On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Health investment complementarities under competing risks

Applying the competing--risks model to multi--cause mortality,this paper provides a theoretical and empirical investigation of the positive complementarities that occur between disease--specific policy interventions. We argue that since an individual cannot die twice, competing risks imply that individuals will not waste resources on causes that are not the most immediate, but will make health investments so as to equalize cause--specific mortality. However, equal mortality risk from a variety of diseases does not imply that disease--specific public health interventions are a waste. Rather, a cause--specific intervention produces spillovers to other disease risks, so that the overall reduction in mortality will generally be larger than the direct effect measured on the targeted disease. The assumption that mortality from non--targeted diseases remains the same after a cause--specific intervention under--estimates the true effect of such programs, since the background mortality is also altered as a result of intervention. Analyzing data from one of the most important public health programs ever introduced, the Expanded Program on Immunization (EPI) of the United Nations, we find evidence for the existence of such complementarities, involving causes that are not biomedically, but behaviorally, linked.

Competing risks to breast cancer mortality in Catalonia

Background: Breast cancer mortality has experienced important changes over the last century. Breast cancer occurs in the presence of other competing risks which can influence breast cancer incidence and mortality trends. The aim of the present work is: 1) to assess the impact of breast cancer deaths among mortality from all causes in Catalonia (Spain), by age and birth cohort and 2) to estimate the risk of death from other causes than breast cancer, one of the inputs needed to model breast cancer mortality reduction due to screening or therapeutic interventions. Methods: The multi-decrement life table methodology was used. First, all-cause mortality probabilities were obtained by age and cohort. Then mortality probability for breast cancer was subtracted from the all-cause mortality probabilities to obtain cohort life tables for causes other than breast cancer. These life tables, on one hand, provide an estimate of the risk of dying from competing risks, and on the other hand, permit to assess the impact of breast cancer deaths on all-cause mortality using the ratio of the probability of death for causes other than breast cancer by the all-cause probability of death. Results: There was an increasing impact of breast cancer on mortality in the first part of the 20th century, with a peak for cohorts born in 1945–54 in the 40–49 age groups (for which approximately 24% of mortality was due to breast cancer). Even though for cohorts born after 1955 there was only information for women under 50, it is also important to note that the impact of breast cancer on all-cause mortality decreased for those cohorts. Conclusion: We have quantified the effect of removing breast cancer mortality in different age groups and birth cohorts. Our results are consistent with US findings. We also have obtained an estimate of the risk of dying from competing-causes mortality, which will be used in the assessment of the effect of mammography screening on breast cancer mortality in Catalonia.

‘Modeling and Analysis of Competing Risks Data’

there has been much research on analyzing various forms of competing risks data. Nevertheless, there are several occasions in survival studies, where the existing models and methodologies are inadequate for the analysis competing risks data. ldentifiabilty problem and various types of and censoring induce more complications in the analysis of competing risks data than in classical survival analysis. Parametric models are not adequate for the analysis of competing risks data since the assumptions about the underlying lifetime distributions may not hold well. Motivated by this, in the present study. we develop some new inference procedures, which are completely distribution free for the analysis of competing risks data.

Longitudinal outcomes of high-risk human papillomavirus (HPV) infections as competing-risks events following cervical HPV test at baseline visit in the *NIS-LAMS** cohort

Background: The complex natural history of human papillomavirus (HPV) infections following a single HPV test can be modeled as competing-risks events (i.e., no-, transient- or persistent infection) in a longitudinal setting. The covariates associated with these compet ng events have not been previously assessed using competing-risks regression models. Objectives: To gain further insights in the outcomes of cervical HPV infections, we used univariate- and multivariate competing-risks regression models to assess the covariaies associated with these competing events. Study Design and Methods: Covariates associated with three competing outcomes (no-, transient- or persistent HR-HPV infection) were analysed in a sub-cohort of 1,865 women prospectively followed-up in the NIS (n = 3,187) and LAMS Study (n = 12,114). Results: In multivariate competing-risks models (with two other outcomes as competing events), permanently HR-HPV negative outcome was significantly predicted only by the clearance of ASCUS+Pap during FU, while three independent covariates predicted transient HR-HPV infections: i) number of recent (< 12 months) sexual partners (risk increased), ii) previous Pap screening history (protective), and history of previous CIN (increased risk). The two most powerful predictors of persistent HR-HPV infections were persistent ASCUS+Pap (risk increased), and previous Pap screening history (protective). In pair-wise comparisons, number of recent sexual partners and previous CIN history increase the probability of transient HR-HPV infection against the HR-HPV negative competing event, while previous Pap screening history is protective. Persistent ASCUS+Pap during FU and no previous Pap screening history are significantly associated with the persistent HR-HPV outcome (compared both with i) always negative, and ii) transient events), whereas multiparity is protective. Conclusions: Different covariates are associated with the three main outcomes of cervical HPV infections. The most significant covariates of each competing events are probably distinct enough to enable constructing of a risk-profile for each main outcome.

Covariates of high-risk human papillomavirus (HPV) infections are distinct for incident CIN1, CIN2 and CIN3 as disclosed by competing-risks regression models

Background: In addition to the oncogenic human papillomavirus (HPV), several cofactors are needed in cervical carcinogenesis, but whether the HPV covariates associated with incident i) CIN1 are different from those of incident ii) CIN2 and iii) CIN3 needs further assessment. Objectives: To gain further insights into the true biological differences between CIN1, CIN2 and CIN3, we assessed HPV covariates associated with incident CIN1, CIN2, and CIN3. Study Design and Methods: HPV covariates associated with progression to CIN1, CIN2 and CIN3 were analysed in the combined cohort of the NIS (n = 3,187) and LAMS study (n = 12,114), using competing-risks regression models (in panel data) for baseline HR-HPV-positive women (n = 1,105), who represent a sub-cohort of all 1,865 women prospectively followed-up in these two studies. Results: Altogether, 90 (4.8%), 39 (2.1%) and 14 (1.4%) cases progressed to CIN1, CIN2, and CIN3, respectively. Among these baseline HR-HPV-positive women, the risk profiles of incident GIN I, CIN2 and CIN3 were unique in that completely different HPV covariates were associated with progression to CIN1, CIN2 and CIN3, irrespective which categories (non-progression, CIN1, CIN2, CIN3 or all) were used as competing-risks events in univariate and multivariate models. Conclusions: These data confirm our previous analysis based on multinomial regression models implicating that distinct covariates of HR-HPV are associated with progression to CIN1, CIN2 and CIN3. This emphasises true biological differences between the three grades of GIN, which revisits the concept of combining CIN2 with CIN3 or with CIN1 in histological classification or used as a common end-point, e.g., in HPV vaccine trials.

Impact of age and comorbidities on long-term survival of patients with high-risk prostate cancer treated with radical prostatectomy: a multi-institutional competing-risks analysis

Survival after surgical treatment using competing-risk analysis has been previously examined in patients with prostate cancer (PCa). However, the combined effect of age and comorbidities has not been assessed in patients with high-risk PCa who might have heterogeneous rates of competing mortality despite the presence of aggressive disease.

Semiparametric Methods for Semi-competing Risks Problem with Censoring and Truncation

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Since mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. Firstly, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Influence of patient age and implantation technique on the probability of re-replacement of the homograft aortic valve

Background and aim of the study: Results of valve re-replacement (reoperation) in 898 patients undergoing aortic valve replacement with cryopreserved homograft valves between 1975 and 1998 are reported. The study aim was to provide estimates of unconditional probability of valve reoperation and cumulative incidence function (actual risk) of reoperation. Methods: Valves were implanted by subcoronary insertion (n = 500), inclusion cylinder (n = 46), and aortic root replacement (n = 352). Probability of reoperation was estimated by adopting a mixture model framework within which estimates were adjusted for two risk factors: patient age at initial replacement, and implantation technique. Results: For a patient aged 50 years, the probability of reoperation in his/her lifetime was estimated as 44% and 56% for non-root and root replacement techniques, respectively. For a patient aged 70 years, estimated probability of reoperation was 16% and 25%, respectively. Given that a reoperation is required, patients with non-root replacement have a higher hazard rate than those with root replacement (hazards ratio = 1.4), indicating that non-root replacement patients tend to undergo reoperation earlier before death than root replacement patients. Conclusion: Younger patient age and root versus non-root replacement are risk factors for reoperation. Valve durability is much less in younger patients, while root replacement patients appear more likely to live longer and hence are more likely to require reoperation.

An analysis of valve re-replacement after aortic valve replacement with biologic devices

Biologic valve re-replacement was examined in a series of 1343 patients who underwent aortic valve replacement at The Prince Charles Hospital, Brisbane, with a cryopreserved or 4 degrees C stored allograft valve or a xenograft valve, A parametric model approach was used to simultaneously model the competing risks of death without re-replacement and re-replacement before death, One hundred eleven patients underwent a first re-replacement for a variety of reasons (69 patients with xenograft valves, 28 patients with 4 degrees C stored allograft valves, and 14 patients with cryopreserved allograft valves), By multivariable analysis younger age at operation was associated with xenograft, 4 degrees C stored allograft, and cryopreserved allograft valve re-replacement, However, this effect was examined in the context of longer survival of younger patients, which increases their exposure to the risk of re-replacement as compared with that in older patients whose decreased survival reduced their probability of requiring valve re-replacement, In patients older than 60 years at the time of aortic valve replacement, the probability of re-replacement (for any reason) before death was similar for xenografts and cryopreserved allograft valves but higher for 4 degrees C stored valves, However, in patients younger than 60 years, the probability of re-replacement at any time during the remainder of the life of the patient was lower with the cryopreserved allograft valve compared with the xenograft valve and 4 degrees C stored allografts.

Classification Performance of Multilayer Perceptrons with Different Risk Functionals

In the present paper we assess the performance of information-theoretic inspired risks functionals in multilayer perceptrons with reference to the two most popular ones, Mean Square Error and Cross-Entropy. The information-theoretic inspired risks, recently proposed, are: HS and HR2 are, respectively, the Shannon and quadratic Rényi entropies of the error; ZED is a risk reflecting the error density at zero errors; EXP is a generalized exponential risk, able to mimic a wide variety of risk functionals, including the information-thoeretic ones. The experiments were carried out with multilayer perceptrons on 35 public real-world datasets. All experiments were performed according to the same protocol. The statistical tests applied to the experimental results showed that the ubiquitous mean square error was the less interesting risk functional to be used by multilayer perceptrons. Namely, mean square error never achieved a significantly better classification performance than competing risks. Cross-entropy and EXP were the risks found by several tests to be significantly better than their competitors. Counts of significantly better and worse risks have also shown the usefulness of HS and HR2 for some datasets.