On the choice of time scales in competing risks predictions

In the standard analysis of competing risks data, proportional hazards models are fit to the cause-specific hazard functions for all causes on the same time scale. These regression analyses are the foundation for predictions of cause-specific cumulative incidence functions based on combining the estimated cause-specific hazard functions. However, in predictions arising from disease registries, where only subjects with disease enter the database, disease-related mortality may be more naturally modeled on the time since diagnosis time scale while death from other causes may be more naturally modeled on the age time scale. The single time scale methodology may be biased if an incorrect time scale is employed for one of the causes and an alternative methodology is not available. We propose inferences for the cumulative incidence function in which regression models for the cause-specific hazard functions may be specified on different time scales. Using the disease registry data, the analysis of other cause mortality on the age scale requires left truncating the event time at the age of disease diagnosis, complicating the analysis. In addition, standard Martingale theory is not applicable when combining regression models on different time scales. We establish that the covariate conditional predictions are consistent and asymptotically normal using empirical process techniques and propose consistent variance estimators for constructing confidence intervals. Simulation studies show that the proposed two time scales method performs well, outperforming the single time-scale predictions when the time scale is misspecified. The methods are illustrated with stage III colon cancer data obtained from the Surveillance, Epidemiology, and End Results program of National Cancer Institute.

Joint modeling of longitudinal, recurrent events and failure time data for survivor's population

Recurrent events together with longitudinal measurements are commonly observed in follow-up studies where the observation is terminated by censoring or a primary failure event. In this article, we developed a joint model where the dependence of longitudinal measurements, recurrent event process and time to failure event is modeled through rescaling the time index. The general idea is that the trajectories of all biology processes of subjects in the survivors' population are elongated or shortened by the rate identified from a model for the failure event. To avoid making disputing assumptions on recurrent events or biomarkers after the failure event (such as death), the model is constructed on the basis of survivors' population. The model also possesses a specific feature that, by aligning failure events as time origins, the backward-in-time model of recurrent events and longitudinal measurements shares the same parameter values with the forward time model. The statistical properties, simulation studies and real data examples are conducted. The proposed method can be generalized to analyze left-truncated data.

A comparison of statistical methods to predict the residual lifetime risk

Lifetime risk measures the cumulative risk for developing a disease over one's lifespan. Modeling the lifetime risk must account for left truncation, the competing risk of death, and inference at a fixed age. In addition, statistical methods to predict the lifetime risk should account for covariate-outcome associations that change with age. In this paper, we review and compare statistical methods to predict the lifetime risk. We first consider a generalized linear model for the lifetime risk using pseudo-observations of the Aalen-Johansen estimator at a fixed age, allowing for left truncation. We also consider modeling the subdistribution hazard with Fine-Gray and Royston-Parmar flexible parametric models in left truncated data with time-covariate interactions, and using these models to predict lifetime risk. In simulation studies, we found the pseudo-observation approach had the least bias, particularly in settings with crossing or converging cumulative incidence curves. We illustrate our method by modeling the lifetime risk of atrial fibrillation in the Framingham Heart Study. We provide technical guidance to replicate all analyses in R.

Nonparametric and semiparametric regression estimation for length-biased survival data

For the past several decades, nonparametric and semiparametric modeling for conventional right-censored survival data has been investigated intensively under a noninformative censoring mechanism. However, these methods may not be applicable for analyzing right-censored survival data that arise from prevalent cohorts when the failure times are subject to length-biased sampling. This review article is intended to provide a summary of some newly developed methods as well as established methods for analyzing length-biased data.

Eliminating bias due to censoring in Kendall's tau estimators for quasi-independence of truncation and failure

While the currently available estimators for the conditional Kendall's tau measure of association between truncation and failure are valid for testing the null hypothesis of quasi-independence, they are biased when the null does not hold. This is because they converge to quantities that depend on the censoring distribution. The magnitude of the bias relative to the theoretical Kendall's tau measure of association between truncation and failure due to censoring has not been studied, and so its importance in real problems is not known. We quantify this bias in order to assess the practical usefulness of the estimators. Furthermore, we propose inverse probability weighted versions of the conditional Kendall's tau estimators to remove the effects of censoring and provide asymptotic results for the estimators. In simulations, we demonstrate the decrease in bias achieved by these inverse probability weighted estimators. We apply the estimators to the Channing House data set and an AIDS incubation data set.

A semiparametric mixture cure survival model for left-truncated and right-censored data

In follow-up studies, the disease event time can be subject to left truncation and right censoring. Furthermore, medical advancements have made it possible for patients to be cured of certain types of diseases. In this article, we consider a semiparametric mixture cure model for the regression analysis of left-truncated and right-censored data. The model combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. We investigate two techniques for estimating model parameters. The first approach is based on martingale estimating equations (EEs). The second approach is based on the conditional likelihood function given truncation variables. The asymptotic properties of both proposed estimators are established. Simulation studies indicate that the conditional maximum-likelihood estimator (cMLE) performs well while the estimator based on EEs is very unstable even though it is shown to be consistent. This is a special and intriguing phenomenon for the EE approach under cure model. We provide insights into this issue and find that the EE approach can be improved significantly by assigning appropriate weights to the censored observations in the EEs. This finding is useful in overcoming the instability of the EE approach in some more complicated situations, where the likelihood approach is not feasible. We illustrate the proposed estimation procedures by analyzing the age at onset of the occiput-wall distance event for patients with ankylosing spondylitis.

Semiparametric model and inference for spontaneous abortion data with a cured proportion and biased sampling

Evaluating and understanding the risk and safety of using medications for autoimmune disease in a woman during her pregnancy will help both clinicians and pregnant women to make better treatment decisions. However, utilizing spontaneous abortion (SAB) data collected in observational studies of pregnancy to derive valid inference poses two major challenges. First, the data from the observational cohort are not random samples of the target population due to the sampling mechanism. Pregnant women with early SAB are more likely to be excluded from the cohort, and there may be substantial differences between the observed SAB time and those in the target population. Second, the observed data are heterogeneous and contain a "cured" proportion. In this article, we consider semiparametric models to simultaneously estimate the probability of being cured and the distribution of time to SAB for the uncured subgroup. To derive the maximum likelihood estimators, we appropriately adjust the sampling bias in the likelihood function and develop an expectation-maximization algorithm to overcome the computational challenge. We apply the empirical process theory to prove the consistency and asymptotic normality of the estimators. We examine the finite sample performance of the proposed estimators in simulation studies and illustrate the proposed method through an application to SAB data from pregnant women.

Varying coefficient subdistribution regression for left-truncated semi-competing risks data

Semi-competing risks data frequently arise in biomedical studies when time to a disease landmark event is subject to dependent censoring by death, the observation of which however is not precluded by the occurrence of the landmark event. In observational studies, the analysis of such data can be further complicated by left truncation. In this work, we study a varying co-efficient subdistribution regression model for left-truncated semi-competing risks data. Our method appropriately accounts for the specifical truncation and censoring features of the data, and moreover has the flexibility to accommodate potentially varying covariate effects. The proposed method can be easily implemented and the resulting estimators are shown to have nice asymptotic properties. We also present inference, such as Kolmogorov-Smirnov type and Cramér Von-Mises type hypothesis testing procedures for the covariate effects. Simulation studies and an application to the Denmark diabetes registry demonstrate good finite-sample performance and practical utility of the proposed method.

Nonidentifiability in the presence of factorization for truncated data

A time to event, [Formula: see text], is left-truncated by [Formula: see text] if [Formula: see text] can be observed only if [Formula: see text]. This often results in oversampling of large values of [Formula: see text], and necessitates adjustment of estimation procedures to avoid bias. Simple risk-set adjustments can be made to standard risk-set-based estimators to accommodate left truncation when [Formula: see text] and [Formula: see text] are quasi-independent. We derive a weaker factorization condition for the conditional distribution of [Formula: see text] given [Formula: see text] in the observable region that permits risk-set adjustment for estimation of the distribution of [Formula: see text], but not of the distribution of [Formula: see text]. Quasi-independence results when the analogous factorization condition for [Formula: see text] given [Formula: see text] holds also, in which case the distributions of [Formula: see text] and [Formula: see text] are easily estimated. While we can test for factorization, if the test does not reject, we cannot identify which factorization condition holds, or whether quasi-independence holds. Hence we require an unverifiable assumption in order to estimate the distribution of [Formula: see text] or [Formula: see text] based on truncated data. This contrasts with the common understanding that truncation is different from censoring in requiring no unverifiable assumptions for estimation. We illustrate these concepts through a simulation of left-truncated and right-censored data.

Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation

It is well known that the nonparametric maximum likelihood estimator (NPMLE) can severely underestimate the survival probabilities at early times for left-truncated and interval-censored (LT-IC) data. For arbitrarily truncated and censored data, Pan and Chappel (JAMA Stat Probab Lett 38:49-57, 1998a, Biometrics 54:1053-1060, 1998b) proposed a nonparametric estimator of the survival function, called the iterative Nelson estimator (INE). Their simulation study showed that the INE performed well in overcoming the under-estimation of the survival function from the NPMLE for LT-IC data. In this article, we revisit the problem of inconsistency of the NPMLE. We point out that the inconsistency is caused by the likelihood function of the left-censored observations, where the left-truncated variables are used as the left endpoints of censoring intervals. This can lead to severe underestimation of the survival function if the NPMLE is obtained using Turnbull's (JAMA 38:290-295, 1976) EM algorithm. To overcome this problem, we propose a modified maximum likelihood estimator (MMLE) based on a modified likelihood function, where the left endpoints of censoring intervals for left-censored observations are the maximum of left-truncated variables and the estimated left endpoint of the support of the left-censored times. Simulation studies show that the MMLE performs well for finite sample and outperforms both the INE and NPMLE.

Nonparametric estimation of transition probabilities for a general progressive multi-state model under cross-sectional sampling

Nonparametric estimation of the transition probability matrix of a progressive multi-state model is considered under cross-sectional sampling. Two different estimators adapted to possibly right-censored and left-truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub-samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left-truncation times associated with the cross-sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs).

A new flexible dependence measure for semi-competing risks

Semi-competing risks data are often encountered in chronic disease follow-up studies that record both nonterminal events (e.g., disease landmark events) and terminal events (e.g., death). Studying the relationship between the nonterminal event and the terminal event can provide insightful information on disease progression. In this article, we propose a new sensible dependence measure tailored to addressing such an interest. We develop a nonparametric estimator, which is general enough to handle both independent right censoring and left truncation. Our strategy of connecting the new dependence measure with quantile regression enables a natural extension to adjust for covariates with minor additional assumptions imposed. We establish the asymptotic properties of the proposed estimators and develop inferences accordingly. Simulation studies suggest good finite-sample performance of the proposed methods. Our proposals are illustrated via an application to Denmark diabetes registry data.

Maximum likelihood estimation for length-biased and interval-censored data with a nonsusceptible fraction

Left-truncated data are often encountered in epidemiological cohort studies, where individuals are recruited according to a certain cross-sectional sampling criterion. Length-biased data, a special case of left-truncated data, assume that the incidence of the initial event follows a homogeneous Poisson process. In this article, we consider an analysis of length-biased and interval-censored data with a nonsusceptible fraction. We first point out the importance of a well-defined target population, which depends on the prior knowledge for the support of the failure times of susceptible individuals. Given the target population, we proceed with a length-biased sampling and draw valid inferences from a length-biased sample. When there is no covariate, we show that it suffices to consider a discrete version of the survival function for the susceptible individuals with jump points at the left endpoints of the censoring intervals when maximizing the full likelihood function, and propose an EM algorithm to obtain the nonparametric maximum likelihood estimates of nonsusceptible rate and the survival function of the susceptible individuals. We also develop a novel graphical method for assessing the stationarity assumption. When covariates are present, we consider the Cox proportional hazards model for the survival time of the susceptible individuals and the logistic regression model for the probability of being susceptible. We construct the full likelihood function and obtain the nonparametric maximum likelihood estimates of the regression parameters by employing the EM algorithm. The large sample properties of the estimates are established. The performance of the method is assessed by simulations. The proposed model and method are applied to data from an early-onset diabetes mellitus study.

Cause-Specific Hazard Regression for Competing Risks Data Under Interval Censoring and Left Truncation

Inference for cause-specific hazards from competing risks data under interval censoring and possible left truncation has been understudied. Aiming at this target, a penalized likelihood approach for a Cox-type proportional cause-specific hazards model is developed, and the associated asymptotic theory is discussed. Monte Carlo simulations show that the approach performs very well for moderate sample sizes. An application to a longitudinal study of dementia illustrates the practical utility of the method. In the application, the age-specific hazards of AD, other dementia and death without dementia are estimated, and risk factors of all competing risks are studied.

Estimating cross quantile residual ratio with left-truncated semi-competing risks data

A semi-competing risks setting often arises in biomedical studies, involving both a nonterminal event and a terminal event. Cross quantile residual ratio (Yang and Peng in Biometrics 72:770-779, 2016) offers a flexible and robust perspective to study the dependency between the nonterminal and the terminal events which can shed useful scientific insight. In this paper, we propose a new nonparametric estimator of this dependence measure with left truncated semi-competing risks data. The new estimator overcomes the limitation of the existing estimator that is resulted from demanding a strong assumption on the truncation mechanism. We establish the asymptotic properties of the proposed estimator and develop inference procedures accordingly. Simulation studies suggest good finite-sample performance of the proposed method. Our proposal is illustrated via an application to Denmark diabetes registry data.

Conditional Independence Test of Failure and Truncation Times: Essential Tool for Method Selection

Conditional independence assumption of truncation and failure times conditioning on covariates is a fundamental and common assumption in the regression analysis of left-truncated and right-censored data. Testing for this assumption is essential to ensure the correct inference on the failure time, but this has often been overlooked in the literature. With consideration of challenges caused by left truncation and right censoring, tests for this conditional independence assumption are developed in which the generalized odds ratio derived from a Cox proportional hazards model on the failure time and the concept of Kendall's tau are combined. Except for the Cox proportional hazards model, no additional model assumptions are imposed, and the distributions of the truncation time and conditioning variables are unspecified. The asymptotic properties of the test statistic are established and an easy implementation for obtaining its distribution is developed. The performance of the proposed test has been evaluated through simulation studies and two real studies.

Evaluation of the natural history of disease by combining incident and prevalent cohorts: application to the Nun Study

The Nun study is a well-known longitudinal epidemiology study of aging and dementia that recruited elderly nuns who were not yet diagnosed with dementia (i.e., incident cohort) and who had dementia prior to entry (i.e., prevalent cohort). In such a natural history of disease study, multistate modeling of the combined data from both incident and prevalent cohorts is desirable to improve the efficiency of inference. While important, the multistate modeling approaches for the combined data have been scarcely used in practice because prevalent samples do not provide the exact date of disease onset and do not represent the target population due to left-truncation. In this paper, we demonstrate how to adequately combine both incident and prevalent cohorts to examine risk factors for every possible transition in studying the natural history of dementia. We adapt a four-state nonhomogeneous Markov model to characterize all transitions between different clinical stages, including plausible reversible transitions. The estimating procedure using the combined data leads to efficiency gains for every transition compared to those from the incident cohort data only.

Bias in cohort-based comparisons of immigrants' health outcomes between countries: a simulation study

Background

Cohort-type data are increasingly used to compare health outcomes of immigrants between countries, e.g. to assess the effects of different national integration policies. In such international comparisons, small differences in cardiovascular diseases risk or mortality rates have been interpreted as showing effects of different policies. We conjecture that cohort-type data sets available for such comparisons might not provide unbiased relative risk estimates between countries because of differentials in migration patterns occurring before the cohorts are being observed.

Method

Two simulation studies were performed to assess whether comparisons are biased if there are differences in 1. the way migrants arrived in the host countries, i.e. in a wave or continuously; 2. the effects on health of exposure to the host country; or 3., patterns of return-migration before a cohort is recruited. In the first simulation cardiovascular disease was the outcome and immortality in the second. Bias was evaluated using a Cox regression model adjusted for age and other dependant variables.

Results

Comparing populations from wave vs. continuous migration may lead to bias only if the duration of stay has a dose-response effect (increase in simulated cardiovascular disease risk by 5% every 5 years vs. no risk: hazard-ratio 1.20(0.15); by 10% every 5 years: 1.47(0.14)). Differentials in return-migration patterns lead to bias in mortality rate ratios (MRR). The direction (under- or overestimation) and size of the bias depends on the model (MRR from 0.92(0.01) to 1.09(0.01)).

Conclusion

The order of magnitude of the effects interpreted as due to integration policies in the literature is the same as the bias in our simulations. Future studies need to take into account duration and relevance of exposure and return-migration to make valid inferences about the effects of integration policies on the health of immigrants.

Electronic supplementary material

The online version of this article (10.1186/s12889-019-7267-2) contains supplementary material, which is available to authorized users.

The impact of left truncation of exposure in environmental case-control studies: evidence from breast cancer risk associated with airborne dioxin

In epidemiology, left-truncated data may bias exposure effect estimates. We analyzed the bias induced by left truncation in estimating breast cancer risk associated with exposure to airborne dioxins. Simulations were run with exposure estimates from a Geographic Information System (GIS)-based metric and considered two hypotheses for historical exposure, three scenarios for intra-individual correlation of annual exposures, and three exposure-effect models. For each correlation/model combination, 500 nested matched case-control studies were simulated and data fitted using a conditional logistic regression model. Bias magnitude was assessed by estimated odds-ratios (ORs) versus theoretical relative risks (TRRs) comparisons. With strong intra-individual correlation and continuous exposure, left truncation overestimated the Beta parameter associated with cumulative dioxin exposure. Versus a theoretical Beta of 4.17, the estimated mean Beta (5%; 95%) was 73.2 (67.7; 78.8) with left-truncated exposure and 4.37 (4.05; 4.66) with lifetime exposure. With exposure categorized in quintiles, the TRR was 2.0, the estimated OR_{Q5 vs. Q1} 2.19 (2.04; 2.33) with truncated exposure versus 2.17 (2.02; 2.32) with lifetime exposure. However, the difference in exposure between Q5 and Q1 was 18× smaller with truncated data, indicating an important overestimation of the dose effect. No intra-individual correlation resulted in effect dilution and statistical power loss. Left truncation induced substantial bias in estimating breast cancer risk associated with exposure with continuous and categorical models. With strong intra-individual exposure correlation, both models detected associations, but categorical models provided better estimates of effect trends. This calls for careful consideration of left truncation-induced bias in interpreting environmental epidemiological data.

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.

A Sexual Partnership Duration: Characterizing Sampling Conditions That Permit unbiased Estimation of Survivorship and Effect on It of Covariates

Partnership duration data are commonly obtained through surveys that collect information on relationships that are ongoing during a fixed time window. This sampling mechanism leads to duration data that are left truncated and right censored; such data have been analysed using the standard truncation product limit estimator (TPLE). In this paper, we describe a common sampling scheme for collecting sexual partnership data, discuss a key assumption required for the TPLE to be unbiased, and provide the conditions under which the nonparametric maximum likelihood estimator of the relationship duration distribution is unique and consistent. We also investigate the conditions required for the consistency of the regression coefcient from a Cox proportional hazards model that apply even when the distribution of duration is not completely identifiable due to restrictions on the support of the truncation distribution. Lastly, we will provide some illustrative examples on estimating distribution of most recent partnerships and present spline regression results based on partnership data collected from sexual behavior survey in Mochudi, Botswana.

Regression analysis of a graphical proportional hazards model for informatively left-truncated current status data

In survival analysis, researchers commonly focus on variable selection issues in real-world data, particularly when complex network structures exist among covariates. Additionally, due to factors such as data collection costs and delayed entry, real-world data often exhibit censoring and truncation phenomena.This paper addresses left-truncated current status data by employing a copula-based approach to model the relationship between censoring time and failure time. Based on this, we investigate the problem of variable selection in the context of complex network structures among covariates. To this end, we integrate Markov Random Field (MRF) with the Proportional Hazards (PH) model, and extend the latter to more flexibly characterize the correlation structure among covariates. For solving the constructed model, we propose a penalized optimization method and utilize spline functions to estimate the baseline hazard function. Through numerical simulation experiments and case studies of clinical trial data, we comprehensively evaluate the effectiveness and performance of the proposed model and its parameter inference strategy. This evaluation not only demonstrates the robustness of the proposed model in handling complex disease data but also further verifies the high precision and reliability of the parameter estimation method.

Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, samples are often selected at a later time, which results in delayed entry so that only individuals who have not yet experienced the terminal event will be included. In joint frailty models such left truncation has effects on the frailty distribution that need to be accounted for in both the recurrence process and the terminal event process, if the two are associated. We demonstrate, in a comprehensive simulation study, the effects that not adjusting for late entry can have and derive the correctly adjusted marginal likelihood, which can be expressed as a ratio of two integrals over the frailty distribution. We extend the estimation method of Liu and Huang (Stat Med 27:2665-2683, 2008. https://doi.org/10.1002/sim.3077 ) to include potential left truncation. Numerical integration is performed by Gaussian quadrature, the baseline intensities are specified as piecewise constant functions, potential covariates are assumed to have multiplicative effects on the intensities. We apply the method to estimate age-specific intensities of recurrent urinary tract infections and mortality in an older population.

Combined estimating equation approaches for the additive hazards model with left-truncated and interval-censored data

Interval-censored failure time data arise commonly in various scientific studies where the failure time of interest is only known to lie in a certain time interval rather than observed exactly. In addition, left truncation on the failure event may occur and can greatly complicate the statistical analysis. In this paper, we investigate regression analysis of left-truncated and interval-censored data with the commonly used additive hazards model. Specifically, we propose a conditional estimating equation approach for the estimation, and further improve its estimation efficiency by combining the conditional estimating equation and the pairwise pseudo-score-based estimating equation that can eliminate the nuisance functions from the marginal likelihood of the truncation times. Asymptotic properties of the proposed estimators are discussed including the consistency and asymptotic normality. Extensive simulation studies are conducted to evaluate the empirical performance of the proposed methods, and suggest that the combined estimating equation approach is obviously more efficient than the conditional estimating equation approach. We then apply the proposed methods to a set of real data for illustration.

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.