Multiple Hazards Model Research Articles

MULTIPLE HAZARDS MODEL, ANALYSIS OF THE GEOMORPHOLOGICAL HAZARDS OF FLASH FLOODS ON THE ARCHAEOLOGICAL SITES OF THE EL-AMBAGI BASIN, EASTERN DESERT, EGYPT

MULTIPLE HAZARDS MODEL, ANALYSIS OF THE GEOMORPHOLOGICAL HAZARDS OF FLASH FLOODS ON THE ARCHAEOLOGICAL SITES OF THE EL-AMBAGI BASIN, EASTERN DESERT, EGYPT

Impact of perineural invasion on the outcome of patients with synchronous colorectal liver metastases treated with neoadjuvant chemotherapy and surgery

PurposeTo analyze the prognostic value of variables of the primary tumor in patients with synchronous liver metastases in colorectal cancer (CLRMs) treated with neoadjuvant chemotherapy and surgery.Methods/PatientsFrom a prospective database, we retrospectively identified all patients with synchronous CLRMs who were treated with neoadjuvant chemotherapy and liver resection. Using univariate and multivariate analyses, we identified the variables associated with tumor recurrence. Overall survival and disease-free survival were calculated using the Kaplan–Meier method with differences determined by the Cox multiple hazards model. Results were compared using the log-rank test.ResultsNinety-eight patients with synchronous CLRMs were identified. With a median follow-up of 39.8 months, overall survival and disease-free survival at 5 and 10 years were 53%, 41.7%, 29% and 29%, respectively. Univariate analysis identified three variables associated with tumor recurrence: location in the colon (p = 0.025), lymphovascular invasion (p = 0.011) and perineural invasion (p = 0.005). Multivariate analysis identified two variables associated with worse overall survival: perineural invasion (HR 2.36, 95% CI 1.162–4.818, p = 0.018) and performing frontline colectomy (HR 3.286, 95% CI 1.256–8.597, p = 0.015). Perineural invasion remained as the only variable associated with lower disease-free survival (HR 1.867, 95% CI 1.013–3.441, p = 0.045). Overall survival at 5 and 10 years in patients with and without perineural invasion was 68.2%, 54.4% and 29.9% and 21.3%, respectively (HR 5.920, 95% CI 2.241–15.630, p < 0.001).ConclusionsPerineural invasion in the primary tumor is the variable with most impact on survival in patients with synchronous CLRMs treated with neoadjuvant chemotherapy and surgery.

Parameter Estimation for Additive Hazard Model Recurrent Event Using Counting Process Approach

The Cox regression model is widely used for survival data analysis. The Cox model requires a proportional hazard. If the proportional hazard assumption is doubtful, then the additive hazard model can be used, where the covariates act in an additively to the baseline hazard function. If the observed survival time is more than once for one individual during the observation, it is called a recurrent event. The additive hazard model measures risk difference to the effect of a covariate in absolutely, while the proportional hazards model measure hazard ratio in relatively. The risk coefficients estimation in the additive hazard model mimics the multiplicative hazard model, using partial likelihood methods. The derivation of these estimators, outlined in the technical notes, is based on the counting process approach. The counting process approach was first developed by Aalen on 1975 which combines elements of stochastic integration, martingale theory and counting process theory. The method is applied to study about the effect of supplementation on infant growth and development. Based on the processing results, the factors that affect the growth and development of the infant are gender, treatment and mother's education.

On Some Properties of $$\alpha $$-Mixtures

The $$\alpha $$ -mixtures is a new, flexible family of distributions that includes many mixture models as special cases. This paper is mainly focused on relevant stochastic comparisons and ageing properties of $$\alpha $$ -mixtures of survival functions. In particular, we prove that ageing properties of $$\alpha $$ -mixtures for additive and multiplicative hazards models depend on the properties of the baseline failure rate functions and the corresponding conditional moments of mixing distributions. Partial orderings of the finite $$\alpha $$ -mixtures in the sense of the usual stochastic order and the hazard rate order are discussed. Finally, we extend some results on the shape of the mixture failure rate obtained in the literature for usual mixtures to the case of $$\alpha $$ -mixtures.

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

Left-censored dementia incidences in estimating cohort effects

We estimate the dementia incidence hazard in Germany for the birth cohorts 1900 until 1954 from a simple sample of Germany’s largest health insurance company. Followed from 2004 to 2012, 36,000 uncensored dementia incidences are observed and further 200,000 right-censored insurants included. From a multiplicative hazard model we find a positive and linear trend in the dementia hazard over the cohorts. The main focus of the study is on 11,000 left-censored persons who have already suffered from the disease in 2004. After including the left-censored observations, the slope of the trend declines markedly due to Simpson’s paradox, left-censored persons are imbalanced between the cohorts. When including left-censoring, the dementia hazard increases differently for different ages, we consider omitted covariates to be the reason. For the standard errors from large sample theory, left-censoring requires an adjustment to the conditional information matrix equality.

SURVIVAL MODELS IN THE CONTEXT OF MULTIPLICATIVE AND ADDITIVE HAZARDS

In survival analysis, multiplicative and additive hazards models provide the two principal frameworks to study the association between the hazard and covariates. When these models are considered for analyzing a given survival dataset, it becomes relevant to evaluate the overall goodness-of-fit and how well each model can predict those subjects who subsequently will or will not experience the event. In this paper, this evaluation is based on a graphical representation of the Cox-Snell residuals and also on a time-dependent version of the area under the receiver operating characteristic (ROC) curve, denoted by AUC(t). A simulation study is carried out to evaluate the performance of the AUC(t) as a tool for comparing the predictive accuracy of survival models. A dataset from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver is also considered to illustrate the usefulness of these tools to compare survival models formulated under distinct hazards frameworks.

Evaluating quality of hospital care using time-to-event endpoints based on patient follow-up data

Revisions of hip and knee arthroplasty implants and cardiac pacemakers pose a large medical and economic burden for society. Consequently, the identification of health care providers with potential for quality improvements regarding the reduction of revision rates is a central aim of quality assurance in any healthcare system. Even though the time span between initial and possible subsequent operations is a classical time-to-event endpoint, hospital-specific quality indicators are in practice often measured as revisions within a fixed follow-up period and subsequently analyzed by traditional methods like proportions or logistic regression. Methods from survival analysis, in contrast, allow the inclusion of all observations, i.e. also those with early censoring or events, and make thus more efficient and more timely use of the available data than traditional methods. This may be obvious to a statistician but in an applied context with historic traditions, the introduction of more complicated methods needs a clear presentation of their added value. We demonstrate how standard survival methods like the Kaplan–Meier estimator and a multiplicative hazards model outperform traditional methods with regard to the identification of performance outliers. Following that, we use the proposed methods to analyze 640,000 hip and knee replacement operations with about 13,000 revisions between 2015 and 2016 in more than 1200 German hospitals in the annual evaluation of quality of care. Based on the results, performance outliers are identified which are to be further investigated qualitatively with regard to their provided quality of care and possible necessary measures for improvement. Survival analysis is a sound statistical framework for analyzing data in the context of quality assurance and survival methods outperform the statistical methods that are traditionally used in this area.

Confidence Bands for Multiplicative Hazards Models: Flexible Resampling Approaches

We propose new resampling‐based approaches to construct asymptotically valid time‐simultaneous confidence bands for cumulative hazard functions in multistate Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time‐dependent covariates, where the data may be subject to independent right‐censoring or left‐truncation. We use simulations to investigate their finite sample behavior. Finally, the methods are utilized to analyze two empirical examples with survival and competing risks data.

Additive-multiplicative hazards regression models for interval-censored semi-competing risks data with missing intermediate events

BackgroundIn clinical trials and survival analysis, participants may be excluded from the study due to withdrawal, which is often referred to as lost-to-follow-up (LTF). It is natural to argue that a disease would be censored due to death; however, when an LTF is present it is not guaranteed that the disease has been censored. This makes it important to consider both cases; the disease is censored or not censored. We also note that the illness process can be censored by LTF. We will consider a multi-state model in which LTF is not regarded as censoring but as a non-fatal event.MethodsWe propose a multi-state model for analyzing semi-competing risks data with interval-censored or missing intermediate events. More precisely, we employ the additive and multiplicative hazards model with log-normal frailty and construct the conditional likelihood to estimate the transition intensities among states in the multi-state model. Marginalization of the full likelihood is accomplished using adaptive importance sampling, and the optimal solution of the regression parameters is achieved through the iterative quasi-Newton algorithm.ResultsSimulation is performed to investigate the finite-sample performance of the proposed estimation method in terms of the relative bias and coverage probability of the regression parameters. The proposed estimators turned out to be robust to misspecifications of the frailty distribution. PAQUID data have been analyzed and yielded somewhat prominent results.ConclusionsWe propose a multi-state model for semi-competing risks data for which there exists information on fatal events, but information on non-fatal events may not be available due to lost to follow-up. Simulation results show that the coverage probabilities of the regression parameters are close to a nominal level of 0.95 in most cases. Regarding the analysis of real data, the risk of transition from a healthy state to dementia is higher for women; however, the risk of death after being diagnosed with dementia is higher for men.

Long term risk of developing type 1 diabetes after HPV vaccination in males and females

IntroductionDespite minimal evidence, public concerns that the human papillomavirus (HPV) vaccine can cause autoimmune diseases (AD) persist. We evaluated whether HPV vaccine is associated with a long-term increased risk of diabetes mellitus type 1 (DM1). MethodsThis was a retrospective cohort study in which we identified all potential DM1 cases from Kaiser Permanente Northern California (KPNC) members who were between 11 and 26 years old any time after June 2006 through December 2015. We chart reviewed a random sample of 100 DM1 cases to confirm diagnosis and to develop a computer algorithm that reliably determined symptom onset date. Our DM1 Analysis Population comprised all individuals who met membership criteria and who were age and sex eligible to have received HPV vaccine. We adjusted for age, sex, race, Medicaid, and years of prior KPNC membership by stratification using a Cox multiplicative hazards model with a calendar timeline. ResultsOur DM1 analysis included 911,648 individuals. Of 2613 DM1 cases identified, 338 remained in the analysis after applying our algorithm, HPV vaccine eligibility and membership criteria. Over the 10 years of the study period, comparing vaccinated with unvaccinated persons, we did not find an increased risk of DM1 associated with HPV vaccine receipt (hazard ratio 1.21, 95% Confidence Interval 0.94, 1.57). ConclusionsWe found no increased risk for development of DM1 following HPV vaccination. Our study provides reassurance that during the 10-year time period after HPV vaccine was introduced, there was no substantial increased risk for DM1 following HPV vaccination.

The estimation for the general additive–multiplicative hazard model using the length-biased survival data

We use the general additive–multiplicative hazard model to analyze the length biased data with right censorship and use the estimating equation method that incorporates the information about length-biased sampling scheme to do the inference. In addition, some graphical and numerical methods are developed for assessing the adequacy of the general additive–multiplicative hazard model. The procedures are derived from cumulative sums of martingale-based residuals over follow-up time and covariate values. The simulations are conducted to insure the good performance of this method. An application to the Oscar data is also illustrated.

Joint analysis of recurrent event data with additive–multiplicative hazards model for the terminal event time

Recurrent event data are often collected in longitudinal follow-up studies. In this article, we propose a semiparametric method to model the recurrent and terminal events jointly. We present an additive–multiplicative hazards model for the terminal event and a proportional intensity model for the recurrent events, and a shared frailty is used to model the dependence between the recurrent and terminal events. We adopt estimating equation approaches for inference, and the asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies. An application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is illustrated.

Additive–multiplicative hazards model with current status data

The additive–multiplicative hazards (AMH) regression model specifies an additive and multiplicative form on the hazard function for the counting process associated with a multidimensional covariate process, which contains the Cox proportional hazards model and the additive hazards model as its special cases. In this paper, we study the AMH model with current status data, where the cumulative hazard hazard function is assumed to be nonparametric and is estimated using B-splines with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood estimation is proposed to estimate regression parameters. The proposed estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The B-splines estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and a real data example is presented for illustration.

The generalized moment estimation of the additive–multiplicative hazard model with auxiliary survival information

Additive–multiplicative hazard model is a natural extension of the proportional hazard model and the additive hazard model in survival analysis. It is classical for applying the martingale estimating functions to estimate the regression parameters. However, the generalized moment method is employed to estimate the coefficients via synthesizing the auxiliary subgroup survival information. The estimators are established to be consistent and asymptotically normal. Furthermore, the method is more efficient than the famous martingale approach. In particular, these asymptotic variance–covariances are identical as the number of subgroups is equal to one. The large sample property of the Breslow estimator for the baseline cumulative hazard function is also investigated. Some extensive simulation studies are conducted to evaluate the finite-sample performances of the proposed method. A real data study is analyzed to show its practical utility.

Multiple frailty model for clustered interval-censored data with frailty selection.

Interval-censored time-to-event data often occur in studies of diseases where the symptoms of interest are not directly observable but require lab examinations for detection. Furthermore, the independence assumption among observations may not be valid if they are from clusters. Some methods have been developed for analysing clustered interval-censored data with a shared frailty to account for overall heterogeneity. In this paper, we propose a multiple frailty proportional hazards model, where we not only account for the baseline heterogeneity and effect variation across clusters for predictors, but also quantify the probabilities of the existence of such frailties. This proposed model will be especially useful for analysing multi-center randomised clinical trials for HIV, infections or progression-free survival in oncology studies.

Frailty models for pneumonia to death with a left-censored covariate.

Frailty models are multiplicative hazard models for studying association between survival time and important clinical covariates. When some values of a clinical covariate are unobserved but known to be below a threshold called the limit of detection (LOD), naive approaches ignoring this problem, such as replacing the undetected value by the LOD or half of the LOD, often produce biased parameter estimate with larger mean squared error of the estimate. To address the LOD problem in a frailty model, we propose a flexible smooth nonparametric density estimator along with Simpson's numerical integration technique. This is an extension of an existing method in the likelihood framework for the estimation and inference of the model parameters. The proposed new method shows the estimators are asymptotically unbiased and gives smaller mean squared error of the estimates. Compared with the existing method, the proposed new method does not require distributional assumptions for the underlying covariates. Simulation studies were conducted to evaluate the performance of the new method in realistic scenarios. We illustrate the use of the proposed method with a data set from Genetic and Inflammatory Markers of Sepsis study in which interlekuin-10 was subject to LOD.

Gene expression markers of efficacy and resistance to cetuximab treatment in metastatic colorectal cancer: results from CALGB 80203 (Alliance).

Formalin-fixed, paraffin-embedded tumor samples from CALGB 80203 were analyzed for expression of EGFR axis-related genes to identify prognostic or predictive biomarkers for cetuximab treatment. Patients (238 total) with first-line metastatic colorectal cancer (mCRC) were randomized to FOLFOX or FOLFIRI chemotherapy ± cetuximab. qRT-PCR analyses were conducted on tissues from 103 patients at baseline to measure gene expression levels of HER-related genes, including amphiregulin (AREG), betacellulin (BTC), NT5E (CD73), DUSP4, EGF, EGFR, epigen (EPGN), epiregulin (EREG), HBEGF, ERBB2 (HER2), ERBB3 (HER3), ERBB4 (HER4), PHLDA1, and TGFA. The interactions between expression levels and treatment with respect to progression-free survival (PFS) and overall survival (OS) were modeled using multiplicative Cox proportional hazards models. High tumor mRNA levels of HER2 [hazard ratio (HR), 0.64; P = 0.002] and EREG (HR, 0.89; P = 0.016) were prognostic markers associated with longer PFS across all patients. HER3 and CD73 expression levels were identified as potential predictive markers of benefit from cetuximab. In KRAS wild-type (WT) tumors, low HER3 expression was associated with longer OS from cetuximab treatment, whereas high HER3 expression was associated with shorter OS from cetuximab treatment (chemo + cetuximab: HR, 1.15; chemo-only: HR, 0.48; Pinteraction = 0.029). High CD73 expression was associated with longer PFS from cetuximab treatment in patients with KRAS-WT (chemo + cetuximab: HR, 0.91; chemo-only: HR, 1.57; Pinteraction = 0.026) and KRAS-mutant (Mut) tumors (chemo + cetuximab: HR, 0.80; chemo-only: HR, 1.29; P = 0.025). Gene expression of HER3 and CD73 was identified as a potential predictive marker for cetuximab. These data implicate HER axis signaling and immune modulation as potential mechanisms of cetuximab action and sensitivity.

Application of Multiplicative and Additive Hazards Models to Injury Prevention among Healthcare Workers

Application of Multiplicative and Additive Hazards Models to Injury Prevention among Healthcare Workers

Is perineural invasion (PN) a determinant of disease free survival in early stage colorectal cancer?

The prognostic importance of perineural invasion (PN) in colorectal cancer (CRC) is unclear. The aim of this study to find out whether the PN was an independent stratification factor of postoperative relapse in curatively resected high-risk stage II & III CRC patients who were treated with adjuvant therapy. Data of patients with high risk stage II & all stage III CRCs treated with adjuvant chemotherapy were retrospectively analyzed. Pathological features of final surgical specimen were noted. Disease-free survival was determined by Kaplan-Meier estimator, with differences determined by multivariate analysis using the Cox multiple hazards model. Results were compared using the log-rank test. PN was found to be positive in 26% in the files of 593 eligible patients. In 21% of the reports PN status was not reported. Presence of PN in the resected primary tumors did not have independent effect on DFS. Further analyses for importance of PN on DFS of colon or rectal cancers did not show any effect. This study had failed to demonstrate any prognostic effect of PN for DFS in surgically resected stage II and III CRC patients who received adjuvant treatments.