Fitting a progressive three-state colorectal cancer model to interval-censored surveillance data under outcome-dependent sampling using a weighted likelihood approach.

To optimize colorectal cancer (CRC) surveillance, accurate information on the risk of developing CRC from premalignant lesions is essential. However, directly observing this risk is challenging since precursor lesions, i.e., advanced adenomas (AAs), are removed upon detection. Statistical methods for multistate models can estimate risks, but estimation is challenging due to low CRC incidence. We propose an outcome-dependent sampling (ODS) design for this problem in which we oversample CRCs. More specifically, we propose a three-state model for jointly estimating the time distributions from baseline colonoscopy to AA and from AA onset to CRC accounting for the ODS design using a weighted likelihood approach. We applied the methodology to a sample from a Norwegian adenoma cohort (1993-2007), comprising 1, 495 individuals (median follow-up 6.8 years [IQR: 1.1 - 12.8 years]) of whom 648 did and 847 did not develop CRC. We observed a 5-year AA risk of 13% and 34% for individuals having non-advanced adenoma (NAA) and AA removed at baseline colonoscopy, respectively. Upon AA development, the subsequent risk to develop CRC in 5 years was 17% and age-dependent. These estimates provide a basis for optimizing surveillance intensity and determining the optimal trade-off between CRC prevention, costs, and use of colonoscopy resources.

Conditional modeling of panel count data with partly interval-censored failure event.

In longitudinal follow-up studies, panel count data arise from discrete observations on recurrent events. We investigate a more general situation where a partly interval-censored failure event is informative to recurrent events. The existing methods for the informative failure event are based on the latent variable model, which provides indirect interpretation for the effect of failure event. To solve this problem, we propose a failure-time-dependent proportional mean model with panel count data through an unspecified link function. For estimation of model parameters, we consider a conditional expectation of least squares function to overcome the challenges from partly interval-censoring, and develop a two-stage estimation procedure by treating the distribution function of the failure time as a functional nuisance parameter and using the B-spline functions to approximate unknown baseline mean and link functions. Furthermore, we derive the overall convergence rate of the proposed estimators and establish the asymptotic normality of finite-dimensional estimator and functionals of infinite-dimensional estimator. The proposed estimation procedure is evaluated by extensive simulation studies, in which the finite-sample performances coincide with the theoretical results. We further illustrate our method with a longitudinal healthy longevity study and draw some insightful conclusions.

Weighted Expectile Regression Neural Networks for Right Censored Data.

As a favorable alternative to the censored quantile regression, censored expectile regression has been popular in survival analysis due to its flexibility in modeling the heterogeneous effect of covariates. The existing weighted expectile regression (WER) method assumes that the censoring variable and covariates are independent, and that the covariates effects has a global linear structure. However, these two assumptions are too restrictive to capture the complex and nonlinear pattern of the underlying covariates effects. In this article, we developed a novel weighted expectile regression neural networks (WERNN) method by incorporating the deep neural network structure into the censored expectile regression framework. To handle the random censoring, we employ the inverse probability of censoring weighting (IPCW) technique in the expectile loss function. The proposed WERNN method is flexible enough to fit nonlinear patterns and therefore achieves more accurate prediction performance than the existing WER method for right censored data. Our findings are supported by extensive Monte Carlo simulation studies and a real data application.

Exploratory subgroup identification in the heterogeneous Cox model: A relatively simple procedure.

For survival analysis applications we propose a novel procedure for identifying subgroups with large treatment effects, with focus on subgroups where treatment is potentially detrimental. The approach, termed forest search, is relatively simple and flexible. All-possible subgroups are screened and selected based on hazard ratio thresholds indicative of harm with assessment according to the standard Cox model. By reversing the role of treatment one can seek to identify substantial benefit. We apply a splitting consistency criteria to identify a subgroup considered "maximally consistent with harm." The type-1 error and power for subgroup identification can be quickly approximated by numerical integration. To aid inference we describe a bootstrap bias-corrected Cox model estimator with variance estimated by a Jacknife approximation. We provide a detailed evaluation of operating characteristics in simulations and compare to virtual twins and generalized random forests where we find the proposal to have favorable performance. In particular, in our simulation setting, we find the proposed approach favorably controls the type-1 error for falsely identifying heterogeneity with higher power and classification accuracy for substantial heterogeneous effects. Two real data applications are provided for publicly available datasets from a clinical trial in oncology, and HIV.

Conditional score approaches to errors-in-variables competing risks data in discrete time.

Analysis of competing risks data has been an important topic in survival analysis due to the need to account for the dependence among the competing events. Also, event times are often recorded on discrete time scales, rendering the models tailored for discrete-time nature useful in the practice of survival analysis. In this work, we focus on regression analysis with discrete-time competing risks data, and consider the errors-in-variables issue where the covariates are prone to measurement errors. Viewing the true covariate value as a parameter, we develop the conditional score methods for various discrete-time competing risks models, including the cause-specific and subdistribution hazards models that have been popular in competing risks data analysis. The proposed estimators can be implemented by efficient computation algorithms, and the associated large sample theories can be simply obtained. Simulation results show satisfactory finite sample performances, and the application with the competing risks data from the scleroderma lung study reveals the utility of the proposed methods.

A new and unified method for regression analysis of interval-censored failure time data under semiparametric transformation models with missing covariates.

This paper discusses regression analysis of interval-censored failure time data arising from semiparametric transformation models in the presence of missing covariates. Although some methods have been developed for the problem, they either apply only to limited situations or may have some computational issues. Corresponding to these, we propose a new and unified two-step inference procedure that can be easily implemented using the existing or standard software. The proposed method makes use of a set of working models to extract partial information from incomplete observations and yields a consistent estimator of regression parameters assuming missing at random. An extensive simulation study is conducted and indicates that it performs well in practical situations. Finally, we apply the proposed approach to an Alzheimer's Disease study that motivated this study.

Joint modeling approaches for censored predictors due to detection limits with applications to metabolites data.

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, exact measures cannot be obtained, and thus are left censored. The problem becomes more challenging when the censored data come from heterogeneous populations consisting of exposed and non-exposed subjects. If the censored data come from non-exposed subjects, their measures are always zero and hence censored, forming a latent class governed by a distinct censoring mechanism compared with the exposed subjects. The exposed group's censored measurements are always greater than zero, but less than the detection limit. It is very often that the exposed and non-exposed subjects may have different disease traits or different relationships with outcomes of interest, so we need to disentangle the two different populations for valid inference. In this article, we aim to fill the methodological gaps in the literature by developing a novel joint modeling approach to not only address the censoring issue in predictors, but also untangle different relationships of exposed and non-exposed subjects with the outcome. Simulation studies are performed to assess the numerical performance of our proposed approach when the sample size is small to moderate. The joint modeling approach is also applied to examine associations between plasma metabolites and blood pressure in Bogalusa Heart Study, and identify new metabolites that are highly associated with blood pressure.

Nonparametric empirical Bayes biomarker imputation and estimation.

Biomarkers are often measured in bulk to diagnose patients, monitor patient conditions, and research novel drug pathways. The measurement of these biomarkers often suffers from detection limits that result in missing and untrustworthy measurements. Frequently, missing biomarkers are imputed so that down-stream analysis can be conducted with modern statistical methods that cannot normally handle data subject to informative censoring. This work develops an empirical Bayes g $$ g $$ -modeling method for imputing and denoising biomarker measurements. We establish superior estimation properties compared to popular methods in simulations and with real data, providing the useful biomarker measurement estimations for down-stream analysis.

The 2017 Women's Health Initiative study and use of hormone therapy: an emulated repeated cross-sectional study.

BACKGROUND: Hormone therapy (HT) use among menopausal women declined after negative information from the 2002 Women's Health Initiative (WHI) HT study. The 2017 post-intervention follow-up WHI study revealed that HT did not increase long-term mortality. However, studies on the effects of the updated WHI findings are lacking. Thus, we assessed the impact of the 2017 WHI findings on HT use in Taiwan. METHODS: We identified 1,869,050 women aged 50-60 years, between June and December 2017, from health insurance claims data to compare HT use in the 3 months preceding and following September 2017. To address the limitations associated with interval-censored data, we employed an emulated repeated cross-sectional design. Using logistic regression analysis, we evaluated the impact of the 2017 WHI study on menopausal symptom-related outpatient visits and HT use. In a scenario analysis, we examined the impact of the 2002 trial on HT use to validate our study design. RESULTS: Study participants' baseline characteristics before and after the 2017 WHI study were not significantly different. Logistic regressions demonstrated that the 2017 study had no significant effect on outpatient visits for menopause-related symptoms or HT use among women with outpatient visits. The scenario analysis confirmed the negative impact of the 2002 WHI trial on HT use. CONCLUSIONS: The 2017 WHI study did not demonstrate any impact on either menopause-related outpatient visits or HT use among middle-aged women in Taiwan. Our emulated cross-sectional study design may be employed in similar population-based policy intervention studies using interval-censored data.

Nonparametric analysis of delayed treatment effects using single-crossing constraints.

Clinical trials involving novel immuno-oncology therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and, in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related. A main advantage of our approach is that it provides an estimate of a crossing time if such a crossing exists, and, moreover, our method generates interpretable measures of treatment benefit including crossing-conditional survival probabilities and crossing-conditional estimates of restricted residual mean life. Our estimates of these measures may be used together with efficacy measures from a primary analysis to provide further insight into differences in survival across treatment arms. We demonstrate the use and effectiveness of our approach with a large simulation study and an analysis of reconstructed outcomes from a recent combination therapy trial.

A Bayesian proportional hazards mixture cure model for interval-censored data.

The proportional hazards mixture cure model is a popular analysis method for survival data where a subgroup of patients are cured. When the data are interval-censored, the estimation of this model is challenging due to its complex data structure. In this article, we propose a computationally efficient semiparametric Bayesian approach, facilitated by spline approximation and Poisson data augmentation, for model estimation and inference with interval-censored data and a cure rate. The spline approximation and Poisson data augmentation greatly simplify the MCMC algorithm and enhance the convergence of the MCMC chains. The empirical properties of the proposed method are examined through extensive simulation studies and also compared with the R package "GORCure". The use of the proposed method is illustrated through analyzing a data set from the Aerobics Center Longitudinal Study.

Regression analysis of doubly censored failure time data with ancillary information.

Doubly censored failure time data occur in many areas and for the situation, the failure time of interest usually represents the elapsed time between two related events such as an infection and the resulting disease onset. Although many methods have been proposed for regression analysis of such data, most of them are conditional on the occurrence time of the initial event and ignore the relationship between the two events or the ancillary information contained in the initial event. Corresponding to this, a new sieve maximum likelihood approach is proposed that makes use of the ancillary information, and in the method, the logistic model and Cox proportional hazards model are employed to model the initial event and the failure time of interest, respectively. A simulation study is conducted and suggests that the proposed method works well in practice and is more efficient than the existing methods as expected. The approach is applied to an AIDS study that motivated this investigation.

Tail Risk Dynamics under Price-Limited Constraint: A Censored Autoregressive Conditional Fréchet Model.

This paper proposes a novel censored autoregressive conditional Fréchet (CAcF) model with a flexible evolution scheme for the time-varying parameters, which allows deciphering tail risk dynamics constrained by price limits from the viewpoints of different risk preferences. The proposed model can well accommodate many important empirical characteristics of financial data, such as heavy-tailedness, volatility clustering, extreme event clustering, and price limits. We then investigate tail risk dynamics via the CAcF model in the price-limited stock markets, taking entropic value at risk (EVaR) as a risk measurement. Our findings suggest that tail risk will be seriously underestimated in price-limited stock markets when the censored property of limit prices is ignored. Additionally, the evidence from the Chinese Taiwan stock market shows that widening price limits would lead to a decrease in the incidence of extreme events (hitting limit-down) but a significant increase in tail risk. Moreover, we find that investors with different risk preferences may make opposing decisions about an extreme event. In summary, the empirical results reveal the effectiveness of our model in interpreting and predicting time-varying tail behaviors in price-limited stock markets, providing a new tool for financial risk management.

Statistical Challenges When Analyzing SARS-CoV-2 RNA Measurements Below the Assay Limit of Quantification in COVID-19 Clinical Trials.

Most clinical trials evaluating coronavirus disease 2019 (COVID-19) therapeutics include assessments of antiviral activity. In recently completed outpatient trials, changes in nasal severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA levels from baseline were commonly assessed using analysis of covariance (ANCOVA) or mixed models for repeated measures (MMRM) with single imputation for results below assay lower limits of quantification (LLoQ). Analyzing changes in viral RNA levels with singly imputed values can lead to biased estimates of treatment effects. In this article, using an illustrative example from the ACTIV-2 trial, we highlight potential pitfalls of imputation when using ANCOVA or MMRM methods, and illustrate how these methods can be used when considering values

Group variable selection for the Cox model with interval-censored failure time data.

Group variable selection is often required in many areas, and for this many methods have been developed under various situations. Unlike the individual variable selection, the group variable selection can select the variables in groups, and it is more efficient to identify both important and unimportant variables or factors by taking into account the existing group structure. In this paper, we consider the situation where one only observes interval-censored failure time data arising from the Cox model, for which there does not seem to exist an established method. More specifically, a penalized sieve maximum likelihood variable selection and estimation procedure is proposed and the oracle property of the proposed method is established. Also, an extensive simulation study is performed and suggests that the proposed approach works well in practical situations. An application of the method to a set of real data is provided.

Semiparametric probit regression model with misclassified current status data.

Current status data arise when each subject under study is examined only once at an observation time, and one only knows the failure status of the event of interest at the observation time rather than the exact failure time. Moreover, the obtained failure status is frequently subject to misclassification due to imperfect tests, yielding misclassified current status data. This article conducts regression analysis of such data with the semiparametric probit model, which serves as an important alternative to existing semiparametric models and has recently received considerable attention in failure time data analysis. We consider the nonparametric maximum likelihood estimation and develop an expectation-maximization (EM) algorithm by incorporating the generalized pool-adjacent-violators (PAV) algorithm to maximize the intractable likelihood function. The resulting estimators of regression parameters are shown to be consistent, asymptotically normal, and semiparametrically efficient. Furthermore, the numerical results in simulation studies indicate that the proposed method performs satisfactorily in finite samples and outperforms the naive method that ignores misclassification. We then apply the proposed method to a real dataset on chlamydia infection.

Ball divergence for the equality test of crossing survival curves.

It is a very common problem to test survival equality using the right-censored time-to-event data in clinical research. Although the log-rank test is popularly used in various studies, it may become insensitive when the proportional hazards assumption is violated. As follows, there have a variety of statistical methods being proposed to identify the discrepancy between crossing survival curves or hazard functions. The omnibus tests against general alternatives are usually preferred due to their wide applicability to complicated scenarios in real applications. In this paper, we propose two novel statistics to estimate the ball divergence using the right-censored survival data, and then implement them in the equality test on survival time in two independent groups. The simulation analysis demonstrates their efficiency in identifying the survival discrepancy. Compared to the existing methods, our proposed methods present higher power in situations with complex distributions, especially when there is a scale shift between groups. Real examples illustrate its advantage in practical applications.

New late-emphasis and combination tests based on infimum and supremum logrank statistics with application in oncology trials.

Immunotherapy cancer clinical trials routinely feature an initial period during which the treatment is given without evident therapeutic benefit, which may be followed by a period during which an effective therapy reduces the hazard for event occurrence. The nature of this treatment effect is incompatible with the proportional hazards assumption, which has prompted much work on the development of alternative effect measures of frameworks for testing. We consider tests based on individual and combination of early- and late-emphasis infimum and supremum logrank statistics, describe how they can be implemented, and evaluate their performance in simulation studies. Through this work and illustrative applications we conclude that this class of test statistics offers a new and powerful framework for assessing treatment effects in cancer clinical trials involving immunotherapies.

Generalized mean residual life models for survival data with missing censoring indicators.

The mean residual life (MRL) function is an important and attractive alternative to the hazard function for characterizing the distribution of a time-to-event variable. In this article, we study the modeling and inference of a family of generalized MRL models for right-censored survival data with censoring indicators missing at random. To estimate the model parameters, augmented inverse probability weighted estimating equation approaches are developed, in which the non-missingness probability and the conditional probability of an uncensored observation are estimated by parametric methods or nonparametric kernel smoothing techniques. Asymptotic properties of the proposed estimators are established and finite sample performance is evaluated by extensive simulation studies. An application to brain cancer data is presented to illustrate the proposed methods.

Towards robust and accurate estimates of the incubation time distribution, with focus on upper tail probabilities and SARS-CoV-2 infection.

Quarantine length for individuals who have been at risk for infection with SARS-CoV-2 has been based on estimates of the incubation time distribution. The time of infection is often not known exactly, yielding data with an interval censored time origin. We give a detailed account of the data structure, likelihood formulation and assumptions usually made in the literature: (i) the risk of infection is assumed constant on the exposure window and (ii) the incubation time follows a specific parametric distribution. The impact of these assumptions remains unclear, especially for the right tail of the distribution which informs quarantine policy. We quantified bias in percentiles by means of simulation studies that mimic reality as close as possible. If assumption (i) is not correct, then median and upper percentiles are affected similarly, whereas misspecification of the parametric approach (ii) mainly affects upper percentiles. The latter may yield considerable bias. We suggest a semiparametric method that provides more robust estimates without the need of a parametric choice. Additionally, we used a simulation study to evaluate a method that has been suggested if all infection times are left censored. It assumes that the width of the interval from infection to latest possible exposure follows a uniform distribution. This assumption gave biased results in the exponential phase of an outbreak. Our application to open source data suggests that focus should be on the level of information in the observations, as expressed by the width of exposure windows, rather than the number of observations.