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.     

Nonparametric maximum likelihood estimation for competing risks survival data subject to interval censoring and truncation

We derive the nonparametric maximum likelihood estimate (NPMLE) of the cumulative incidence functions for competing risks survival data subject to interval censoring and truncation. Since the cumulative incidence function NPMLEs give rise to an estimate of the survival distribution which can be undefined over a potentially larger set of regions than the NPMLE of the survival function obtained ignoring failure type, we consider an alternative pseudolikelihood estimator. The methods are then applied to data from a cohort of injecting drug users in Thailand susceptible to infection from HIV-1 subtypes B and E.     

Fast approximations of pseudo-observations in the context of right censoring and interval censoring

In the context of right-censored and interval-censored data, we develop asymptotic formulas to compute pseudo-observations for the survival function and the restricted mean survival time (RMST). These formulas are based on the original estimators and do not involve computation of the jackknife estimators. For right-censored data, Von Mises expansions of the Kaplan–Meier estimator are used to derive the pseudo-observations. For interval-censored data, a general class of parametric models for the survival function is studied. An asymptotic representation of the pseudo-observations is derived involving the Hessian matrix and the score vector. Theoretical results that justify the use of pseudo-observations in regression are also derived. The formula is illustrated on the piecewise-constant-hazard model for the RMST. The proposed approximations are extremely accurate, even for small sample sizes, as illustrated by Monte Carlo simulations and real data. We also study the gain in terms of computation time, as compared to the original jackknife method, which can be substantial for a large dataset.     

Life expectancy of oil palm (Elaeis guineensis) infected by Ganoderma boninense in coastal soils,Malaysia: a case study

Ganoderma boninense basal stem rot poses a serious threat to the oil palm industry. The effects of external disease symptoms and coastal soils (Briah – Typic Endoaquepts, Jawa – Typic Sulfaquepts, and Selangor – Typic Humaquepts) on the life expectancy of the infected palms, from disease detection to death, were studied. Six-monthly censuses on disease classes for each palm were recorded between 2004 and 2012. Survival curves of disease symptoms and soil types were compared using Kaplan–Meier and log-rank methods, respectively. Ganoderma-infected palms in acid-sulphate (AS) and potential AS soils recorded lower life expectancy. Survival duration of infected palms with foliar symptoms was 12-months shorter. External factors, such as soil type may influence the survival of infected palms and soil types may pre-dispose oil palm to higher risk of Ganoderma infection. More effective Ganoderma management for palms planted on Coastal soils (with and without AS layer) have been proposed.     

Small-sample inference for incomplete longitudinal data with truncation and censoring in tumor xenograft models

In cancer drug development, demonstrating activity in xenograft models, where mice are grafted with human cancer cells, is an important step in bringing a promising compound to humans. A key outcome variable is the tumor volume measured in a given period of time for groups of mice given different doses of a single or combination anticancer regimen. However, a mouse may die before the end of a study or may be sacrificed when its tumor volume quadruples, and its tumor may be suppressed for some time and then grow back. Thus, incomplete repeated measurements arise. The incompleteness or missingness is also caused by drastic tumor shrinkage (<0.01 cm3) or random truncation. Because of the small sample sizes in these models, asymptotic inferences are usually not appropriate. We propose two parametric test procedures based on the EM algorithm and the Bayesian method to compare treatment effects among different groups while accounting for informative censoring. A real xenograft study on a new antitumor agent, temozolomide, combined with irinotecan is analyzed using the proposed methods.     

Woodland caribou calf mortality in Newfoundland: insights into the role of climate,predation and population density over three decades of study

The rates and causes of juvenile mortality are central features of the dynamics and conservation of large mammals, like woodland caribou (Rangifer tarandus caribou (Gmelin, 1788)), but intrinsic and extrinsic factors may be modified by variations in animal abundance. We tested the influences of population size, climate, calf weight and sex on survival to 6 months of age of 1241 radio-collared caribou calves over three decades, spanning periods of population growth (1979–1997) and decline (2003–2012) in Newfoundland, Canada. Daily survival rates were higher and rose more quickly with calf age during the population growth period compared to the decline. Population size (negatively) and calf weight (positively) affected survival during the decline but neither had a detectable influence during the growth phase. Sex, climate and plant productivity (the latter two derived from the North Atlantic Oscillation and Normalized Difference Vegetation Index, respectively) exerted minimal influence during either phase. Predation was the dominant source of mortality. The mean percentage of calves killed by predators was 30 % higher during the decline compared to the growth phase. Black bears (Ursus americanus) and lynx (Lynx canadensis) were the major predators during the population increase but this changed during the decrease to black bears and coyotes (Canis latrans). Our findings are consistent with the hypothesis that Newfoundland caribou experienced phase-dependent survival mediated proximally by predation and competition for food.     

Discrete-time nonparametric estimation for semi-Markov models of chain-of-events data subject to interval censoring and truncation

Chain-of-events data are longitudinal observations on a succession of events that can only occur in a prescribed order. One goal in an analysis of this type of data is to determine the distribution of times between the successive events. This is difficult when individuals are observed periodically rather than continuously because the event times are then interval censored. Chain-of-events data may also be subject to truncation when individuals can only be observed if a certain event in the chain (e.g., the final event) has occurred. We provide a nonparametric approach to estimate the distributions of times between successive events in discrete time for data such as these under the semi-Markov assumption that the times between events are independent. This method uses a self-consistency algorithm that extends Turnbull's algorithm (1976, Journal of the Royal Statistical Society, Series B 38, 290-295). The quantities required to carry out the algorithm can be calculated recursively for improved computational efficiency. Two examples using data from studies involving HIV disease are used to illustrate our methods.     

Divergent estimates of herd‐wide caribou calf survival: Ecological factors and methodological biases

Population monitoring is a critical part of effective wildlife management, but methods are prone to biases that can hinder our ability to accurately track changes in populations through time. Calf survival plays an important role in ungulate population dynamics and can be monitored using telemetry and herd composition surveys. These methods, however, are susceptible to unrepresentative sampling and violations of the assumption of equal detectability, respectively. Here, we capitalized on 55 herd‐wide estimates of woodland caribou (Rangifer tarandus caribou) calf survival in Newfoundland, Canada, using telemetry (n = 1,175 calves) and 249 herd‐wide estimates of calf:cow ratios (C:C) using herd composition surveys to investigate these potential biases. These data included 17 herd‐wide estimates replicated from both methods concurrently (n = 448 calves and n = 17 surveys) which we used to understand which processes and sampling biases contributed to disagreement between estimates of herd‐wide calf survival. We used Cox proportional hazards models to determine whether estimates of calf mortality risk were biased by the date a calf was collared. We also used linear mixed‐effects models to determine whether estimates of C:C ratios were biased by survey date and herd size. We found that calves collared later in the calving season had a higher mortality risk and that C:C tended to be higher for surveys conducted later in the autumn. When we used these relationships to modify estimates of herd‐wide calf survival derived from telemetry and herd composition surveys concurrently, we found that formerly disparate estimates of woodland caribou calf survival now overlapped (within a 95% confidence interval) in a majority of cases. Our case study highlights the potential of under‐appreciated biases to impact our understanding of population dynamics and suggests ways that managers can limit the influence of these biases in the two widely applied methods for estimating herd‐wide survival.     

Inference for the effect of treatment on survival probability in randomized trials with noncompliance and administrative censoring

In many clinical studies with a survival outcome, administrative censoring occurs when follow-up ends at a prespecified date and many subjects are still alive. An additional complication in some trials is that there is noncompliance with the assigned treatment. For this setting, we study the estimation of the causal effect of treatment on survival probability up to a given time point among those subjects who would comply with the assignment to both treatment and control. We first discuss the standard instrumental variable (IV) method for survival outcomes and parametric maximum likelihood methods, and then develop an efficient plug-in nonparametric empirical maximum likelihood estimation (PNEMLE) approach. The PNEMLE method does not make any assumptions on outcome distributions, and makes use of the mixture structure in the data to gain efficiency over the standard IV method. Theoretical results of the PNEMLE are derived and the method is illustrated by an analysis of data from a breast cancer screening trial. From our limited mortality analysis with administrative censoring times 10 years into the follow-up, we find a significant benefit of screening is present after 4 years (at the 5% level) and this persists at 10 years follow-up.     

Evaluating food availability and nest predation risk as sources of bias in aural bird surveys

ABSTRACT The use of aural surveys to estimate population parameters is widespread in avian studies. Despite efforts to increase the efficacy of this method, the potential for ecological context to bias population estimates remains largely unexplored. For example, food availability and nest predation risk can influence singing activity independent of density and, therefore, may bias aural estimates where these ecological factors vary systematically among habitats or other categories of ecological interest. We used a natural fire event in a mixed‐conifer forest that experienced variation in fire severity (low, intermediate, and high) to determine if aural surveys produce accurate density estimates of Dark‐eyed Juncos ( Junco hyemalis) independent of ecological context. During the first 2‐yr postfire, we censused junco populations in each burn type with intensive spot‐mapping and nest searching, locating 168 nests. Simultaneously, we conducted fixed‐radius point‐count surveys and estimated food availability and nest predation risk in each burn type to test whether ecological context may influence aural detection probability independent of actual density. We found no difference in nesting densities among patches burned at different severity. Arthropod food availability was inversely related to fire severity during the first postfire breeding season, but increased to higher levels across all severities during the second. In both years, aural detections were significantly greater in intermediate severity patches that consistently represented the habitat with the lowest nest predation risk. These results suggest that nest predation risk may significantly bias aural estimates of avian populations. Although traditional aural survey methods such as the Breeding Bird Survey measure habitat attributes, our findings highlight the difficulty in assessing relevant covariates in estimates of avian population. Future research must consider the potential for nest predation and other ecological factors to drive interannual or interhabitat variation in avian population estimates independent of true changes in population size.     

Diagnosis and prognosis potential of four gene promoter hypermethylation in prostate cancer

The current prostate special antigen (PSA) test causes the overtreatment of indolent prostate cancer (PCa). It also increases the risk of delayed treatment of aggressive PCa. DNA methylation aberrations are important events for gene expression dysregulation during tumorigenesis and have been suggested as novel candidate biomarkers for PCa. This may improve the diagnosis and prognosis of PCa. This study assessed the differential methylation and messenger RNA (mRNA) expression between normal and PCa samples. Correlation between promoter methylation and mRNA expression was estimated using Pearson's correlation coefficients. Moreover, the diagnostic potential of candidate methylation markers was estimated by the receiver operating characteristic (ROC) curve using continuous beta values. Survival and Cox analysis was performed to evaluate the prognostic potential of the candidate methylation markers. A total of 359 hypermethylated sites 3435 hypomethylation sites, 483 upregulated genes, and 1341 downregulated genes were identified from The Cancer Genome Atlas database. Furthermore, 17 hypermethylated sites (covering 13 genes), including known genes associated with hypermethylation in PCa (e.g., AOX1 and C1orf114), showed high discrimination between adjacent normal tissues and PCa samples with the area under the ROC curve from 0.88 to 0.94. Notably, ANXA2, FGFR2, HAAO, and KCNE3 were identified as valuable prognostic markers of PCa through the Kaplan–Meier analysis. Using gene methylation as a continuous variable, four promoter hypermethylation was significantly associated with disease-free survival in univariate Cox regression and multivariate Cox regression. This study identified four novel diagnostic and prognostic markers for PCa. The markers provide important strategies for improving the timely diagnosis and prognosis of PCa.     

Factors Influencing Survival of Radiotagged and Banded Northern Bobwhites in Georgia

Abstract: Numerous studies of behavior and ecology of northern bobwhites (Colinus virginianus) have depended on radiotagging and telemetry for data collection. Excluding the presumably short-term effects of trapping, handling, and attaching radiotransmitters, researchers often assume that little bias is associated with estimating survival and behavioral parameters associated with this technique. However, researchers have not adequately examined these effects on organisms being investigated and have thus assumed demographic information obtained from such methods are valid. In light of this conjecture, it is imperative to evaluate methodological assumptions to ensure research is statistically valid and biologically meaningful. Therefore, we used Burnham's model and program MARK to analyze survival estimates of individually banded and radiotagged bobwhites during an 8-year period (1997–2004) consisting of 6,568 individuals (2,527 radiotagged) via combined analysis of mark—recapture, dead recovery (via harvest), and radiotelemetry data to test the effects of radiotransmitters on bobwhite survival. We also compared band—recapture survival estimates to Kaplan—Meier survival estimates, and we examined the effects of various other factors (e.g., temporal, spatial) on bobwhite survival. Based on Akaike's model selection criterion, the best model including the radiotransmitter covariate (Akaike's Information Criterion adjusted for small sample size bias and overdispersion relative value = 0.72) did not explain more of the variation in survival than models without this effect. Thus, we found the effect of radiotransmitters as negligible. Bobwhite survival varied relative to spatial (e.g., site), temporal (e.g., yr and season), and gender effects. Average annual survival for the 8-year period was 22.76% (1.50 SE) for banded-only and 21.72% (1.49 SE) for radiotagged birds. Survival rate varied annually, ranging from 12.42% (7.51 SE) to 37.16% (8.27 SE), and seasonally, ranging from 23.82% (2.71 SE) to 65.06% (3.23 SE); however, between group (banded-only, radiotagged) survival differences were still inconsequential. We conclude that for our study, radiotelemetry provided reliable survival estimates of an intensively managed bobwhite population, where supplemental food was provided, and this information provided useful data to make practical habitat management decisions. We believe that future radiotelemetry studies would benefit as a whole if researchers conducted similar analyses prior to presenting their results from radiotelemetry data, especially for populations that are more food limited.     

Correcting bias due to missing stage data in the non-parametric estimation of stage-specific net survival for colorectal cancer using multiple imputation

BackgroundPopulation-based net survival by tumour stage at diagnosis is a key measure in cancer surveillance. Unfortunately, data on tumour stage are often missing for a non-negligible proportion of patients and the mechanism giving rise to the missingness is usually anything but completely at random. In this setting, restricting analysis to the subset of complete records gives typically biased results. Multiple imputation is a promising practical approach to the issues raised by the missing data, but its use in conjunction with the Pohar-Perme method for estimating net survival has not been formally evaluated.MethodsWe performed a resampling study using colorectal cancer population-based registry data to evaluate the ability of multiple imputation, used along with the Pohar-Perme method, to deliver unbiased estimates of stage-specific net survival and recover missing stage information. We created 1000 independent data sets, each containing 5000 patients. Stage data were then made missing at random under two scenarios (30% and 50% missingness).ResultsComplete records analysis showed substantial bias and poor confidence interval coverage. Across both scenarios our multiple imputation strategy virtually eliminated the bias and greatly improved confidence interval coverage.ConclusionsIn the presence of missing stage data complete records analysis often gives severely biased results. We showed that combining multiple imputation with the Pohar-Perme estimator provides a valid practical approach for the estimation of stage-specific colorectal cancer net survival. As usual, when the percentage of missing data is high the results should be interpreted cautiously and sensitivity analyses are recommended.     

Integrated survival analysis using an event‐time approach in a Bayesian framework

Event‐time or continuous‐time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval‐censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece‐wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event‐time analyses can be used by eliminating the need for having completely known fate data.