Maximum likelihood estimation for semiparametric transformation models with interval-censored data

Maximum likelihood estimation for semiparametric regression models with interval-censored multistate data

Interval-censored multistate data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur over a broad time interval. We relate potentially time-dependent covariates to multistate processes through semiparametric proportional intensity models with random effects. We study nonparametric maximum likelihood estimation under general interval censoring and develop a stable expectation-maximization algorithm. We show that the resulting parameter estimators are consistent and that the finite-dimensional components are asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we demonstrate through extensive simulation studies that the proposed numerical and inferential procedures perform well in realistic settings. Finally, we provide an application to a major epidemiologic cohort study.

Statistical analysis of self-reported health conditions in cohort studies: handling of missing onset age

OBJECTIVES

This paper discusses methodological challenges in epidemiological association analysis of a time-to-event outcome and hypothesized risk factors, where age/time at the onset of the outcome may be missing in some cases, a condition commonly encountered when the outcome is self-reported.

STUDY DESIGN AND SETTING

A cohort study with long-term follow-up for outcome ascertainment such as the Childhood Cancer Survivor Study (CCSS), a large cohort study of 5-year survivors of childhood cancer diagnosed in 1970-1999 in which occurrences and age at onset of various chronic health conditions (CHCs) are self-reported in surveys. Simple methods for handling missing onset age and their potential bias in the exposure-outcome association inference are discussed. The interval-censored method is discussed as a remedy for handling this problem. The finite sample performance of these approaches is compared through Monte Carlo simulations. Examples from the CCSS include four CHCs (diabetes, myocardial infarction, osteoporosis/osteopenia, and growth hormone deficiency).

RESULTS

The interval-censored method is useable in practice using the standard statistical software. The simulation study showed that the regression coefficient estimates from the 'Interval censored' method consistently displayed reduced bias and, in most cases, smaller standard deviations, resulting in smaller mean square errors, compared to those from the simple approaches, regardless of the proportion of subjects with an event of interest, the proportion of missing onset age, and the sample size.

CONCLUSION

The interval-censored method is a statistically valid and practical approach to the association analysis of self-reported time-to-event data when onset age may be missing. While the simpler approaches that force such data into complete data may enable the standard analytic methods to be applicable, there is considerable loss in both accuracy and precision relative to the interval-censored method.

Improving estimation efficiency of case-cohort studies with interval-censored failure time data

The case-cohort design is a commonly used cost-effective sampling strategy for large cohort studies, where some covariates are expensive to measure or obtain. In this paper, we consider regression analysis under a case-cohort study with interval-censored failure time data, where the failure time is only known to fall within an interval instead of being exactly observed. A common approach to analyzing data from a case-cohort study is the inverse probability weighting approach, where only subjects in the case-cohort sample are used in estimation, and the subjects are weighted based on the probability of inclusion into the case-cohort sample. This approach, though consistent, is generally inefficient as it does not incorporate information outside the case-cohort sample. To improve efficiency, we first develop a sieve maximum weighted likelihood estimator under the Cox model based on the case-cohort sample and then propose a procedure to update this estimator by using information in the full cohort. We show that the update estimator is consistent, asymptotically normal, and at least as efficient as the original estimator. The proposed method can flexibly incorporate auxiliary variables to improve estimation efficiency. A weighted bootstrap procedure is employed for variance estimation. Simulation results indicate that the proposed method works well in practical situations. An application to a Phase 3 HIV vaccine efficacy trial is provided for illustration.

Factor-augmented transformation models for interval-censored failure time data

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

Mosquitocidal effect of ivermectin-treated nettings and sprayed walls on Anopheles gambiae s.s

Ivermectin (IVM) has been proposed as a new tool for malaria control as it is toxic on vectors feeding on treated humans or cattle. Nevertheless, IVM may have a direct mosquitocidal effect when applied on bed nets or sprayed walls. The potential for IVM application as a new insecticide for long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS) was tested in this proof-of-concept study in a laboratory and semi-field environment. Laboratory-reared, insecticide-susceptible Kisumu Anopheles gambiae were exposed to IVM on impregnated netting materials and sprayed plastered- and mud walls using cone bioassays. The results showed a direct mosquitocidal effect of IVM on this mosquito strain as all mosquitoes died by 24 h after exposure to IVM. The effect was slower on the IVM-sprayed walls compared to the treated nettings. Further work to evaluate possibility of IVM as a new insecticide formulation in LLINs and IRS will be required.

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.

Noninferiority of Silver Diamine Fluoride vs Sealants for Reducing Dental Caries Prevalence and Incidence: A Randomized Clinical Trial

Importance

Dental caries is the world's most prevalent noncommunicable disease and a source of health inequity; school dental sealant programs are a common preventive measure. Silver diamine fluoride (SDF) may provide an alternative therapy to prevent and control caries if shown to be noninferior to sealant treatment.

Objective

To determine whether school-based application of SDF is noninferior to dental sealants and atraumatic restorative treatment (ART) in the prevalence of dental caries.

Design, Setting, and Participants

The Silver Diamine Fluoride Versus Therapeutic Sealants for the Arrest and Prevention of Dental Caries in Low-Income Minority Children (CariedAway) study was a pragmatic noninferiority cluster-randomized clinical trial conducted from February 2018 to June 2023 to compare silver diamine fluoride vs therapeutic sealants for the arrest and prevention of dental caries. Children at primary schools in New York, New York, with at least 50% of the student population reporting as Black or Hispanic and at least 80% receiving free or reduced lunch were included. This population was selected as they are at the highest risk of caries in New York. Students were randomized to receive either SDF or sealant with ART; those aged 5 to 13 years were included in the analysis. Treatment was provided at every visit based on need, and the number of visits varied by child. Schools with preexisting oral health programs were excluded, as were children who did not speak English. Of 17 741 students assessed for eligibility, 7418 were randomized, and 4100 completed follow-up and were included in the final analysis.

Interventions

Participants were randomized at the school level to receive either a 38% concentration SDF solution or glass ionomer sealants and ART. Each participant also received fluoride varnish.

Main Outcomes and Measures

Primary study outcomes were the prevalence and incidence of dental caries.

Results

A total of 7418 children (mean [SD] age, 7.58 [1.90] years; 4006 [54.0%] female; 125 [1.7%] Asian, 1246 [16.8%] Black, 3648 [49.2%] Hispanic, 153 [2.1%] White, 114 [1.5%] multiple races or ethnicities, 90 [1.2%] other [unspecified], 2042 [27.5%] unreported) were enrolled and randomized to receive either SDF (n = 3739) or sealants with ART (n = 3679). After initial treatment, 4100 participants (55.0%) completed at least 1 follow-up observation. The overall baseline prevalence of dental caries was approximately 27.2% (95% CI, 25.7-28.6). The odds of decay prevalence decreased longitudinally (odds ratio [OR], 0.79; 95% CI, 0.75-0.83) and SDF was noninferior compared to sealants and ART (OR, 0.94; 95% CI, 0.80-1.11). The crude incidence of dental caries in children treated with SDF was 10.2 per 1000 tooth-years vs 9.8 per 1000 tooth-years in children treated with sealants and ART (rate ratio, 1.05; 95% CI, 0.97-1.12).

Conclusions and Relevance

In this school-based pragmatic randomized clinical trial, application of SDF resulted in nearly identical caries incidence compared to dental sealants and ART and was noninferior in the longitudinal prevalence of caries. These findings suggest that SDF may provide an effective alternative for use in school caries prevention.

Trial Registration

ClinicalTrials.gov Identifier: NCT03442309.

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.

Predicting Conversion Time from Mild Cognitive Impairment to Dementia with Interval-Censored Models

Background

Mild cognitive impairment (MCI) patients are at a high risk of developing Alzheimer's disease and related dementias (ADRD) at an estimated annual rate above 10%. It is clinically and practically important to accurately predict MCI-to-dementia conversion time.

Objective

It is clinically and practically important to accurately predict MCI-to-dementia conversion time by using easily available clinical data.

Methods

The dementia diagnosis often falls between two clinical visits, and such survival outcome is known as interval-censored data. We utilized the semi-parametric model and the random forest model for interval-censored data in conjunction with a variable selection approach to select important measures for predicting the conversion time from MCI to dementia. Two large AD cohort data sets were used to build, validate, and test the predictive model.

Results

We found that the semi-parametric model can improve the prediction of the conversion time for patients with MCI-to-dementia conversion, and it also has good predictive performance for all patients.

Conclusions

Interval-censored data should be analyzed by using the models that were developed for interval- censored data to improve the model performance.

Semiparametric estimation and testing for panel count data with informative interval-censored failure event

Panel count data and interval-censored data are two types of incomplete data that often occur in event history studies. Almost all existing statistical methods are developed for their separate analysis. In this paper, we investigate a more general situation where a recurrent event process and an interval-censored failure event occur together. To intuitively and clearly explain the relationship between the recurrent current process and failure event, we propose a failure time-dependent mean model through a completely unspecified link function. To overcome the challenges arising from the blending of nonparametric components and parametric regression coefficients, we develop a two-stage conditional expected likelihood-based estimation procedure. We establish the consistency, the convergence rate and the asymptotic normality of the proposed two-stage estimator. Furthermore, we construct a class of two-sample tests for comparison of mean functions from different groups. The proposed methods are evaluated by extensive simulation studies and are illustrated with the skin cancer data that motivated this study.

A semiparametric Cox-Aalen transformation model with censored data

We propose a broad class of so-called Cox-Aalen transformation models that incorporate both multiplicative and additive covariate effects on the baseline hazard function within a transformation. The proposed models provide a highly flexible and versatile class of semiparametric models that include the transformation models and the Cox-Aalen model as special cases. Specifically, it extends the transformation models by allowing potentially time-dependent covariates to work additively on the baseline hazard and extends the Cox-Aalen model through a predetermined transformation function. We propose an estimating equation approach and devise an expectation-solving (ES) algorithm that involves fast and robust calculations. The resulting estimator is shown to be consistent and asymptotically normal via modern empirical process techniques. The ES algorithm yields a computationally simple method for estimating the variance of both parametric and nonparametric estimators. Finally, we demonstrate the performance of our procedures through extensive simulation studies and applications in two randomized, placebo-controlled human immunodeficiency virus (HIV) prevention efficacy trials. The data example shows the utility of the proposed Cox-Aalen transformation models in enhancing statistical power for discovering covariate effects.

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.

Bayesian transformation model for spatial partly interval-censored data

The transformation model with partly interval-censored data offers a highly flexible modeling framework that can simultaneously support multiple common survival models and a wide variety of censored data types. However, the real data may contain unexplained heterogeneity that cannot be entirely explained by covariates and may be brought on by a variety of unmeasured regional characteristics. Due to this, we introduce the conditionally autoregressive prior into the transformation model with partly interval-censored data and take the spatial frailty into account. An efficient Markov chain Monte Carlo method is proposed to handle the posterior sampling and model inference. The approach is simple to use and does not include any challenging Metropolis steps owing to four-stage data augmentation. Through several simulations, the suggested method's empirical performance is assessed and then the method is used in a leukemia study.

Marginal proportional hazards models for multivariate interval-censored data

Multivariate interval-censored data arise when there are multiple types of events or clusters of study subjects, such that the event times are potentially correlated and when each event is only known to occur over a particular time interval. We formulate the effects of potentially time-varying covariates on the multivariate event times through marginal proportional hazards models while leaving the dependence structures of the related event times unspecified. We construct the nonparametric pseudolikelihood under the working assumption that all event times are independent, and we provide a simple and stable EM-type algorithm. The resulting nonparametric maximum pseudolikelihood estimators for the regression parameters are shown to be consistent and asymptotically normal, with a limiting covariance matrix that can be consistently estimated by a sandwich estimator under arbitrary dependence structures for the related event times. We evaluate the performance of the proposed methods through extensive simulation studies and present an application to data from the Atherosclerosis Risk in Communities Study.

Concave likelihood-based regression with finite-support response variables

We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume a model which includes models previously considered for interval-censored variables with log-concave distributions as special cases. The resulting log-likelihood is concave, which we use to establish asymptotic normality of its maximizer as the number of observations n tends to infinity with the number of parameters d fixed, and rates of convergence of L1 -regularized estimators when the true parameter vector is sparse and d and n both tend to infinity withlog ( d ) / n → 0 $\log (d) / n \rightarrow 0$ . We consider an inexact proximal Newton algorithm for computing estimates and give theoretical guarantees for its convergence. The range of possible applications is wide, including but not limited to survival analysis in discrete time, the modeling of outcomes on scored surveys and questionnaires, and, more generally, interval-censored regression. The applicability and usefulness of the proposed methods are illustrated in simulations and data examples.

An augmented likelihood approach for the Cox proportional hazards model with interval-censored auxiliary and validated outcome data-with application to the Hispanic Community Health Study/Study of Latinos

In large epidemiologic studies, it is typical for an inexpensive, non-invasive procedure to be used to record disease status during regular follow-up visits, with less frequent assessment by a gold standard test. Inexpensive outcome measures like self-reported disease status are practical to obtain, but can be error-prone. Association analysis reliant on error-prone outcomes may lead to biased results; however, restricting analyses to only data from the less frequently observed error-free outcome could be inefficient. We have developed an augmented likelihood that incorporates data from both error-prone outcomes and a gold standard assessment. We conduct a numerical study to show how we can improve statistical efficiency by using the proposed method over standard approaches for interval-censored survival data that do not leverage auxiliary data. We extend this method for the complex survey design setting so that it can be applied in our motivating data example. Our method is applied to data from the Hispanic Community Health Study/Study of Latinos to assess the association between energy and protein intake and the risk of incident diabetes. In our application, we demonstrate how our method can be used in combination with regression calibration to additionally address the covariate measurement error in self-reported diet.

Validation of eGFR for Detecting Associations Between Serum Protein Biomarkers and Subsequent GFR Decline

SIGNIFICANCE STATEMENT

eGFR from creatinine, cystatin C, or both has been primarily used in search of biomarkers for GFR decline. Whether the relationships between biomarkers and eGFR decline are similar to associations with measured GFR (mGFR) decline has not been investigated. This study revealed that some biomarkers showed statistically significant different associations with eGFR decline compared with mGFR decline, particularly for eGFR from cystatin C. The findings indicate that non-GFR-related factors, such as age, sex, and body mass index, influence the relationship between biomarkers and eGFR decline. Therefore, the results of biomarker studies using eGFR, particularly eGFRcys, should be interpreted with caution and perhaps validated with mGFR.

BACKGROUND

Several serum protein biomarkers have been proposed as risk factors for GFR decline using eGFR from creatinine or cystatin C. We investigated whether eGFR can be used as a surrogate end point for measured GFR (mGFR) when searching for biomarkers associated with GFR decline.

METHODS

In the Renal Iohexol Clearance Survey, GFR was measured with plasma iohexol clearance in 1627 individuals without diabetes, kidney, or cardiovascular disease at baseline. After 11 years of follow-up, 1409 participants had one or more follow-up GFR measurements. Using logistic regression and interval-censored Cox regression, we analyzed the association between baseline levels of 12 serum protein biomarkers with the risk of accelerated GFR decline and incident CKD for both mGFR and eGFR.

RESULTS

Several biomarkers exhibited different associations with eGFR decline compared with their association with mGFR decline. More biomarkers showed different associations with eGFRcys decline than with eGFRcre decline. Most of the different associations of eGFR decline versus mGFR decline remained statistically significant after adjustment for age, sex, and body mass index, but several were attenuated and not significant after adjusting for the corresponding baseline mGFR or eGFR.

CONCLUSIONS

In studies of some serum protein biomarkers, eGFR decline may not be an appropriate surrogate outcome for mGFR decline. Although the differences from mGFR decline are attenuated by adjustment for confounding factors in most cases, some persist. Therefore, proposed biomarkers from studies using eGFR should preferably be validated with mGFR.

Analysis of the Cox Model with Longitudinal Covariates with Measurement Errors and Partly Interval Censored Failure Times, with Application to an AIDS Clinical Trial

Time-dependent covariates are often measured intermittently and with measurement errors. Motivated by the AIDS Clinical Trials Group (ACTG) 175 trial, this paper develops statistical inferences for the Cox model for partly interval censored failure times and longitudinal covariates with measurement errors. The conditional score methods developed for the Cox model with measurement errors and right censored data are no longer applicable to interval censored data. Assuming an additive measurement error model for a longitudinal covariate, we propose a nonparametric maximum likelihood estimation approach by deriving the measurement error induced hazard model that shows the attenuating effect of using the plug-in estimate for the true underlying longitudinal covariate. An EM algorithm is devised to facilitate maximum likelihood estimation that accounts for the partly interval censored failure times. The proposed methods can accommodate different numbers of replicates for different individuals and at different times. Simulation studies show that the proposed methods perform well with satisfactory finite-sample performances and that the naive methods ignoring measurement error or using the plug-in estimate can yield large biases. A hypothesis testing procedure for the measurement error model is proposed. The proposed methods are applied to the ACTG 175 trial to assess the associations of treatment arm and time-dependent CD4 cell count on the composite clinical endpoint of AIDS or death.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12561-023-09372-y.

A pairwise pseudo-likelihood approach for regression analysis of left-truncated failure time data with various types of censoring

BACKGROUND

Failure time data frequently occur in many medical studies and often accompany with various types of censoring. In some applications, left truncation may occur and can induce biased sampling, which makes the practical data analysis become more complicated. The existing analysis methods for left-truncated data have some limitations in that they either focus only on a special type of censored data or fail to flexibly utilize the distribution information of the truncation times for inference. Therefore, it is essential to develop a reliable and efficient method for the analysis of left-truncated failure time data with various types of censoring.

METHOD

This paper concerns regression analysis of left-truncated failure time data with the proportional hazards model under various types of censoring mechanisms, including right censoring, interval censoring and a mixture of them. The proposed pairwise pseudo-likelihood estimation method is essentially built on a combination of the conditional likelihood and the pairwise likelihood that eliminates the nuisance truncation distribution function or avoids its estimation. To implement the presented method, a flexible EM algorithm is developed by utilizing the idea of self-consistent estimating equation. A main feature of the algorithm is that it involves closed-form estimators of the large-dimensional nuisance parameters and is thus computationally stable and reliable. In addition, an R package LTsurv is developed.

RESULTS

The numerical results obtained from extensive simulation studies suggest that the proposed pairwise pseudo-likelihood method performs reasonably well in practical situations and is obviously more efficient than the conditional likelihood approach as expected. The analysis results of the MHCPS data with the proposed pairwise pseudo-likelihood method indicate that males have significantly higher risk of losing active life than females. In contrast, the conditional likelihood method recognizes this effect as non-significant, which is because the conditional likelihood method often loses some estimation efficiency compared with the proposed method.

CONCLUSIONS

The proposed method provides a general and helpful tool to conduct the Cox's regression analysis of left-truncated failure time data under various types of censoring.

Modeling and maximum likelihood based inference of interval-censored data with unknown upper limits and time-dependent covariates

Due to the nature of study design or other reasons, the upper limits of the interval-censored data with multiple visits are unknown. A naïve approach is to treat the last observed time as the exact event time, which may induce biased estimators of the model parameters. In this paper, we first develop a Cox model with time-dependent covariates for the event time and a proportional hazards model with frailty for the gap time. We then construct the upper limits using the latent gap times to resolve the issue of interval-censored event time data with unknown upper limits. A data-augmentation technique and a Monte Carlo EM (MCEM) algorithm are developed to facilitate computation. Theoretical properties of the computational algorithm are also investigated. Additionally, new model comparison criteria are developed to assess the fit of the gap time data as well as the fit of the event time data conditional on the gap time data. Our proposed method compares favorably with competing methods in both simulation study and real data analysis.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

Temporal development of unfavourable urodynamic parameters during the first year after spinal cord injury

OBJECTIVES

To describe the temporal development of and risk factors for the occurrence of unfavourable urodynamic parameters during the first year after spinal cord injury (SCI).

PATIENTS AND METHODS

This population-based longitudinal study used data from 97 adult patients with a single-event traumatic or ischaemic SCI who underwent video-urodynamic investigation (UDI) at a university SCI centre. The first occurrences of unfavourable urodynamic parameters (detrusor overactivity combined with detrusor sphincter dyssynergia [DO-DSD], maximum storage detrusor pressure ≥40 cmH₂ O, bladder compliance <20 mL/cmH₂ O, vesico-ureteric reflux [VUR] and any unfavourable parameter [composite outcome]) were evaluated using time-to-event analysis.

RESULTS

The majority of the population (87/97 [90%]) had at least one unfavourable urodynamic parameter. Most unfavourable urodynamic parameters were initially identified during the 1- or 3-month UDI, including 92% of the DO-DSD (78/85), 82% of the maximum storage pressure ≥40 cmH₂ O (31/38), and 100% of the VUR (seven of seven) observations. No low bladder compliance was observed. The risk of DO-DSD was elevated in patients with thoracic SCI compared to those with lumbar SCI (adjusted hazard ratio [aHR] 2.38, 95% confidence interval [CI] 1.16-4.89). Risk of maximum storage detrusor pressure ≥40 cmH₂ O was higher in males than females (aHR 8.33, 95% CI 2.51-27.66), in patients with a cervical SCI compared to those with lumbar SCI (aHR 14.89, 95% CI 3.28-67.55), and in patients with AIS Grade B or C compared to AIS Grade D SCI (aHR 6.17, 95% CI 1.78-21.39). No risk factors were identified for the composite outcome of any unfavourable urodynamic parameter.

CONCLUSIONS

The first UDI should take place within 3 months after SCI as to facilitate early diagnosis of unfavourable urodynamic parameters and timely treatment. Neuro-urological guidelines and individualised management strategies for patients with SCI may be strengthened by considering sex and SCI characteristics in the scheduling of UDIs.

Cox models with time-varying covariates and partly-interval censoring-A maximum penalised likelihood approach

Time-varying covariates can be important predictors when model based predictions are considered. A Cox model that includes time-varying covariates is usually referred to as an extended Cox model. When only right censoring is presented in the observed survival times, the conventional partial likelihood method is still applicable to estimate the regression coefficients of an extended Cox model. However, if there are interval-censored survival times, then the partial likelihood method is not directly available unless an imputation, such as the middle point imputation, is used to replaced the left- and interval-censored data. However, such imputation methods are well known for causing biases. This paper considers fitting of the extended Cox models using the maximum penalised likelihood method allowing observed survival times to be partly interval censored, where a penalty function is used to regularise the baseline hazard estimate. We present simulation studies to demonstrate the performance of our proposed method, and illustrate our method with applications to two real datasets from medical research.

Instrumental variable estimation of complier causal treatment effect with interval-censored data

Assessing causal treatment effect on a time-to-event outcome is of key interest in many scientific investigations. Instrumental variable (IV) is a useful tool to mitigate the impact of endogenous treatment selection to attain unbiased estimation of causal treatment effect. Existing development of IV methodology, however, has not attended to outcomes subject to interval censoring, which are ubiquitously present in studies with intermittent follow-up but are challenging to handle in terms of both theory and computation. In this work, we fill in this important gap by studying a general class of causal semiparametric transformation models with interval-censored data. We propose a nonparametric maximum likelihood estimator of the complier causal treatment effect. Moreover, we design a reliable and computationally stable expectation-maximization (EM) algorithm, which has a tractable objective function in the maximization step via the use of Poisson latent variables. The asymptotic properties of the proposed estimators, including the consistency, asymptotic normality, and semiparametric efficiency, are established with empirical process techniques. We conduct extensive simulation studies and an application to a colorectal cancer screening data set, showing satisfactory finite-sample performance of the proposed method as well as its prominent advantages over naive methods.

Risk prediction with imperfect survival outcome information from electronic health records

Readily available proxies for the time of disease onset such as the time of the first diagnostic code can lead to substantial risk prediction error if performing analyses based on poor proxies. Due to the lack of detailed documentation and labor intensiveness of manual annotation, it is often only feasible to ascertain for a small subset the current status of the disease by a follow-up time rather than the exact time. In this paper, we aim to develop risk prediction models for the onset time efficiently leveraging both a small number of labels on the current status and a large number of unlabeled observations on imperfect proxies. Under a semiparametric transformation model for onset and a highly flexible measurement error model for proxy onset time, we propose the semisupervised risk prediction method by combining information from proxies and limited labels efficiently. From an initially estimator solely based on the labeled subset, we perform a one-step correction with the full data augmenting against a mean zero rank correlation score derived from the proxies. We establish the consistency and asymptotic normality of the proposed semisupervised estimator and provide a resampling procedure for interval estimation. Simulation studies demonstrate that the proposed estimator performs well in a finite sample. We illustrate the proposed estimator by developing a genetic risk prediction model for obesity using data from Mass General Brigham Healthcare Biobank.

Semiparametric regression analysis of bivariate censored events in a family study of Alzheimer's disease

Assessing disease comorbidity patterns in families represents the first step in gene mapping for diseases and is central to the practice of precision medicine. One way to evaluate the relative contributions of genetic risk factor and environmental determinants of a complex trait (e.g., Alzheimer's disease [AD]) and its comorbidities (e.g., cardiovascular diseases [CVD]) is through familial studies, where an initial cohort of subjects are recruited, genotyped for specific loci, and interviewed to provide extensive disease history in family members. Because of the retrospective nature of obtaining disease phenotypes in family members, the exact time of disease onset may not be available such that current status data or interval-censored data are observed. All existing methods for analyzing these family study data assume single event subject to right-censoring so are not applicable. In this article, we propose a semiparametric regression model for the family history data that assumes a family-specific random effect and individual random effects to account for the dependence due to shared environmental exposures and unobserved genetic relatedness, respectively. To incorporate multiple events, we jointly model the onset of the primary disease of interest and a secondary disease outcome that is subject to interval-censoring. We propose nonparametric maximum likelihood estimation and develop a stable Expectation-Maximization (EM) algorithm for computation. We establish the asymptotic properties of the resulting estimators and examine the performance of the proposed methods through simulation studies. Our application to a real world study reveals that the main contribution of comorbidity between AD and CVD is due to genetic factors instead of environmental factors.

Simultaneous variable selection in regression analysis of multivariate interval-censored data

Multivariate interval-censored data arise when each subject under study can potentially experience multiple events and the onset time of each event is not observed exactly but is known to lie in a certain time interval formed by adjacent examination times with changed statuses of the event. This type of incomplete and complex data structure poses a substantial challenge in practical data analysis. In addition, many potential risk factors exist in numerous studies. Thus, conducting variable selection for event-specific covariates simultaneously becomes useful in identifying important variables and assessing their effects on the events of interest. In this paper, we develop a variable selection technique for multivariate interval-censored data under a general class of semiparametric transformation frailty models. The minimum information criterion (MIC) method is embedded in the optimization step of the proposed expectation-maximization (EM) algorithm to obtain the parameter estimator. The proposed EM algorithm greatly reduces the computational burden in maximizing the observed likelihood function, and the MIC naturally avoids selecting the optimal tuning parameter as needed in many other popular penalties, making the proposed algorithm promising and reliable. The proposed method is evaluated through extensive simulation studies and illustrated by an analysis of patient data from the Aerobics Center Longitudinal Study.

A new approach to estimation of the proportional hazards model based on interval-censored data with missing covariates

This paper discusses the fitting of the proportional hazards model to interval-censored failure time data with missing covariates. Many authors have discussed the problem when complete covariate information is available or the missing is completely at random. In contrast to this, we will focus on the situation where the missing is at random. For the problem, a sieve maximum likelihood estimation approach is proposed with the use of I-spline functions to approximate the unknown cumulative baseline hazard function in the model. For the implementation of the proposed method, we develop an EM algorithm based on a two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. The proposed approach is then applied to a set of the data concerning Alzheimer Disease that motivated this study.

Mixture survival trees for cancer risk classification

In oncology studies, it is important to understand and characterize disease heterogeneity among patients so that patients can be classified into different risk groups and one can identify high-risk patients at the right time. This information can then be used to identify a more homogeneous patient population for developing precision medicine. In this paper, we propose a mixture survival tree approach for direct risk classification. We assume that the patients can be classified into a pre-specified number of risk groups, where each group has distinct survival profile. Our proposed tree-based methods are devised to estimate latent group membership using an EM algorithm. The observed data log-likelihood function is used as the splitting criterion in recursive partitioning. The finite sample performance is evaluated by extensive simulation studies and the proposed method is illustrated by a case study in breast cancer.

SEMIPARAMETRIC LATENT-CLASS MODELS FOR MULTIVARIATE LONGITUDINAL AND SURVIVAL DATA

In long-term follow-up studies, data are often collected on repeated measures of multivariate response variables as well as on time to the occurrence of a certain event. To jointly analyze such longitudinal data and survival time, we propose a general class of semiparametric latent-class models that accommodates a heterogeneous study population with flexible dependence structures between the longitudinal and survival outcomes. We combine nonparametric maximum likelihood estimation with sieve estimation and devise an efficient EM algorithm to implement the proposed approach. We establish the asymptotic properties of the proposed estimators through novel use of modern empirical process theory, sieve estimation theory, and semiparametric efficiency theory. Finally, we demonstrate the advantages of the proposed methods through extensive simulation studies and provide an application to the Atherosclerosis Risk in Communities study.

Maximum Likelihood Estimation for Semiparametric Regression Models With Panel Count Data

Panel count data, in which the observation for each study subject consists of the number of recurrent events between successive examinations, are commonly encountered in industrial reliability testing, medical research, and various other scientific investigations. We formulate the effects of potentially time-dependent covariates on one or more types of recurrent events through non-homogeneous Poisson processes with random effects. We adopt nonparametric maximum likelihood estimation under arbitrary examination schemes and develop a simple and stable EM algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that achieves the semiparametric efficiency bound and can be estimated through profile likelihood. We evaluate the performance of the proposed methods through extensive simulation studies and present a skin cancer clinical trial.

A simulation-extrapolation approach for regression analysis of misclassified current status data with the additive hazards model

Current status data arise when each subject is observed only once and the failure time of interest is only known to be either smaller or larger than the observation time rather than observed exactly. For the situation, due to the use of imperfect diagnostic tests, the failure status could often suffer misclassification or one observes misclassified data, which may result in severely biased estimation if not taken into account. In this article, we discuss regression analysis of such misclassified current status data arising from the additive hazards model, and a simulation-extrapolation (SIMEX) approach is developed for the estimation. Furthermore, the asymptotic properties of the proposed estimators are established, and a simulation study is conducted to assess the empirical performance of the method, which indicates that the proposed procedure performs well. In particular, it can correct the estimation bias given by the naive method that ignores the existence of misclassification. An application to a medical study on gonorrhea is also provided.

A semiparametric mixture model approach for regression analysis of partly interval-censored data with a cured subgroup

Failure time data with a cured subgroup are frequently confronted in various scientific fields and many methods have been proposed for their analysis under right or interval censoring. However, a cure model approach does not seem to exist in the analysis of partly interval-censored data, which consist of both exactly observed and interval-censored observations on the failure time of interest. In this article, we propose a two-component mixture cure model approach for analyzing such type of data. We employ a logistic model to describe the cured probability and a proportional hazards model to model the latent failure time distribution for uncured subjects. We consider maximum likelihood estimation and develop a new expectation-maximization algorithm for its implementation. The asymptotic properties of the resulting estimators are established and the finite sample performance of the proposed method is examined through simulation studies. An application to a set of real data on childhood mortality in Nigeria is provided.

Semiparametric regression analysis of partly interval-censored failure time data with application to an AIDS clinical trial

Failure time data subject to various types of censoring commonly arise in epidemiological and biomedical studies. Motivated by an AIDS clinical trial, we consider regression analysis of failure time data that include exact and left-, interval-, and/or right-censored observations, which are often referred to as partly interval-censored failure time data. We study the effects of potentially time-dependent covariates on partly interval-censored failure time via a class of semiparametric transformation models that includes the widely used proportional hazards model and the proportional odds model as special cases. We propose an EM algorithm for the nonparametric maximum likelihood estimation and show that it unifies some existing approaches developed for traditional right-censored data or purely interval-censored data. In particular, the proposed method reduces to the partial likelihood approach in the case of right-censored data under the proportional hazards model. We establish that the resulting estimator is consistent and asymptotically normal. In addition, we investigate the proposed method via simulation studies and apply it to the motivating AIDS clinical trial.

Semiparametric analysis of zero-inflated recurrent events with a terminal event

Recurrent event data frequently arise in longitudinal studies and observations on recurrent events could be terminated by a major failure event such as death. In many situations, there exist a large fraction of subjects without any recurrent events of interest. Among these subjects, some are unsusceptible to recurrent events, while others are susceptible but have no recurrent events being observed due to censoring. In this article, we propose a zero-inflated generalized joint frailty model and a sieve maximum likelihood approach to analyze zero-inflated recurrent events with a terminal event. The model provides a considerable flexibility in formulating the effects of covariates on both recurrent events and the terminal event by specifying various transformation functions. In addition, Bernstein polynomials are employed to approximate the unknown cumulative baseline hazard (intensity) function. The estimation procedure can be easily implemented and is computationally fast. Extensive simulation studies are conducted and demonstrate that our proposed method works well for practical situations. Finally, we apply the method to analyze myocardial infarction recurrences in the presence of death in a clinical trial with cardiovascular outcomes.

Evaluating Vaccine Efficacy Against SARS-CoV-2 Infection

Although interim results from several large placebo-controlled phase 3 trials demonstrated high vaccine efficacy (VE) against symptomatic COVID-19, it is unknown how effective the vaccines are in preventing people from becoming asymptomatically infected and potentially spreading the virus unwittingly. It is more difficult to evaluate VE against SARS-CoV-2 infection than against symptomatic COVID-19 because infection is not observed directly but rather is known to occur between two antibody or RT-PCR tests. Additional challenges arise as community transmission changes over time and as participants are vaccinated on different dates because of staggered enrollment or crossover before the end of the study. Here, we provide valid and efficient statistical methods for estimating potentially waning VE against SARS-CoV-2 infection with blood or nasal samples under time-varying community transmission, staggered enrollment, and blinded or unblinded crossover. We demonstrate the usefulness of the proposed methods through numerical studies mimicking the BNT162b2 phase 3 trial and the Prevent COVID U study. In addition, we assess how crossover and the frequency of diagnostic tests affect the precision of VE estimates.

SUMMARY

We show how to estimate potentially waning efficacy of COVID-19 vaccines against SARS-CoV-2 infection using blood or nasal samples collected periodically from clinical trials with staggered enrollment of participants and crossover of placebo recipients.