Semi-parametric Statistical Inference For Complex Interval-Censored Data

Censored data has become a focal point of research in current research,with interval-censored data being a particularly complex and prevalent structure across various felds.Unlike right-censored data,interval-censored data does not contain any precise failure times,making its modeling more challenging.Many scholars have recognized that existing traditional analytical theories are insuffcient to address the complexities and implicit information within interval-censored data,necessitating new research methods for further exploration and discussion.The most efective approach to dealing with complex interval-censored data is to address it through targeted structures.In this thesis,we propose semi-parametric inference methods for interval-censored data with diferent complex structures.Throughout the study,we have undertaken a systematic efort to assess the level of structural complexity of interval-censored data from various perspectives,levels,and perspectives.This thesis includes fve parts.1.Semi-parametric analysis of left-truncated and interval-censored data.Left truncation is usually caused by the researchers including only those subjects whose characteristics match those of their study,which typically introduces a selection bias into the study.The existing literature suggested a conditional likelihood approach,which is straightforward but overlooks the information contained in the left truncation,resulting in lower effciency and potential adverse impacts on subsequent statistical inference analyses.To address this issue,we develop a pairwise likelihood that utilizes the left truncation of each individual in this chapter.Using semi-parametric transformation models,we address the left truncation problem for case K interval-censored data and establish the corresponding statistical inference theories and asymptotic properties by using the sieve maximum likelihood approach.Simulation results demonstrate the validity of the proposed theory,resulting in an improvement in estimation effciency.The validity of addressing left truncation issues arising from HIV infection in AIDS research is further illustrated by case studies.2.Semi-parametric analysis of informatively interval-censored data with a cured subgroup.Informatively censoring and cure structures are common latent structures in interval-censored data.Dependent censoring refers to the correlation between a subject’s failure time and the observation process,while cure structures refer to the phenomenon where some individuals are immune to the failure event.Ignoring these structures can signifcantly impact statistical inference results.To address this issue,we develop a highly implementable two-step estimation method by using the frailty models and non-mixture cure models.We employ the sieve maximum likelihood method and establish the asymptotic properties of the estimators.Numerical results demonstrate that the proposed method performs well under fnite samples while ignoring informatively censoring structures leads to biased results.The validation and discussion of cure structures and dependent structures in Alzheimer’s disease research further highlight the broad applicability of the proposed method.3.Semi-parametric analysis of interval-censored data with missing at random covariates.It is well known that missing data is a signifcant problem in current research,and if this issue is not addressed correctly during analysis,the results will be less efective and reliable.The most common methods for addressing missing data are complete-case analysis and inverse probability weighting.It is noteworthy,however,that both approaches have signifcant shortcomings,as they fail to account for individuals within the cohort who experience partial covariate missingness during the modeling of failure times,which can result in a signifcant loss of estimation accuracy.In order to address this issue,we construct multiple auxiliary models based on the classic inverse probability weighting method,to maximize the utilization of information implicit in individuals with only partial covariates.As a result,we propose an efective and easily implementable algorithm to handle the missing covariates in interval-censored data,signifcantly increasing the effciency of estimation.The numerical results indicate that the proposed method performs consistently and effciently,with notable improvements in estimation accuracy and effciency over existing methods.The validity of this method is illustrated through case studies in an Alzheimer’s disease study.4.Semi-parametric analysis of bivariate interval-censored data under casecohort studies.In epidemiological research and clinical trials,where cost considerations play a signifcant role in the design of the study,it is common for covariates to be missing by design.The case-cohort study is a classical design methodology in this feld.In a case-cohort study,we focus on the bivariate interval-censored data and investigate the dependence structure within the bivariate data utilizing a Gamma frailty term.Missing information is handled using the classical inverse probability weighting method.We establish an estimation model and asymptotic theory for estimated covariate efects using the sieve maximum likelihood approach and Bernstein polynomials to approximate the baseline cumulative hazard function.It is demonstrated in numerical simulations that the method performs well when applied to fnite samples,and that ignoring dependence in binary interval-censored data will result in signifcant estimation bias.The application of the proposed method in practical situations can be demonstrated by further case studies analyzing the real data from an age-related eye disease study.5.Semi-parametric inference of competing risk interval-censored data with all-or-nothing compliance.Subjects may experience multiple events that compete with each other,in which the occurrence of one type of outcome hinders another.Due to the fundamental change in the data structure,existing methods for analyzing competing risk interval-censored data become inefective.Moreover,it is widely accepted that randomized controlled trials are the gold standard in medical research in light of the urgent need to evaluate treatment efectiveness.Unfortunately,it is nearly impossible to conduct such trials due to practical constraints,requiring researchers to rely on observational studies.Observational studies are frequently plagued by confounding factors that lead to serious doubts about the conclusions from the traditional methods.To the best of our knowledge,there are no existing methods for dealing with this issue.To address it,we employ an instrumental variable approach to divide the study population into four potential compliance subgroups and,assuming that the cumulative incidence function follows a semiparametric transformation model,determine the likelihood function that corresponds to these subgroups.Using the sieve maximum likelihood method,we establish the asymptotic properties of the estimators and provide a more intuitive class of causal functions.It has been demonstrated through numerical simulations and case studies that the proposed semiparametric causal inference method is highly efective in estimating causal relationships under fnite samples and that neglecting any factor in this complex data structure will lead to an inability to estimate causal relationships.