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.     

Partner status and survival after cancer: A competing risks analysis

ObjectiveThe survival benefits of having a partner for all cancers combined is well recognized, however its prognostic importance for individual cancer types, including competing mortality causes, is less clear. This study was undertaken to quantify the impact of partner status on survival due to cancer-specific and competing mortality causes.MethodsData were obtained from the population-based Queensland Cancer Registry on 176,050 incident cases of ten leading cancers diagnosed in Queensland (Australia) from 1996 to 2012. Flexible parametric competing-risks models were used to estimate cause-specific hazards and cumulative probabilities of death, adjusting for age, stage (breast, colorectal and melanoma only) and stratifying by sex.ResultsBoth unpartnered males and females had higher total cumulative probability of death than their partnered counterparts for each site. For example, the survival disadvantage for unpartnered males ranged from 3% to 30% with higher mortality burden from both the primary cancer and competing mortality causes. The cause-specific age-adjusted hazard ratios were also consistent with patients without a partner having increased mortality risk although the specific effect varied by site, sex and cause of death. For all combined sites, unpartnered males had a 46%, 18% and 44% higher risk of cancer-specific, other cancer and non-cancer mortality respectively with similar patterns for females. The higher mortality risk persisted after adjustment for stage.ConclusionsIt is important to better understand the mechanisms by which having a partner is beneficial following a cancer diagnosis, so that this can inform improvements in cancer management for all people with cancer.     

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.     

On testing dependence between time to failure and cause of failure when causes of failure are missing

The hypothesis of independence between the failure time and the cause of failure is studied by using the conditional probabilities of failure due to a specific cause given that there is no failure up to certain fixed time. In practice, there are situations when the failure times are available for all units but the causes of failures might be missing for some units. We propose tests based on U-statistics to test for independence of the failure time and the cause of failure in the competing risks model when all the causes of failure cannot be observed. The asymptotic distribution is normal in each case. Simulation studies look at power comparisons for the proposed tests for two families of distributions. The one-sided and the two-sided tests based on Kendall type statistic perform exceedingly well in detecting departures from independence.     

Biologically Based Prediction of Empirical Nonlinearity in Lung Cancer Risk vs. Residential/ Occupational Radon Exposure

Ecologic U.S. county data suggest negative associations between residential radon exposure and lung cancer mortality (LCM) that are inconsistent with clearly positive ones revealed by individual data on underground miners. If this inconsistency is due to competing effects of induced cell killing vs. mutations in alpha-radiation exposed bronchial epithelium, then linear extrapolation from miner data may overestimate typical residential radon risks. To investigate the plausibility of this hypothesis, a biologically based “cytodynamic 2-stage” (CD2) cancer-risk model was fit to combined 1950 to 1954 age-specific person-year data on white females of age 40+ y in 2821 U.S. counties (～90% never-smokers), and on five cohorts of underground miners who never smoked, conditional on a realistic rate of alpha-radiation-induced killing of human lung cells, and on linear-no-threshold dose-response relations for both processes assumed to affect cancer risk (alpha-induced mutations and cell killing). As summarized previously (Bogen, K.T., Hum. Exper. Toxicol. 17:691-6, 1998), a good CD2 fit was obtained that involved biologically plausible parameter values and (without further optimization) also predicted inverse dose-rate effects observed in the nonsmoking miners. The present paper reports mathematical details of the CD2 model used, as well as additional modeling results involving the same combined data set. The results obtained are consistent with the hypotheses that low-level radon exposure is nonlinearly related to LCM risk, and that current linear no-threshold extrapolation models overestimate LCM risk associated with relatively low residential radon concentrations (<～200?Bq m^?3). Testing this hypothesis would require more extensive individual-level epidemiological data relating residential radon exposures to LCM than are currently available.     

Mixed-effect hybrid models for longitudinal data with nonignorable dropout

Summary .  Selection models and pattern-mixture models are often used to deal with nonignorable dropout in longitudinal studies. These two classes of models are based on different factorizations of the joint distribution of the outcome process and the dropout process. We consider a new class of models, called mixed-effect hybrid models (MEHMs), where the joint distribution of the outcome process and dropout process is factorized into the marginal distribution of random effects, the dropout process conditional on random effects, and the outcome process conditional on dropout patterns and random effects. MEHMs combine features of selection models and pattern-mixture models: they directly model the missingness process as in selection models, and enjoy the computational simplicity of pattern-mixture models. The MEHM provides a generalization of shared-parameter models (SPMs) by relaxing the conditional independence assumption between the measurement process and the dropout process given random effects. Because SPMs are nested within MEHMs, likelihood ratio tests can be constructed to evaluate the conditional independence assumption of SPMs. We use data from a pediatric AIDS clinical trial to illustrate the models.     

Spatio-temporal trends in gastric cancer mortality in Spain: 1975–2008

Aim of the study: There has been a downward trend in gastric cancer mortality worldwide. In Spain, a marked spatial aggregation of areas with excess mortality due to this cause has long been reported. This paper sought to analyse the evolution of gastric cancer mortality risk in Spanish provinces and explore the possible attenuation of the geographical pattern. Methods: We studied a series of gastric cancer mortality data by province, year of death, sex and age group using a conditional autoregressive (CAR) model that incorporated space, time and spatio-temporal interactions. Results: Gastric cancer mortality risk decreased in all Spanish provinces in both males and females. Overall, decreasing trends were more pronounced during the first years of the study period, largely due to a sharper fall in gastric cancer mortality risk among the older population. Recent decades have witnessed a slowing in the rate of decrease, especially among the younger age groups. In most areas, risk declined at a similar rate, thus serving to maintain interprovincial differences and the persistence of the geographical pattern, though with some differences. The north and northwest provinces were the areas with higher mortality risks in both sexes and age groups over the entire study period. Concluding statement: Despite the decline in gastric cancer mortality risk observed for the 50 Spanish provinces studied, geographical differences still persist in Spain, and the cluster of excess mortality in the north-west of the country remains in evidence.     

Regression modeling of competing crude failure probabilities

In a randomized trial of tamoxifen therapy for breast cancer, women can experience tumor recurrence or die from competing causes. One goal of analysis is to describe the effect of tamoxifen on the probabilities of recurrence or death from other causes. To this end, we propose a semi-parametric transformation model for the crude failure probabilities of a competing risk, conditional on covariates. The model is developed as an extension of the standard approach to survival data with independent right censoring. Estimation of the regression coefficients is achieved with a rank-based least squares criterion. Simulations show that the procedure works well with practical sample sizes. A separate estimating function is developed for the baseline parameter. Prediction of covariate-adjusted failure probabilities is considered. The methodology is motivated and illustrated with data from the tamoxifen trial.     

Semiparametric Bayesian analysis of case-control data under conditional gene-environment independence

In case-control studies of gene-environment association with disease, when genetic and environmental exposures can be assumed to be independent in the underlying population, one may exploit the independence in order to derive more efficient estimation techniques than the traditional logistic regression analysis (Chatterjee and Carroll, 2005, Biometrika92, 399-418). However, covariates that stratify the population, such as age, ethnicity and alike, could potentially lead to nonindependence. In this article, we provide a novel semiparametric Bayesian approach to model stratification effects under the assumption of gene-environment independence in the control population. We illustrate the methods by applying them to data from a population-based case-control study on ovarian cancer conducted in Israel. A simulation study is conducted to compare our method with other popular choices. The results reflect that the semiparametric Bayesian model allows incorporation of key scientific evidence in the form of a prior and offers a flexible, robust alternative when standard parametric model assumptions do not hold.     

Quantifying Cancer Absolute Risk and Cancer Mortality in the Presence of Competing Events after a Myotonic Dystrophy Diagnosis

Recent studies show that patients with myotonic dystrophy (DM) have an increased risk of specific malignancies, but estimates of absolute cancer risk accounting for competing events are lacking. Using the Swedish Patient Registry, we identified 1,081 patients with an inpatient and/or outpatient diagnosis of DM between 1987 and 2007. Date and cause of death and date of cancer diagnosis were extracted from the Swedish Cause of Death and Cancer Registries. We calculated non-parametric estimates of absolute cancer risk and cancer mortality accounting for the high non-cancer competing mortality associated with DM. Absolute cancer risk after DM diagnosis was 1.6% (95% CI=0.4-4%), 5% (95% CI=3-9%) and 9% (95% CI=6-13%) at ages 40, 50 and 60 years, respectively. Females had a higher absolute risk of all cancers combined than males: 9% (95% CI=4-14), and 13% (95% CI=9-20) vs. 2% (95%CI= 0.7-6) and 4% (95%CI=2-8) by ages 50 and 60 years, respectively) and developed cancer at younger ages (median age =51 years, range=22-74 vs. 57, range=43-84, respectively, p=0.02). Cancer deaths accounted for 10% of all deaths, with an absolute cancer mortality risk of 2% (95%CI=1-4.5%), 4% (95%CI=2-6%), and 6% (95%CI=4-9%) by ages 50, 60, and 70 years, respectively. No gender difference in cancer-specific mortality was observed (p=0.6). In conclusion, cancer significantly contributes to morbidity and mortality in DM patients, even after accounting for high competing DM mortality from non-neoplastic causes. It is important to apply population-appropriate, validated cancer screening strategies in DM patients.     

Marginal hazard ratio estimates in joint frailty models for heart failure trials

This work is motivated by clinical trials in chronic heart failure disease, where treatment has effects both on morbidity (assessed as recurrent non‐fatal hospitalisations) and on mortality (assessed as cardiovascular death, CV death). Recently, a joint frailty proportional hazards model has been proposed for these kind of efficacy outcomes to account for a potential association between the risk rates for hospital admissions and CV death. However, more often clinical trial results are presented by treatment effect estimates that have been derived from marginal proportional hazards models, that is, a Cox model for mortality and an Andersen–Gill model for recurrent hospitalisations. We show how these marginal hazard ratios and their estimates depend on the association between the risk processes, when these are actually linked by shared or dependent frailty terms. First we derive the marginal hazard ratios as a function of time. Then, applying least false parameter theory, we show that the marginal hazard ratio estimate for the hospitalisation rate depends on study duration and on parameters of the underlying joint frailty model. In particular, we identify parameters, for example the treatment effect on mortality, that determine if the marginal hazard ratio estimate for hospitalisations is smaller, equal or larger than the conditional one. How this affects rejection probabilities is further investigated in simulation studies. Our findings can be used to interpret marginal hazard ratio estimates in heart failure trials and are illustrated by the results of the CHARM‐Preserved trial (where CHARM is the ‘Candesartan in Heart failure Assessment of Reduction in Mortality and morbidity’ programme).     

A general approach to sample size determination for prevalence surveys that use dual test protocols

We develop a Bayesian simulation based approach for determining the sample size required for estimating a binomial probability and the difference between two binomial probabilities where we allow for dependence between two fallible diagnostic procedures. Examples include estimating the prevalence of disease in a single population based on results from two imperfect diagnostic tests applied to sampled individuals, or surveys designed to compare the prevalences of two populations using diagnostic outcomes that are subject to misclassification. We propose a two stage procedure in which the tests are initially assumed to be independent conditional on true disease status (i.e. conditionally independent). An interval based sample size determination scheme is performed under this assumption and data are collected and used to test the conditional independence assumption. If the data reveal the diagnostic tests to be conditionally dependent, structure is added to the model to account for dependence and the sample size routine is repeated in order to properly satisfy the criterion under the correct model. We also examine the impact on required sample size when adding an extra heterogeneous population to a study.     

Composite Hazard Functions Reflecting Competing Latent Processes

A method for fitting parametric models to apparently complex hazard rates in survival data is suggested. Hazard complexity may indicate competing causes of failure. A competing risks model is constructed on the assumption that a failure time can be considered as the first passage time of possibly several latent, stochastic processes competing in reaching a barrier. An additional assumption of independence between the hidden processes leads directly to a composite hazard function as the sum of the cause specific hazards. We show how this composite hazard model based on Wiener processes can serve as a flexible tool for modelling complex hazards by varying the number of processes and their starting conditions. An example with real data is presented. Parameter estimation and model assessment are based on Markov Chain Monte Carlo methods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lifetime Smoking History and Cause-Specific Mortality in a Cohort Study with 43 Years of Follow-Up

BackgroundIn general, smoking increases the risk of mortality. However, it is less clear how the relative risk varies by cause of death. The exact impact of changes in smoking habits throughout life on different mortality risks is less studied.MethodsWe studied the impact of baseline and lifetime smoking habits, and duration of smoking on the risk of all-cause mortality, mortality of cardiovascular diseases (CVD), chronic obstructive pulmonary disease (COPD), any cancer and of the four most common types of cancer (lung, colorectal, prostate, and breast cancer) in a cohort study (Vlagtwedde-Vlaardingen 1965–1990, with a follow-up on mortality status until 2009, n = 8,645). We used Cox regression models adjusted for age, BMI, sex, and place of residence. Since previous studies suggested a potential effect modification of sex, we additionally stratified by sex and tested for interactions. In addition, to determine which cause of death carried the highest risk we performed competing-risk analyses on mortality due to CVD, cancer, COPD and other causes.ResultsCurrent smoking (light, moderate, and heavy cigarette smoking) and lifetime persistent smoking were associated with an increased risk of all-cause, CVD, COPD, any cancer, and lung cancer mortality. Higher numbers of pack years at baseline were associated with an increased risk of all-cause, CVD, COPD, any cancer, lung, colorectal, and prostate cancer mortality. Males who were lifetime persistent pipe/cigar smokers had a higher risk of lung cancer [HR (95% CI) = 7.72 (1.72–34.75)] as well as all-cause and any cancer mortality. A longer duration of smoking was associated with a higher risk of COPD, any and lung cancer [HR (95% CI) = 1.06 (1.00–1.12), 1.03 (1.00–1.06) and 1.10 (1.03–1.17) respectively], but not with other mortality causes. The competing risk analyses showed that ex- and current smokers had a higher risk of cancer, CVD, and COPD mortality compared to all other mortality causes. In addition, heavy smokers had a higher risk for COPD mortality compared to cancer, and CVD mortality.ConclusionOur study indicates that lifetime numbers of cigarettes smoked and the duration of smoking have different impacts for different causes of mortality. Moreover, our findings emphasize the importance of smoking-related competing risks when studying the smoking-related cancer mortality in a general population and that smoking cessation immediately effectively reduces the risk of all-cause and any cancer mortality.     

Competing risks regression for clustered data

A population average regression model is proposed to assess the marginal effects of covariates on the cumulative incidence function when there is dependence across individuals within a cluster in the competing risks setting. This method extends the Fine-Gray proportional hazards model for the subdistribution to situations, where individuals within a cluster may be correlated due to unobserved shared factors. Estimators of the regression parameters in the marginal model are developed under an independence working assumption where the correlation across individuals within a cluster is completely unspecified. The estimators are consistent and asymptotically normal, and variance estimation may be achieved without specifying the form of the dependence across individuals. A simulation study evidences that the inferential procedures perform well with realistic sample sizes. The practical utility of the methods is illustrated with data from the European Bone Marrow Transplant Registry.     

A Unimodal Model for Double Observer Distance Sampling Surveys

Distance sampling is a widely used method to estimate animal population size. Most distance sampling models utilize a monotonically decreasing detection function such as a half-normal. Recent advances in distance sampling modeling allow for the incorporation of covariates into the distance model, and the elimination of the assumption of perfect detection at some fixed distance (usually the transect line) with the use of double-observer models. The assumption of full observer independence in the double-observer model is problematic, but can be addressed by using the point independence assumption which assumes there is one distance, the apex of the detection function, where the 2 observers are assumed independent. Aerially collected distance sampling data can have a unimodal shape and have been successfully modeled with a gamma detection function. Covariates in gamma detection models cause the apex of detection to shift depending upon covariate levels, making this model incompatible with the point independence assumption when using double-observer data. This paper reports a unimodal detection model based on a two-piece normal distribution that allows covariates, has only one apex, and is consistent with the point independence assumption when double-observer data are utilized. An aerial line-transect survey of black bears in Alaska illustrate how this method can be applied.     

Flexible maximum likelihood methods for bivariate proportional hazards models

This article presents methodology for multivariate proportional hazards (PH) regression models. The methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional PH models, along with assumptions about the association among lifetimes. Because the models are parametric, ordinary maximum likelihood can be applied; it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes, unlike existing semiparametric methods. A bivariate Clayton model (1978, Biometrika 65, 141-151) is used to illustrate the approach taken. Because a parametric assumption about association is made, efficiency and robustness comparisons are made between estimation based on the bivariate Clayton model and "working independence" methods that specify only marginal distributions for each lifetime variable.     

The Very High Premature Mortality Rate among Active Professional Wrestlers Is Primarily Due to Cardiovascular Disease

Purpose

Recently, much media attention has been given to the premature deaths in professional wrestlers. Since no formal studies exist that have statistically examined the probability of premature mortality in professional wrestlers, we determined survival estimates for active wresters over the past quarter century to establish the factors contributing to the premature mortality of these individuals.

Methods

Data including cause of death was obtained from public records and wrestling publications in wrestlers who were active between January 1, 1985 and December 31, 2011. 557 males were considered consistently active wrestlers during this time period. 2007 published mortality rates from the Center for Disease Control were used to compare the general population to the wrestlers by age, BMI, time period, and cause of death. Survival estimates and Cox hazard regression models were fit to determine incident premature deaths and factors associated with lower survival. Cumulative incidence function (CIF) estimates given years wrestled was obtained using a competing risks model for cause of death.

Results

The mortality for all wrestlers over the 26-year study period was.007 deaths/total person-years or 708 per 100,000 per year, and 16% of deaths occurred below age 50 years. Among wrestlers, the leading cause of deaths based on CIF was cardiovascular-related (38%). For cardiovascular-related deaths, drug overdose-related deaths and cancer deaths, wrestler mortality rates were respectively 15.1, 122.7 and 6.4 times greater than those of males in the general population. Survival estimates from hazard models indicated that BMI is significantly associated with the hazard of death from total time wrestling (p<0.0001).

Conclusion

Professional wrestlers are more likely to die prematurely from cardiovascular disease compared to the general population and morbidly obese wrestlers are especially at risk. Results from this study may be useful for professional wrestlers, as well as wellness policy and medical care implementation.     

Cancer mortality in a population-based cohort of American Indians – The strong heart study

BackgroundCancer mortality among American Indian (AI) people varies widely, but factors associated with cancer mortality are infrequently assessed.MethodsCancer deaths were identified from death certificate data for 3516 participants of the Strong Heart Study, a population-based cohort study of AI adults ages 45–74 years in Arizona, Oklahoma, and North and South Dakota. Cancer mortality was calculated by age, sex and region. Cox proportional hazards model was used to assess independent associations between baseline factors in 1989 and cancer death by 2010.ResultsAfter a median follow-up of 15.3 years, the cancer death rate per 1000 person-years was 6.33 (95 % CI 5.67–7.04). Cancer mortality was highest among men in North/South Dakota (8.18; 95 % CI 6.46–10.23) and lowest among women in Arizona (4.57; 95 % CI 2.87–6.92). Factors independently associated with increased cancer mortality included age, current or former smoking, waist circumference, albuminuria, urinary cadmium, and prior cancer history. Factors associated with decreased cancer mortality included Oklahoma compared to Dakota residence, higher body mass index and total cholesterol. Sex was not associated with cancer mortality. Lung cancer was the leading cause of cancer mortality overall (1.56/1000 person-years), but no lung cancer deaths occurred among Arizona participants. Mortality from unspecified cancer was relatively high (0.48/100 person-years; 95 % CI 0.32−0.71).ConclusionsRegional variation in AI cancer mortality persisted despite adjustment for individual risk factors. Mortality from unspecified cancer was high. Better understanding of regional differences in cancer mortality, and better classification of cancer deaths, will help healthcare programs address cancer in AI communities.     

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.