What characteristics of dogs help them stay shorter in shelters? Evidence from a polish animal shelter

Staying in animal shelters can be stressful for dogs because of exposure to noise, unfamiliar environment, and social separation. Consequently, the wellbeing of sheltered dogs could be improved through reduction of length of stay in a shelter (LOS). To help inform the development of interventions aimed at LOS reduction, we analyze dogs' characteristics affecting their LOS. We use econometric modeling to identify the characteristics's influence by simultaneously controlling for multiple factors. We use data from Poland's largest animal shelter (11805 observations from the years 2000-2020). We compare two modeling approaches: a Cox survival model, commonly used in animal welfare studies, and an accelerated failure time model, theoretically better fitted to studying time-dependent factors but not yet applied in the context of LOS. We conclude that the latter approach is preferable for studying factors affecting LOS. Male sex, mixed-breed, dark fur, large size, and older age appear to be associated with longer time to adoption for dogs. To our knowledge, this is the first econometric examination of factors affecting LOS in a country in Central and Eastern Europe.

An Accelerated Failure Time Model to Predict Cause-Specific Survival and Prognostic Factors of Lung and Bronchus Cancer Patients with at Least Bone or Brain Metastases: Development and Internal Validation Using a SEER-Based Study

BACKGROUND

This study addresses the significant challenge of low survival rates in patients with cause-specific lung cancer accompanied by bone or brain metastases. Recognizing the critical need for an effective predictive model, the research aims to establish survival prediction models using both parametric and non-parametric approaches.

METHODS

Clinical data from lung cancer patients with at least one bone or brain metastasis between 2000 and 2020 from the SEER database were utilized. Four models were constructed: Cox proportional hazard, Weibull accelerated failure time (AFT), log-normal AFT, and Zografos-Balakrishnan log-normal (ZBLN). Independent prognostic factors for cause-specific survival were identified, and model fit was evaluated using Akaike's and Bayesian information criteria. Internal validation assessed predictive accuracy and discriminability through the Harriel Concordance Index (C-index) and calibration plots.

RESULTS

A total of 20,412 patients were included, with 14,290 (70%) as the training cohort and 6122 (30%) validation. Independent prognostic factors selected for the study were age, race, sex, primary tumor site, disease grade, total malignant tumor in situ, metastases, treatment modality, and histology. Among the accelerated failure time (AFT) models considered, the ZBLN distribution exhibited the most robust model fit for the 3- and 5-year survival, as evidenced by the lowest values of Akaike's information criterion of 6322 and 79,396, and the Bayesian information criterion of 63,495 and 79,396, respectively. This outperformed other AFT and Cox models (AIC = [156,891, 211,125]; BIC = [158,848, 211,287]). Regarding predictive accuracy, the ZBLN AFT model achieved the highest concordance C-index (0.682, 0.667), a better performance than the Cox model (0.669, 0.643). The calibration curves of the ZBLN AFT model demonstrated a high degree of concordance between actual and predicted values. All variables considered in this study demonstrated significance at the 0.05 level for the ZBLN AFT model. However, differences emerged in the significant variations in survival times between subgroups. The study revealed that patients with only bone metastases have a higher chance of survival compared to only brain and those with bone and brain metastases.

CONCLUSIONS

The study highlights the underutilized but accurate nature of the accelerated failure time model in predicting lung cancer survival and identifying prognostic factors. These findings have implications for individualized clinical decisions, indicating the potential for screening and professional care of lung cancer patients with at least one bone or brain metastasis in the future.

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.

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.

Regularized Buckley-James method for right-censored outcomes with block-missing multimodal covariates

High-dimensional data with censored outcomes of interest are prevalent in medical research. To analyze such data, the regularized Buckley-James estimator has been successfully applied to build accurate predictive models and conduct variable selection. In this paper, we consider the problem of parameter estimation and variable selection for the semiparametric accelerated failure time model for high-dimensional block-missing multimodal neuroimaging data with censored outcomes. We propose a penalized Buckley-James method that can simultaneously handle block-wise missing covariates and censored outcomes. This method can also perform variable selection. The proposed method is evaluated by simulations and applied to a multimodal neuroimaging dataset and obtains meaningful results.

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.

Prediction of the generalization of myasthenia gravis with purely ocular symptoms at onset: a multivariable model development and validation

Background

About half of myasthenia gravis (MG) patients with purely ocular symptoms at onset progress to generalized myasthenia gravis (gMG).

Objectives

To develop and validate a model to predict the generalization of MG at 6 months after disease onset in patients with ocular-onset myasthenia gravis (OoMG).

Methods

Data of patients with OoMG were retrospectively collected from two tertiary hospitals in Germany and China. An accelerated failure time model was developed using the backward elimination method based on the German cohort to predict the generalization of OoMG. The model was then externally validated in the Chinese cohort, and its performance was assessed using Harrell's C-index and calibration plots.

Results

Four hundred and seventy-seven patients (275 from Germany and 202 from China) were eligible for inclusion. One hundred and three (37.5%) patients in the German cohort progressed from OoMG to gMG with a median follow-up time of 69 (32-116) months. The median time to generalization was 29 (16-71) months. The estimated cumulative probability of generalization was 30.5% [95% CI (confidence interval), 24.3-36.2%) at 5 years after disease onset. The final model, which was represented as a nomogram, included five clinical variables: sex, titer of anti-AChR antibody, status of anti-MuSK antibody, age at disease onset and the presence of other autoimmune disease. External validation of the model using the bootstrap showed a C-index of 0.670 (95% CI, 0.602-0.738). Calibration curves revealed moderate agreement of predicted and observed outcomes.

Conclusion

The nomogram is a good predictor for generalization in patients with OoMG that can be used to inform of the individual generalization risk, which might improve the clinical decision-making.

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.

Multistate Models for the Recovery Process in the Covid-19 Context: An Empirical Study of Chinese Enterprises

The Covid-19 pandemic has severely affected enterprises worldwide. It is thus of practical significance to study the process of enterprise recovery from Covid-19. However, the research on the effects of relevant determinants of business recovery is limited. This article presents a multistate modeling framework that considers the determinants, recovery time, and transition likelihood of Chinese enterprises by the state of those enterprises as a result of the pandemic (recovery state), with the help of an accelerated failure time model. Empirical data from 750 enterprises were used to evaluate the recovery process. The results indicate that the main problems facing non-manufacturing industries are supply shortages and order cancellations. With the increase of supplies and orders, the probability of transition between different recovery states gradually increases, and the recovery time of enterprises becomes shorter. For manufacturing industries, the factors that hinder recovery are more complex. The main problems are employee panic and order cancellations in the initial stage, employee shortages in the middle stage, and raw material shortages in the full recovery stage. This study can provide a reference for enterprise recovery in the current pandemic context and help policymakers and business managers take necessary measures to accelerate recovery.

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.

An Investigation of the Initial Recovery Time of Chinese Enterprises Affected by COVID-19 Using an Accelerated Failure Time Model

COVID-19 has had a great impact on the economy, society, and people's lives in China and globally. The production and operations of Chinese enterprises have also faced tremendous challenges. To understand the economic impact of COVID-19 on enterprises and the key affecting factors, this study adds to the literature by investigating the business recovery process of enterprises from the micro perspective. Specific attention is paid to the initial stage of business recovery. A questionnaire survey of 750 enterprises explored the impact during the pandemic period from July to September 2020. An accelerated failure time model in survival analysis was adopted to analyze the data. The results show that the manufacturing industry is mainly faced by affecting factors such as enterprise ownership, employees' panic and order cancellation on initial enterprise recovery. As for the non-manufacturing industry, more factors, including clients' distribution, employees' panic, raw material shortage, cash flow shortage and order cancellation, are found to be significant. Acceleration factors that estimate the effects of those covariates on acceleration/deceleration of the recovery time are presented. For instance, the acceleration factor of employees' panic is 1.319 for non-manufacturing, which implies that, compared with enterprises where employees are less panicked, enterprises with employees obviously panicked will recover 1.319 times slower at any quantile of probability of recovery time. This study provides a scientific reference for the post-pandemic recovery of enterprises, and can support the formulation of government policies and enterprise decisions.

Analysis of Factors Associated With Length of Stay of Opioid-Related Emergency Department Visits

Introduction and Objective: Emergency department (ED) length of stay (LOS) is an important indicator of the quality of care in ED and is associated with patients’ outcomes and healthcare costs. However, there is limited data on how the patient characteristics affect the ED LOS of opioid-related visits. This study aims to identify and quantify the effect of patient-related characteristics on LOS of opioid-related ED visits.

Methods: This is a retrospective analysis of electronic health records (EHR) of patients with diagnoses of opioid abuse. The study included patients with a diagnosis of opioid abuse who visited the ED at Christiana Care Hospital from January 1, 2017, to December 31, 2018 (N=5,661). The opioid-related visits were identified using ICD-10 diagnosis codes. We used accelerated failure time (AFT) models, a time-to-event analysis approach to evaluate the relationships of different patient characteristics with ED LOS.

Results: The mean age of the study population was 39 years. The study population had 40% female, 20% Black/African American, and 5% Hispanic or Latino. The prevalence of co-use of cocaine and co-use of alcohol was 11%, and 9%, respectively. Also, 58% had mental health comorbidity, and 1% were homeless. The distribution of ED LOS was right-skewed with a median of 4.3 (IQR: 2.6, 6.8). Co-use of alcohol (time ratio, TR: 1.31, CI: 1.23-1.40), co-use of cocaine (TR: 1.18, CI: 1.11-1.25), the presence of mental health comorbidity (TR: 1.05, CI 1.01-1.09), and homelessness (TR: 1.57, CI: 1.32-1.86) were associated with increased ED LOS.

Conclusions: Co-use of alcohol, co-use of cocaine, homelessness, and mental health comorbidity are associated with the longer LOS of opioid-related ED visits.

A Practical Overview and Reporting Strategies for Statistical Analysis of Survival Studies

Survival (time-to-event) analysis is commonly used in clinical research. Key features of performing a survival analysis include checking proportional hazards assumptions, reporting CIs for hazards ratios and relative risks, graphically displaying the findings, and analyzing with consideration of competing risks. This article provides a brief overview of important statistical considerations for survival analysis. Censoring schemes, different methods of survival function estimation, and ways to compare survival curves are described. We also explain competing risk and how to model survival data in the presence of it. Different kinds of bias that influence survival estimation and avenues to model the data under these circumstances are also described. Several analysis techniques are accompanied by graphical representations illustrating proper reporting strategies. We provide a list of guiding statements for researchers and reviewers.

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.

[Subgroup identification based on accelerated failure time model combined with adaptive elastic net]

OBJECTIVE

To solve the problem of identifying subgroup in a randomized clinical trial with respect to survival time, we present a strategy based on accelerated failure time model to identify the subgroup with an enhanced treatment effect.

OBJECTIVE

We fitted and compared univariate accelerated failure time (AFT) models and penalized AFT models regularized by adaptive elastic net to identify the candidate covariates. Based on these covariates, we utilized change-point algorithm to classify the patient subgroups. A two-stage adaptive design was adopted to verify the treatment effect in certain subgroups. Simulations were conducted across different scenarios to evaluate the performance of the models.

OBJECTIVE

As the correlation between covariates differed, the power of the models with an adaptive design was stable. In the two-stage adaptive design, the power of the models was the highest when the two significance levels (α1 and α2) were allocated to be 0.035 and 0.015, respectively. A better effect of the responder subgroup was associated with a higher power of the models. For a fixed sample size, the power decreased as the covariate number to sample size ratio increased, but the power showed a stable trend when the ratio was above 1. The univariate models showed different distribution patterns of the parameters for different survival time, while their distribution was relatively stable in the penalized AFT models.

OBJECTIVE

The correlation between the covariates does not affect the performance of univariate AFT models and penalized AFT models. (0.035, 0.015) can be used as a reference for the significance level of an adaptive design. For small differences in the treatment effect between the responder and the non-responder, the penalized AFT model including the main effect of covariate (Penalized, Eq_in) outperforms the univariate AFT model excluding the main effect of covariate (Univariate, Eq_ex). Univariate, Eq_ex performs better when the covariate number to sample size ratio is less than 1, but is outperformed by Penalized, Eq_in when the ratio is above 1. The parameter distribution of survival time has a greater impact on the univariate models but a smaller impact on the penalized models.

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.

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.

Germination Data Analysis by Time-to-Event Approaches

Germination data are analyzed by several methods, which can be mainly classified as germination indexes and traditional regression techniques to fit non-linear parametric functions to the temporal sequence of cumulative germination. However, due to the nature of germination data, often different from other biological data, the abovementioned methods may present some limits, especially when ungerminated seeds are present at the end of an experiment. A class of methods that could allow addressing these issues is represented by the so-called “time-to-event analysis”, better known in other scientific fields as “survival analysis” or “reliability analysis”. There is relatively little literature about the application of these methods to germination data, and some reviews dealt only with parts of the possible approaches such as either non-parametric and semi-parametric or parametric ones. The present study aims to give a contribution to the knowledge about the reliability of these methods by assessing all the main approaches to the same germination data provided by sugar beet (Beta vulgaris L.) seeds cohorts. The results obtained confirmed that although the different approaches present advantages and disadvantages, they could generally represent a valuable tool to analyze germination data providing parameters whose usefulness depends on the purpose of the research.

[Subgroup identification based on an accelerated failure time model combined with adaptive elastic net]

OBJECTIVE

We propose a strategy for identifying subgroups with the treatment effect from the survival data of a randomized clinical trial based on accelerated failure time (AFT) model.

METHODS

We applied adaptive elastic net to the AFT model (designated as the penalized model) and identified the candidate covariates based on covariate-treatment interactions. To classify the patient subgroups, we utilized a likelihood-based change-point algorithm to determine the threshold cutoff point. A two-stage adaptive design was adopted to verify if the treatment effect existed within the identified subgroups.

RESULTS

The penalized model with the main effect of the covariates considerably outperformed the univariate model without the main effect for the trial data with a small sample size, a high censoring rate, a small subgroup size, or a sample size that did not exceed the number of covariates; in other scenarios, the latter model showed better performances. Compared with the traditional design, the adaptive design improved the power for detecting the treatment effect where subgroup effect exists with a well-controlled type Ⅰ error.

CONCLUSIONS

The penalized AFT model with the main effect of the covariates has advantages in subgroup identification from the survival data of clinical trials. Compared with the traditional design, the two-stage adaptive design has better performance in evaluation of the treatment effect when a subgroup effect exists.

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.

Phase II trial design with growth modulation index as the primary endpoint

Molecularly targeted, genomic-driven, and immunotherapy-based clinical trials continue to be advanced for the treatment of relapse or refractory cancer patients, where the growth modulation index (GMI) is often considered a primary endpoint of treatment efficacy. However, there little literature is available that considers the trial design with GMI as the primary endpoint. In this article, we derived a sample size formula for the score test under a log-linear model of the GMI. Study designs using the derived sample size formula are illustrated under a bivariate exponential model, the Weibull frailty model, and the generalized treatment effect size. The proposed designs provide sound statistical methods for a single-arm phase II trial with GMI as the primary endpoint.

Pathway aggregation for survival prediction via multiple kernel learning

Attempts to predict prognosis in cancer patients using high-dimensional genomic data such as gene expression in tumor tissue can be made difficult by the large number of features and the potential complexity of the relationship between features and the outcome. Integrating prior biological knowledge into risk prediction with such data by grouping genomic features into pathways and networks reduces the dimensionality of the problem and could improve prediction accuracy. Additionally, such knowledge-based models may be more biologically grounded and interpretable. Prediction could potentially be further improved by allowing for complex nonlinear pathway effects. The kernel machine framework has been proposed as an effective approach for modeling the nonlinear and interactive effects of genes in pathways for both censored and noncensored outcomes. When multiple pathways are under consideration, one may efficiently select informative pathways and aggregate their signals via multiple kernel learning (MKL), which has been proposed for prediction of noncensored outcomes. In this paper, we propose MKL methods for censored survival outcomes. We derive our approach for a general survival modeling framework with a convex objective function and illustrate its application under the Cox proportional hazards and semiparametric accelerated failure time models. Numerical studies demonstrate that the proposed MKL-based prediction methods work well in finite sample and can potentially outperform models constructed assuming linear effects or ignoring the group knowledge. The methods are illustrated with an application to 2 cancer data sets.

Induced smoothing for rank-based regression with recurrent gap time data

Various semiparametric regression models have recently been proposed for the analysis of gap times between consecutive recurrent events. Among them, the semiparametric accelerated failure time (AFT) model is especially appealing owing to its direct interpretation of covariate effects on the gap times. In general, estimation of the semiparametric AFT model is challenging because the rank-based estimating function is a nonsmooth step function. As a result, solutions to the estimating equations do not necessarily exist. Moreover, the popular resampling-based variance estimation for the AFT model requires solving rank-based estimating equations repeatedly and hence can be computationally cumbersome and unstable. In this paper, we extend the induced smoothing approach to the AFT model for recurrent gap time data. Our proposed smooth estimating function permits the application of standard numerical methods for both the regression coefficients estimation and the standard error estimation. Large-sample properties and an asymptotic variance estimator are provided for the proposed method. Simulation studies show that the proposed method outperforms the existing nonsmooth rank-based estimating function methods in both point estimation and variance estimation. The proposed method is applied to the data analysis of repeated hospitalizations for patients in the Danish Psychiatric Center Register.

Semiparametric regression analysis for alternating recurrent event data

Alternating recurrent event data arise frequently in clinical and epidemiologic studies, where 2 types of events such as hospital admission and discharge occur alternately over time. The 2 alternating states defined by these recurrent events could each carry important and distinct information about a patient's underlying health condition and/or the quality of care. In this paper, we propose a semiparametric method for evaluating covariate effects on the 2 alternating states jointly. The proposed methodology accounts for the dependence among the alternating states as well as the heterogeneity across patients via a frailty with unspecified distribution. Moreover, the estimation procedure, which is based on smooth estimating equations, not only properly addresses challenges such as induced dependent censoring and intercept sampling bias commonly confronted in serial event gap time data but also is more computationally tractable than the existing rank-based methods. The proposed methods are evaluated by simulation studies and illustrated by analyzing psychiatric contacts from the South Verona Psychiatric Case Register.

Sparse boosting for high-dimensional survival data with varying coefficients

Motivated by high-throughput profiling studies in biomedical research, variable selection methods have been a focus for biostatisticians. In this paper, we consider semiparametric varying-coefficient accelerated failure time models for right censored survival data with high-dimensional covariates. Instead of adopting the traditional regularization approaches, we offer a novel sparse boosting (SparseL₂ Boosting) algorithm to conduct model-based prediction and variable selection. One main advantage of this new method is that we do not need to perform the time-consuming selection of tuning parameters. Extensive simulations are conducted to examine the performance of our sparse boosting feature selection techniques. We further illustrate our methods using a lung cancer data analysis.

How serious is bias in effect estimation in randomised trials with survival data given risk heterogeneity and informative censoring?

It is often assumed that randomisation will prevent bias in estimation of treatment effects from clinical trials, but this is not true of the semiparametric Proportional Hazards model for survival data when there is underlying risk heterogeneity. Here, a new formula is proposed for estimation of this bias, improving on a previous formula through ease of use and clarity regarding the role of the mid-study cumulative hazard rate, shown to be an important factor for the bias magnitude. Informative censoring (IC) is recognised as a source of bias. Here, work on selection effects among survivors due to risk heterogeneity is extended to include IC. A new formula shows that bias in causal effect estimation under IC has two sources: one consequent on heterogeneity and one from the additional impact of IC. The formula provides new insights not previously shown: there may less bias under IC than when there is no IC and even, in principle, zero bias. When tested against simulated data, the new formulae are shown to be very accurate for prediction of bias in Proportional Hazards and accelerated failure time analyses which ignore heterogeneity. These data are also used to investigate the performance of accelerated failure time models which explicitly model risk heterogeneity ('frailty models') and G estimation. These methods remove bias when there is simple censoring but not with informative censoring when they may lead to overestimation of treatment effects. The new formulae may be used to help researchers judge the possible extent of bias in past studies. Copyright © 2017 John Wiley & Sons, Ltd.

Mediation Analysis for Censored Survival Data Under an Accelerated Failure Time Model

Recent advances in causal mediation analysis have formalized conditions for estimating direct and indirect effects in various contexts. These approaches have been extended to a number of models for survival outcomes including accelerated failure time models, which are widely used in a broad range of health applications given their intuitive interpretation. In this setting, it has been suggested that under standard assumptions, the "difference" and "product" methods produce equivalent estimates of the indirect effect of exposure on the survival outcome. We formally show that these two methods may produce substantially different estimates in the presence of censoring or truncation, due to a form of model misspecification. Specifically, we establish that while the product method remains valid under standard assumptions in the presence of independent censoring, the difference method can be biased in the presence of such censoring whenever the error distribution of the accelerated failure time model fails to be collapsible upon marginalizing over the mediator. This will invariably be the case for most choices of mediator and outcome error distributions. A notable exception arises in case of normal mediator-normal outcome where we show consistency of both difference and product estimators in the presence of independent censoring. These results are confirmed in simulation studies and two data applications.

Investigation of contributing factors to extremely severe traffic crashes using survival theory

This study aimed to investigate the contributing factors to serious casualty crashes in China. Crashes with deaths greater than 10 people are defined as serious casualty crashes in China. The serious casualty crash data were collected from 2009 to 2014. The random forest analysis was first conducted to select the candidate variables that affect the risks of serious casualty crashes. The Bayesian random parameters accelerated failure time (AFT) model was then developed to link the probability of the serious casualty crash with road geometric conditions, pavement conditions, environmental characteristics, collision characteristics, vehicle conditions, and driver characteristics. The AFT model estimation results indicate that overload driving, country road, northwest china region, turnover crash, private car, snowy or icy road surface and sight distance conditions have significant fixed effects on the likelihood of serious casualty crashes. In addition to these fixed-parameter variables, freeway, clear weather conditions, coach drivers, and upgrade horizontal curve affect the likelihood of serious casualty crashes with varying magnitude across observations. One of the important findings is that the serious casualty crash likelihood does not always decrease with an increase in the driving experience (number of years driven). Before the inflection point of 7 years, the serious casualty crash likelihood increases as the driving experience grows. The results of this study can help to develop effective countermeasures and policy initiatives for the prevention of serious casualty crashes.

Joint two-part Tobit models for longitudinal and time-to-event data

In this article, we show how Tobit models can address problems of identifying characteristics of subjects having left-censored outcomes in the context of developing a method for jointly analyzing time-to-event and longitudinal data. There are some methods for handling these types of data separately, but they may not be appropriate when time to event is dependent on the longitudinal outcome, and a substantial portion of values are reported to be below the limits of detection. An alternative approach is to develop a joint model for the time-to-event outcome and a two-part longitudinal outcome, linking them through random effects. This proposed approach is implemented to assess the association between the risk of decline of CD4/CD8 ratio and rates of change in viral load, along with discriminating between patients who are potentially progressors to AIDS from patients who do not. We develop a fully Bayesian approach for fitting joint two-part Tobit models and illustrate the proposed methods on simulated and real data from an AIDS clinical study.

Application of Correlated Time-to-Event Models to Ecological Momentary Assessment Data

Ecological momentary assessment data consist of in-the-moment sampling several times per day aimed at capturing phenomena that are highly variable. When research questions are focused on the association between a construct measured repeatedly and an event that occurs sporadically over time interspersed between repeated measures, the data consist of correlated observed or censored times to an event. In such a case, specialized time-to-event models that account for correlated observations are required to properly assess the relationships under study. In the current study, we apply two time-to-event analysis techniques, proportional hazards, and accelerated failure time modeling, to data from a study of affective states and sexual behavior in depressed adolescents and illustrate differing interpretations from the models.

Gene-Gene Interaction Analysis for the Accelerated Failure Time Model Using a Unified Model-Based Multifactor Dimensionality Reduction Method

Although a large number of genetic variants have been identified to be associated with common diseases through genome-wide association studies, there still exits limitations in explaining the missing heritability. One approach to solving this missing heritability problem is to investigate gene-gene interactions, rather than a single-locus approach. For gene-gene interaction analysis, the multifactor dimensionality reduction (MDR) method has been widely applied, since the constructive induction algorithm of MDR efficiently reduces high-order dimensions into one dimension by classifying multi-level genotypes into high- and low-risk groups. The MDR method has been extended to various phenotypes and has been improved to provide a significance test for gene-gene interactions. In this paper, we propose a simple method, called accelerated failure time (AFT) UM-MDR, in which the idea of a unified model-based MDR is extended to the survival phenotype by incorporating AFT-MDR into the classification step. The proposed AFT UM-MDR method is compared with AFT-MDR through simulation studies, and a short discussion is given.

A censored quantile regression approach for the analysis of time to event data

The commonly used statistical model for studying time to event data, the Cox proportional hazards model, is limited by the assumption of a constant hazard ratio over time (i.e., proportionality), and the fact that it models the hazard rate rather than the survival time directly. The censored quantile regression model, defined on the quantiles of time to event, provides an alternative that is more flexible and interpretable. However, the censored quantile regression model has not been widely adopted in clinical research, due to the complexity involved in interpreting its results properly and consequently the difficulty to appreciate its advantages over the Cox proportional hazards model, as well as the absence of adequate validation procedure. In this paper, we addressed these limitations by (1) using both simulated examples and data from National Wilms' Tumor clinical trials to illustrate proper interpretation of the censored quantile regression model and the differences and the advantages of the model compared to the Cox proportional hazards model; and (2) developing a validation procedure for the predictive censored quantile regression model. The performance of this procedure was examined using simulation studies. Overall, we recommend the use of censored quantile regression model, which permits a more sensitive analysis of time to event data together with the Cox proportional hazards model.

Generalizing Quantile Regression for Counting Processes with Applications to Recurrent Events

In survival analysis, quantile regression has become a useful approach to account for covariate effects on the distribution of an event time of interest. In this paper, we discuss how quantile regression can be extended to model counting processes, and thus lead to a broader regression framework for survival data. We specifically investigate the proposed modeling of counting processes for recurrent events data. We show that the new recurrent events model retains the desirable features of quantile regression such as easy interpretation and good model flexibility, while accommodating various observation schemes encountered in observational studies. We develop a general theoretical and inferential framework for the new counting process model, which unifies with an existing method for censored quantile regression. As another useful contribution of this work, we propose a sample-based covariance estimation procedure, which provides a useful complement to the prevailing bootstrapping approach. We demonstrate the utility of our proposals via simulation studies and an application to a dataset from the US Cystic Fibrosis Foundation Patient Registry (CFFPR).

Accelerated failure time model for case-cohort design with longitudinal covariates subject to measurement error and detection limits

Biomarkers are often measured over time in epidemiological studies and clinical trials for better understanding of the mechanism of diseases. In large cohort studies, case-cohort sampling provides a cost effective method to collect expensive biomarker data for revealing the relationship between biomarker trajectories and time to event. However, biomarker measurements are often limited by the sensitivity and precision of a given assay, resulting in data that are censored at detection limits and prone to measurement errors. Additionally, the occurrence of an event of interest may preclude biomarkers from being further evaluated. Inappropriate handling of these types of data can lead to biased conclusions. Under a classical case cohort design, we propose a modified likelihood-based approach to accommodate these special features of longitudinal biomarker measurements in the accelerated failure time models. The maximum likelihood estimators based on the full likelihood function are obtained by Gaussian quadrature method. We evaluate the performance of our case-cohort estimator and compare its relative efficiency to the full cohort estimator through simulation studies. The proposed method is further illustrated using the data from a biomarker study of sepsis among patients with community acquired pneumonia.

Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry. We propose a general noninformative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions. We extend these propriety results to cases where the response variables are censored. The latter scenario is of interest in the context of accelerated failure time models, which are relevant in survival analysis. We present a simulation study that demonstrates good frequentist properties of the posterior credible intervals associated with the proposed priors. This study also sheds some light on the trade-off between increased model flexibility and the risk of over-fitting. We illustrate the performance of the proposed models with real data. Although we focus on models with univariate response variables, we also present some extensions to the multivariate case in the Supporting Information. Copyright © 2016 John Wiley & Sons, Ltd.

A Bayesian approach for instrumental variable analysis with censored time-to-event outcome

Instrumental variable (IV) analysis has been widely used in economics, epidemiology, and other fields to estimate the causal effects of covariates on outcomes, in the presence of unobserved confounders and/or measurement errors in covariates. However, IV methods for time-to-event outcome with censored data remain underdeveloped. This paper proposes a Bayesian approach for IV analysis with censored time-to-event outcome by using a two-stage linear model. A Markov chain Monte Carlo sampling method is developed for parameter estimation for both normal and non-normal linear models with elliptically contoured error distributions. The performance of our method is examined by simulation studies. Our method largely reduces bias and greatly improves coverage probability of the estimated causal effect, compared with the method that ignores the unobserved confounders and measurement errors. We illustrate our method on the Women's Health Initiative Observational Study and the Atherosclerosis Risk in Communities Study.

Time trends and payer differences in lengths of initial hospitalization for preterm infants, Arkansas, 2004 to 2010

OBJECTIVE

The objective of this study was to examine the time trend in length of stay (LOS) and explore potential differences in neonatal LOS by insurance type for preterm infants in Arkansas between 2004 and 2010.

STUDY DESIGN

There were 18,712 preterm infants included in our analyses. Accelerated failure time models were used to model neonatal LOS as a function of insurance type and discharge year while adjusting for key maternal and infant characteristics, and complication/anomaly indicators.

RESULTS

Before adjusting for the complication/anomaly indicators, the LOS for preterm infants delivered to mothers in the Medicaid group was 3.2% shorter than those in the private payer group. Furthermore, each subsequent year was associated with a 1.6% increase in the expected LOS. However, after accounting for complications and anomalies, insurance coverage differences in neonatal LOS were not statistically significant while the trend in LOS persisted at a 0.59% increase for each succeeding year.

CONCLUSION

All of the apparent differences in LOS by insurance type and more than half of the apparent increase in LOS over time are accounted for by higher rates of complications among privately insured preterm infants and increasing rates of complications for all surviving preterm infants between 2004 and 2010.

Survival analysis and regression models

Time-to-event outcomes are common in medical research as they offer more information than simply whether or not an event occurred. To handle these outcomes, as well as censored observations where the event was not observed during follow-up, survival analysis methods should be used. Kaplan-Meier estimation can be used to create graphs of the observed survival curves, while the log-rank test can be used to compare curves from different groups. If it is desired to test continuous predictors or to test multiple covariates at once, survival regression models such as the Cox model or the accelerated failure time model (AFT) should be used. The choice of model should depend on whether or not the assumption of the model (proportional hazards for the Cox model, a parametric distribution of the event times for the AFT model) is met. The goal of this paper is to review basic concepts of survival analysis. Discussions relating the Cox model and the AFT model will be provided. The use and interpretation of the survival methods model are illustrated using an artificially simulated dataset.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan-Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

A new insight into fecal hemoglobin concentration-dependent predictor for colorectal neoplasia

We sought to assess how much of the variation in incidence of colorectal neoplasia is explained by baseline fecal hemoglobin concentration (FHbC) and also to assess the additional predictive value of conventional risk factors. We enrolled subjects aged 40 years and over who attended screening for colorectal cancer with the fecal immunochemical test (FIT) in Keelung community-based integrated screening program. The accelerated failure time model was used to train the clinical weights of covariates in the prediction model. Datasets from two external communities were used for external validation. The area under curve (AUC) for the model containing only FHbC was 83.0% (95% CI: 81.5-84.4%), which was considerably greater than the one containing only conventional risk factors (65.8%, 95% CI: 64.2-67.4%). Adding conventional risk factors did not make significant additional contribution (p = 0.62, AUC = 83.5%, 95% CI: 82.1-84.9%) to the predictive model with FHbC only. Males showed a stronger linear dose-response relationship than females, yielding gender-specific FHbC predictive models. External validation confirms these results. The high predictive ability supported by a dose-dependent relationship between baseline FHbC and the risk of developing colorectal neoplasia suggests that FHbC may be useful for identifying cases requiring closer postdiagnosis clinical surveillance as well as being an early indicator of colorectal neoplasia risk in the general population. Our findings may also make contribution to the development of the FHbC-guided screening policy but its pros and cons in connection with cost and effectiveness of screening should be evaluated before it can be applied to population-based screening for colorectal cancer.

Fast Censored Linear Regression

Weighted log-rank estimating function has become a standard estimation method for the censored linear regression model, or the accelerated failure time model. Well established statistically, the estimator defined as a consistent root has, however, rather poor computational properties because the estimating function is neither continuous nor, in general, monotone. We propose a computationally efficient estimator through an asymptotics-guided Newton algorithm, in which censored quantile regression methods are tailored to yield an initial consistent estimate and a consistent derivative estimate of the limiting estimating function. We also develop fast interval estimation with a new proposal for sandwich variance estimation. The proposed estimator is asymptotically equivalent to the consistent root estimator and barely distinguishable in samples of practical size. However, computation time is typically reduced by two to three orders of magnitude for point estimation alone. Illustrations with clinical applications are provided.

A general semiparametric hazards regression model: efficient estimation and structure selection

We consider a general semiparametric hazards regression model that encompasses the Cox proportional hazards model and the accelerated failure time model for survival analysis. To overcome the nonexistence of the maximum likelihood, we derive a kernel-smoothed profile likelihood function and prove that the resulting estimates of the regression parameters are consistent and achieve semiparametric efficiency. In addition, we develop penalized structure selection techniques to determine which covariates constitute the accelerated failure time model and which covariates constitute the proportional hazards model. The proposed method is able to estimate the model structure consistently and model parameters efficiently. Furthermore, variance estimation is straightforward. The proposed estimation performs well in simulation studies and is applied to the analysis of a real data set.

smcure: an R-package for estimating semiparametric mixture cure models

The mixture cure model is a special type of survival models and it assumes that the studied population is a mixture of susceptible individuals who may experience the event of interest, and cure/non-susceptible individuals who will never experience the event. For such data, standard survival models are usually not appropriate because they do not account for the possibility of cure. This paper presents an R package smcure to fit the semiparametric proportional hazards mixture cure model and the accelerated failure time mixture cure model.

Evaluating traditional Chinese medicine using modern clinical trial design and statistical methodology: application to a randomized controlled acupuncture trial

Traditional Chinese medicine (TCM), used in China and other Asian counties for thousands of years, is increasingly utilized in Western countries. However, due to inherent differences in how Western medicine and this ancient modality are practiced, employing the so-called Western medicine-based gold standard research methods to evaluate TCM is challenging. This paper is a discussion of the obstacles inherent in the design and statistical analysis of clinical trials of TCM. It is based on our experience in designing and conducting a randomized controlled clinical trial of acupuncture for post-operative dental pain control in which acupuncture was shown to be statistically and significantly better than placebo in lengthening the median survival time to rescue drug. We demonstrate here that PH assumptions in the common Cox model did not hold in that trial and that TCM trials warrant more thoughtful modeling and more sophisticated models of statistical analysis. TCM study design entails all the challenges encountered in trials of drugs, devices, and surgical procedures in the Western medicine. We present possible solutions to some but leave many issues unresolved.

Risk Prediction for Prostate Cancer Recurrence Through Regularized Estimation with Simultaneous Adjustment for Nonlinear Clinical Effects

In biomedical studies, it is of substantial interest to develop risk prediction scores using high-dimensional data such as gene expression data for clinical endpoints that are subject to censoring. In the presence of well-established clinical risk factors, investigators often prefer a procedure that also adjusts for these clinical variables. While accelerated failure time (AFT) models are a useful tool for the analysis of censored outcome data, it assumes that covariate effects on the logarithm of time-to-event are linear, which is often unrealistic in practice. We propose to build risk prediction scores through regularized rank estimation in partly linear AFT models, where high-dimensional data such as gene expression data are modeled linearly and important clinical variables are modeled nonlinearly using penalized regression splines. We show through simulation studies that our model has better operating characteristics compared to several existing models. In particular, we show that there is a non-negligible effect on prediction as well as feature selection when nonlinear clinical effects are misspecified as linear. This work is motivated by a recent prostate cancer study, where investigators collected gene expression data along with established prognostic clinical variables and the primary endpoint is time to prostate cancer recurrence. We analyzed the prostate cancer data and evaluated prediction performance of several models based on the extended c statistic for censored data, showing that 1) the relationship between the clinical variable, prostate specific antigen, and the prostate cancer recurrence is likely nonlinear, i.e., the time to recurrence decreases as PSA increases and it starts to level off when PSA becomes greater than 11; 2) correct specification of this nonlinear effect improves performance in prediction and feature selection; and 3) addition of gene expression data does not seem to further improve the performance of the resultant risk prediction scores.

Semiparametric analysis of recurrent events: artificial censoring, truncation, pairwise estimation and inference

The analysis of recurrent failure time data from longitudinal studies can be complicated by the presence of dependent censoring. There has been a substantive literature that has developed based on an artificial censoring device. We explore in this article the connection between this class of methods with truncated data structures. In addition, a new procedure is developed for estimation and inference in a joint model for recurrent events and dependent censoring. Estimation proceeds using a mixed U-statistic based estimating function approach. New resampling-based methods for variance estimation and model checking are also described. The methods are illustrated by application to data from an HIV clinical trial as with a limited simulation study.

An accelerated failure time mixture cure model with masked event

We extend the Dahlberg and Wang (Biometrics 2007, 63, 1237-1244) proportional hazards (PH) cure model for the analysis of time-to-event data that is subject to a cure rate with masked event to a setting where the PH assumption does not hold. Assuming an accelerated failure time (AFT) model with unspecified error distribution for the time to the event of interest, we propose rank-based estimating equations for the model parameters and use a generalization of the EM algorithm for parameter estimation. Applying our proposed AFT model to the same motivating breast cancer dataset as Dahlberg and Wang (Biometrics 2007, 63, 1237-1244), our results are more intuitive for the treatment arm in which the PH assumption may be violated. We also conduct a simulation study to evaluate the performance of the proposed method.