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)     

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.     

The analysis of failure times in the presence of competing risks.

Distinct problems in the analysis of failure times with competing causes of failure include the estimation of treatment or exposure effects on specific failure types, the study of interrelations among failure types, and the estimation of failure rates for some causes given the removal of certain other failure types. The usual formation of these problems is in terms of conceptual or latent failure times for each failure type. This approach is criticized on the basis of unwarranted assumptions, lack of physical interpretation and identifiability problems. An alternative approach utilizing cause-specific hazard functions for observable quantities, including time-dependent covariates, is proposed. Cause-specific hazard functions are shown to be the basic estimable quantities in the competing risks framework. A method, involving the estimation of parameters that relate time-dependent risk indicators for some causes to cause-specific hazard functions for other causes, is proposed for the study of interrelations among failure types. Further, it is argued that the problem of estimation of failure rates under the removal of certain causes is not well posed until a mechanism for cause removal is specified. Following such a specification, one will sometimes be in a position to make sensible extrapolations from available data to situations involving cause removal. A clinical program in bone marrow transplantation for leukemia provides a setting for discussion and illustration of each of these ideas. Failure due to censoring in a survivorship study leads to further discussion.     

Estimation of competing risks with general missing pattern in failure types

In competing risks data, missing failure types (causes) is a very common phenomenon. In this work, we consider a general missing pattern in which, if a failure type is not observed, one observes a set of possible types containing the true type, along with the failure time. We first consider maximum likelihood estimation with missing-at-random assumption via the expectation maximization (EM) algorithm. We then propose a Nelson-Aalen type estimator for situations when certain information on the conditional probability of the true type given a set of possible failure types is available from the experimentalists. This is based on a least-squares type method using the relationships between hazards for different types and hazards for different combinations of missing types. We conduct a simulation study to investigate the performance of this method, which indicates that bias may be small, even for high proportion of missing data, for sufficiently large number of observations. The estimates are somewhat sensitive to misspecification of the conditional probabilities of the true types when the missing proportion is high. We also consider an example from an animal experiment to illustrate our methodology.     

Analysis of competing risks survival data when some failure types are missing

We propose a method to analyse competing risks survival datawhen failure types are missing for some individuals. Our approachis based on a standard proportional hazards structure for eachof the failure types, and involves the solution to estimatingequations. We present consistent and asymptotically normal estimatorsof the regression coefficients and related score tests. An appealingfeature is that individuals with known failure types make thesame contributions as they would to a standard proportionalhazards analysis. Contributions of individuals with unknownfailure types are weighted according to the probability thatthey failed from the cause of interest. Efficiency and robustnessare discussed. Results are illustrated with data from a breastcancer trial.     

Analysis of a partially observed binary covariate process and a censored failure time in the presence of truncation and competing risks

We develop methods for assessing the association between a binary time-dependent covariate process and a failure time endpoint when the former is observed only at a single time point and the latter is right censored, and when the observations are subject to truncation and competing causes of failure. Using a proportional hazards model for the effect of the covariate process on the failure time of interest, we develop an approach utilizing EM algorithm and profile likelihood for estimating the relative risk parameter and cause-specific hazards for failure. The methods are extended to account for other covariates that can influence the time-dependent covariate process and cause-specific risks of failure. We illustrate the methods with data from a recent study on the association between loss of hepatitis B e antigen and the development of hepatocellular carcinoma in a population of chronic carriers of hepatitis B.     

Responses of vasoactive hormones in congestive cardiac failure

Congestive cardiac failure causes activation of various neurohumoral responses that increase total peripheral resistance and promote salt and water retention. These effects increase blood pressure and organ perfusion in the short term, but ultimately cause further cardiac decompensation by increasing ventricular afterload and cardiac work. The role of the renin-angiotensin-aldosterone system and the catecholamines is partially understood, and blockade of these systems as a treatment of heart failure is now established. The role of vasopressin in heart failure is more controversial, but there is now compelling evidence that vasopressin may have important vasoconstrictor actions in addition to its fluid retaining properties. Atrial natriuretic factor is a newly described cardiac hormone released from the atrium. Atrial natriuretic factor causes natriuresis, diuresis, vasodilatation, suppression of thirst, and suppression of both renin and aldosterone. These actions largely counteract the effects of the renin-angiotensin system and vasopressin. Plasma atrial natriuretic factor has been reported to be markedly elevated in human and experimental heart failure, and may act to limit the neurohumoral response to reduced cardiac output. This review summarizes our understanding of the vasoactive hormones and reports experimental evidence supporting a pathophysiological role for vasopressin and atrial natriuretic factor in congestive cardiac failure.     

Opportunities to replace the use of animals in sepsis research. The report and recommendations of a Focus on Alternatives workshop

Sepsis and multiple organ failure are common causes of death in patients admitted to intensive care units. The incidence of sepsis and associated mortalities has been steadily increasing over the past 20 years. Sepsis is a complex inflammatory condition, the precise causes of which are still poorly understood. Animal models of sepsis have the potential to cause substantial suffering, and many of them have been poorly representative of the human syndrome. However, a number of non-animal approaches, including in vitro, in silico and clinical studies, show promise for addressing this situation. This report is based on discussions held at an expert workshop convened by Focus on Alternatives and held in 2004 at the Wellcome Trust, London. It provides an overview of some non-animal approaches to sepsis research, including their strengths and weaknesses, and argues that they should be prioritised for further development.     

Joint modeling of progression of HIV resistance mutations measured with uncertainty and failure time data

Development of HIV resistance mutations is a major cause for failure of antiretroviral treatment. This article proposes a method for jointly modeling the processes of viral genetic changes and treatment failure. Because the viral genome is measured with uncertainty, a hidden Markov model is used to fit the viral genetic process. The uncertain viral genotype is included as a time-dependent covariate in a Cox model for failure time, and an expectation-maximization algorithm is used to estimate the model parameters. This model allows simultaneous evaluation of the sequencing uncertainty and the effect of resistance mutation on the risk of virological and immunological failures. Various model checking tests are provided to assess the appropriateness of the model. Simulation studies are performed to investigate the finite-sample properties of the proposed methods, which are then applied to data collected in three phase II clinical trials testing antiretroviral treatments containing the drug efavirenz.     

The application of training to failure in periodized multiple-set resistance exercise programs

Few studies and reports in the body of literature have directly addressed the issue of whether resistance exercise sets should be performed to failure. Research has clearly demonstrated the superiority of performing multiple sets vs. single sets for increases in maximal strength. However, there is little direct evidence to decide conclusively whether or not multiple sets should be performed to failure. Therefore, the purpose of this research note was to discuss what is currently known concerning the application of training to failure and to stimulate further research on this topic. Although not essential for increases in muscular characteristics such as strength and hypertrophy, training to failure might allow advanced lifters to break through training plateaus when incorporated periodically into short-term microcycles. Because muscular hypertrophy is a key contributor to long-term increases in maximal strength, advanced lifters should consider training to failure occasionally. The potential mechanisms by which training to failure might provide an advantage are through greater activation of motor units and secretion of growth-promoting hormones. However, training to failure is not an effective stimulus without lifting at a sufficient intensity (percentage of 1 repetition maximum). Furthermore, training to failure should not be performed repeatedly over long periods, due to the high potential for overtraining and overuse injuries. Therefore, the training status and the goals of the lifter should guide the decision-making process on this issue.     

Quantile regression models with multivariate failure time data

As an alternative to the mean regression model, the quantile regression model has been studied extensively with independent failure time data. However, due to natural or artificial clustering, it is common to encounter multivariate failure time data in biomedical research where the intracluster correlation needs to be accounted for appropriately. For right-censored correlated survival data, we investigate the quantile regression model and adapt an estimating equation approach for parameter estimation under the working independence assumption, as well as a weighted version for enhancing the efficiency. We show that the parameter estimates are consistent and asymptotically follow normal distributions. The variance estimation using asymptotic approximation involves nonparametric functional density estimation. We employ the bootstrap and perturbation resampling methods for the estimation of the variance-covariance matrix. We examine the proposed method for finite sample sizes through simulation studies, and illustrate it with data from a clinical trial on otitis media.     

Regression analysis of doubly censored failure time data with frailty

In doubly censored failure time data, the survival time of interest is defined as the elapsed time between an initial event and a subsequent event, and the occurrences of both events cannot be observed exactly. Instead, only right- or interval-censored observations on the occurrence times are available. For the analysis of such data, a number of methods have been proposed under the assumption that the survival time of interest is independent of the occurrence time of the initial event. This article investigates a different situation where the independence may not be true with the focus on regression analysis of doubly censored data. Cox frailty models are applied to describe the effects of covariates and an EM algorithm is developed for estimation. Simulation studies are performed to investigate finite sample properties of the proposed method and an illustrative example from an acquired immune deficiency syndrome (AIDS) cohort study is provided.     

A random effects model for multivariate failure time data from multicenter clinical trials

A random effects model for analyzing multivariate failure time data is proposed. The work is motivated by the need for assessing the mean treatment effect in a multicenter clinical trial study, assuming that the centers are a random sample from an underlying population. An estimating equation for the mean hazard ratio parameter is proposed. The proposed estimator is shown to be consistent and asymptotically normally distributed. A variance estimator, based on large sample theory, is proposed. Simulation results indicate that the proposed estimator performs well in finite samples. The proposed variance estimator effectively corrects the bias of the naive variance estimator, which assumes independence of individuals within a group. The methodology is illustrated with a clinical trial data set from the Studies of Left Ventricular Dysfunction. This shows that the variability of the treatment effect is higher than found by means of simpler models.     

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.     

Late renal failure due to prostatic outflow obstruction: a preventable disease.

Nineteen patients presenting with late renal failure due to prostatic outflow obstruction (mean age 68.7 years; mean serum creatinine concentration 1158 mumol/l) were identified from the admission records of two renal units. As late renal failure secondary to prostatic enlargement is preventable case records were analysed retrospectively in an attempt to identify aspects of management in which preventive efforts might be of value. Delays in referral were common, with a mean of 2.8 years between the onset of prostatic symptoms and time of referral, six patients being referred who had had symptoms for more than three years. Four of five patients who had had a prostatectomy were known to be in renal failure at the time of operation but were not referred until 2-13 years later, when prostatic symptoms had recurred and there was evidence of progressive nephropathy with dilatation of the upper urinary tract. Two patients died on admission and eight (47% of survivors) required long term dialysis, most patients (80%) requiring some dialysis support during the initial period. These findings suggest that progressive nephropathy caused by prostatic outflow obstruction might, in part, be averted by more adequate screening of renal function in men with untreated prostatism and closer follow up of patients with uraemia at the time of prostatectomy.     

Testing homogeneity in Weibull-regression models

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data.     

A proportional hazards model for multivariate interval-censored failure time data

This paper focuses on the methodology developed for analyzing a multivariate interval-censored data set from an AIDS observational study. A purpose of the study was to determine the natural history of the opportunistic infection cytomeglovirus (CMV) in an HIV-infected individual. For this observational study, laboratory tests were performed at scheduled clinic visits to test for the presence of the CMV virus in the blood and in the urine (called CMV shedding in the blood and urine). The study investigators were interested in determining whether the stage of HIV disease at study entry was predictive of an increased risk for CMV shedding in either the blood or the urine. If all patients had made each clinic visit, the data would be multivariate grouped failure time data and published methods could be used. However, many patients missed several visits, and when they returned, their lab tests indicated a change in their blood and/or urine CMV shedding status, resulting in interval-censored failure time data. This paper outlines a method for applying the proportional hazards model to the analysis of multivariate interval-censored failure time data from a study of CMV in HIV-infected patients.     

Complete fertilization failure in ICSI

Abstract  Fertilization failure is one of the causes of infertility that becomes evident only after in vitro fertilization (TVF) and intracytoplasmic sperm injection (ICSI) have been attempted. Although the frequency of incidence of fertilization failure is low, if fertilization failure is encountered, medical treatment is usually stopped and serious psychological damage may occur to the patient.
While fertilization failure in IVF can be dealt with using ICSI, there is no treatment for fertilization failure in ICSI. At present, clinical investigations are being conducted to evaluate oocyte activation in combination with ICSI to cope with fertilization failure of ICSI.     

Independence tests for VNTR alleles defined as quantile bins.

VNTR fragment lengths in three databases maintained by the FBI for forensic purposes were partitioned into quantile bins, and tests for independence of the two bins at each of six loci were conducted. Whether independence was declared depended on the number of quantiles used. For a large number of quantile bins, equal to the number of fixed bins used by the FBI, 10 of 18 likelihood-ratio tests showed significant departures from independence when all genotypes were considered, and this changed to 7 of 18 when only heterozygotes were tested. This is in contrast to likelihood-ratio tests on fixed bins, when there were five significant departures over all genotypes and two departures for heterozygotes.     

Estimating regression parameters and degree of dependence for multivariate failure time data

Multivariate failure time data are frequently encountered in longitudinal studies when subjects may experience several events or when there is a grouping of individuals into a cluster. To take into account the dependence of the failure times within the unit (the individual or the cluster) as well as censoring, two multivariate generalizations of the Cox proportional hazards model are commonly used. The marginal hazard model is used when the purpose is to estimate mean regression parameters, while the frailty model is retained when the purpose is to assess the degree of dependence within the unit. We propose a new approach based on the combination of the two aforementioned models to estimate both these quantities. This two-step estimation procedure is quicker and more simple to implement than the EM algorithm used in frailty models estimation. Simulation results are provided to illustrate robustness, consistency, and large-sample properties of estimators. Finally, this method is exemplified on a diabetic retinopathy study in order to assess the effect of photocoagulation in delaying the onset of blindness as well as the dependence between the two eyes blindness times of a patient.