Competing risk models to estimate the excess mortality and the first recurrent-event hazards

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.

A bayesian approach to model the underlying predictors of early recurrence and postoperative death in patients with colorectal Cancer

Objective

This study aimed at utilizing a Bayesian approach semi-competing risks technique to model the underlying predictors of early recurrence and postoperative Death in patients with colorectal cancer (CRC).

Methods

In this prospective cohort study, 284 patients with colorectal cancer, who underwent surgery, referred to Imam Khomeini clinic in Hamadan from 2001 to 2017. The primary outcomes were the probability of recurrence, the probability of Mortality without recurrence, and the probability of Mortality after recurrence. The patients ‘recurrence status was determined from patients’ records. The Bayesian survival modeling was carried out by semi-competing risks illness-death models, with accelerated failure time (AFT) approach, in R 4.1 software. The best model was chosen according to the lowest deviance information criterion (DIC) and highest logarithm of the pseudo marginal likelihood (LPML).

Results

The log-normal model (DIC = 1633, LPML = -811), was the optimal model. The results showed that gender(Time Ratio = 0.764: 95% Confidence Interval = 0.456–0.855), age at diagnosis (0.764: 0.538–0.935 ), T₃ stage (0601: 0.530–0.713), N₂ stage (0.714: 0.577–0.935 ), tumor size (0.709: 0.610–0.929), grade of differentiation at poor (0.856: 0.733–0.988), and moderate (0.648: 0.503–0.955) levels, and the number of chemotherapies (1.583: 1.367–1.863) were significantly related to recurrence. Also, age at diagnosis (0.396: 0.313–0.532), metastasis to other sites (0.566: 0.490–0.835), T₃ stage (0.363: 0.592 − 0.301), T₄ stage (0.434: 0.347–0.545), grade of differentiation at moderate level (0.527: 0.387–0.674), tumor size (0.595: 0.500–0.679), and the number of chemotherapies (1.541: 1.332–2.243) were the significantly predicted the death. Also, age at diagnosis (0.659: 0.559–0.803), and the number of chemotherapies (2.029: 1.792–2.191) were significantly related to mortality after recurrence.

Conclusion

According to specific results obtained from the optimal Bayesian log-normal model for terminal and non-terminal events, appropriate screening strategies and the earlier detection of CRC leads to substantial improvements in the survival of patients.

Integrating relative survival in multi-state models—a non-parametric approach

Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate.

Specific causes of recurrence after surgery and mortality in patients with colorectal cancer: A competing risks survival analysis

Background

In situation where there are more than one cause of occurring the outcome such as recurrence after surgery and death, the assumption of classical survival analyses are not satisfied. To cover this issue, this study aimed at utilizing competing risks survival analysis to assess the specific risk factors of local-distance recurrence and mortality in patients with colorectal cancer (CRC) undergoing surgery.

Materials and Methods

In this retrospective cohort study, 254 patients with CRC undergoing resection surgery were studied. Data of the outcome from the available documents in the hospital were gathered. Furthermore, based on pathological report, the diagnosis of CRC was considered. We model the risk factors on the hazard of recurrence and death using competing risk survival in R3.6.1 software.

Results

A total of 114 patients had local or distant recurrence (21 local recurrences, 72 distant recurrences, and 21 local and distant recurrence). Pathological stage (adjusted hazard ratio [AHR] = 4.28 and 5.37 for stage 3 and 4, respectively), tumor site (AHR = 2.45), recurrence (AHR = 3.92) and age (AHR = 3.15 for age >70) was related to hazard of death. Also based on cause-specific hazard model, pathological stage (AHR = 7.62 for stage 4), age (AHR = 1.46 for age >70), T stage (AHR = 1.8 and 2.7 for T3 and T4, respectively), N stage (AHR = 2.59 for N2), and white blood cells (AHR = 1.95) increased the hazard of recurrence in patients with CRC.

Conclusion

This study showed that older age, higher pathological, rectum tumor site and presence of recurrence were independent risk factors for mortality among CRC patients. Also age, higher T/N stage, higher pathological stage and higher values of WBC were significantly related to higher hazard of local/distance recurrence of patients with CRC.

Vascular Diseases In Patients With Chronic Myeloproliferative Neoplasms - Impact Of Comorbidity

Background

Patients with chronic myeloproliferative neoplasms (MPNs), including essential thrombocythemia (ET), polycythemia vera (PV), and primary myelofibrosis (PMF), are at high risk of vascular complications. However, the magnitude of this is risk not well known and the possible effect of comorbidity is poorly understood.

Aim

Our aim was to compare the risk of vascular diseases in patients with MPNs and matched comparisons from the general population and to study the effect modification of comorbidity.

Methods

We followed 3087 patients with ET, 6076 with PV, 3719 with PMF or unspecified MPN, and age- and sex-matched general population comparisons to estimate the risks of cardiovascular diseases such as myocardial infarction and stroke. We computed 5-year cumulative incidences (risks) for vascular disease in patients with MPNs and comparisons as well as 1-year and 5-year risks, risk differences, and hazard ratios (HRs) for vascular diseases comparing rates in each group of patients with their comparison cohort by level of comorbidity based on the Charlson Comorbidity Index (CCI) [score of 0 (low comorbidity), of 1–2 (moderate comorbidity), and of >2 (severe comorbidity)], as well as other comorbid conditions.

Results

The overall 5-year risk of vascular disease ranged from 0.5% to 7.7% in patients with MPNs, which was higher than the risk in the general population. In the same period, the adjusted HRs for vascular disease were 1.3 to 3.7 folds higher in patients with MPNs compared to the general population. An increase in CCI score was associated with an equally increased rate of most types of vascular diseases during the first 5 years of follow-up in both MPN and comparisons.

Conclusion

Patients with MPNs have a higher risk of vascular diseases during the first 5 years than that of the general population; however, comorbidity modifies the rates similarly in MPN and in the general population.

Estimation of the adjusted cause-specific cumulative probability using flexible regression models for the cause-specific hazards

In competing risks setting, we account for death according to a specific cause and the quantities of interest are usually the cause-specific hazards (CSHs) and the cause-specific cumulative probabilities. A cause-specific cumulative probability can be obtained with a combination of the CSHs or via the subdistribution hazard. Here, we modeled the CSH with flexible hazard-based regression models using B-splines for the baseline hazard and time-dependent (TD) effects. We derived the variance of the cause-specific cumulative probabilities at the population level using the multivariate delta method and showed how we could easily quantify the impact of a covariate on the cumulative probability scale using covariate-adjusted cause-specific cumulative probabilities and their difference. We conducted a simulation study to evaluate the performance of this approach in its ability to estimate the cumulative probabilities using different functions for the cause-specific log baseline hazard and with or without a TD effect. In the scenario with TD effect, we tested both well-specified and misspecified models. We showed that the flexible regression models perform nearly as well as the nonparametric method, if we allow enough flexibility for the baseline hazards. Moreover, neglecting the TD effect hardly affects the cumulative probabilities estimates of the whole population but impacts them in the various subgroups. We illustrated our approach using data from people diagnosed with monoclonal gammopathy of undetermined significance and provided the R-code to derive those quantities, as an extension of the R-package mexhaz.

Improving survival in end-stage renal disease: A case study

Background: With the increase of life expectancy, *On behalf of the REIN registry. end-stage renal disease (ESRD) is affecting a growing number of people. Simultaneously, renal replacement therapies (RRTs) have considerably improved patient survival. We investigated the way current RRT practices would affect patients' survival.

Methods: We used a multi-state model to represent the transitions between RRTs and the transition to death. The concept of “crude probability of death” combined with this model allowed estimating the proportions of ESRD-related and ESRD-unrelated deaths. Estimating the ESRD-related death rate requires comparing the mortality rate between ESRD patients and the general population. Predicting patients' courses through RRTs and Death states could be obtained by solving a system of Kolmogorov differential equations. The impact of practice on patient survival was quantified using the restricted mean survival time (RMST) which was compared with that of healthy subjects with same characteristics.

Results: The crude probability of ESRD-unrelated death was nearly zero in the youngest patients (18–45 years) but was a sizeable part of deaths in the oldest (≥70 years). Moreover, in the oldest patients, the proportion of expected death was higher in patient without vs. with diabetes because the former live older. In men aged 75 years at first RRT, the predicted RMSTs in patients with and without diabetes were, respectively, 61% and 69% those of comparable healthy men.

Conclusion: Using the concept of “crude probability of death” with multi-state models is feasible and useful to assess the relative benefits of various treatments in ESRD and help patient long-term management.

A multilevel excess hazard model to estimate net survival on hierarchical data allowing for non-linear and non-proportional effects of covariates

The excess hazard regression model is an approach developed for the analysis of cancer registry data to estimate net survival, that is, the survival of cancer patients that would be observed if cancer was the only cause of death. Cancer registry data typically possess a hierarchical structure: individuals from the same geographical unit share common characteristics such as proximity to a large hospital that may influence access to and quality of health care, so that their survival times might be correlated. As a consequence, correct statistical inference regarding the estimation of net survival and the effect of covariates should take this hierarchical structure into account. It becomes particularly important as many studies in cancer epidemiology aim at studying the effect on the excess mortality hazard of variables, such as deprivation indexes, often available only at the ecological level rather than at the individual level. We developed here an approach to fit a flexible excess hazard model including a random effect to describe the unobserved heterogeneity existing between different clusters of individuals, and with the possibility to estimate non-linear and time-dependent effects of covariates. We demonstrated the overall good performance of the proposed approach in a simulation study that assessed the impact on parameter estimates of the number of clusters, their size and their level of unbalance. We then used this multilevel model to describe the effect of a deprivation index defined at the geographical level on the excess mortality hazard of patients diagnosed with cancer of the oral cavity. Copyright © 2016 John Wiley & Sons, Ltd.

A multistate additive relative survival semi-Markov model

Medical researchers are often interested to investigate the relationship between explicative variables and times-to-events such as disease progression or death. Such multiple times-to-events can be studied using multistate models. For chronic diseases, it may be relevant to consider semi-Markov multistate models because the transition intensities between two clinical states more likely depend on the time already spent in the current state than on the chronological time. When the cause of death for a patient is unavailable or not totally attributable to the disease, it is not possible to specifically study the associations with the excess mortality related to the disease. Relative survival analysis allows an estimate of the net survival in the hypothetical situation where the disease would be the only possible cause of death. In this paper, we propose a semi-Markov additive relative survival (SMRS) model that combines the multistate and the relative survival approaches. The usefulness of the SMRS model is illustrated by two applications with data from a French cohort of kidney transplant recipients. Using simulated data, we also highlight the effectiveness of the SMRS model: the results tend to those obtained if the different causes of death are known.

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

In chronic diseases, such as cancer, recurrent events (such as relapses) are commonly observed; these could be interrupted by death. With such data, a joint analysis of recurrence and mortality processes is usually conducted with a frailty parameter shared by both processes. We examined a joint modeling of these processes considering death under two aspects: 'death due to the disease under study' and 'death due to other causes', which enables estimating the disease-specific mortality hazard. The excess hazard model was used to overcome the difficulties in determining the causes of deaths (unavailability or unreliability); this model allows estimating the disease-specific mortality hazard without needing the cause of death but using the mortality hazards observed in the general population. We propose an approach to model jointly recurrence and disease-specific mortality processes within a parametric framework. A correlation between the two processes is taken into account through a shared frailty parameter. This approach allows estimating unbiased covariate effects on the hazards of recurrence and disease-specific mortality. The performance of the approach was evaluated by simulations with different scenarios. The method is illustrated by an analysis of a population-based dataset on colon cancer with observations of colon cancer recurrences and deaths. The benefits of the new approach are highlighted by comparison with the 'classical' joint model of recurrence and overall mortality. Moreover, we assessed the goodness of fit of the proposed model. Comparisons between the conditional hazard and the marginal hazard of the disease-specific mortality are shown, and differences in interpretation are discussed.