Characterizing quantile-varying covariate effects under the accelerated failure time model.

An important task in survival analysis is choosing a structure for the relationship between covariates of interest and the time-to-event outcome. For example, the accelerated failure time (AFT) model structures each covariate effect as a constant multiplicative shift in the outcome distribution across all survival quantiles. Though parsimonious, this structure cannot detect or capture effects that differ across quantiles of the distribution, a limitation that is analogous to only permitting proportional hazards in the Cox model. To address this, we propose a general framework for quantile-varying multiplicative effects under the AFT model. Specifically, we embed flexible regression structures within the AFT model and derive a novel formula for interpretable effects on the quantile scale. A regression standardization scheme based on the g-formula is proposed to enable the estimation of both covariate-conditional and marginal effects for an exposure of interest. We implement a user-friendly Bayesian approach for the estimation and quantification of uncertainty while accounting for left truncation and complex censoring. We emphasize the intuitive interpretation of this model through numerical and graphical tools and illustrate its performance through simulation and application to a study of Alzheimer's disease and dementia.

Choice of baseline hazards in joint modeling of longitudinal and time-to-event cancer survival data.

Longitudinal time-to-event analysis is a statistical method to analyze data where covariates are measured repeatedly. In survival studies, the risk for an event is estimated using Cox-proportional hazard model or extended Cox-model for exogenous time-dependent covariates. However, these models are inappropriate for endogenous time-dependent covariates like longitudinally measured biomarkers, Carcinoembryonic Antigen (CEA). Joint models that can simultaneously model the longitudinal covariates and time-to-event data have been proposed as an alternative. The present study highlights the importance of choosing the baseline hazards to get more accurate risk estimation. The study used colon cancer patient data to illustrate and compare four different joint models which differs based on the choice of baseline hazards [piecewise-constant Gauss-Hermite (GH), piecewise-constant pseudo-adaptive GH, Weibull Accelerated Failure time model with GH & B-spline GH]. We conducted simulation study to assess the model consistency with varying sample size (N = 100, 250, 500) and censoring (20 %, 50 %, 70 %) proportions. In colon cancer patient data, based on Akaike information criteria (AIC) and Bayesian information criteria (BIC), piecewise-constant pseudo-adaptive GH was found to be the best fitted model. Despite differences in model fit, the hazards obtained from the four models were similar. The study identified composite stage as a prognostic factor for time-to-event and the longitudinal outcome, CEA as a dynamic predictor for overall survival in colon cancer patients. Based on the simulation study Piecewise-PH-aGH was found to be the best model with least AIC and BIC values, and highest coverage probability(CP). While the Bias, and RMSE for all the models showed a competitive performance. However, Piecewise-PH-aGH has shown least bias and RMSE in most of the combinations and has taken the shortest computation time, which shows its computational efficiency. This study is the first of its kind to discuss on the choice of baseline hazards.

Reply to "Matters arising: cost-effectiveness of first-line immunotherapy combinations with or without chemotherapy for advanced non-small cell lung cancer: a modelling approach".

In this article, we read with great attention the correspondence by Bullement et al., regarding our published study on cost-effectiveness of first-line immunotherapy combinations with or without chemotherapy for advanced non-small cell lung cancer. We referred to a few the most important comments from Bullement et al. in our opinion, including proportional hazard (PH) assumption, accelerated failure time (AFT) model, and health utility, and made some explanations.

A Network-Constrain Weibull AFT Model for Biomarkers Discovery.

We propose AFTNet, a novel network-constraint survival analysis method based on the Weibull accelerated failure time (AFT) model solved by a penalized likelihood approach for variable selection and estimation. When using the log-linear representation, the inference problem becomes a structured sparse regression problem for which we explicitly incorporate the correlation patterns among predictors using a double penalty that promotes both sparsity and grouping effect. Moreover, we establish the theoretical consistency for the AFTNet estimator and present an efficient iterative computational algorithm based on the proximal gradient descent method. Finally, we evaluate AFTNet performance both on synthetic and real data examples.

The role of body mass index at diagnosis of colorectal cancer on Black-White disparities in survival: a density regression mediation approach.

The study of racial/ethnic inequalities in health is important to reduce the uneven burden of disease. In the case of colorectal cancer (CRC), disparities in survival among non-Hispanic Whites and Blacks are well documented, and mechanisms leading to these disparities need to be studied formally. It has also been established that body mass index (BMI) is a risk factor for developing CRC, and recent literature shows BMI at diagnosis of CRC is associated with survival. Since BMI varies by racial/ethnic group, a question that arises is whether differences in BMI are partially responsible for observed racial/ethnic disparities in survival for CRC patients. This article presents new methodology to quantify the impact of the hypothetical intervention that matches the BMI distribution in the Black population to a potentially complex distributional form observed in the White population on racial/ethnic disparities in survival. Our density mediation approach can be utilized to estimate natural direct and indirect effects in the general causal mediation setting under stronger assumptions. We perform a simulation study that shows our proposed Bayesian density regression approach performs as well as or better than current methodology allowing for a shift in the mean of the distribution only, and that standard practice of categorizing BMI leads to large biases when BMI is a mediator variable. When applied to motivating data from the Cancer Care Outcomes Research and Surveillance (CanCORS) Consortium, our approach suggests the proposed intervention is potentially beneficial for elderly and low-income Black patients, yet harmful for young or high-income Black populations.

Maximum approximate likelihood estimation in accelerated failure time model for interval-censored data.

The approximate Bernstein polynomial model, a mixture of beta distributions, is applied to obtain maximum likelihood estimates of the regression coefficients, the baseline density and the survival functions in an accelerated failure time model based on interval censored data including current status data. The estimators of the regression coefficients and the underlying baseline density function are shown to be consistent with almost parametric rates of convergence under some conditions for uncensored and/or interval censored data. Simulation shows that the proposed method is better than its competitors. The proposed method is illustrated by fitting the Breast Cosmetic and the HIV infection time data using the accelerated failure time model.

Gaussian process regression for survival time prediction with genome-wide gene expression.

Predicting the survival time of a cancer patient based on his/her genome-wide gene expression remains a challenging problem. For certain types of cancer, the effects of gene expression on survival are both weak and abundant, so identifying non-zero effects with reasonable accuracy is difficult. As an alternative to methods that use variable selection, we propose a Gaussian process accelerated failure time model to predict survival time using genome-wide or pathway-wide gene expression data. Using a Monte Carlo expectation-maximization algorithm, we jointly impute censored log-survival time and estimate model parameters. We demonstrate the performance of our method and its advantage over existing methods in both simulations and real data analysis. The real data that we analyze were collected from 513 patients with kidney renal clear cell carcinoma and include survival time, demographic/clinical variables, and expression of more than 20 000 genes. In addition to the right-censored survival time, our method can also accommodate left-censored or interval-censored outcomes; and it provides a natural way to combine multiple types of high-dimensional -omics data. An R package implementing our method is available in the Supplementary material available at Biostatistics online.

Semiparametric analysis of a generalized linear model with multiple covariates subject to detection limits.

Studies on the health effects of environmental mixtures face the challenge of limit of detection (LOD) in multiple correlated exposure measurements. Conventional approaches to deal with covariates subject to LOD, including complete-case analysis, substitution methods, and parametric modeling of covariate distribution, are feasible but may result in efficiency loss or bias. With a single covariate subject to LOD, a flexible semiparametric accelerated failure time (AFT) model to accommodate censored measurements has been proposed. We generalize this approach by considering a multivariate AFT model for the multiple correlated covariates subject to LOD and a generalized linear model for the outcome. A two-stage procedure based on semiparametric pseudo-likelihood is proposed for estimating the effects of these covariates on health outcome. Consistency and asymptotic normality of the estimators are derived for an arbitrary fixed dimension of covariates. Simulations studies demonstrate good large sample performance of the proposed methods vs conventional methods in realistic scenarios. We illustrate the practical utility of the proposed method with the LIFECODES birth cohort data, where we compare our approach to existing approaches in an analysis of multiple urinary trace metals in association with oxidative stress in pregnant women.

Scalable algorithms for semiparametric accelerated failure time models in high dimensions.

Semiparametric accelerated failure time (AFT) models are a useful alternative to Cox proportional hazards models, especially when the assumption of constant hazard ratios is untenable. However, rank-based criteria for fitting AFT models are often nondifferentiable, which poses a computational challenge in high-dimensional settings. In this article, we propose a new alternating direction method of multipliers algorithm for fitting semiparametric AFT models by minimizing a penalized rank-based loss function. Our algorithm scales well in both the number of subjects and number of predictors, and can easily accommodate a wide range of popular penalties. To improve the selection of tuning parameters, we propose a new criterion which avoids some common problems in cross-validation with censored responses. Through extensive simulation studies, we show that our algorithm and software is much faster than existing methods (which can only be applied to special cases), and we show that estimators which minimize a penalized rank-based criterion often outperform alternative estimators which minimize penalized weighted least squares criteria. Application to nine cancer datasets further demonstrates that rank-based estimators of semiparametric AFT models are competitive with estimators assuming proportional hazards in high-dimensional settings, whereas weighted least squares estimators are often not. A software package implementing the algorithm, along with a set of auxiliary functions, is available for download at github.com/ajmolstad/penAFT.

Examining Risk Factors Accelerating Time-to-Chronic Obstructive Pulmonary Disease (COPD) Diagnosis among Asthma Patients.

Asthma patients may have an increased risk for diagnosis of chronic obstructive pulmonary disease (COPD). However, risk factors accelerating time-to-COPD diagnosis are unclear. This study aims to estimate risk factors associated with the incidence of COPD diagnosis in asthma patients. Canada's Population Data BC (PopData BC) was used to identify asthma patients without prior COPD diagnosis between January 1, 1998, to December 31, 1999. Patients were assessed for time-to-incidence of COPD diagnosis from January 1, 2000, to December 31, 2018. The study estimated the effects of several risk factors in predicting the incidence of COPD in asthma patients during the 18-year follow-up period. Patient factors such as Medication Adherence (MA) were assessed by the proportion of days covered (PDC) and the medication possession ratio (MPR). The log-logistic mixed-effects accelerated failure time model was used to estimate the adjusted failure time ratios (aFTR) and 95% Confidence Interval (95% CI) for factors predicting time-to-COPD diagnosis among asthma patients. We identified 68,211 asthma patients with a mean age of 48.2 years included in the analysis. Risk factors accelerating time-to-COPD diagnosis included: male sex (aFTR: 0.62, 95% CI:0.56-0.68), older adults (age > 40 years) [aFTR: 0.03, 95% CI: 0.02-0.04], history of tobacco smoking (aFTR: 0.29, 95% CI: 0.13-0.68), asthma exacerbations (aFTR: 0.81, 95%CI: 0.70, 0.94), frequent emergency admissions (aFTR:0.21, 95% CI: 0.17-0.25), longer hospital stay (aFTR:0.07, 95% CI: 0.06-0.09), patients with increased burden of comorbidities (aFTR:0.28, 95% CI: 0.22-0.34), obese male sex (aFTR:0.38, 95% CI: 0.15-0.99), SABA overuse (aFTR: 0.61, 95% CI: 0.44-0.84), moderate (aFTR:0.23, 95% CI: 0.21-0.26), and severe asthma (aFTR:0.10, 95% CI: 0.08-0.12). After adjustment, MA ≥0.80 was significantly associated with 83% delayed time-to-COPD diagnosis [i.e. aFTR =1.83, 95%CI: 1.54-2.17 for PDC]. However, asthma severity significantly modifies the effect of MA independent of tobacco smoking history. The targeted intervention aimed to mitigate early diagnosis of COPD may prioritize enhancing medication adherence among asthma patients to prevent frequent exacerbation during follow-up.

Detection of multiple change points in a Weibull accelerated failure time model using sequential testing.

With improvements to cancer diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation. We propose a sequential testing approach for detecting multiple change points in the Weibull accelerated failure time model, since this is sufficiently flexible to accommodate increasing, decreasing, or constant hazard rates and is also the only continuous distribution for which the accelerated failure time model can be reparameterized as a proportional hazards model. Our sequential testing procedure does not require the number of change points to be known; this information is instead inferred from the data. We conduct a simulation study to show that the method accurately detects change points and estimates the model. The numerical results along with real data applications demonstrate that our proposed method can detect change points in the hazard rate.

Spline-based accelerated failure time model.

The accelerated failure time (AFT) model has been suggested as an alternative to the Cox proportional hazards model. However, a parametric AFT model requires the specification of an appropriate distribution for the event time, which is often difficult to identify in real-life studies and may limit applications. A semiparametric AFT model was developed by Komárek et al based on smoothed error distribution that does not require such specification. In this article, we develop a spline-based AFT model that also does not require specification of the parametric family of event time distribution. The baseline hazard function is modeled by regression B-splines, allowing for the estimation of a variety of smooth and flexible shapes. In comprehensive simulations, we validate the performance of our approach and compare with the results from parametric AFT models and the approach of Komárek. Both the proposed spline-based AFT model and the approach of Komárek provided unbiased estimates of covariate effects and survival curves for a variety of scenarios in which the event time followed different distributions, including both simple and complex cases. Spline-based estimates of the baseline hazard showed also a satisfactory numerical stability. As expected, the baseline hazard and survival probabilities estimated by the misspecified parametric AFT models deviated from the truth. We illustrated the application of the proposed model in a study of colon cancer.

Using generalized linear models to implement g-estimation for survival data with time-varying confounding.

Using data from observational studies to estimate the causal effect of a time-varying exposure, repeatedly measured over time, on an outcome of interest requires careful adjustment for confounding. Standard regression adjustment for observed time-varying confounders is unsuitable, as it can eliminate part of the causal effect and induce bias. Inverse probability weighting, g-computation, and g-estimation have been proposed as being more suitable methods. G-estimation has some advantages over the other two methods, but until recently there has been a lack of flexible g-estimation methods for a survival time outcome. The recently proposed Structural Nested Cumulative Survival Time Model (SNCSTM) is such a method. Efficient estimation of the parameters of this model required bespoke software. In this article we show how the SNCSTM can be fitted efficiently via g-estimation using standard software for fitting generalised linear models. The ability to implement g-estimation for a survival outcome using standard statistical software greatly increases the potential uptake of this method. We illustrate the use of this method of fitting the SNCSTM by reanalyzing data from the UK Cystic Fibrosis Registry, and provide example R code to facilitate the use of this approach by other researchers.

Accelerated failure time model for data from outcome-dependent sampling.

Outcome-dependent sampling designs such as the case-control or case-cohort design are widely used in epidemiological studies for their outstanding cost-effectiveness. In this article, we propose and develop a smoothed weighted Gehan estimating equation approach for inference in an accelerated failure time model under a general failure time outcome-dependent sampling scheme. The proposed estimating equation is continuously differentiable and can be solved by the standard numerical methods. In addition to developing asymptotic properties of the proposed estimator, we also propose and investigate a new optimal power-based subsamples allocation criteria in the proposed design by maximizing the power function of a significant test. Simulation results show that the proposed estimator is more efficient than other existing competing estimators and the optimal power-based subsamples allocation will provide an ODS design that yield improved power for the test of exposure effect. We illustrate the proposed method with a data set from the Norwegian Mother and Child Cohort Study to evaluate the relationship between exposure to perfluoroalkyl substances and women's subfecundity.

Adjusting for time-varying confounders in survival analysis using structural nested cumulative survival time models.

Accounting for time-varying confounding when assessing the causal effects of time-varying exposures on survival time is challenging. Standard survival methods that incorporate time-varying confounders as covariates generally yield biased effect estimates. Estimators using weighting by inverse probability of exposure can be unstable when confounders are highly predictive of exposure or the exposure is continuous. Structural nested accelerated failure time models (AFTMs) require artificial recensoring, which can cause estimation difficulties. Here, we introduce the structural nested cumulative survival time model (SNCSTM). This model assumes that intervening to set exposure at time t to zero has an additive effect on the subsequent conditional hazard given exposure and confounder histories when all subsequent exposures have already been set to zero. We show how to fit it using standard software for generalized linear models and describe two more efficient, double robust, closed-form estimators. All three estimators avoid the artificial recensoring of AFTMs and the instability of estimators that use weighting by the inverse probability of exposure. We examine the performance of our estimators using a simulation study and illustrate their use on data from the UK Cystic Fibrosis Registry. The SNCSTM is compared with a recently proposed structural nested cumulative failure time model, and several advantages of the former are identified.

Censored linear regression in the presence or absence of auxiliary survival information.

There has been a rising interest in better exploiting auxiliary summary information from large databases in the analysis of smaller-scale studies that collect more comprehensive patient-level information. The purpose of this paper is twofold: first, we propose a novel approach to synthesize information from both the aggregate summary statistics and the individual-level data in censored linear regression. We show that the auxiliary information amounts to a system of nonsmooth estimating equations and thus can be combined with the conventional weighted log-rank estimating equations by using the generalized method of moments (GMM) approach. The proposed methodology can be further extended to account for the potential inconsistency in information from different sources. Second, in the absence of auxiliary information, we propose to improve estimation efficiency by combining the overidentified weighted log-rank estimating equations with different weight functions via the GMM framework. To deal with the nonsmooth GMM-type objective functions, we develop an asymptotics-guided algorithm for parameter and variance estimation. We establish the asymptotic normality of the proposed GMM-type estimators. Simulation studies show that the proposed estimators can yield substantial efficiency gain over the conventional weighted log-rank estimators. The proposed methods are applied to a pancreatic cancer study for illustration.

Generalized scale-change models for recurrent event processes under informative censoring.

Two major challenges arise in regression analyses of recurrent event data: first, popular existing models, such as the Cox proportional rates model, may not fully capture the covariate effects on the underlying recurrent event process; second, the censoring time remains informative about the risk of experiencing recurrent events after accounting for covariates. We tackle both challenges by a general class of semiparametric scale-change models that allow a scale-change covariate effect as well as a multiplicative covariate effect. The proposed model is flexible and includes several existing models as special cases, such as the popular proportional rates model, the accelerated mean model, and the accelerated rate model. Moreover, it accommodates informative censoring through a subject-level latent frailty whose distribution is left unspecified. A robust estimation procedure which requires neither a parametric assumption on the distribution of the frailty nor a Poisson assumption on the recurrent event process is proposed to estimate the model parameters. The asymptotic properties of the resulting estimator are established, with the asymptotic variance estimated from a novel resampling approach. As a byproduct, the structure of the model provides a model selection approach among the submodels via hypothesis testing of model parameters. Numerical studies show that the proposed estimator and the model selection procedure perform well under both noninformative and informative censoring scenarios. The methods are applied to data from two transplant cohorts to study the risk of infections after transplantation.

Analysis of clustered failure time data with cure fraction using copula.

Clustered survival data in the presence of cure has received increasing attention. In this paper, we consider a semiparametric mixture cure model which incorporates a logistic regression model for the cure fraction and a semiparametric regression model for the failure time. We utilize Archimedean copula (AC) models to assess the strength of association for both susceptibility and failure times between susceptible individuals in the same cluster. Instead of using the full likelihood approach, we consider a composite likelihood function and a two-stage estimation procedure for both marginal and association parameters. A Jackknife procedure that takes out one cluster at a time is proposed for the variance estimation of the estimators. Akaike information criterion is applied to select the best model among ACs. Simulation studies are performed to validate our estimating procedures, and two real data sets are analyzed to demonstrate the practical use of our proposed method.

Mediation analysis in a case-control study when the mediator is a censored variable.

Mediation analysis is an approach for assessing the direct and indirect effects of an initial variable on an outcome through a mediator. In practice, mediation models can involve a censored mediator (eg, a woman's age at menopause). The current research for mediation analysis with a censored mediator focuses on scenarios where outcomes are continuous. However, the outcomes can be binary (eg, type 2 diabetes). Another challenge when analyzing such a mediation model is to use data from a case-control study, which results in biased estimations for the initial variable-mediator association if a standard approach is directly applied. In this study, we propose an approach (denoted as MAC-CC) to analyze the mediation model with a censored mediator given data from a case-control study, based on the semiparametric accelerated failure time model along with a pseudo-likelihood function. We adapted the measures for assessing the indirect and direct effects using counterfactual definitions. We conducted simulation studies to investigate the performance of MAC-CC and compared it to those of the naïve approach and the complete-case approach. MAC-CC accurately estimates the coefficients of different paths, the indirect effects, and the proportions of the total effects mediated. We applied the proposed and existing approaches to the mediation study of genetic variants, a woman's age at menopause, and type 2 diabetes based on a case-control study of type 2 diabetes. Our results indicate that there is no mediating effect from the age at menopause on the association between the genetic variants and type 2 diabetes.

SEMIPARAMETRIC REGRESSION MODEL FOR RECURRENT BACTERIAL INFECTIONS AFTER HEMATOPOIETIC STEM CELL TRANSPLANTATION.

Patients who undergo hematopoietic stem cell transplantation (HSCT) often experience multiple bacterial infections during the early post-transplant period. In this article, we consider a semiparametric regression model that correlates patient- and transplant-related risk factors with inter-infection gap times. Existing regression methods for recurrent gap times are not directly applicable to study post-transplant infection because the initiating event (transplant) is different than the recurrent events of interest (post-transplant infections); as a result, the time from transplant to the first infection and the time elapsed between consecutive infections have distinct biological meanings and hence follow different distributions. Moreover, risk factors may have different effects on these two types of gap times. We propose a semiparametric estimation procedure to evaluate the covariate effects on time from transplant to thefirst infection and on gap times between consecutive infections simultaneously. The proposed estimator accounts for dependent censoring induced by within-subject correlation among recurrent gap times and length bias in the last censored gap time due to intercept sampling. We study the finite sample properties through simulations and present an application of the proposed method to the post-HSCT bacterial infection data collected at the University of Minnesota.