A semiparametric mixture cure survival model for left‐truncated and right‐censored data

In follow‐up studies, the disease event time can be subject to left truncation and right censoring. Furthermore, medical advancements have made it possible for patients to be cured of certain types of diseases. In this article, we consider a semiparametric mixture cure model for the regression analysis of left‐truncated and right‐censored data. The model combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. We investigate two techniques for estimating model parameters. The first approach is based on martingale estimating equations (EEs). The second approach is based on the conditional likelihood function given truncation variables. The asymptotic properties of both proposed estimators are established. Simulation studies indicate that the conditional maximum‐likelihood estimator (cMLE) performs well while the estimator based on EEs is very unstable even though it is shown to be consistent. This is a special and intriguing phenomenon for the EE approach under cure model. We provide insights into this issue and find that the EE approach can be improved significantly by assigning appropriate weights to the censored observations in the EEs. This finding is useful in overcoming the instability of the EE approach in some more complicated situations, where the likelihood approach is not feasible. We illustrate the proposed estimation procedures by analyzing the age at onset of the occiput‐wall distance event for patients with ankylosing spondylitis.     

Cause‐Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring

Summary The standard estimator for the cause‐specific cumulative incidence function in a competing risks setting with left truncated and/or right censored data can be written in two alternative forms. One is a weighted empirical cumulative distribution function and the other a product‐limit estimator. This equivalence suggests an alternative view of the analysis of time‐to‐event data with left truncation and right censoring: individuals who are still at risk or experienced an earlier competing event receive weights from the censoring and truncation mechanisms. As a consequence, inference on the cumulative scale can be performed using weighted versions of standard procedures. This holds for estimation of the cause‐specific cumulative incidence function as well as for estimation of the regression parameters in the Fine and Gray proportional subdistribution hazards model. We show that, with the appropriate filtration, a martingale property holds that allows deriving asymptotic results for the proportional subdistribution hazards model in the same way as for the standard Cox proportional hazards model. Estimation of the cause‐specific cumulative incidence function and regression on the subdistribution hazard can be performed using standard software for survival analysis if the software allows for inclusion of time‐dependent weights. We show the implementation in the R statistical package. The proportional subdistribution hazards model is used to investigate the effect of calendar period as a deterministic external time varying covariate, which can be seen as a special case of left truncation, on AIDS related and non‐AIDS related cumulative mortality.     

An additive‐multiplicative mean residual life model for right‐censored data

Many studies have focused on determining the effect of the body mass index (BMI) on the mortality in different cohorts. In this article, we propose an additive‐multiplicative mean residual life (MRL) model to assess the effects of BMI and other risk factors on the MRL function of survival time in a cohort of Chinese type 2 diabetic patients. The proposed model can simultaneously manage additive and multiplicative risk factors and provide a comprehensible interpretation of their effects on the MRL function of interest. We develop an estimation procedure through pseudo partial score equations to obtain parameter estimates. We establish the asymptotic properties of the proposed estimators and conduct simulations to demonstrate the performance of the proposed method. The application of the procedure to a study on the life expectancy of type 2 diabetic patients reveals new insights into the extension of the life expectancy of such patients.     

Marginal Models for Clustered Time‐to‐Event Data with Competing Risks Using Pseudovalues

Summary Many time‐to‐event studies are complicated by the presence of competing risks and by nesting of individuals within a cluster, such as patients in the same center in a multicenter study. Several methods have been proposed for modeling the cumulative incidence function with independent observations. However, when subjects are clustered, one needs to account for the presence of a cluster effect either through frailty modeling of the hazard or subdistribution hazard, or by adjusting for the within‐cluster correlation in a marginal model. We propose a method for modeling the marginal cumulative incidence function directly. We compute leave‐one‐out pseudo‐observations from the cumulative incidence function at several time points. These are used in a generalized estimating equation to model the marginal cumulative incidence curve, and obtain consistent estimates of the model parameters. A sandwich variance estimator is derived to adjust for the within‐cluster correlation. The method is easy to implement using standard software once the pseudovalues are obtained, and is a generalization of several existing models. Simulation studies show that the method works well to adjust the SE for the within‐cluster correlation. We illustrate the method on a dataset looking at outcomes after bone marrow transplantation.     

On Distance‐Based Permutation Tests for Between‐Group Comparisons

Summary Permutation tests based on distances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo‐F tests arising from a distance‐based extension of multivariate analysis of variance. In this article, we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data.     

Hazard ratio estimation for two‐sample case under interval‐censored failure time data

This paper discusses two‐sample comparison in the case of interval‐censored failure time data. For the problem, one common approach is to employ some nonparametric test procedures, which usually give some p‐values but not a direct or exact quantitative measure of the survival or treatment difference of interest. In particular, these procedures cannot provide a hazard ratio estimate, which is commonly used to measure the difference between the two treatments or samples. For interval‐censored data, a few nonparametric test procedures have been developed, but it does not seem to exist as a procedure for hazard ratio estimation. Corresponding to this, we present two procedures for nonparametric estimation of the hazard ratio of the two samples for interval‐censored data situations. They are generalizations of the corresponding procedures for right‐censored failure time data. An extensive simulation study is conducted to evaluate the performance of the two procedures and indicates that they work reasonably well in practice. For illustration, they are applied to a set of interval‐censored data arising from a breast cancer study.     

Design‐based inference on Bernstein type estimators for continuous populations

The estimation of the values of a variable at any point of a study area is performed using Bernstein polynomials when the sampling scheme is implemented by selecting a point in each polygon of a regular grid overimposed onto the area. The evaluation of the precision of the resulting estimates is investigated under a completely design‐based framework. Moreover, as the main contribution to the mean squared error of the Bernstein‐type estimator is due to the bias, also a pseudo‐jackknife estimator is proposed. The performance of both estimators is investigated theoretically and by means of a simulation study. An application to a soil survey performed in Berkshire Downs in Oxfordshire (UK) is considered.     

A comparison of abundance estimates from extended batch‐marking and Jolly–Seber‐type experiments

Little attention has been paid to the use of multi‐sample batch‐marking studies, as it is generally assumed that an individual's capture history is necessary for fully efficient estimates. However, recently, Huggins et al. ( 2010 ) present a pseudo‐likelihood for a multi‐sample batch‐marking study where they used estimating equations to solve for survival and capture probabilities and then derived abundance estimates using a Horvitz–Thompson‐type estimator. We have developed and maximized the likelihood for batch‐marking studies. We use data simulated from a Jolly–Seber‐type study and convert this to what would have been obtained from an extended batch‐marking study. We compare our abundance estimates obtained from the Crosbie–Manly–Arnason–Schwarz (CMAS) model with those of the extended batch‐marking model to determine the efficiency of collecting and analyzing batch‐marking data. We found that estimates of abundance were similar for all three estimators: CMAS, Huggins, and our likelihood. Gains are made when using unique identifiers and employing the CMAS model in terms of precision; however, the likelihood typically had lower mean square error than the pseudo‐likelihood method of Huggins et al. ( 2010 ). When faced with designing a batch‐marking study, researchers can be confident in obtaining unbiased abundance estimators. Furthermore, they can design studies in order to reduce mean square error by manipulating capture probabilities and sample size.     

Right‐ and left‐handed three‐helix proteins. I. Experimental and simulation analysis of differences in folding and structure

Despite the large number of publications on three‐helix protein folding, there is no study devoted to the influence of handedness on the rate of three‐helix protein folding. From the experimental studies, we make a conclusion that the left‐handed three‐helix proteins fold faster than the right‐handed ones. What may explain this difference? An important question arising in this paper is whether the modeling of protein folding can catch the difference between the protein folding rates of proteins with similar structures but with different folding mechanisms. To answer this question, the folding of eight three‐helix proteins (four right‐handed and four left‐handed), which are similar in size, was modeled using the Monte Carlo and dynamic programming methods. The studies allowed us to determine the orders of folding of the secondary‐structure elements in these domains and amino acid residues which are important for the folding. The obtained data are in good correlation with each other and with the experimental data. Structural analysis of these proteins demonstrated that the left‐handed domains have a lesser number of contacts per residue and a smaller radius of cross section than the right‐handed domains. This may be one of the explanations of the observed fact. The same tendency is observed for the large dataset consisting of 332 three‐helix proteins (238 right‐ and 94 left‐handed). From our analysis, we found that the left‐handed three‐helix proteins have some less‐dense packing that should result in faster folding for some proteins as compared to the case of right‐handed proteins.Proteins 2013; © 2013 Wiley Periodicals, Inc.     

Cox proportional hazards models with left truncation and time‐varying coefficient: Application of age at event as outcome in cohort studies

When analyzing time‐to‐event cohort data, two different ways of choosing a time scale have been discussed in the literature: time‐on‐study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time‐varying coefficient for left‐truncated and right‐censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well‐established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.     

Risk‐adjusted monitoring of time to event in the presence of long‐term survivors

The use of control charts for monitoring schemes in medical context should consider adjustments to incorporate the specific risk for each individual. Some authors propose the use of a risk‐adjusted survival time cumulative sum (RAST CUSUM) control chart to monitor a time‐to‐event outcome, possibly right censored, using conventional survival models, which do not contemplate the possibility of cure of a patient. We propose to extend this approach considering a risk‐adjusted CUSUM chart, based on a cure rate model. We consider a regression model in which the covariates affect the cure fraction. The CUSUM scores are obtained for Weibull and log‐logistic promotion time model to monitor a scale parameter for nonimmune individuals. A simulation study was conducted to evaluate and compare the performance of the proposed chart (RACUF CUSUM) with RAST CUSUM, based on optimal control limits and average run length in different situations. As a result, we note that the RAST CUSUM chart is inappropriate when applied to data with a cure rate, while the proposed RACUF CUSUM chart seems to have similar performance if applied to data without a cure rate. The proposed chart is illustrated with simulated data and with a real data set of patients with heart failure treated at the Heart Institute (InCor), at the University of São Paulo, Brazil.     

Joint regression analysis for survival data in the presence of two sets of semi‐competing risks

In many clinical trials, multiple time‐to‐event endpoints including the primary endpoint (e.g., time to death) and secondary endpoints (e.g., progression‐related endpoints) are commonly used to determine treatment efficacy. These endpoints are often biologically related. This work is motivated by a study of bone marrow transplant (BMT) for leukemia patients, who may experience the acute graft‐versus‐host disease (GVHD), relapse of leukemia, and death after an allogeneic BMT. The acute GVHD is associated with the relapse free survival, and both the acute GVHD and relapse of leukemia are intermediate nonterminal events subject to dependent censoring by the informative terminal event death, but not vice versa, giving rise to survival data that are subject to two sets of semi‐competing risks. It is important to assess the impacts of prognostic factors on these three time‐to‐event endpoints. We propose a novel statistical approach that jointly models such data via a pair of copulas to account for multiple dependence structures, while the marginal distribution of each endpoint is formulated by a Cox proportional hazards model. We develop an estimation procedure based on pseudo‐likelihood and carry out simulation studies to examine the performance of the proposed method in finite samples. The practical utility of the proposed method is further illustrated with data from the motivating example.     

A Note on Variance Estimation of the Aalen–Johansen Estimator of the Cumulative Incidence Function in Competing Risks,with a View towards Left‐Truncated Data

The Aalen–Johansen estimator is the standard nonparametric estimator of the cumulative incidence function in competing risks. Estimating its variance in small samples has attracted some interest recently, together with a critique of the usual martingale‐based estimators. We show that the preferred estimator equals a Greenwood‐type estimator that has been derived as a recursion formula using counting processes and martingales in a more general multistate framework. We also extend previous simulation studies on estimating the variance of the Aalen–Johansen estimator in small samples to left‐truncated observation schemes, which may conveniently be handled within the counting processes framework. This investigation is motivated by a real data example on spontaneous abortion in pregnancies exposed to coumarin derivatives, where both competing risks and left‐truncation have recently been shown to be crucial methodological issues (Meister and Schaefer (2008), Reproductive Toxicology 26 , 31–35). Multistate‐type software and data are available online to perform the analyses. The Greenwood‐type estimator is recommended for use in practice.     

The Identity Objection to the future‐like‐ours argument

Some critics of Don Marquis's ‘future‐like‐ours’ anti‐abortion argument launch what has been called the Identity Objection. The upshot of this objection is that under a psychological theory of personal identity, a non‐sentient fetus lacks precisely what Marquis believes gives it a right to life – a future like ours. However, Eric Vogelstein, in a recent article, has argued that under this theory of personal identity a non‐sentient fetus, in fact, has a future like ours, which he believes dissolves the Identity Objection. But Vogelstein is mistaken. Even if he is correct that there is a sense in which a non‐sentient fetus has a future of value under a psychological theory of personal identity, the sense in which it has one is importantly different from the sense in which we have one, meaning that, under such a theory, a non‐sentient fetus does not have a future like ours.     

Confidence bands for multiplicative hazards models: Flexible resampling approaches

We propose new resampling‐based approaches to construct asymptotically valid time‐simultaneous confidence bands for cumulative hazard functions in multistate Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time‐dependent covariates, where the data may be subject to independent right‐censoring or left‐truncation. We use simulations to investigate their finite sample behavior. Finally, the methods are utilized to analyze two empirical examples with survival and competing risks data.     

Long non‐coding RNA MALAT1 mediates hypoxia‐induced pro‐survival autophagy of endometrial stromal cells in endometriosis

Endometriosis is a common gynecological disease characterized by diminished apoptosis, sustained ectopic survival of dysfunctional endometrial cells. Hypoxia has been implicated as a crucial microenvironmental factor that contributes to endometriosis. It has been reported that long non‐coding RNA MALAT1 (lncRNA‐MALAT1) highly expressed in endometriosis and up‐regulated by hypoxia. Hypoxia may also induce autophagy, which might act as cell protective mechanism. However, the relationship between lncRNA‐MALAT1 and autophagy under hypoxia conditions in endometriosis remains unknown. In the present study, we found that both lncRNA‐MALAT1 and autophagy level were up‐regulated in ectopic endometrium from patients with endometriosis, and its expression level correlates positively with that of hypoxia‐inducible factor‐1α (HIF‐1α). In cultured human endometrial stromal cells, both lncRNA‐MALAT1 and autophagy were induced by hypoxia in a time‐dependent manner and lncRNA‐MALAT1 up‐regulation was dependent on HIF‐1α signalling. Our analyses also show that knockdown of lncRNA‐MALAT1 suppressed hypoxia induced autophagy. Furthermore, inhibiting autophagy with specific inhibitor 3‐Methyladenine (3‐MA) and Beclin1 siRNA enhanced apoptosis of human endometrial stromal cells under hypoxia condition. Collectively, our findings identify that lncRNA‐MALAT1 mediates hypoxia‐induced pro‐survival autophagy of endometrial stromal cells in endometriosis.     

Self‐assembling study of sarcolipin and its mutants in multiple molecular dynamic simulations

The Sarcolipin (SLN) is a single trans‐membrane protein that can self‐assembly to dimer and oligomer for playing importantphysiological function. In this work, we addressed the dimerization of wild type SLN (wSLN) and its mutants (mSLNs) – I17A and I20A, using both coarse‐grained (CG) and atomistic (AT) molecular dynamics (MD) simulations. Our results demonstrated that wSLN homodimer assembled as a left‐handed helical complex, while mSLNs heterodimers assembled as right‐handed complexes. Analysis of residue‐residue contacts map indicated that isoleucine (Ile)‐leucione (Leu) zipper domain played an important role in dimerization. The potential of mean force (PMF) demonstrated that wSLN homodimer was more stable than mSLNs heterodimers. Meanwhile, the mSLNs heterodimers preferred right‐handed rather than left‐handed helix. AT‐MD simulations for wSLN and mSLNs were also in line with CG‐MD simulations. These results provided the insights for understanding the mechanisms of SLNs self‐assembling. Proteins 2017; 85:1065–1077. © 2017 Wiley Periodicals, Inc.     

Pseudo‐real‐time retinal layer segmentation for high‐resolution adaptive optics optical coherence tomography

We present a pseudo‐real‐time retinal layer segmentation for high‐resolution Sensorless Adaptive Optics‐Optical Coherence Tomography (SAO‐OCT). Our pseudo‐real‐time segmentation method is based on Dijkstra's algorithm that uses the intensity of pixels and the vertical gradient of the image to find the minimum cost in a geometric graph formulation within a limited search region. It segments six retinal layer boundaries in an iterative process according to their order of prominence. The segmentation time is strongly correlated to the number of retinal layers to be segmented. Our program permits en face images to be extracted during data acquisition to guide the depth specific focus control and depth dependent aberration correction for high‐resolution SAO‐OCT systems. The average processing times for our entire pipeline for segmenting six layers in a retinal B‐scan of 496 × 400 and 240 × 400 pixels are around 25.60 and 13.76 ms, respectively. When reducing the number of layers segmented to only two layers, the time required for a 240 × 400 pixel image is 8.26 ms.     

Defective regression models for cure rate modeling with interval‐censored data

Regression models in survival analysis are most commonly applied for right‐censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval‐censored mechanism is ignored. We present a cure rate defective model for interval‐censored event‐time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.     

Time‐dependent classification accuracy curve under marker‐dependent sampling

Evaluating the classification accuracy of a candidate biomarker signaling the onset of disease or disease status is essential for medical decision making. A good biomarker would accurately identify the patients who are likely to progress or die at a particular time in the future or who are in urgent need for active treatments. To assess the performance of a candidate biomarker, the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are commonly used. In many cases, the standard simple random sampling (SRS) design used for biomarker validation studies is costly and inefficient. In order to improve the efficiency and reduce the cost of biomarker validation, marker‐dependent sampling (MDS) may be used. In a MDS design, the selection of patients to assess true survival time is dependent on the result of a biomarker assay. In this article, we introduce a nonparametric estimator for time‐dependent AUC under a MDS design. The consistency and the asymptotic normality of the proposed estimator is established. Simulation shows the unbiasedness of the proposed estimator and a significant efficiency gain of the MDS design over the SRS design.