Quantile regression for longitudinal data with values below the limit of detection and time-dependent covariates-application to modeling carbon nanotube and nanofiber exposures.

BACKGROUND: In studies of occupational health, longitudinal environmental exposure, and biomonitoring data are often subject to right skewing and left censoring, in which measurements fall below the limit of detection (LOD). To address right-skewed data, it is common practice to log-transform the data and model the geometric mean, assuming a log-normal distribution. However, if the transformed data do not follow a known distribution, modeling the mean of exposure may result in bias and reduce efficiency. In addition, when examining longitudinal data, it is possible that certain covariates may vary over time. OBJECTIVE: To develop predictive quantile regression models to resolve the issues of left censoring and time-dependent covariates and to quantitatively evaluate if previous and current covariates can predict current and/or future exposure levels. METHODS: To address these gaps, we suggested incorporating different substitution approaches into quantile regression and utilizing a method for selecting a working type of time dependency for covariates. RESULTS: In a simulation study, we demonstrated that, under different types of time-dependent covariates, the approach of multiple random value imputation outperformed the other approaches. We also applied our methods to a carbon nanotube and nanofiber exposure study. The dependent variables are the left-censored mass of elemental carbon at both the respirable and inhalable aerosol size fractions. In this study, we identified some potential time-dependent covariates with respect to worker-level determinants and job tasks. CONCLUSION: Time dependency for covariates is rarely accounted for when analyzing longitudinal environmental exposure and biomonitoring data with values less than the LOD through predictive modeling. Mistreating the time-dependency as time-independency will lead to an efficiency loss of regression parameter estimation. Therefore, we addressed time-varying covariates in longitudinal exposure and biomonitoring data with left-censored measurements and illustrated an entire conditional distribution through different quantiles.

Evaluation of Left Truncation and Censoring When Changing the Use of the International Classification of Diseases Eighth Revision Codes to Tenth Revision Codes in the Danish National Patient Registry.

Purpose: In the Danish National Patient Registry (DNPR), covering all Danish hospitals and widely used in research, diseases have been recorded using International Classification of Diseases (ICD) codes, transitioning from the Eighth to the Tenth revision in 1994. Uncertainty exists regarding whether including ICD-8 codes alongside ICD-10 is needed for complete disease identification. We assessed the extent of left-truncation and left-censoring in the DNPR arising from omitting ICD-8 codes. Patients and Methods: We sampled 500,000 Danes ≥40 years of age in 1995, 2010, and 2018. From the DNPR, we identified cardiovascular, endocrine, gastrointestinal, neurological, pulmonary, rheumatic, and urogenital diseases as well as fractures. We obtained the number of people with a disease recorded with ICD-8 codes only (ie, the ICD-8 record would be left-truncated by not using ICD-8 codes), ICD-8 plus ICD-10 codes (ie, the ICD-8 record would be left-censored by not using ICD-8 codes), and ICD-10 codes only. For each ICD group, we calculated the proportion of people with the disease relative to the total sample (ie, 500,000 people) and the total number of people with the disease across all ICD groups. Results: Overall, the left-truncation issue decreased over the years. Relative to all people with a disease, the left-truncated proportion was for example 59% in 1995 and <2% in 2018 for diabetes mellitus; 93% in 1995, and 54% in 2018 for appendicitis. The left-truncation issue increased with age group for most diseases. The proportion of disease records left-censored by not using ICD-8 codes was generally low but highest for chronic diseases. Conclusion: The left-truncation issue diminished over sample years, particularly for chronic diseases, yet remained rather high for selected surgical diseases. The left-truncation issue increased with age group for most diseases. Left-censoring was overall a minor issue that primarily concerned chronic diseases.

Compare the marginal effects for environmental exposure and biomonitoring data with repeated measurements and values below the limit of detection.

BACKGROUND: Environmental exposure and biomonitoring data with repeated measurements from environmental and occupational studies are commonly right-skewed and in the presence of limits of detection (LOD). However, existing model has not been discussed for small-sample properties and highly skewed data with non-detects and repeated measurements. OBJECTIVE: Marginal modeling provides an alternative to analyzing longitudinal and cluster data, in which the parameter interpretations are with respect to marginal or population-averaged means. METHODS: We outlined the theories of three marginal models, i.e., generalized estimating equations (GEE), quadratic inference functions (QIF), and generalized method of moments (GMM). With these approaches, we proposed to incorporate the fill-in methods, including single and multiple value imputation techniques, such that any measurements less than the limit of detection are assigned values. RESULTS: We demonstrated that the GEE method works well in terms of estimating the regression parameters in small sample sizes, while the QIF and GMM outperform in large-sample settings, as parameter estimates are consistent and have relatively smaller mean squared error. No specific fill-in method can be deemed superior as each has its own merits. IMPACT: Marginal modeling is firstly employed to analyze repeated measures data with non-detects, in which only the mean structure needs to be correctly provided to obtain consistent parameter estimates. After replacing non-detects through substitution methods and utilizing small-sample bias corrections, in a simulation study we found that the estimating approaches used in the marginal models have corresponding advantages under a wide range of sample sizes. We also applied the models to longitudinal and cluster working examples.

A marginalized two-part joint model for a longitudinal biomarker and a terminal event with application to advanced head and neck cancers.

The sum of the longest diameter (SLD) of the target lesions is a longitudinal biomarker used to assess tumor response in cancer clinical trials, which can inform about early treatment effect. This biomarker is semicontinuous, often characterized by an excess of zeros and right skewness. Conditional two-part joint models were introduced to account for the excess of zeros in the longitudinal biomarker distribution and link it to a time-to-event outcome. A limitation of the conditional two-part model is that it only provides an effect of covariates, such as treatment, on the conditional mean of positive biomarker values, and not an overall effect on the biomarker, which is often of clinical relevance. As an alternative, we propose in this article, a marginalized two-part joint model (M-TPJM) for the repeated measurements of the SLD and a terminal event, where the covariates affect the overall mean of the biomarker. Our simulation studies assessed the good performance of the marginalized model in terms of estimation and coverage rates. Our application of the M-TPJM to a randomized clinical trial of advanced head and neck cancer shows that the combination of panitumumab in addition with chemotherapy increases the odds of observing a disappearance of all target lesions compared to chemotherapy alone, leading to a possible indirect effect of the combined treatment on time to death.

Time-to-Event Analysis with Unknown Time Origins via Longitudinal Biomarker Registration.

In observational studies, the time origin of interest for time-to-event analysis is often unknown, such as the time of disease onset. Existing approaches to estimating the time origins are commonly built on extrapolating a parametric longitudinal model, which rely on rigid assumptions that can lead to biased inferences. In this paper, we introduce a flexible semiparametric curve registration model. It assumes the longitudinal trajectories follow a flexible common shape function with person-specific disease progression pattern characterized by a random curve registration function, which is further used to model the unknown time origin as a random start time. This random time is used as a link to jointly model the longitudinal and survival data where the unknown time origins are integrated out in the joint likelihood function, which facilitates unbiased and consistent estimation. Since the disease progression pattern naturally predicts time-to-event, we further propose a new functional survival model using the registration function as a predictor of the time-to-event. The asymptotic consistency and semiparametric efficiency of the proposed models are proved. Simulation studies and two real data applications demonstrate the effectiveness of this new approach.

Robust joint modelling of left-censored longitudinal data and survival data with application to HIV vaccine studies.

In jointly modelling longitudinal and survival data, the longitudinal data may be complex in the sense that they may contain outliers and may be left censored. Motivated from an HIV vaccine study, we propose a robust method for joint models of longitudinal and survival data, where the outliers in longitudinal data are addressed using a multivariate t-distribution for b-outliers and using an M-estimator for e-outliers. We also propose a computationally efficient method for approximate likelihood inference. The proposed method is evaluated by simulation studies. Based on the proposed models and method, we analyze the HIV vaccine data and find a strong association between longitudinal biomarkers and the risk of HIV infection.

Bayesian modelling of response to therapy and drug-sensitivity in acute lymphoblastic leukemia.

Acute lymphoblastic leukemia (ALL) is a heterogeneous haematologic malignancy involving the abnormal proliferation of immature lymphocytes and accounts for most paediatric cancer cases. The management of ALL in children has seen great improvement in the last decades thanks to greater understanding of the disease leading to improved treatment strategies evidenced through clinical trials. Common therapy regimens involve a first course of chemotherapy (induction phase), followed by treatment with a combination of anti-leukemia drugs. A measure of the efficacy early in the course of therapy is the presence of minimal residual disease (MRD). MRD quantifies residual tumor cells and indicates the effiectiveness of the treatment over the course of therapy. MRD positivity is defined for values of MRD greater than 0.01%, yielding left-censored MRD observations. We propose a Bayesian model to study the relationship between patient features (leukemia subtype, baseline characteristics, and drug sensitivity profile) and MRD observed at two time points during the induction phase. Specifically, we model the observed MRD values via an auto-regressive model, accounting for left-censoring of the data and for the fact that some patients are already in remission after the first stage of induction therapy. Patient characteristics are included in the model via linear regression terms. In particular, patient-specific drug sensitivity based on ex vivo assays of patient samples is exploited to identify groups of subjects with similar profiles. We include this information as a covariate in the model for MRD. We adopt horseshoe priors for the regression coefficients to perform variable selection to identify important covariates. We fit the proposed approach to data from three prospective paediatric ALL clinical trials carried out at the St. Jude Children's Research Hospital. Our results highlight that drug sensitivity profiles and leukemic subtypes play an important role in the response to induction therapy as measured by serial MRD measures.

Comparing and combining data from immune assays based on left-censored multivariate normal model assuming common assay differences across settings.

In vaccine research towards the prevention of infectious diseases, immune response biomarkers serve as an important tool for comparing and ranking vaccine candidates based on their immunogenicity and predicted protective effect. However, analyses of immune response outcomes can be complicated by differences across assays when immune response data are acquired from multiple groups/laboratories. Motivated by a real-world problem to accommodate the use of two different neutralization assays in COVID-19 vaccine trials, we propose methods based on left-censored multivariate normal model assuming common assay differences across settings, to adjust for differences between assays with respect to measurement error and the lower limit of detection. Our proposed methods integrate external paired-sample data with bridging assumptions to achieve two objectives, both using pooled data acquired from different assays: (i) comparing immunogenicity between vaccine regimens, and (ii) evaluating correlates of risk. In simulation studies, for the first objective, our method leads to unbiased calibrated assay mean with good coverage of bootstrap confidence interval, as well as valid test for immunogenicity comparison, while the alternative method assuming constant calibration model between assays leads to biased estimate of assay mean with undercoverage problem and invalid test with inflated type-I error; for the second objective, in the presence of noticeable left-censoring rate, our proposed method can drastically outperform the existing method that ignores left-censoring, in terms of reduced bias and improved precision. We apply the proposed methods to SARS-CoV-2 spike-pseudotyped virus neutralization assay data generated in vaccine and convalescent samples by two different laboratories.

Self-reporting and screening: Data with right-censored, left-censored, and complete observations.

We consider survival data that combine three types of observations: uncensored, right-censored, and left-censored. Such data arises from screening a medical condition, in situations where self-detection arises naturally. Our goal is to estimate the failure-time distribution, based on these three observation types. We propose a novel methodology for distribution estimation using both semiparametric and nonparametric techniques. We then evaluate the performance of these estimators via simulated data. Finally, as a case study, we estimate the patience of patients who arrive at an emergency department and wait for treatment. Three categories of patients are observed: those who leave the system and announce it, and thus their patience time is observed; those who get service and thus their patience time is right-censored by the waiting time; and those who leave the system without announcing it. For this third category, the patients' absence is revealed only when they are called to service, which is after they have already left; formally, their patience time is left-censored. Other applications of our proposed methodology are discussed.

Collider Bias in Administrative Workers' Compensation Claims Data: A Challenge for Cross-Jurisdictional Research.

PURPOSE: Workers' compensation claims consist of occupational injuries severe enough to meet a compensability threshold. Theoretically, systems with higher thresholds should have fewer claims but greater average severity. For research that relies on claims data, particularly cross-jurisdictional comparisons of compensation systems, this results in collider bias that can lead to spurious associations confounding analyses. In this study, I use real and simulated claims data to demonstrate collider bias and problems with methods used to account for it. METHODS: Using Australian claims data, I used a linear regression to test the association between claim rate and mean disability durations across Statistical Areas. Analyses were repeated with nesting by state/territory to account for variations in compensability thresholds across compensation systems. Both analyses are repeated on left-censored data. Simulated claims data are analysed with Cox survival analyses to illustrate how left-censoring can reverse effects. RESULTS: The claim rate within a Statistical Area was inversely associated with disability duration. However, this reversed when Statistical Areas were nested by state/territory. Left-censoring resulted in an attenuation of the unnested association to non-significance, while the nested association remained significantly positive. Cox regressions with simulated claims data demonstrated how left-censoring can reverse effects. CONCLUSIONS: Collider bias can seriously confound work disability research, particularly cross-jurisdictional comparisons. Work disability researchers must grapple with this challenge by using appropriate study designs and analytical approaches, and considering how it affects the interpretation of results.

Between-group comparison of area under the curve in clinical trials with censored follow-up: Application to HIV therapeutic vaccines.

In clinical trials, longitudinal data are commonly analyzed and compared between groups using a single summary statistic such as area under the outcome versus time curve (AUC). However, incomplete data, arising from censoring due to a limit of detection or missing data, can bias these analyses. In this article, we present a statistical test based on splines-based mixed-model accounting for both the censoring and missingness mechanisms in the AUC estimation. Inferential properties of the proposed method were evaluated and compared to ad hoc approaches and to a non-parametric method through a simulation study based on two-armed trial where trajectories and the proportion of missing data were varied. Simulation results highlight that our approach has significant advantages over the other methods. A real working example from two HIV therapeutic vaccine trials is presented to illustrate the applicability of our approach.

Quantile regression for exposure data with repeated measures in the presence of non-detects.

BACKGROUND: Exposure data with repeated measures from occupational studies are frequently right-skewed and left-censored. To address right-skewed data, data are generally log-transformed and analyses modeling the geometric mean operate under the assumption the data are log-normally distributed. However, modeling the mean of exposure may lead to bias and loss of efficiency if the transformed data do not follow a known distribution. In addition, left censoring occurs when measurements are below the limit of detection (LOD). OBJECTIVE: To present a complete illustration of the entire conditional distribution of an exposure outcome by examining different quantiles, rather than modeling the mean. METHODS: We propose an approach combining the quantile regression model, which does not require any specified error distributions, with the substitution method for skewed data with repeated measurements and non-detects. RESULTS: In a simulation study and application example, we demonstrate that this method performs well, particularly for highly right-skewed data, as parameter estimates are consistent and have smaller mean squared error relative to existing approaches. SIGNIFICANCE: The proposed approach provides an alternative insight into the conditional distribution of an exposure outcome for repeated measures models.

Inflammation correction in micronutrient deficiency with censored inflammatory biomarkers.

BACKGROUND: Biomarkers of micronutrient status vary with inflammation, and can be corrected by a regression-based approach [Biomarkers Reflecting Inflammation and Nutritional Determinants of Anemia (BRINDA)] using measured concentrations of inflammation biomarkers, e.g., C-reactive protein (CRP) and/or α1-acid-glycoprotein (AGP). However, this is confounded when inflammation is measured with multiple assays with variable limits of detection (LOD) and lower limits of quantification (LLOQ). OBJECTIVES: We aimed to develop a probability approach for the estimation of prevalence of micronutrient deficiency using the distribution of true serum/plasma micronutrient concentrations in the population. METHODS: Left-censoring of an inflammation biomarker due to varying values of LOD or LLOQ was addressed by estimating the distribution of the inflammation biomarker at concentrations lower than the LOD and using this for the probability estimation of prevalence of nutrient deficiency. This method was evaluated using 2 publicly available data sets for children <5 y old: BRINDA and the Indian Comprehensive National Nutrition Survey. Each data set included measures of serum ferritin (SF), vitamin A, zinc, and CRP measured using different assays with variable LLOQs. RESULTS: The empirical distribution of SF after correction for CRP and AGP by the BRINDA method was comparable with the estimated probability distribution of SF, yielding similar estimates of iron deficiency prevalence when evaluated in the BRINDA data (17.4%; 95% CI: 15.2%, 19.7% compared with 16.8%; 95% CI: 13.9%, 20.0%; BRINDA compared with the probability method). The BRINDA method-adjusted iron deficiency prevalence was linearly associated with the proportion of left-censored CRP data, whereas these were not associated in the probability method. In the Indian survey data, estimates of prevalence of iron and zinc deficiency were comparable but vitamin A deficiency was lower by the probability method (17.6%; 95% CI: 16.7%, 20.2% compared with 15.7%; 95% CI: 15.2%, 16.3%; BRINDA compared with the probability method). CONCLUSIONS: The proposed probability method is a robust alternate approach to the estimation of the prevalence of nutrient deficiency with left-censored inflammation biomarker data.

Factors Related to Diabetes Mellitus in the Middle-Aged and Over in Taiwan.

Study Objective: to investigate the factors related to diabetes mellitus in the middle-aged and over in Taiwan. Method: data from seven surveys (in 1989-2011) from the "Taiwan Longitudinal Study on Aging" (TLSA), among cohort B (above the age 60 in 1989), cohort A (aged 50-66 in 1996), and cohort C (aged 50-66 in 2003), were analyzed by the interval-censored Cox model. Results: in the early aging stage (aged 60-64), diabetes mellitus prevalence among the same age appeared the lowest in cohort B, followed by cohort A; cohort C reveals the highest than the young generation. Moreover, suffering from hypertension and kidney diseases are closely related to diabetes mellitus, with the diabetes mellitus suffering hazard ratio of 2.53 (95%: 2.35, 2.73) and 1.26 (95%: 1.11, 1.44) times, respectively. For people with fair and poor self-rated health, the risk of suffering from diabetes mellitus is 1.16 (95%: 1.07, 1.27) and 1.50 (95%: 1.35, 1.67) times compared to people with good self-rated health, respectively. Conclusions: in this study, it is considered that an advanced interval censoring model analysis could more accurately grasp the characteristics of factors in people who are middle-aged and over suffering from diabetes mellitus in Taiwan.

Regression models with asymmetric data for estimating thyroglobulin levels one year after the ablation of thyroid cancer.

A key biomarker in the study of differentiated thyroid cancer is thyroglobulin. Measurements of the levels of this protein in the blood are determined using laboratory instruments that cannot detect very small concentrations below a threshold, generating left-censored measurements. In the presence of censoring, ordinary least-squares regression models generate biased parameter estimates; therefore, it is necessary to resort to more complex models that consider the censored observations and the behavior of the distribution of the response variable, such as censored and mixed regression models. These techniques were used to model the relationship between thyroglobulin levels in individuals with differentiated thyroid cancer before and after treatment with radioactive iodine (I-131). Log-normal, log-skew-normal, log-power-normal, and log-generalized-gamma probability distributions were used to model the behavior of errors in the adjusted models. Log-generalized-gamma distribution yielded the best results according to the established model selection criteria.

A multiple imputation method based on weighted quantile regression models for longitudinal censored biomarker data with missing values at early visits.

BACKGROUND: In patient-based studies, biomarker data are often subject to left censoring due to the detection limits, or to incomplete sample or data collection. In the context of longitudinal regression analysis, inappropriate handling of these issues could lead to biased parameter estimates. We developed a specific multiple imputation (MI) strategy based on weighted censored quantile regression (CQR) that not only accounts for censoring, but also missing data at early visits when longitudinal biomarker data are modeled as a covariate. METHODS: We assessed through simulation studies the performances of developed imputation approach by considering various scenarios of covariance structures of longitudinal data and levels of censoring. We also illustrated the application of the proposed method to the Prospective Study of Outcomes in Ankylosing spondylitis (AS) (PSOAS) data to address the issues of censored or missing C-reactive protein (CRP) level at early visits for a group of patients. RESULTS: Our findings from simulation studies indicated that the proposed method performs better than other MI methods by having a higher relative efficiency. We also found that our approach is not sensitive to the choice of covariance structure as compared to other methods that assume normality of biomarker data. The analysis results of PSOAS data from the imputed CRP levels based on our method suggested that higher CRP is significantly associated with radiographic damage, while those from other methods did not result in a significant association. CONCLUSION: The MI based on weighted CQR offers a more valid statistical approach to evaluate a biomarker of disease in the presence of both issues with censoring and missing data in early visits.

Imputation of Gait Speed for Noncompleters in the 400-Meter Walk: Application to the Lifestyle Interventions for Elders Study.

When a 400-m walk test with time constraint (in 15 minutes) is administered, analysis of the associated 400-m gait speed can be challenging because some older adults are unable to complete the distance in time (noncompleters). A simplistic imputation method is to calculate the observed speeds of the noncompleters as the partially completed distance divided by the corresponding amount of elapsed time as an estimate of gait speed over the full 400-m distance. This common practice has not been validated to the best of our knowledge. We propose a Bayesian multiple imputation (MI) method to impute the unobserved 400-m gait speed for noncompleters. Briefly, MI is performed under the assumption that the unobserved 400-m gait speed of noncompleters is left-censored from a normal distribution. We illustrate the application of the Bayesian MI method using longitudinal data collected from the Lifestyle Interventions for Elders (LIFE) study. A simulation study was performed to assess the bias in estimation of the mean 400-m gait speed using both methods. The results indicate that the simplistic imputation method tends to overestimate the population mean, whereas the Bayesian MI method yields minimal bias as the sample size increases.

Bivariate Left-Censored Bayesian Model for Predicting Exposure: Preliminary Analysis of Worker Exposure during the Deepwater Horizon Oil Spill.

In April 2010, the Deepwater Horizon oil rig caught fire and exploded, releasing almost 5 million barrels of oil into the Gulf of Mexico over the ensuing 3 months. Thousands of oil spill workers participated in the spill response and clean-up efforts. The GuLF STUDY being conducted by the National Institute of Environmental Health Sciences is an epidemiological study to investigate potential adverse health effects among these oil spill clean-up workers. Many volatile chemicals were released from the oil into the air, including total hydrocarbons (THC), which is a composite of the volatile components of oil including benzene, toluene, ethylbenzene, xylene, and hexane (BTEXH). Our goal is to estimate exposure levels to these toxic chemicals for groups of oil spill workers in the study (hereafter called exposure groups, EGs) with likely comparable exposure distributions. A large number of air measurements were collected, but many EGs are characterized by datasets with a large percentage of censored measurements (below the analytic methods' limits of detection) and/or a limited number of measurements. We use THC for which there was less censoring to develop predictive linear models for specific BTEXH air exposures with higher degrees of censoring. We present a novel Bayesian hierarchical linear model that allows us to predict, for different EGs simultaneously, exposure levels of a second chemical while accounting for censoring in both THC and the chemical of interest. We illustrate the methodology by estimating exposure levels for several EGs on the Development Driller III, a rig vessel charged with drilling one of the relief wells. The model provided credible estimates in this example for geometric means, arithmetic means, variances, correlations, and regression coefficients for each group. This approach should be considered when estimating exposures in situations when multiple chemicals are correlated and have varying degrees of censoring.

A multivariate cure model for left-censored and right-censored data with application to colorectal cancer screening patterns.

We develop a multivariate cure survival model to estimate lifetime patterns of colorectal cancer screening. Screening data cover long periods of time, with sparse observations for each person. Some events may occur before the study begins or after the study ends, so the data are both left-censored and right-censored, and some individuals are never screened (the 'cured' population). We propose a multivariate parametric cure model that can be used with left-censored and right-censored data. Our model allows for the estimation of the time to screening as well as the average number of times individuals will be screened. We calculate likelihood functions based on the observations for each subject using a distribution that accounts for within-subject correlation and estimate parameters using Markov chain Monte Carlo methods. We apply our methods to the estimation of lifetime colorectal cancer screening behavior in the SEER-Medicare data set. Copyright © 2016 John Wiley & Sons, Ltd.

Model averaging quantiles from data censored by a limit of detection.

In chemical risk assessment, it is important to determine the quantiles of the distribution of concentration data. The selection of an appropriate distribution and the estimation of particular quantiles of interest are largely hindered by the omnipresence of observations below the limit of detection, leading to left-censored data. The log-normal distribution is a common choice, but this distribution is not the only possibility and alternatives should be considered as well. Here, we focus on several distributions that are related to the log-normal distribution or that are seminonparametric extensions of the log-normal distribution. Whereas previous work focused on the estimation of the cumulative distribution function, our interest here goes to the estimation of quantiles, particularly in the left tail of the distribution where most of the left-censored data are located. Two different model averaged quantile estimators are defined and compared for different families of candidate models. The models and methods of selection and averaging are further investigated through simulations and illustrated on data of cadmium concentration in food products. The approach is extended to include covariates and to deal with uncertainty about the values of the limit of detection. These extensions are illustrated with (134) cesium measurements from Fukushima Prefecture, Japan. We can conclude that averaged models do achieve good performance characteristics in case no useful prior knowledge about the true distribution is available; that there is no structural difference in the performance of the direct and indirect method; and that, not surprisingly, only the true or closely approximating model can deal with extremely high percentages of censoring.