Analysis of cause of death: Competing risks or progressive illness‐death model?

The analysis of cause of death is increasingly becoming a topic in oncology. It is usually distinguished between disease‐related and disease‐unrelated death. A frequently used approach is to define death as disease‐related when a progression to advanced phases has occurred before, otherwise as disease‐unrelated. The data are often analyzed as competing risks, while a progressive illness‐death model might in fact describe the situation more precisely. In this study, we investigated under which circumstances this misspecification leads to biased estimations of the state occupation probabilities. We simulated data according to the progressive illness‐death model in various settings, analyzed them with a competing risks model and with a progressive illness‐death model and compared them to the true state occupation probabilities. Censoring was either added independently of the status or based on the patients' status. The simulations showed that the censoring mechanism was decisive for the bias while neither the progression hazard nor the Markov property was important. Further, we found a slightly increased standard deviation for the competing risk estimator when censoring was independent of the patients' status. For illustration, both methods were applied to two practical examples of chronic myeloid leukemia (CML): one randomized controlled trial and one registry data set. While in the first case both estimators yielded almost identical results, in the latter case, visible differences were found between both methods.     

A review and critique of some models used in competing risk analysis.

We have introduced a notation which allows one to define competing risk models easily and to examine underlying assumptions. We have treated the actuarial model for competing risk in detail, comparing it with other models and giving useful variance formulae both for the case when times of death are available and for the case when they are not. The generality of these methods is illustrated by an example treating two dependent competing risks.     

Multiple Decrement Analysis with Dependent Risks

In a competing risks problem where a well-defined population is exposed simultaneously to several causes of death, interest has centered on the estimation of the probability of death from a given cause when one or more other causes have been eliminated. A basic component of all available procedures for estimating these probabilities is the assumption that the several causes of death act independently—an unrealistic assumption in the context of human and animal populations. This article considers the estimation of these probabilities assuming the existence ofinterdependencies among the various causes of death. A general formula is derived based on a given set of crude probabilities of death as well as the characteristics of the joint distribution of random variables indicating death from the various causes. This formula identifies alternative assumptions, less restrictive than that of independent risks, which may he used for estimation purposes.     

Estimating Subject‐Specific Dependent Competing Risk Profile with Censored Event Time Observations

Summary In a longitudinal study, suppose that the primary endpoint is the time to a specific event. This response variable, however, may be censored by an independent censoring variable or by the occurrence of one of several dependent competing events. For each study subject, a set of baseline covariates is collected. The question is how to construct a reliable prediction rule for the future subject's profile of all competing risks of interest at a specific time point for risk‐benefit decision making. In this article, we propose a two‐stage procedure to make inferences about such subject‐specific profiles. For the first step, we use a parametric model to obtain a univariate risk index score system. We then estimate consistently the average competing risks for subjects who have the same parametric index score via a nonparametric function estimation procedure. We illustrate this new proposal with the data from a randomized clinical trial for evaluating the efficacy of a treatment for prostate cancer. The primary endpoint for this study was the time to prostate cancer death, but had two types of dependent competing events, one from cardiovascular death and the other from death of other causes.     

Joint Modeling for Cognitive Trajectory and Risk of Dementia in the Presence of Death

Summary .  Dementia is characterized by accelerated cognitive decline before and after diagnosis as compared to normal aging. It has been known that cognitive impairment occurs long before the diagnosis of dementia. For individuals who develop dementia, it is important to determine the time when the rate of cognitive decline begins to accelerate and the subsequent gap time to dementia diagnosis. For normal aging individuals, it is also useful to understand the trajectory of cognitive function until their death. A Bayesian change-point model is proposed to fit the trajectory of cognitive function for individuals who develop dementia. In real life, people in older ages are subject to two competing risks, e.g., dementia and dementia-free death. Because the majority of people do not develop dementia, a mixture model is used for survival data with competing risks, which consists of dementia onset time after the change point of cognitive function decline for demented individuals and death time for nondemented individuals. The cognitive trajectories and the survival process are modeled jointly and the parameters are estimated using the Markov chain Monte Carlo method. Using data from the Honolulu Asia Aging Study, we show the trajectories of cognitive function and the effect of education, apolipoprotein E 4 genotype, and hypertension on cognitive decline and the risk of dementia.     

Utilizing Cause-of-Death Information to Estimate Conditional Probabilities of Disease and Death

Conditional probabilities that do not require the assumption of independence among competing risks for identifiability are proposed for the analysis of carcinogenesis bioassay data as a reasonable adjustment for deaths or other removals due to competing risks. These conditional probabilities permit consideration of one type of tumor at a time, but in such a way that inferences are relevant to actual experimental conditions under which other diseases and causes of death are present and operating. The importance of assigning cause of death in bioassays is demonstrated by the fact that it allows the definition and identification of functions useful in the interpretation of carcinogenesis data, without requiring that a disease of interest be independent from competing risks. However, one proposed conditional probability does require sacrifice data for its identifiability.     

A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.     

On a probability Model for Classifying the Unknown Causes of Death Due to Two Competing Risks into Assignable Causes

A probability model to classify the otherwise unclassified causes of death due to two competing risks R₁ and R₂ has been evolved in this paper. A simple model based on Poisson inputs has been illustrated by numerical illustrations. Further generalization of the model with more than two competing risks is straightforward for the given model.     

Population regulation by dispersal over patchy environment;

A mathematical model for the population regulation is presented, which takes into account the environmental heterogeneity and the animal dispersal, and does not contain any direct density effect on reproduction or death processes. Generally speaking, there are two kinds of dispersal, one is the density independent dispersal, the other is the density dependent. It is shown that a population equilibrium can be maintained by the density dependent dispersal or threshold dispersal which occurs only when the population density exceeds a certain threshold level, but that density independent dispersal by itself can not continue to maintain a population equilibrium.     

Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data

Summary In many instances, a subject can experience both a nonterminal and terminal event where the terminal event (e.g., death) censors the nonterminal event (e.g., relapse) but not vice versa. Typically, the two events are correlated. This situation has been termed semicompeting risks (e.g., Fine, Jiang, and Chappell, 2001 , Biometrika 88, 907–939; Wang, 2003 , Journal of the Royal Statistical Society, Series B 65, 257–273), and analysis has been based on a joint survival function of two event times over the positive quadrant but with observation restricted to the upper wedge. Implicitly, this approach entertains the idea of latent failure times and leads to discussion of a marginal distribution of the nonterminal event that is not grounded in reality. We argue that, similar to models for competing risks, latent failure times should generally be avoided in modeling such data. We note that semicompeting risks have more classically been described as an illness–death model and this formulation avoids any reference to latent times. We consider an illness–death model with shared frailty, which in its most restrictive form is identical to the semicompeting risks model that has been proposed and analyzed, but that allows for many generalizations and the simple incorporation of covariates. Nonparametric maximum likelihood estimation is used for inference and resulting estimates for the correlation parameter are compared with other proposed approaches. Asymptotic properties, simulations studies, and application to a randomized clinical trial in nasopharyngeal cancer evaluate and illustrate the methods. A simple and fast algorithm is developed for its numerical implementation.     

A Bayesian multi-risks survival (MRS) model in the presence of double censorings

Semi-competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi-competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi-risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right-censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate-specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer.     

Empirical, free of genetic model, estimation of recurrence risks in multifactorial diseases: conditional probability approach]

Conditional probability approach in estimation of recurrence risks in sibships of different parental phenotypic matings with the different set of affected and normal siblings is considered. The formulae are presented for calculation of recurrence risks in cases of equal and different susceptibility of two sexes under different ways of sampling of family data: direct selection of offsprings through the parents; indirect selection of offsprings through affected siblings--the probands, under different ascertainment probability--from pi = 1.0 ("exhaustive selection") up to pi----0 ("single selection"); for the case of different susceptibility of the two sexes a possibility of the differences in the ascertainment probabilities of men (pi m) and of women (pi w) is allowed, unlike "independent ascertainment model", which requires the constancy of pi. The case of multiple incompatible subforms is considered for estimation of the recurrence risks of the specified subforms. The methods of the risks estimation proposed are free of genetic models being universal both for classical mendelian traits (with the constant risks) and for multifactorial ones (with variable risks).     

A Multiple‐Absorbent Markov Process in Survival Studies: Application to Breast Cancer

A Markov process with several absorbent states is applied for analyzing a breast cancer dataset. The study examines the evolution of patients until death, and shows that two well‐differentiated ways can be considered in the evolution of patients towards the death state: those who relapse and those who not. The risk groups we have considered are determined by the application of treatments radiotherapy and chemotherapy, which are introduced as covariates. Four states are distinguished: no relapse, relapse, death after metastasis, and death without metastasis, the last two absorbent. We apply a methodology that uses algorithmic procedures, avoiding differential equations. The transition probability functions and the likelihood function in the model are calculated. For the dataset, the survival functions and the mean times in states for the different group of risks are determined. We show that the metastasis is the main cause of death in this cohort, but the number of deaths by relapse is not negligible.     

A Bayesian hierarchical approach to account for left-censored and missing radiation doses prone to classical measurement error when analyzing lung cancer mortality due to γ-ray exposure in the French cohort of uranium miners

Epidemiological data on cohorts of occupationally exposed uranium miners are currently used to assess health risks associated with chronic exposure to low doses of ionizing radiation. Nevertheless, exposure uncertainty is ubiquitous and questions the validity of statistical inference in these cohorts. This paper highlights the flexibility and relevance of the Bayesian hierarchical approach to account for both missing and left-censored (i.e. only known to be lower than a fixed detection limit) radiation doses that are prone to measurement error, when estimating radiation-related risks. Up to the authors’ knowledge, this is the first time these three sources of uncertainty are dealt with simultaneously in radiation epidemiology. To illustrate the issue, this paper focuses on the specific problem of accounting for these three sources of uncertainty when estimating the association between occupational exposure to low levels of γ-radiation and lung cancer mortality in the post-55 sub-cohort of French uranium miners. The impact of these three sources of dose uncertainty is of marginal importance when estimating the risk of death by lung cancer among French uranium miners. The corrected excess hazard ratio (EHR) is 0.81 per 100 mSv (95% credible interval: [0.28; 1.75]). Interestingly, even if the 95% credible interval of the corrected EHR is wider than the uncorrected one, a statistically significant positive association remains between γ-ray exposure and the risk of death by lung cancer, after accounting for dose uncertainty. Sensitivity analyses show that the results obtained are robust to different assumptions. Because of its flexible and modular nature, the Bayesian hierarchical models proposed in this work could be easily extended to account for high proportions of missing and left-censored dose values or exposure data, prone to more complex patterns of measurement error.

     

Dependent competing risks: a stochastic process model

Analyses of human mortality data classified according to cause of death frequently are based on competing risk theory. In particular, the times to death for different causes often are assumed to be independent. In this paper, a competing risk model with a weaker assumption of conditional independence of the times to death, given an assumed stochastic covariate process, is developed and applied to cause specific mortality data from the Framingham Heart Study. The results generated under this conditional independence model are compared with analogous results under the standard marginal independence model. Under the assumption that this conditional independence model is valid, the comparison suggests that the standard model overestimates by 4% the effect on life expectancy at age 30 due to the hypothetical elimination of cancer and by 7% the effect for cardiovascular/cerebrovascular disease. By age 80 the overestimates were 11% for cancer and 16% for heart disease. These results suggest the importance of avoiding the marginal independence assumption when appropriate data are available — especially when focusing on mortality at advanced ages.     

昆虫细胞程序性死亡的研究进展

在昆虫发育和抵抗病原微生物的入侵过程中,细胞凋亡与自噬性死亡现象十分常见。昆虫细胞凋亡的研究已经取得了许多的成果,但是有关细胞自噬程序性死亡的研究还正在深入。昆虫细胞凋亡的信号通路至少有3条：一条类似于线虫细胞的凋亡信号通路,另一条类似于哺乳动物细胞的凋亡信号通路, 还有一条不依赖于胱天蛋白酶的凋亡信号通路。在昆虫的多种组织细胞中,细胞凋亡与自噬程序性死亡在信号通路上存在互串(cross talking),可以相互促进、抑制或替代。了解昆虫细胞程序性死亡对防治害虫具有一定的意义。     

The natural history of cytogenetically abnormal fetuses detected at midtrimester amniocentesis which are not terminated electively: new data and estimates of the excess and relative risk of late fetal death associated with 47,+21 and some other abnormal karyotypes.

We report the results of an ongoing survey of rates of spontaneous death of fetuses with chromosome abnormalities detected at second-trimester amniocentesis in which the mother did not elect abortion. Estimated excess risks (and conservative 90% confidence intervals) of spontaneous fetal death for various cytogenetic abnormalities are as follows: 47,+21, 25.6% (18.0%-34.0%); 47,+18, 63.8% (49.3%-79.8%); 47,+13, 36.5% (11%-69.7%); 45,X, 65.3% (41.0%-84.2%); and mosaic 45,X/46,XX, 10.8% (1.0%-26.8%). There is little evidence for an excess risk of fetal death, at least following amniocentesis, for 47,XXX, 47,XXY, or 47,XYY. The excess risks of fetal death were adjusted for the likelihood that a fetus of normal karyotype would undergo spontaneous fetal death in a population of older maternal age similar to that in which prenatal cytogenetic diagnosis is undertaken. The absolute fetal death rates when this factor is ignored are about 3.5% higher (i.e., may be derived by adding 3.5% to the values given). The excess risks are those which are most appropriate for use in estimating the contribution of chromosome abnormalities to spontaneous fetal death.     

Comparison between Frailty Index of Deficit Accumulation and Phenotypic Model to Predict Risk of Falls: Data from the Global Longitudinal Study of Osteoporosis in Women (GLOW) Hamilton Cohort

Objectives

To compare the predictive accuracy of the frailty index (FI) of deficit accumulation and the phenotypic frailty (PF) model in predicting risks of future falls, fractures and death in women aged ≥55 years.

Methods

Based on the data from the Global Longitudinal Study of Osteoporosis in Women (GLOW) 3-year Hamilton cohort (n = 3,985), we compared the predictive accuracy of the FI and PF in risks of falls, fractures and death using three strategies: (1) investigated the relationship with adverse health outcomes by increasing per one-fifth (i.e., 20%) of the FI and PF; (2) trichotomized the FI based on the overlap in the density distribution of the FI by the three groups (robust, pre-frail and frail) which were defined by the PF; (3) categorized the women according to a predicted probability function of falls during the third year of follow-up predicted by the FI. Logistic regression models were used for falls and death, while survival analyses were conducted for fractures.

Results

The FI and PF agreed with each other at a good level of consensus (correlation coefficients ≥ 0.56) in all the three strategies. Both the FI and PF approaches predicted adverse health outcomes significantly. The FI quantified the risks of future falls, fractures and death more precisely than the PF. Both the FI and PF discriminated risks of adverse outcomes in multivariable models with acceptable and comparable area under the curve (AUCs) for falls (AUCs ≥ 0.68) and death (AUCs ≥ 0.79), and c-indices for fractures (c-indices ≥ 0.69) respectively.

Conclusions

The FI is comparable with the PF in predicting risks of adverse health outcomes. These findings may indicate the flexibility in the choice of frailty model for the elderly in the population-based settings.     

A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction

In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (EM)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.