areas was attenuated with simulated LT, but trends in the social gradient remained, except for prostate cancer, for which the social gradient reversed. Flexible modelling additionally showed a loss of effect of EDI upon the excess mortality hazard of esophagus, bladder and kidney cancers in men and bladder cancer in women using simulated LT.

CONCLUSIONS

For most cancers the results were similar using simulated LT. However, inconsistent results, particularly for prostate cancer, highlight the need for deprivation-specific LT in order to produce accurate results.

How to achieve sustainable buyer-seller relationship in social commerce? The effect of network closure on ties evolution

The fact that most buyer-seller ties in the social commerce community are easy to form but hard to keep has brought the "social bubble" into social commerce. Following the literature streams of network closure and social commerce and based on the longitudinal dataset of an online social commerce community over a year, this article explores the buyer-seller ties evolution in the social commerce community through two stages, that is, ties emergence versus ties persistence. In this study, the authors build a hazard model and estimate with a semiparametric partial likelihood method. Our results show an asymmetric effect of network closure mechanisms across different stages of buyer-seller ties evolution. In the early stage of buyer-seller ties, due to the information asymmetry, buyers usually rely on informative signals that either reflect the "popular others" (i.e., the popularity and content sharing) or the "ideal self" (i.e., the value homophily and status homophily) to form ties with sellers, which makes the community more "transactional." As very few ties can survive through the periods of 3 months or more, the normative social influence, which relies heavily on the structure of extant relationships among community members, becomes the dominant driver of ties persistence, which makes the community more "social." This study contributes to the ongoing research of network analysis and social commerce. It provides valuable tactics to sellers who want to develop long-term relationships with buyers in the social commerce community.

Difference in net survival using regional and national life tables in Japan

BACKGROUND

National life table is commonly used for estimating cancer net survival. However, the national life table does not reflect condition of people in local area accurately, because there are disparities in cancer mortality rates among the local area in many cases. We investigated magnitude of difference in cancer net survival using the local area in Japan and Japanese life tables.

METHODS

We analyzed data from 32,942 cancer patients diagnosed between 2010 and 2012 in Aomori prefecture, Japan. Expected survival rates in Aomori (ESA) and Japan (ESJ) were estimated based on the life table of each area. Five-year net survival rates using ESA and the ESJ were estimated using the Pohar-Perme method.

RESULTS

The difference between net survival rates using the ESA (NSA) and the ESJ (NSJ) were larger than in men (0.3－3.0%) than in women (0.1－0.8%). The largest difference in the net survival rate was observed in prostate cancer patients, because the difference in the expected survival in oldest old men was remarkable.

CONCLUSION

Two factors affected the difference in the net survival rates resulting from the sensitivity analysis. The difference was larger (1) among older patients or (2) with a longer observation period (person-years).

A Flexible Bayesian Parametric Proportional Hazard Model: Simulation and Applications to Right-Censored Healthcare Data

Survival analysis is a collection of statistical techniques which examine the time it takes for an event to occur, and it is one of the most important fields in biomedical sciences and other variety of scientific disciplines. Furthermore, the computational rapid advancements in recent decades have advocated the application of Bayesian techniques in this field, giving a powerful and flexible alternative to the classical inference. The aim of this study is to consider the Bayesian inference for the generalized log-logistic proportional hazard model with applications to right-censored healthcare data sets. We assume an independent gamma prior for the baseline hazard parameters and a normal prior is placed on the regression coefficients. We then obtain the exact form of the joint posterior distribution of the regression coefficients and distributional parameters. The Bayesian estimates of the parameters of the proposed model are obtained using the Markov chain Monte Carlo (McMC) simulation technique. All computations are performed in Bayesian analysis using Gibbs sampling (BUGS) syntax that can be run with Just Another Gibbs Sampling (JAGS) from the R software. A detailed simulation study was used to assess the performance of the proposed parametric proportional hazard model. Two real-survival data problems in the healthcare are analyzed for illustration of the proposed model and for model comparison. Furthermore, the convergence diagnostic tests are presented and analyzed. Finally, our research found that the proposed parametric proportional hazard model performs well and could be beneficial in analyzing various types of survival data.

Inverse probability weighting and doubly robust standardization in the relative survival framework

A commonly reported measure when interested in the survival of cancer patients is relative survival. Relative survival circumvents issues with inaccurate cause of death information by incorporating the expected mortality rates of cancer individuals from population lifetables of the general population. A summary of the cancer population prognosis can be obtained using the marginal relative survival. To explore differences between exposure groups, such as socioeconomic groups, the difference in marginal relative survival between exposed and unexposed can be obtained and under assumptions is interpreted as the average causal effect of exposure to survival. In a modeling context, this is usually estimated by applying regression standardization as the average of the individual-specific estimates after fitting a relative survival model. Regression standardization yields an estimator that consistently estimates the causal effect under standard causal inference assumptions and if the relative survival model is correctly specified. We extend inverse probability weighting (IPW) and doubly robust standardization methods in the relative survival framework as additional valuable tools for obtaining average causal effects when correct model specification might not hold for the relative survival model. IPW yields an unbiased estimate of the average causal effect if a correctly specified model has been fitted for the exposure (propensity score) whereas doubly robust standardization requires that at least one of the propensity score model or the relative survival model is correctly specified. An example using data on melanoma is provided and a simulation study is conducted to investigate how sensitive are the methods to model misspecification, including different ways for obtaining standard errors.

Association between multimorbidity and socioeconomic deprivation on short-term mortality among patients with diffuse large B-cell or follicular lymphoma in England: a nationwide cohort study

OBJECTIVES

We aimed to assess the association between multimorbidity and deprivation on short-term mortality among patients with diffuse large B-cell (DLBCL) and follicular lymphoma (FL) in England.

SETTING

The association of multimorbidity and socioeconomic deprivation on survival among patients diagnosed with DLBCL and FL in England between 2005 and 2013. We linked the English population-based cancer registry with electronic health records databases and estimated adjusted mortality rate ratios by multimorbidity and deprivation status. Using flexible hazard-based regression models, we computed DLBCL and FL standardised mortality risk by deprivation and multimorbidity at 1 year.

RESULTS

Overall, 41 422 patients aged 45-99 years were diagnosed with DLBCL or FL in England during 2005-2015. Most deprived patients with FL with multimorbidities had three times higher hazard of 1-year mortality (HR: 3.3, CI 2.48 to 4.28, p<0.001) than least deprived patients without comorbidity; among DLBCL, there was approximately twice the hazard (HR: 1.9, CI 1.70 to 2.07, p<0.001).

CONCLUSIONS

Multimorbidity, deprivation and their combination are strong and independent predictors of an increased short-term mortality risk among patients with DLBCL and FL in England. Public health measures targeting the reduction of multimorbidity among most deprived patients with DLBCL and FL are needed to reduce the short-term mortality gap.

A tractable Bayesian joint model for longitudinal and survival data

We introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modeled using generalized linear mixed models, while the survival process is modeled using a parametric general hazard structure. The two processes are linked by sharing fixed and random effects, separating the effects that play a role at the time scale from those that affect the hazard scale. This strategy allows for the inclusion of nonlinear and time-dependent effects while avoiding the need for numerical integration, which facilitates the implementation of the proposed joint model. We explore the use of flexible parametric distributions for modeling the baseline hazard function which can capture the basic shapes of interest in practice. We discuss prior elicitation based on the interpretation of the parameters. We present an extensive simulation study, where we analyze the inferential properties of the proposed models, and illustrate the trade-off between flexibility, sample size, and censoring. We also apply our proposal to two real data applications in order to demonstrate the adaptability of our formulation both in univariate time-to-event data and in a competing risks framework. The methodology is implemented in rstan.

Marginal measures and causal effects using the relative survival framework

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.

Understanding disparities in cancer prognosis: An extension of mediation analysis to the relative survival framework

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.

Correcting inaccurate background mortality in excess hazard models through breakpoints

BACKGROUND

Methods for estimating relative survival are widely used in population-based cancer survival studies. These methods are based on splitting the observed (the overall) mortality into excess mortality (due to cancer) and background mortality (due to other causes, as expected in the general population). The latter is derived from life tables usually stratified by age, sex, and calendar year but not by other covariates (such as the deprivation level or the socioeconomic status) which may lack though they would influence background mortality. The absence of these covariates leads to inaccurate background mortality, thus to biases in estimating the excess mortality. These biases may be avoided by adjusting the background mortality for these covariates whenever available.

METHODS

In this work, we propose a regression model of excess mortality that corrects for potentially inaccurate background mortality by introducing age-dependent multiplicative parameters through breakpoints, which gives some flexibility. The performance of this model was first assessed with a single and two breakpoints in an intensive simulation study, then the method was applied to French population-based data on colorectal cancer.

RESULTS

The proposed model proved to be interesting in the simulations and the applications to real data; it limited the bias in parameter estimates of the excess mortality in several scenarios and improved the results and the generalizability of Touraine's proportional hazards model.

CONCLUSION

Finally, the proposed model is a good approach to correct reliably inaccurate background mortality by introducing multiplicative parameters that depend on age and on an additional variable through breakpoints.