Semiparametric Additive Hazards Model Research Articles

Semiparametric varying-coefficient additive hazards model for informatively interval-censored failure time data

The analysis of interval-censored data with informative observation processes has recently attracted much attention and a few methods have been developed. However, all of the existing methods assume that covariate effects are constant and this may not be true sometimes in practice. To address this, in this paper, we propose a varying-coefficient additive hazards model and in the proposed method, frailty variables are used to describe the dependence between the failure time and the informative observation process. For inference, a Bernstein polynomials-based, two-step sieve maximum likelihood method is developed and the proposed method can be easily implemented. Furthermore, the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed approach works well for practical situations. The proposed method is applied to a cardiac allograft vasculopathy (CAV) study that motivated this investigation.

Semiparametric Additive Hazards Model with Doubly Truncated Data

Semiparametric Additive Hazards Model with Doubly Truncated Data

Shape restricted additive hazards models: Monotone, unimodal, and U-shape hazard functions.

We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time-dependent covariate with monotone or U-shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study.

A Genetic Association Test Accounting for Skewed X-Inactivation With Application to Biotherapy Immunogenicity in Patients With Autoimmune Diseases.

Despite being assayed on commercialized DNA chips, the X chromosome is commonly excluded from genome-wide association studies (GWAS). One of the reasons is the complexity to analyze the data taking into account the X-chromosome inactivation (XCI) process in women and in particular the XCI process with a potentially skewed pattern. This is the case when investigating the role of X-linked genetic variants in the occurrence of anti-drug antibodies (ADAs) in patients with autoimmune diseases treated by biotherapies. In this context, we propose a novel test statistic for selecting loci of interest harbored by the X chromosome that are associated with time-to-event data taking into account skewed X-inactivation (XCI-S). The proposed statistic relies on a semi-parametric additive hazard model and is straightforward to implement. Results from the simulation study show that the test provides higher power gains than the score tests from the Cox model (under XCI process or its escape) and the Xu et al.'s XCI-S likelihood ratio test. We applied the test to the data from the real-world observational multicohort study set-up by the IMI-funded ABIRISK consortium for identifying X chromosome susceptibility loci for drug immunogenicity in patients with autoimmune diseases treated by biotherapies. The test allowed us to select two single nucleotide polymorphisms (SNPs) with high linkage disequilibrium (rs5991366 and rs5991394) located in the cytoband Xp22.2 that would have been overlooked by the Cox score tests and the Xu et al.'s XCI-S likelihood ratio test. Both SNPs showed a similar protective effect for drug immunogenicity without any occurrence of ADA positivity for the homozygous females and hemizygous males for the alternative allele. To our knowledge, this is the first study to investigate the association between X chromosome loci and the occurrence of anti-drug antibodies. We think that more X-Chromosome GWAS should be performed and that the test is well-suited for identifying X-Chromosome SNPs, while taking into account all patterns of the skewed X-Chromosome inactivation process.

Semiparametric additive frailty hazard model for clustered failure time data

This article proposes a flexible semiparametric additive frailty hazard model under clustered failure time data, where frailty is assumed to have an additive effect on the hazard function. When there is no frailty, this model degenerates into a semiparametric additive hazard model. Our method can deal simultaneously with both time‐varying and constant covariate effects. The estimate of the covariate effects does not rely on the frailty distribution. The time‐varying coefficient is estimated by utilizing the local linear technique, while we can obtain a ‐consistency convergence rate of the constant‐coefficient estimate by integration. Another advantage of the estimator is that it has a closed form. We establish large sample properties of the estimator and conduct simulation studies under various scenarios to demonstrate its performance. The proposed method is applied to real data for illustration.

Weight calibration to improve efficiency for estimating pure risks from the additive hazards model with the nested case-control design.

We study the efficiency of covariate-specific estimates of pure risk (one minus the survival function) when some covariates are only available for case-control samples nested in a cohort. We focus on the semiparametric additive hazards model in which the hazard function equals a baseline hazard plus a linear combination of covariates with either time-varying or time-invariant coefficients. A published approach uses the design-based inclusion probabilities to reweight the nested case-control data. We obtain more efficient estimates of pure risks by calibrating the design weights to data available in the entire cohort, for both time-varying and time-invariant covariate coefficients. We develop explicit variance formulas for the weight-calibrated estimates based on influence functions. Simulations show the improvement in precision by using weight calibration and confirm the consistency of variance estimators and the validity of inference based on asymptotic normality. Examples are provided using data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study (PLCO).

ANALISIS SURVIVAL UNTUK DURASI PROSES KELAHIRAN MENGGUNAKAN MODEL REGRESI HAZARD ADDITIF

Survival data is the length of time until an event occurs. If the survival time is affected by other factor, it can be modeled with a regression model. The regression model for survival data is commonly based on the Cox proportional hazard model. In the Cox proportional hazard model, the covariate effect act multiplicatively on unknown baseline hazard. Alternative to the multiplicative hazard model is the additive hazard model. One of the additive hazard models is the semiparametric additive hazard model that introduced by Lin Ying in 1994. The regression coefficient estimates in this model mimic the scoring equation in the Cox model. Score equation of Cox model is the derivative of the Partial Likelihood and methods to maximize partial likelihood with Newton Raphson iterasi. Subject from this paper is describe the multiplicative and additive hazard model that applied to the duration of the birth process. The data is obtained from two different clinics,there are clinic that applies gentlebirth method while the other one no gentlebirth. From the data processing obtained the factors that affect on the duration of the birth process are baby’s weight, baby’s height and method of birth. Keywords: survival, additive hazard model, cox proportional hazard, partial likelihood, gentlebirth, duration

Population-Based Study on Cancer Subtypes, Guideline-Concordant Adjuvant Therapy, and Survival Among Women With Stage I-III Breast Cancer.

Breast cancer subtype is a key determinant in treatment decision-making, and also effects survival outcome. In this population-based study, in-depth analyses were performed to examine the impact that breast cancer subtype and receipt of guideline-concordant adjuvant systemic therapy (AST) have on survival using a population-based cancer registry's data. Women aged ≥20 years with microscopically confirmed stage I-III breast cancer diagnosed in 2011 were identified from the Louisiana Tumor Registry. Breast cancer subtypes were categorized based on hormone receptor (HR) and HER2 status. Guideline-concordant treatment was defined using the NCCN Guidelines for Breast Cancer. Logistic regression was applied to identify factors associated with guideline-concordant AST receipt. Kaplan-Meier survival curves were generated to compare survival among subtypes by AST receipt status, and a semiparametric additive hazard model was used to verify the factors impacting survival outcome. Of 2,214 eligible patients, most (70.8%) were HR+/HER2- followed by HR-/HER2- (14.4%), and 78.6% received guideline-concordant AST. Compared with patients with the HR+/HER2+ subtype, women with other subtypes were more likely to be guideline-concordant after adjusting for sociodemographic and clinical variables. Women with the HR-/HER2+ or HR-/HER2- subtype had a higher risk of any-cause and breast cancer-specific death than those with the HR+/HER2+ subtype. Those who did not receive AST had an additional adjusted hazard of 0.0191 (P=.0001) in overall survival and 0.0126 (P=.0011) in cause-specific survival compared with those who received AST. Most patients received guideline-concordant AST, except for those with the HR+/HER2+ subtype. Patients receiving guideline-adherent adjuvant therapy had better survival outcomes across all breast cancer subtypes.

Instrumental variable estimation in semi-parametric additive hazards models.

SummaryInstrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available. Two‐stage least‐squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data. The semi‐parametric additive hazard model which can include time‐independent and time‐dependent covariate effects is particularly suited for the two‐stage residual inclusion method, since it allows direct estimation of time‐independent covariate effects without restricting the effect of the residual on the hazard. In this article, we prove asymptotic normality of two‐stage residual inclusion estimators of regression coefficients in a semi‐parametric additive hazard model with time‐independent and time‐dependent covariate effects. We consider the cases of continuous and binary exposure. Estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands. The new methods are compared to existing ones in a simulation study and are applied to a real data set. The proposed methods perform favorably especially in cases with exposure‐dependent censoring.

Celebrating the 25th International Conference of The International Environmetrics Society

Celebrating the 25th International Conference of The International Environmetrics Society

Additive hazards model with auxiliary subgroup survival information.

The semiparametric additive hazards model is an important way for studying the effect of potential risk factors for right-censored time-to-event data. In this paper, we study the additive hazards model in the presence of auxiliary subgroup [Formula: see text]-year survival information. We formulate the known auxiliary information in the form of estimating equations, and combine them with the conventional score-type estimating equations for the estimation of the regression parameters based on the maximum empirical likelihood method. We prove that the new estimator of the regression coefficients follows asymptotically a multivariate normal distribution with a sandwich-type covariance matrix that can be consistently estimated, and is strictly more efficient, in an asymptotic sense, than the conventional one without incorporation of the available auxiliary information. Simulation studies show that the new proposal has substantial advantages over the conventional one in terms of standard errors, and with the accommodation of more informative information, the proposed estimator becomes more competing. An AIDS data example is used for illustration.

On estimation of the optimal treatment regime with the additive hazards model

We propose a doubly robust estimation method for the optimal treatment regime based on an additive hazards model with censored survival data. Specifically, we introduce a new semiparametric additive hazard model which allows flexible baseline covariate effects in the control group and incorporates marginal treatment effect and its linear interaction with covariates. In addition, we propose a time-dependent propensity score to construct an A-learning type of estimating equations. The resulting estimator is shown to be consistent and asymptotically normal when either the baseline effect model for covariates or the propensity score is correctly specified. The asymptotic variance of the estimator is consistently estimated using a simple resampling method. Simulation studies are conducted to evaluate the finite-sample performance of the estimators and an application to AIDS clinical trial data is also given to illustrate the methodology.

Bayesian inference in time-varying additive hazards models with applications to disease mapping.

Environmental health and disease mapping studies are often concerned with the evaluation of the combined effect of various socio-demographic and behavioral factors, and environmental exposures on time-to-events of interest, such as death of individuals, organisms or plants. In such studies, estimation of the hazard function is often of interest. In addition to known explanatory variables, the hazard function maybe subject to spatial/geographical variations, such that proximally located regions may experience similar hazards than regions that are distantly located. A popular approach for handling this type of spatially-correlated time-to-event data is the Cox's Proportional Hazards (PH) regression model with spatial frailties. However, the PH assumption poses a major practical challenge, as it entails that the effects of the various explanatory variables remain constant over time. This assumption is often unrealistic, for instance, in studies with long follow-ups where the effects of some exposures on the hazard may vary drastically over time. Our goal in this paper is to offer a flexible semiparametric additive hazards model (AH) with spatial frailties. Our proposed model allows both the frailties as well as the regression coefficients to be time-varying, thus relaxing the proportionality assumption. Our estimation framework is Bayesian, powered by carefully tailored posterior sampling strategies via Markov chain Monte Carlo techniques. We apply the model to a dataset on prostate cancer survival from the US state of Louisiana to illustrate its advantages.

Survivor bias in Mendelian randomization analysis.

Mendelian randomization studies employ genotypes as experimental handles to infer the effect of genetically modified exposures (e.g. vitamin D exposure) on disease outcomes (e.g. mortality). The statistical analysis of these studies makes use of the standard instrumental variables framework. Many of these studies focus on elderly populations, thereby ignoring the problem of left truncation, which arises due to the selection of study participants being conditional upon surviving up to the time of study onset. Such selection, in general, invalidates the assumptions on which the instrumental variables analysis rests. We show that Mendelian randomization studies of adult or elderly populations will therefore, in general, return biased estimates of the exposure effect when the considered genotype affects mortality; in contrast, standard tests of the causal null hypothesis that the exposure does not affect the mortality rate remain unbiased, even when they ignore this problem of left truncation. To eliminate "survivor bias" or "truncation bias" from the effect of exposure on mortality, we next propose various simple strategies under a semi-parametric additive hazard model. We examine the performance of the proposed methods in simulation studies and use them to infer the effect of vitamin D on all-cause mortality based on the Monica10 study with the genetic variant filaggrin as instrumental variable.

Instrumental variable with competing risk model.

In this paper, we discuss causal inference on the efficacy of a treatment or medication on a time-to-event outcome with competing risks. Although the treatment group can be randomized, there can be confoundings between the compliance and the outcome. Unmeasured confoundings may exist even after adjustment for measured covariates. Instrumental variable methods are commonly used to yield consistent estimations of causal parameters in the presence of unmeasured confoundings. On the basis of a semiparametric additive hazard model for the subdistribution hazard, we propose an instrumental variable estimator to yield consistent estimation of efficacy in the presence of unmeasured confoundings for competing risk settings. We derived the asymptotic properties for the proposed estimator. The estimator is shown to be well performed under finite sample size according to simulation results. We applied our method to a real transplant data example and showed that the unmeasured confoundings lead to significant bias in the estimation of the effect (about 50% attenuated). Copyright © 2017 John Wiley & Sons, Ltd.

A multiple imputation approach to the analysis of clustered interval-censored failure time data with the additive hazards model

Clustered interval-censored failure time data can occur when the failure time of interest is collected from several clusters and known only within certain time intervals. Regression analysis of clustered interval-censored failure time data is discussed assuming that the data arise from the semiparametric additive hazards model. A multiple imputation approach is proposed for inference. A major advantage of the approach is its simplicity because it avoids estimating the correlation within clusters by implementing a resampling-based method. The presented approach can be easily implemented by using the existing software packages for right-censored failure time data. Extensive simulation studies are conducted, indicating that the proposed imputation approach performs well for practical situations. The proposed approach also performs well compared to the existing methods and can be more conveniently applied to various types of data representation. The proposed methodology is further demonstrated by applying it to a lymphatic filariasis study.

Analysis of two-phase sampling data with semiparametric additive hazards models

Under the case-cohort design introduced by Prentice (Biometrica 73:1-11, 1986), the covariate histories are ascertained only for the subjects who experience the event of interest (i.e., the cases) during the follow-up period and for a relatively small random sample from the original cohort (i.e., the subcohort). The case-cohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times. Most statistical methods developed for the case-cohort design use the proportional hazards model, and few methods allow for time-varying regression coefficients. In addition, most methods disregard data from subjects outside of the subcohort, which can result in inefficient inference. Addressing these issues, this paper proposes an estimation procedure for the semiparametric additive hazards model with case-cohort/two-phase sampling data, allowing the covariates of interest to be missing for cases as well as for non-cases. A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant. An augmented inverse probability weighted estimation procedure is proposed. The proposed method allows utilizing the auxiliary information that correlates with the phase-two covariates to improve efficiency. The asymptotic properties of the proposed estimators are established. An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted complete-case estimation method. The method is applied to analyze data from a preventive HIV vaccine efficacy trial.

Coordinate Descent Methods for the Penalized Semiparametric Additive Hazards Model

For survival data with a large number of explanatory variables, lasso penalized Cox regression is a popular regularization strategy. However, a penalized Cox model may not always provide the best fit to data and can be difficult to estimate in high dimension because of its intrinsic nonlinearity. The semiparametric additive hazards model is a flexible alternative which is a natural survival analogue of the standard linear regression model. Building on this analogy, we develop a cyclic coordinate descent algorithm for fitting the lasso and elastic net penalized additive hazards model. The algorithm requires no nonlinear optimization steps and offers excellent performance and stability. An implementation is available in the R package ahaz. We demonstrate this implementation in a small timing study and in an application to real data.

Regression analysis of competing risks data via semi-parametric additive hazard model

When the subjects in a study possess different demographic and disease characteristics and are exposed to more than one types of failure, a practical problem is to assess the covariate effects on each type of failure as well as on all-cause failure. The most widely used method is to employ the Cox models on each cause-specific hazard and the all-cause hazard. It has been pointed out that this method causes the problem of internal inconsistency. To solve such a problem, the additive hazard models have been advocated. In this paper, we model each cause-specific hazard with the additive hazard model that includes both constant and time-varying covariate effects. We illustrate that the covariate effect on all-cause failure can be estimated by the sum of the effects on all competing risks. Using data from a longitudinal study on breast cancer patients, we show that the proposed method gives simple interpretation of the final results, when the primary covariate effect is constant in the additive manner on each cause-specific hazard. Based on the given additive models on the cause-specific hazards, we derive the inferences for the adjusted survival and cumulative incidence functions.

Assessing cumulative incidence functions under the semiparametric additive risk model

In analyzing competing risks data, a quantity of considerable interest is the cumulative incidence function. Often, the effect of covariates on the cumulative incidence function is modeled via the proportional hazards model for the cause-specific hazard function. As the proportionality assumption may be too restrictive in practice, we consider an alternative more flexible semiparametric additive hazards model of (Biometrika 1994; 81:501-514) for the cause-specific hazard. This model specifies the effect of covariates on the cause-specific hazard to be additive as well as allows the effect of some covariates to be fixed and that of others to be time varying. We present an approach for constructing confidence intervals as well as confidence bands for the cause-specific cumulative incidence function of subjects with given values of the covariates. Furthermore, we also present an approach for constructing confidence intervals and confidence bands for comparing two cumulative incidence functions given values of the covariates. The finite sample property of the proposed estimators is investigated through simulations. We conclude our paper with an analysis of the well-known malignant melanoma data using our method.