Pairwise dependence diagnostics for clustered failure-time data

Frailty and copula models specify a parametric dependence structurefor multivariate failure-time data. Estimation of some jointquantities can be highly sensitive to the assumed parametricform, and hence model fit is an important issue. This paperlays out a general diagnostic framework for evaluating and selectingfrailty and copula models. The approach is based on the cumulativesum of residuals that are calculated in bivariate time. Theresiduals reflect the difference between the observed and expectedbivariate association structures. The proposed model-checkingprocess is interpretable with a limiting distribution whichcan be approximated using the bootstrap. Simulations and a dataexample illustrate the practical application of the method.     

Semiparametric analysis of survival data with left truncation and dependent right censoring

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. Because 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. First, 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.     

Imputing unobserved values with the EM algorithm under left and right-truncation, and interval censoring for estimating the size of hidden populations

Capture–recapture techniques have been used for considerable time to predict population size. Estimators usually rely on frequency counts for numbers of trappings; however, it may be the case that these are not available for a particular problem, for example if the original data set has been lost and only a summary table is available. Here, we investigate techniques for specific examples; the motivating example is an epidemiology study by Mosley et al., which focussed on a cholera outbreak in East Pakistan. To demonstrate the wider range of the technique, we also look at a study for predicting the long-term outlook of the AIDS epidemic using information on number of sexual partners. A new estimator is developed here which uses the EM algorithm to impute unobserved values and then uses these values in a similar way to the existing estimators. The results show that a truncated approach – mimicking the Chao lower bound approach – gives an improved estimate when population homogeneity is violated.     

A Simple Two‐Sample Rank Test for Multivariate Survival Outcomes with Left Truncation and Right Censoring

A distribution‐free two‐sample rank test is proposed for testing for differences between survival distributions in the analysis of biomedical studies in which two groups of subjects are followed over time for a particular outcome, which may recur. This method is motivated by an observational HIV (human immunodeficiency virus) study in which a group of HIV‐seropositive women and a comparable group of HIV‐seronegative women were examined every 6 months for the presence of cervical intraepithelial neoplasia (CIN), the cervical cancer precursor. Women entered the study serially and were subject to random loss to follow‐up. Only women free of CIN at study entry were followed resulting in left‐truncated survival times. If a woman is found to be CIN infected at a later examination, she is treated and then followed until CIN recurs. The two groups of women were compared at both occurrences of CIN on the basis of rank statistics. For the first occurrence of CIN, survival times since the beginning of the study (based on calendar time) are compared. For a recurrence of CIN, survival times since the first development of CIN are compared. The proposed test statistic for an overall difference between the two groups follows a chi‐square distribution with two degrees of freedom. Simulation results demonstrate the usefulness of the proposed test proposed test statistic, which reduces to the Gehan statistic if each person is followed only to the first failure and there is no serial enrollment.     

Role of caspase-3 in tau truncation at D421 is restricted in transgenic mouse models for tauopathies

Truncated tau is widely detected in Alzheimer's disease brain, and caspase-3 has been considered as a major executioner for tau truncation at aspartate421 (D421), according to its capability of cleaving recombinant tau in vitro . Here we investigated the relationship between D421 truncated tau and caspase-3 in two transgenic mouse models for tauopathies. In adult transgenic mice, activated caspase-3 could not be detected in neurons containing truncated tau, with the exception of a few glia-like cells or neurons in postnatal mice. Caspase-3 expression exhibited a dramatic decrease at the early development stage, and kept at constantly low levels during adult stages in both wild type and transgenic mice. On the other hand, co-incubating brain homogenates from adult tau transgenic mice and ethanol-treated postnatal mice promoted tau truncation at D421, which was mildly reduced by caspase inhibitor, but completely suppressed by phosphatase inhibitor, indicating that hyperphosphorylated tau becomes a poor substrate for truncation at D421. Taken together, our study shows that insufficient caspase-3 expression and hyperphosphorylated status of tau in the adult transgenic mouse brain restrict caspase-3 as an efficient enzyme for tau truncation in vivo . Clearly, there is a caspase-3 independent mechanism responsible for tau truncation at D421 in these models.