Competing risk analysis for life table data with known observation times

"Several models have been proposed for the analysis of cohort mortality in the presence of competing risks.... This paper describes a maximum likelihood approach to the analysis of follow up data in life table format for the case of two competing risks--a specific cause and its competing complement. The model developed uses a robust survivorship assumption--the piecewise exponential--and takes into account information on time to death and time to withdrawal." (summary in GER)     

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.     

Concomitant Information in Competing Risk Analysis

A competing risk model, accommodating both Type I censoring and random withdrawals, is expanded to incorporate concomitant information by allowing the parameters of the underlying distributions to be a linear function of two covariates. The model is developed for two competing risks, one following a Weibull distribution and the other a Rayleigh distribution, and random withdrawals following a Weibull distribution. A method is developed for testing the equality of the coefficients for a given covariate for each of the competing risks using MLE'.     

Meta-analysis of clinical trials with competing time-to-event endpoints

Recommendations for the analysis of competing risks in the context of randomized clinical trials are well established. Meta-analysis of individual patient data (IPD) is the gold standard for synthesizing evidence for clinical interpretation based on multiple studies. Surprisingly, no formal guidelines have been yet proposed to conduct an IPD meta-analysis with competing risk endpoints. To fill this gap, this work details (i) how to handle the heterogeneity between trials via a stratified regression model for competing risks and (ii) that the usual metrics of inconsistency to assess heterogeneity can readily be employed. Our proposal is illustrated by the re-analysis of a recently published meta-analysis in nasopharyngeal carcinoma, aiming at quantifying the benefit of the addition of chemotherapy to radiotherapy on each competing endpoint.     

Competing Risk Analysis of Censored Survival Data

A competing risk model is developed to accommodate both planned Type I censoring and random withdrawals. MLE's, their properties, confidence regions for parameters and mean lifetimes are obtained for a model regarding random censoring as a competing risk and compared to those obtained for the model in which withdrawals are regarded as random censoring. Estimated net and crude probabilities are calculated and compared for the two models. The model is developed for two competing risks, one following a Weibull distribution and the other a Rayleigh distribution, and random withdrawals following a Weibull distribution.     

Dominance and deference: Men inhibit creative displays during mate competition when their competitor is strong

Dominance is a form of social status based on an individual's ability to inflict costs (e.g. physical aggression) onto others. Subordinate individuals defer to dominant individuals in order to avoid physical aggression. We hypothesized that relatively subordinate men defer to dominant men by inhibiting creative displays during mate competition. Male participants were led to believe they were competing for a date with an attractive female. Participants believed they were competing against either a strong or weak male. During an interview with the attractive female, participants were prompted to display their creativity to the female by telling funny jokes and interesting stories. We found that participants competing against a strong male were less likely to tell jokes and less likely to tell stories. Additionally, participants competing against a strong male told jokes that were less funny and less elaborate.     

Joint Modeling of Multivariate Longitudinal Data and Competing Risks Using Multiphase Sub-models

In many clinical studies that involve follow-up, it is common to observe one or more sequences of longitudinal measurements, as well as one or more time to event outcomes. A competing risks situation arises when the probability of occurrence of one event is altered/hindered by another time to event. Recently, there has been much attention paid to the joint analysis of a single longitudinal response and a single time to event outcome, when the missing data mechanism in the longitudinal process is non-ignorable. We, in this paper, propose an extension where multiple longitudinal responses are jointly modeled with competing risks (multiple time to events). Our shared parameter joint model consists of a system of multiphase non-linear mixed effects sub-models for the multiple longitudinal responses, and a system of cause-specific non-proportional hazards frailty sub-models for competing risks, with associations among multiple longitudinal responses and competing risks modeled using latent parameters. The joint model is applied to a data set of patients who are on mechanical circulatory support and are awaiting heart transplant, using readily available software. While on the mechanical circulatory support, patient liver and renal functions may worsen and these in turn may influence one of the two possible competing outcomes: (i) death before transplant; (ii) transplant. In one application, we propose a system of multiphase cause-specific non-proportional hazard sub-model where frailty can be time varying. Performance under different scenarios was assessed using simulation studies. By using the proposed joint modeling of the multiphase sub-models, one can identify: (i) non-linear trends in multiple longitudinal outcomes; (ii) time-varying hazards and cumulative incidence functions of the competing risks; (iii) identify risk factors for the both types of outcomes, where the effect may or may not change with time; and (iv) assess the association between multiple longitudinal and competing risks outcomes, where the association may or may not change with time.     

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.     

Solid-phase capture of pathogenic bacteria by using gangliosides and detection with real-time PCR

We developed a method for concentrating pathogens from samples without enrichment. Immobilized gangliosides concentrated bacteria for detection with real-time PCR. A sensitivity of approximately 4 CFU/ml (3 h) in samples without competing microflora was achieved. Samples with competing microflora had a sensitivity of 40,000 CFU/ml. The variance was less than one cycle.     

The effects of chrysomelid beetle grazing and plant competition on the growth of Rumex obtusifolius

Summary The interaction between grazing by Gastrophysa viridula and interspecific plant competition was investigated for Rumex obtusifolius growing in the field. During an eight-month growing season non-competing R. obtusifolius grew larger than competing plants although herbivore loads (beetle productivity per unit leaf area) were similar for competing and non-competing plants. However, grazing significantly reduced the growth of R. obtusifolius only in competing plants thus demonstrating a synergism between plant competition and invertebrate herbivory. The relevance of these findings for the distribution of plant species is discussed.     

Competition and coexistence in regional habitats

Habitat heterogeneity plays a key role in the dynamics and structures of communities. In this article, a two-species metapopulation model that includes local competitive dynamics is analyzed to study the population dynamics of two competing species in spatially structured habitats. When local stochastic extinction can be ignored, there are, as in Lotka-Volterra equations, four outcomes of interspecific competition in this model. The outcomes of competition depend on the competitive intensity between the competing pairs. An inferior competitor and a superior competitor, or two strongly competing species, can never stably coexist, whereas two weak competitors (even if they are very similar species) may coexist over the long term in such environments. Local stochastic extinction may greatly affect the outcomes of interspecific competition. Two competing species can or cannot stably coexist depending not only on the competitive intensity between the competing pairs but also on their precompetitive distributions. Two weak competitors that have similar precompetitive distributions can always regionally coexist. Two strongly competing species that competitively exclude each other in more stable habitats may be able to stably coexist in highly heterogenous environments if they have similar precompetitive distributions. There is also a chance for an inferior competitor to coexist regionally or even to exclude a superior competitor when the superior competitor has a narrow precompetitive distribution and the inferior competitor has a wide precompetitive distribution.     

Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds

The population-dispersal dynamics for predator–prey interactions and two competing species in a two patch environment are studied. It is assumed that both species (i.e., either predators and their prey, or the two competing species) are mobile and their dispersal between patches is directed to the higher fitness patch. It is proved that such dispersal, irrespectively of its speed, cannot destabilize a locally stable predator–prey population equilibrium that corresponds to no movement at all. In the case of two competing species, dispersal can destabilize population equilibrium. Conditions are given when this cannot happen, including the case of identical patches.     

Saturation of transgene protein synthesis from mRNA in cells producing a large number of transgene mRNA

Experimental results have suggested that transgene expression can be saturated when large amounts of plasmid vectors are delivered into cells. To investigate this saturation kinetic behavior, cells were transfected with monitoring and competing plasmids using cationic liposomes. Even although an identical amount of a monitoring plasmid expressing firefly luciferase (FL) was used for transfection, transgene expression from the plasmid was greatly affected by the level of transgene expression from competing plasmids expressing renilla luciferase (RL). Similar results were obtained by exchanging the monitoring and competing plasmids. The competing plasmid‐dependent reduction in transgene expression from the monitoring plasmid was also observed in mouse liver after hydrodynamic injection of plasmids. On the other hand, the mRNA and protein expression level of glyceraldehyde‐3‐phosphate dehydrogenase (GAPDH), an endogenous gene, in the liver hardly changed even when transgene expression process is saturated. The expression of FL from a monitoring plasmid was significantly restored by siRNA‐mediated degradation of RL mRNA that was expressed from a competing plasmid. These results suggest that the efficiency of protein synthesis from plasmid vectors is reduced when a large amount of mRNA is transcribed with no significant changes in endogenous gene expression. Biotechnol. Bioeng. 2011;108: 2380–2389. © 2011 Wiley Periodicals, Inc.     

Competitive binding of fluoroquinolone antibiotics and some other drugs to human serum albumin: a luminescence spectroscopic study

Co‐administration of several drugs in multidrug therapy may alter the binding of each to human serum albumin (HSA) and hence their pharmacological activity. Thirty‐two frequently prescribed drug combinations, consisting of four fluoroquinolone antibiotics and eight competing drugs, have been studied using fluorescence and circular dichroism spectroscopic techniques. Competitive binding studies on the drug combinations are not available in the literature. In most cases, the presence of competing drug decreased the binding affinity of fluoroquinolone, resulting in an increase in the concentration of free pharmacologically active drug. The competitive binding mechanism involved could be interpreted in terms of the site specificity of the binding and competing drugs. For levofloxacin, the change in the binding affinity was small because in the presence of site II‐specific competing drugs, levofloxacin mainly occupied site I. A competitive interference mechanism was operative for sparfloxacin, whereas competitive interference as well as site‐to‐site displacement of competing drugs was observed in the case of ciprofloxacin hydrochloride. For enrofloxacin, a different behavior was observed for different combinations; site‐to‐site displacement and conformational changes as well as independent binding has been observed for various drug combinations. Circular dichroism spectral studies showed that competitive binding did not cause any major structural changes in the HSA molecule. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Predation in multi-prey communities

We consider the effect of a top predator on the stability of a system of competing prey species. In the first instance, this is done in detail for two prey species where the predators either behave in a completely random way, interfere with each other or switch to the more abundant prey at any time. The analysis is then extended to the case of n similar prey species, either competing equally or competing with their two nearest neighbours in exploiting a one-dimensional resource spectrum. It is found that predator switching can produce local stability when the prey species overlap completely and even when the competition coefficients are greater than one. This, however, is more difficult to attain for nearest neighbour competition. In either case switching is advantageous to the predators, since it allows them to coexist successfully with their prey over a wider range of conditions.     

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)     

Independent and competing disease risks: implications for host populations in variable environments

Disease models usually assume disease to act independently of other mortality- and morbidity-causing factors. Alternatively, disease may function as a competing risk factor, for example, killing already moribund hosts. Using tuberculosis (TB) in African buffalo as a model system, we explore consequences of competing or independent disease effects for host population dynamics. We include scenarios with density-dependent and density-independent effects of environmental variation, exemplified by variable food availability (driven by rainfall) and catastrophic droughts, respectively. Independent disease effects reduce population size linearly with prevalence, irrespective of the nature of environmental variation. Competing disease risks alter population size only if density-independent variation is present; then, disease reduces population size nonlinearly. Field data indicate that the net effect of TB on buffalo likely falls between the extremes of total independence and competition with other risk factors: TB increases mortality and decreases fecundity in some prime-aged buffalo, suggesting independent disease risks in these individuals, while similar disease effects in senescent buffalo may act as competing risks. Moreover, increased survival and fecundity of TB-negative buffalo may compensate for some disease-related losses. Model assumptions on independent or competing disease risks and environmental variability should be considered explicitly when assessing disease effects on wildlife populations.     

Transforming growth factor type beta in normal human urine

TGF beta has been identified in normal human urine specimens from five individuals studied for five consecutive days. The peptide was extracted from urine using Sepralyte C1 beads. Detectable levels of [125I]TGF beta competing activity as measured by radioreceptor assay was found in about half of the specimens studied. The protein isolated from urine using C1 Sepralyte beads was further purified using Biogel P-60 column chromatography. Fractions were tested for TGF beta and EGF competing activity using radioreceptor assays. TGF beta and EGF extracted from urine are clearly separated by column chromatography. Two distinct EGF peaks and a single TGF beta peak were observed. Fractions having [125I]TGF beta competing activity were pooled and further purified using reverse-phase HPLC. HPLC fractions having [125I]TGF beta competing activity were tested for bioactivity using a soft agar assay. The fractions were capable of stimulating soft agar growth of AKR-2B (clone 84A) cells and cross reacted with a TGF beta antibody in a radioimmunoassay. The presence of TGF beta in normal human urine was also demonstrated by immunoblotting. These results also suggest that C1 bead extraction of urine specimens can be used as a rapid first step in purification of TGF beta.     

A joint model for longitudinal measurements and survival data in the presence of multiple failure types

Summary .   In this article we study a joint model for longitudinal measurements and competing risks survival data. Our joint model provides a flexible approach to handle possible nonignorable missing data in the longitudinal measurements due to dropout. It is also an extension of previous joint models with a single failure type, offering a possible way to model informatively censored events as a competing risk. Our model consists of a linear mixed effects submodel for the longitudinal outcome and a proportional cause-specific hazards frailty submodel ( Prentice et al., 1978 , Biometrics 34, 541–554) for the competing risks survival data, linked together by some latent random effects. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their standard errors using a profile likelihood method. The developed method works well in our simulation studies and is applied to a clinical trial for the scleroderma lung disease.