The competing risks Cox model with auxiliary case covariates under weaker missing-at-random cause of failure

Weighting estimation in the cause-specific Cox regression with partially missing causes of failure

Complex diseases are often analyzed using disease subtypes classified by multiple biomarkers to study pathogenic heterogeneity. In such molecular pathological epidemiology research, we consider a weighted Cox proportional hazard model to evaluate the effect of exposures on various disease subtypes under competing-risk settings in the presence of partially or completely missing biomarkers. The asymptotic properties of the inverse and augmented inverse probability-weighted estimating equation methods are studied with a general pattern of missing data. Simulation studies have been conducted to demonstrate the double robustness of the estimators. For illustration, we applied this method to examine the association between pack-years of smoking before the age of 30 and the incidence of colorectal cancer subtypes defined by a combination of four tumor molecular biomarkers (statuses of microsatellite instability, CpG island methylator phenotype, BRAF mutation, and KRAS mutation) in the Nurses' Health Study cohort.

Comparison between inverse-probability weighting and multiple imputation in Cox model with missing failure subtype

Identifying and distinguishing risk factors for heterogeneous disease subtypes has been of great interest. However, missingness in disease subtypes is a common problem in those data analyses. Several methods have been proposed to deal with the missing data, including complete-case analysis, inverse-probability weighting, and multiple imputation. Although extant literature has compared these methods in missing problems, none has focused on the competing risk setting. In this paper, we discuss the assumptions required when complete-case analysis, inverse-probability weighting, and multiple imputation are used to deal with the missing failure subtype problem, focusing on how to implement these methods under various realistic scenarios in competing risk settings. Besides, we compare these three methods regarding their biases, efficiency, and robustness to model misspecifications using simulation studies. Our results show that complete-case analysis can be seriously biased when the missing completely at random assumption does not hold. Inverse-probability weighting and multiple imputation estimators are valid when we correctly specify the corresponding models for missingness and for imputation, and multiple imputation typically shows higher efficiency than inverse-probability weighting. However, in real-world studies, building imputation models for the missing subtypes can be more challenging than building missingness models. In that case, inverse-probability weighting could be preferred for its easy usage. We also propose two automated model selection procedures and demonstrate their usage in a study of the association between smoking and colorectal cancer subtypes in the Nurses' Health Study and Health Professional Follow-Up Study.

Semiparametric marginal regression for clustered competing risks data with missing cause of failure

Clustered competing risks data are commonly encountered in multicenter studies. The analysis of such data is often complicated due to informative cluster size (ICS), a situation where the outcomes under study are associated with the size of the cluster. In addition, the cause of failure is frequently incompletely observed in real-world settings. To the best of our knowledge, there is no methodology for population-averaged analysis with clustered competing risks data with an ICS and missing causes of failure. To address this problem, we consider the semiparametric marginal proportional cause-specific hazards model and propose a maximum partial pseudolikelihood estimator under a missing at random assumption. To make the latter assumption more plausible in practice, we allow for auxiliary variables that may be related to the probability of missingness. The proposed method does not impose assumptions regarding the within-cluster dependence and allows for ICS. The asymptotic properties of the proposed estimators for both regression coefficients and infinite-dimensional parameters, such as the marginal cumulative incidence functions, are rigorously established. Simulation studies show that the proposed method performs well and that methods that ignore the within-cluster dependence and the ICS lead to invalid inferences. The proposed method is applied to competing risks data from a large multicenter HIV study in sub-Saharan Africa where a significant portion of causes of failure is missing.

Reflection on modern methods: causal inference considerations for heterogeneous disease etiology

Molecular pathological epidemiology research provides information about pathogenic mechanisms. A common study goal is to evaluate whether the effects of risk factors on disease incidence vary between different disease subtypes. A popular approach to carrying out this type of research is to implement a multinomial regression in which each of the non-zero values corresponds to a bona fide disease subtype. Then, heterogeneity in the exposure effects across subtypes is examined by comparing the coefficients of the exposure between the different subtypes. In this paper, we explain why this common method potentially cannot recover causal effects, even when all confounders are measured, due to a particular type of selection bias. This bias can be explained by recognizing that the multinomial regression is equivalent to a series of logistic regressions; each compares cases of a certain subtype to the controls. We further explain how this bias arises using directed acyclic graphs and we demonstrate the potential magnitude of the bias by analysis of a hypothetical data set and by a simulation study.

The microbiome, genetics, and gastrointestinal neoplasms: the evolving field of molecular pathological epidemiology to analyze the tumor-immune-microbiome interaction

Metagenomic studies using next-generation sequencing technologies have revealed rich human intestinal microbiome, which likely influence host immunity and health conditions including cancer. Evidence indicates a biological link between altered microbiome and cancers in the digestive system. Escherichia coli and Bacteroides fragilis have been found to be enriched in colorectal mucosal tissues from patients with familial adenomatous polyposis that is caused by germline APC mutations. In addition, recent studies have found enrichment of certain oral bacteria, viruses, and fungi in tumor tissue and fecal specimens from patients with gastrointestinal cancer. An integrative approach is required to elucidate the role of microorganisms in the pathogenic process of gastrointestinal cancers, which develop through the accumulation of somatic genetic and epigenetic alterations in neoplastic cells, influenced by host genetic variations, immunity, microbiome, and environmental exposures. The transdisciplinary field of molecular pathological epidemiology (MPE) offers research frameworks to link germline genetics and environmental factors (including diet, lifestyle, and pharmacological factors) to pathologic phenotypes. The integration of microbiology into the MPE model (microbiology-MPE) can contribute to better understanding of the interactive role of environment, tumor cells, immune cells, and microbiome in various diseases. We review major clinical and experimental studies on the microbiome, and describe emerging evidence from the microbiology-MPE research in gastrointestinal cancers. Together with basic experimental research, this new research paradigm can help us to develop new prevention and treatment strategies for gastrointestinal cancers through targeting of the microbiome.

Semiparametric regression and risk prediction with competing risks data under missing cause of failure

The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial.

Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes

This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.

Causal inference in the face of competing events

Purpose of review

Epidemiologists frequently must handle competing events, which prevent the event of interest from occurring. We review considerations for handling competing events when interpreting results causally.

Recent findings

When interpreting statistical associations as causal effects, we recommend following a causal inference "roadmap" as one would in an analysis without competing events. There are, however, special considerations to be made for competing events when choosing the causal estimand that best answers the question of interest, selecting the statistical estimand (e.g. the cause-specific or subdistribution) that will target that causal estimand, and assessing whether causal identification conditions (e.g., conditional exchangeability, positivity, and consistency) have been sufficiently met.

Summary

When doing causal inference in the competing events setting, it is critical to first ascertain the relevant question and the causal estimand that best answers it, with the choice often being between estimands that do and do not eliminate competing events.

Integration of microbiology, molecular pathology, and epidemiology: a new paradigm to explore the pathogenesis of microbiome-driven neoplasms

Molecular pathological epidemiology (MPE) is an integrative transdisciplinary field that addresses heterogeneous effects of exogenous and endogenous factors (collectively termed 'exposures'), including microorganisms, on disease occurrence and consequences, utilising molecular pathological signatures of the disease. In parallel with the paradigm of precision medicine, findings from MPE research can provide aetiological insights into tailored strategies of disease prevention and treatment. Due to the availability of molecular pathological tests on tumours, the MPE approach has been utilised predominantly in research on cancers including breast, lung, prostate, and colorectal carcinomas. Mounting evidence indicates that the microbiome (inclusive of viruses, bacteria, fungi, and parasites) plays an important role in a variety of human diseases including neoplasms. An alteration of the microbiome may be not only a cause of neoplasia but also an informative biomarker that indicates or mediates the association of an epidemiological exposure with health conditions and outcomes. To adequately educate and train investigators in this emerging area, we herein propose the integration of microbiology into the MPE model (termed 'microbiology-MPE'), which could improve our understanding of the complex interactions of environment, tumour cells, the immune system, and microbes in the tumour microenvironment during the carcinogenic process. Using this approach, we can examine how lifestyle factors, dietary patterns, medications, environmental exposures, and germline genetics influence cancer development and progression through impacting the microbial communities in the human body. Further integration of other disciplines (e.g. pharmacology, immunology, nutrition) into microbiology-MPE would expand this developing research frontier. With the advent of high-throughput next-generation sequencing technologies, researchers now have increasing access to large-scale metagenomics as well as other omics data (e.g. genomics, epigenomics, proteomics, and metabolomics) in population-based research. The integrative field of microbiology-MPE will open new opportunities for personalised medicine and public health. Copyright © 2019 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.

Insights into Pathogenic Interactions Among Environment, Host, and Tumor at the Crossroads of Molecular Pathology and Epidemiology

Evidence indicates that diet, nutrition, lifestyle, the environment, the microbiome, and other exogenous factors have pathogenic roles and also influence the genome, epigenome, transcriptome, proteome, and metabolome of tumor and nonneoplastic cells, including immune cells. With the need for big-data research, pathology must transform to integrate data science fields, including epidemiology, biostatistics, and bioinformatics. The research framework of molecular pathological epidemiology (MPE) demonstrates the strengths of such an interdisciplinary integration, having been used to study breast, lung, prostate, and colorectal cancers. The MPE research paradigm not only can provide novel insights into interactions among environment, tumor, and host but also opens new research frontiers. New developments-such as computational digital pathology, systems biology, artificial intelligence, and in vivo pathology technologies-will further transform pathology and MPE. Although it is necessary to address the rarity of transdisciplinary education and training programs, MPE provides an exemplary model of integrative scientific approaches and contributes to advancements in precision medicine, therapy, and prevention.

Integrative analysis of exogenous, endogenous, tumour and immune factors for precision medicine

Immunotherapy strategies targeting immune checkpoints such as the CTLA4 and CD274 (programmed cell death 1 ligand 1, PD-L1)/PDCD1 (programmed cell death 1, PD-1) T-cell coreceptor pathways are revolutionising oncology. The approval of pembrolizumab use for solid tumours with high-level microsatellite instability or mismatch repair deficiency by the US Food and Drug Administration highlights promise of precision immuno-oncology. However, despite evidence indicating influences of exogenous and endogenous factors such as diet, nutrients, alcohol, smoking, obesity, lifestyle, environmental exposures and microbiome on tumour-immune interactions, integrative analyses of those factors and immunity lag behind. Immune cell analyses in the tumour microenvironment have not adequately been integrated into large-scale studies. Addressing this gap, the transdisciplinary field of molecular pathological epidemiology (MPE) offers research frameworks to integrate tumour immunology into population health sciences, and link the exposures and germline genetics (eg, HLA genotypes) to tumour and immune characteristics. Multilevel research using bioinformatics, in vivo pathology and omics (genomics, epigenomics, transcriptomics, proteomics and metabolomics) technologies is possible with use of tissue, peripheral blood circulating cells, cell-free plasma, stool, sputum, urine and other body fluids. This immunology-MPE model can synergise with experimental immunology, microbiology and systems biology. GI neoplasms represent exemplary diseases for the immunology-MPE model, given rich microbiota and immune tissues of intestines, and the well-established carcinogenic role of intestinal inflammation. Proof-of-principle studies on colorectal cancer provided insights into immunomodulating effects of aspirin, vitamin D, inflammatory diets and omega-3 polyunsaturated fatty acids. The integrated immunology-MPE model can contribute to better understanding of environment-tumour-immune interactions, and effective immunoprevention and immunotherapy strategies for precision medicine.

Missingness in the Setting of Competing Risks: from missing values to missing potential outcomes

Purpose of review

The setting of competing risks in which there is an event that precludes the event of interest from occurring is prevalent in epidemiological research. Unless studying all-cause mortality, any study following up individuals is subject to having a competing risk should individuals die during time period that the study covers. While there are prior papers discussing the need for competing risk methods in epidemiologic research, we are not aware of any review that discusses issues of missing data in a competing risk setting.

Recent Findings

We provide an overview of causal inference in competing risks as potential outcomes are missing, provide some strategies in dealing with missing (or misclassified) event type, and missing covariate data in competing risks. The strategies presented are specifically focused on those that may easily be implemented in standard statistical packages. There is ongoing work in terms of causal analyses, dealing with missing event type information, and missing covariate values specific to competing risk analyses.

Summary

Competing events are common in epidemiologic research. While there has been a focus on why one should conduct a proper competing risk analysis, a perhaps unrecognized issue is in terms of missingness. Strategies exist to minimize the impact of missingness in analyses of competing risks.

Utility of inverse probability weighting in molecular pathological epidemiology

As one of causal inference methodologies, the inverse probability weighting (IPW) method has been utilized to address confounding and account for missing data when subjects with missing data cannot be included in a primary analysis. The transdisciplinary field of molecular pathological epidemiology (MPE) integrates molecular pathological and epidemiological methods, and takes advantages of improved understanding of pathogenesis to generate stronger biological evidence of causality and optimize strategies for precision medicine and prevention. Disease subtyping based on biomarker analysis of biospecimens is essential in MPE research. However, there are nearly always cases that lack subtype information due to the unavailability or insufficiency of biospecimens. To address this missing subtype data issue, we incorporated inverse probability weights into Cox proportional cause-specific hazards regression. The weight was inverse of the probability of biomarker data availability estimated based on a model for biomarker data availability status. The strategy was illustrated in two example studies; each assessed alcohol intake or family history of colorectal cancer in relation to the risk of developing colorectal carcinoma subtypes classified by tumor microsatellite instability (MSI) status, using a prospective cohort study, the Nurses' Health Study. Logistic regression was used to estimate the probability of MSI data availability for each cancer case with covariates of clinical features and family history of colorectal cancer. This application of IPW can reduce selection bias caused by nonrandom variation in biospecimen data availability. The integration of causal inference methods into the MPE approach will likely have substantial potentials to advance the field of epidemiology.