A joint frailty model to estimate the recurrence process and the disease-specific mortality process without needing the cause of death

Socioeconomic status and its relation with breast cancer recurrence and survival in young women in the Netherlands

BACKGROUND

Associations between socioeconomic status (SES) and breast cancer survival are most pronounced in young patients. We further investigated the relation between SES, subsequent recurrent events and mortality in breast cancer patients < 40 years. Using detailed data on all recurrences that occur between date of diagnosis of the primary tumor and last observation, we provide a unique insight in the prognosis of young breast cancer patients according to SES.

METHODS

All women < 40 years diagnosed with primary operated stage I-III breast cancer in 2005 were selected from the nationwide population-based Netherlands Cancer Registry. Data on all recurrences within 10 years from primary tumor diagnosis were collected directly from patient files. Recurrence patterns and absolute risks of recurrence, contralateral breast cancer (CBC) and mortality - accounting for competing risks - were analysed according to SES. Relationships between SES, recurrence patterns and excess mortality were estimated using a multivariable joint model, wherein the association between recurrent events and excess mortality (expected mortality derived from the general population) was included.

RESULTS

We included 525 patients. The 10-year recurrence risk was lowest in high SES (18.1%), highest in low SES (29.8%). Death and CBC as first events were rare. In high, medium and low SES 13.2%, 15.3% and 19.1% died following a recurrence. Low SES patients had shorter median time intervals between diagnosis, first recurrence and 10-year mortality (2.6 and 2.7 years, respectively) compared to high SES (3.5 and 3.3 years, respectively). In multivariable joint modeling, high SES was significantly related to lower recurrence rates over 10-year follow-up, compared to low SES. A strong association between the recurrent event process and excess mortality was found.

CONCLUSIONS

High SES is associated with lower recurrence risks, less subsequent events and better prognosis after recurrence over 10 years than low SES. Breast cancer risk factors, adjuvant treatment adherence and treatment of recurrence may possibly play a role in this association.

Assessment of death risk of breast cancer patients with joint frailty models

Objectives:

To investigate the effects of risk factors on recurrence and death in breast cancer patients, taking into account the dependence between recurrence and death as well as the heterogeneity among individuals. The other aim of this study was to make predictions of death risks with a dynamic model that includes patient’s history and different horizons.

Methods:

The data of 465 patients who had undergone surgery at the Istanbul University Oncology Institute, Istanbul, Turkey, between 2009 and 2016 were used. For data analysis in this retrospective study, the authors applied the joint frailty model, and the predictions were obtained using dynamic prediction methods that consider the patient’s history. The Brier score was used to evaluate the accuracy of the estimations.

Results:

A positive relationship was found between recurrence and death, and heterogeneity was found among patients (p<0.001, p=1.008, p=2.945). The effects of Cerb-B2, tumor type, remaining lymph nodes, neoadjuvant chemotherapy, and surgery type were statistically significant for death and recurrence (p<0.05, relative risk [death, recurrence] = [2.5, 11.86], [2.065, 2.798], [1.852, 3.113], [4.211, 9.366], [1.521,1.991]). The Brier score values used in the evaluation of the predictions obtained by the dynamic prediction methods were found to be below 0.30.

Conclusion:

The use of joint frailty models is recommended for the detection of heterogeneity effects and dependence between recurrence and death. Through models in survival analysis, researchers can obtain more accurate parameter estimates. A significant variance of frailty indicates different death risks for the same characteristics.

Percutaneous repair or medical treatment for secondary mitral regurgitation: outcomes at 2 years

AIMS

The MITRA-FR trial showed that among symptomatic patients with severe secondary mitral regurgitation, percutaneous repair did not reduce the risk of death or hospitalization for heart failure at 12 months compared with guideline-directed medical treatment alone. We report the 24-month outcome from this trial.

METHODS AND RESULTS

At 37 centres, we randomly assigned 304 symptomatic heart failure patients with severe secondary mitral regurgitation (effective regurgitant orifice area >20 mm² or regurgitant volume >30 mL), and left ventricular ejection fraction between 15% and 40% to undergo percutaneous valve repair plus medical treatment (intervention group, n = 152) or medical treatment alone (control group, n = 152). The primary efficacy outcome was the composite of all-cause death and unplanned hospitalization for heart failure at 12 months. At 24 months, all-cause death and unplanned hospitalization for heart failure occurred in 63.8% of patients (97/152) in the intervention group and 67.1% (102/152) in the control group [hazard ratio (HR) 1.01, 95% confidence interval (CI) 0.77-1.34]. All-cause mortality occurred in 34.9% of patients (53/152) in the intervention group and 34.2% (52/152) in the control group (HR 1.02, 95% CI 0.70-1.50). Unplanned hospitalization for heart failure occurred in 55.9% of patients (85/152) in the intervention group and 61.8% (94/152) in the control group (HR 0.97, 95% CI 0.72-1.30).

CONCLUSIONS

In patients with severe secondary mitral regurgitation, percutaneous repair added to medical treatment did not significantly reduce the risk of death or hospitalization for heart failure at 2 years compared with medical treatment alone.

A joint model for recurrent events and a semi-competing risk in the presence of multi-level clustering

Clinical trial designs often include multiple levels of clustering in which patients are nested within clinical sites and recurrent outcomes are nested within patients who may also experience a semi-competing risk. Traditional survival methods that analyze these processes separately may lead to erroneous inferences as they ignore possible dependencies. To account for the association between recurrent events and a semi-competing risk in the presence of two levels of clustering, we developed a semi-parametric joint model. The Gaussian quadrature with a piecewise constant baseline hazard was used to estimate the unspecified baseline hazards and the likelihood. Simulations showed that the proposed joint model has good statistical properties (i.e. <5% bias and 95% coverage) compared to the shared frailty and joint frailty models when informative censoring and multiple levels of clustering were present. The proposed method was applied to data from an AIDS clinical trial to investigate the impact of antiretroviral treatment on recurrent AIDS-defining events in the presence of a semi-competing risk of death and multi-level clustering and showed a significant dependency between AIDS-defining events and death at the patient level but not at the clinic level.

A joint frailty model provides for risk stratification of human immunodeficiency virus-infected patients based on unobserved heterogeneity

OBJECTIVES

To investigate the association between recurrent AIDS-defining events and a semicompeting risk of death in patients with advanced, multidrug-resistant human immunodeficiency virus infection and to identify individuals at increased risk for these events using a joint frailty model.

STUDY DESIGN AND SETTING

Three hundred sixty-eight patients with antiretroviral treatment failure in the Options in Management of Antiretrovirals Trial randomized to two antiretroviral treatment strategies using a 2 × 2 factorial design, intensive vs. standard and interruption vs. continuation, and followed for development of AIDS-defining events and death.

RESULTS

Participants were heterogeneous for risk of AIDS-defining events and death (P < 0.001), and AIDS-defining events were strongly associated with death (P < 0.001), irrespective of treatment. The frailty model was used to classify individuals into high- and low-risk groups based on unobserved heterogeneity. Low-risk individuals were unlikely to die (0%) or have an AIDS-defining event (<4%), whereas high-risk individuals had event rates approaching 70%. About one-third of high-risk individuals had accelerated mortality, all who died before experiencing an AIDS-defining event. High-risk was associated with being immunocompromised and higher predicted 5-year mortality.

CONCLUSION

The joint frailty model permits classification of individuals into risk groups based on unobserved heterogeneity that may be identifiable based on observed covariates, providing advantages over the traditional Cox model.

Frailty modelling for multitype recurrent events in clinical trials

Recurrent event outcomes are ubiquitous among clinical trial data which encourages a conventional approach to analysis. Yet a common feature of these data has received less attention, that is, survival times often comprise multiple types of events that may imply a disparity in cost and disease severity. Typically, we neglect this feature of the data by combining event-types or analyzing each type separately, thus ignoring any interdependence among them. This practice may reflect a dearth of readily available methods and software that more appropriately acknowledge the true data structure. We provide a review of the literature on multitype recurrent events and frailty modelling which reflects a renewed interest in the topic over the past decade and the emergence of software for estimation. Thus, a review of available methods seems timely, if not overdue.

Analysis of Survival Data: Challenges and Algorithm-Based Model Selection

Survival data is a special form of time to event data that is often encountered while modelling risk. The classical Cox proportional hazard model, that is popularly used to analyse survival data, cannot be used for modelling risk when the proportional hazard assumption is violated or when there is recurrent time to event data. In this context we conducted this narrative review to develop an algorithm for selection of advanced methods of analysing survival data in the above-mentioned situations. Findings were synthesized from literature retrieved from searches of Pubmed, Embase, and Google Scholar. Existing literature suggest that for non-proportionality, especially due to categorical predictors stratified Cox model may be useful. An accelerated failure time model is applicable in case of different follow-up time among different experimental groups and the median time to event is the outcome of interest instead of hazard. Extended Cox models and marginal models are used in case of multivariate ordered failure events and the type of model depends upon the presence of clustering and nature of ordering. In the presence of heterogeneity, a shared frailty model is used that is analogous to mixed models. More advanced models, including competing risk and multistate models are required for modelling competing risk, multiple states and multiple transitions. Joint models are used for multiple time dependent outcomes with different attributes. We have developed an algorithm based on the review for appropriate model selection to curb the challenge of modeling survival data and the algorithm is expected to help the naïve researchers in analysing survival data.

Challenges in the estimation of Net SURvival: The CENSUR working survival group

BACKGROUND

Net survival, the survival probability that would be observed, in a hypothetical world, where the cancer of interest would be the only possible cause of death, is a key indicator in population-based cancer studies. Accounting for mortality due to other causes, it allows cross-country comparisons or trends analysis and provides a useful indicator for public health decision-making. The objective of this study was to show how the creation and formalization of a network comprising established research teams, which already had substantial and complementary experience in both cancer survival analysis and methodological development, make it possible to meet challenges and thus provide more adequate tools, to improve the quality and the comparability of cancer survival data, and to promote methodological transfers in areas of emerging interest.

METHOD

The Challenges in the Estimation of Net SURvival (CENSUR) working survival group is composed of international researchers highly skilled in biostatistics, methodology, and epidemiology, from different research organizations in France, the United Kingdom, Italy, Slovenia, and Canada, and involved in French (FRANCIM) and European (EUROCARE) cancer registry networks.

RESULTS

The expected advantages are an interdisciplinary, international, synergistic network capable of addressing problems in public health, for decision-makers at different levels; tools for those in charge of net survival analyses; a common methodology that makes unbiased cross-national comparisons of cancer survival feasible; transfer of methods for net survival estimations to other specific applications (clinical research, occupational epidemiology); and dissemination of results during an international training course.

CONCLUSION

The formalization of the international CENSUR working survival group was motivated by a need felt by scientists conducting population-based cancer research to discuss, develop, and monitor implementation of a common methodology to analyze net survival in order to provide useful information for cancer control and cancer policy. A "team science" approach is necessary to address new challenges concerning the estimation of net survival.

Simulating recurrent event data with hazard functions defined on a total time scale

Background

In medical studies with recurrent event data a total time scale perspective is often needed to adequately reflect disease mechanisms. This means that the hazard process is defined on the time since some starting point, e.g. the beginning of some disease, in contrast to a gap time scale where the hazard process restarts after each event. While techniques such as the Andersen-Gill model have been developed for analyzing data from a total time perspective, techniques for the simulation of such data, e.g. for sample size planning, have not been investigated so far.

Methods

We have derived a simulation algorithm covering the Andersen-Gill model that can be used for sample size planning in clinical trials as well as the investigation of modeling techniques. Specifically, we allow for fixed and/or random covariates and an arbitrary hazard function defined on a total time scale. Furthermore we take into account that individuals may be temporarily insusceptible to a recurrent incidence of the event. The methods are based on conditional distributions of the inter-event times conditional on the total time of the preceeding event or study start. Closed form solutions are provided for common distributions. The derived methods have been implemented in a readily accessible R script.

Results

The proposed techniques are illustrated by planning the sample size for a clinical trial with complex recurrent event data. The required sample size is shown to be affected not only by censoring and intra-patient correlation, but also by the presence of risk-free intervals. This demonstrates the need for a simulation algorithm that particularly allows for complex study designs where no analytical sample size formulas might exist.

Conclusions

The derived simulation algorithm is seen to be useful for the simulation of recurrent event data that follow an Andersen-Gill model. Next to the use of a total time scale, it allows for intra-patient correlation and risk-free intervals as are often observed in clinical trial data. Its application therefore allows the simulation of data that closely resemble real settings and thus can improve the use of simulation studies for designing and analysing studies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-015-0005-2) contains supplementary material, which is available to authorized users.

Bayesian imperfect information analysis for clinical recurrent data

In medical research, clinical practice must often be undertaken with imperfect information from limited resources. This study applied Bayesian imperfect information-value analysis to realistic situations to produce likelihood functions and posterior distributions, to a clinical decision-making problem for recurrent events. In this study, three kinds of failure models are considered, and our methods illustrated with an analysis of imperfect information from a trial of immunotherapy in the treatment of chronic granulomatous disease. In addition, we present evidence toward a better understanding of the differing behaviors along with concomitant variables. Based on the results of simulations, the imperfect information value of the concomitant variables was evaluated and different realistic situations were compared to see which could yield more accurate results for medical decision-making.