Identifiability of distributions under competing risks and complementary risks model

Let X₁,X₂,…,X_p be p random variables with cdf's F₁(x),F₂(x),…,F_p(x)respectively. Let U = min(X₁,X₂,…,X_p) and V = max(X₁,X₂,…,X_p).In this paper we study the problem of uniquely determining and estimating the marginal distributions F₁,F₂,…,F_p given the distribution of U or of V.

First the problem of competing and complementary risks are introduced with examples and the corresponding identification problems are considered when the X₁'s are independently distributed and U(V) is identified, as well as the case when U(V) is not identified. The case when the X₁'s are dependent is considered next. Finally the problem of estimation is considered.     

Multistate Survival Models as Transient Electrical Networks

In multistate survival analysis, the sojourn of a patient through various clinical states is shown to correspond to the diffusion of 1 C of electrical charge through an electrical network. The essential comparison has differentials of probability for the patient to correspond to differentials of charge, and it equates clinical states to electrical nodes. Indeed, if the death state of the patient corresponds to the sink node of the circuit, then the transient current that would be seen on an oscilloscope as the sink output is a plot of the probability density for the survival time of the patient. This electrical circuit analogy is further explored by considering the simplest possible survival model with two clinical states, alive and dead (sink), that incorporates censoring and truncation. The sink output seen on an oscilloscope is a plot of the Kaplan–Meier mass function. Thus, the Kaplan–Meier estimator finds motivation from the dynamics of current flow, as a fundamental physical law, rather than as a nonparametric maximum likelihood estimate (MLE). Generalization to competing risks settings with multiple death states (sinks) leads to cause‐specific Kaplan–Meier submass functions as outputs at sink nodes. With covariates present, the electrical analogy provides for an intuitive understanding of partial likelihood and various baseline hazard estimates often used with the proportional hazards model.     

On exact confidence intervals in a competing risks model with generalized hybrid type-I censored exponential data

In a recent paper by Mao, Shi and Sun that appeared in Journal of Statistical Computation and Simulation, the authors discuss, among other approaches, the construction of exact confidence intervals for the underlying parameters by ‘pivoting the cumulative distribution functions’ of the corresponding maximum likelihood estimators (MLEs). The authors assume that this method is applicable without providing the appropriate justification. In this short note the two requirements for the applicability of this method are discussed, namely, the stochastic monotonicity of the MLEs and the existence of solutions to the equations defining the exact confidence interval's endpoints.     

Flexible parametric estimation technique for a competing risks model with unobserved heterogeneity: a Monte Carlo study

We analyse a flexible parametric estimation technique for a competing risks (CR) model with unobserved heterogeneity, by extending a local mixed proportional hazard single risk model for continuous duration time to a local mixture CR (LMCR) model for discrete duration time. The state-specific local hazard function for the LMCR model is per definition a valid density function if we have either one or two destination states. We conduct Monte Carlo experiments to compare the estimated parameters of the LMCR model, and to compare the estimated parameters of a CR model based on a Heckman–Singer-type (HS-type) technique, with the data-generating process parameters. The Monte Carlo results show that the LMCR model performs better or at least as good as the HS-type model with respect to the estimated structure parameters in most of the cases, but relatively poorer with respect to the estimated duration-dependence parameters.     

Point predictors of the latent failure times of censored units in progressively Type-II censored competing risks data from the exponential distributions

In this paper, we discuss the problem of predicting times to the latent failures of units censored in multiple stages in a progressively Type-II censored competing risks model. It is assumed that the lifetime distribution of the latent failure times are independent and exponential-distributed with the different scale parameters. Several classical point predictors such as the maximum likelihood predictor, the best unbiased predictor, the best linear unbiased predictor, the median unbiased predictor and the conditional median predictor are obtained. The Bayesian point predictors are derived under squared error loss criterion. Moreover, the point estimators of the unknown parameters are obtained using the observed data and different point predictors of the latent failure times. Finally, Monte-Carlo simulations are carried out to compare the performances of the different methods of prediction and estimation and one real data is used to illustrate the proposed procedures.     

Nonexclusive Competition in the Market for Lemons

A seller can trade an endowment of a perfectly divisible good, the quality of which she privately knows. Buyers compete by offering menus of nonexclusive contracts, so that the seller can privately trade with several buyers. In this setting, we show that an equilibrium exists under mild conditions and that aggregate equilibrium allocations are generically unique. Although the good for sale is divisible, in equilibrium the seller ends up trading her whole endowment or not trading at all. Trades take place at a price equal to the expected quality of the good, conditional on the seller being ready to trade at that price. Our model thus provides a novel strategic foundation for Akerlof's (1970) results. It also contrasts with competitive screening models in which contracts are assumed to be exclusive, as in Rothschild and Stiglitz (1976). Latent contracts that are issued but not traded in equilibrium play an important role in our analysis.     

我国药品零售企业人力资源逆向选择及风险规避

在药品流通领域,执业药师的＂良＂与其他经资格认证的药学技术人员的＂相对劣或者不确定的良＂,以及一些鱼目混珠的从业人员（营业员）的＂确定劣＂的博弈一直在进行,在执业药师与一般药学技术人员和营业员的竞争中,出现了明显的＂劣币驱赶良币＂现象。其原因主要是药品零售企业人力资源市场上存在＂准入水平＂的＂质＂的不同,但对不同质的人员却采用相同的价值评价标准,执业药师的药学服务和健康收益的价值被忽视。加上信息不对称的存在和法律刚性规定的不足,最终导致逆向选择的发生,出现执业药师被一般药学技术人员所淘汰的不正常现象,并将导致整个药品零售领域从事药学服务工作的人员所代表的实际能力普遍低于岗位本身的素质需要。建议在新医改实施过程中,应加大执业药师制度宣传,尽快为执业药师立法,重构药学技术人员价值评价体系和激励机制,通过规制政策淘汰一些不合要求的从业人员和企业,并让执业准入的执业药师为保障公众用药的安全和有效发挥其应有的作用。     

Competing risks,left truncation and late entry effect in A-bomb survivors cohort

The cohort under study comprises A-bomb survivors residing in Hiroshima Prefecture since 1968. After this year, thousands of survivors were newly recognized every year. The aim of this study is to determine whether the survival experience of the late entrants to the cohort is significantly different from the registered population in 1968. Parametric models that account for left truncation and competing risks were developed by using sub-hazard functions. A Weibull distribution was used to determine the possible existence of a late entry effect in Hiroshima A-bomb survivors. The competing risks framework shows that there might be a late entry effect in the male and female groups. Our findings are congruent with previous studies analysing similar populations.     

Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks

Abstract. An objective of randomized placebo‐controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain represented in the vaccine construct. Motivated by this objective, recently a mark‐specific proportional hazards (PH) model with a continuum of competing risks has been studied, where the genetic distance of the transmitting strain is the continuous ‘mark’ defined and observable only in failures. A high percentage of genetic marks of interest may be missing for a variety of reasons, predominantly because rapid evolution of HIV sequences after transmission before a blood sample is drawn from which HIV sequences are measured. This research investigates the stratified mark‐specific PH model with missing marks where the baseline functions may vary with strata. We develop two consistent estimation approaches, the first based on the inverse probability weighted complete‐case (IPW) technique, and the second based on augmenting the IPW estimator by incorporating auxiliary information predictive of the mark. We investigate the asymptotic properties and finite‐sample performance of the two estimators, and show that the augmented IPW estimator, which satisfies a double robustness property, is more efficient.     

Changing compatibility of cohabitation and childbearing between young British women born in 1958 and 1970

We investigate the effect of parenthood on whether non-marital unions led to marriage or parting for two cohorts of British women when they were aged between 16 and 29. We compare the effect of conceptions leading to births and the presence and characteristics of children on the odds that a cohabitation was dissolved, or that it was converted to marriage, for women born in 1958 and 1970. A multilevel, multiprocess, competing-risks model allows for multiple cohabitations per woman and endogeneity of fertility status. We find that cohabiting couples’ response to impending parenthood and the presence of children changed over time. In particular, the proportion of cohabiting couples who married before a birth decreased and, in the 1970 cohort only, the risk of dissolution declined during pregnancy. There is also evidence that the presence of a child cemented a cohabiting union for women from the 1970, but not the earlier, cohort.