Predicting the Survival Time for Bladder Cancer Using an Additive Hazards Model in Microarray Data

Background:Survival rates for breast cancer (BC) are often based on the outcomes of this disease. The aim of this study was to compare the performance of three survival models, namely Cox regression, Aalen's, and Lin and Ying's additive hazards (AH) models for identifying the prognostic factors regarding the survival time of BC patients.Materials and Methods:This study was a historical cohort study which used 1025 females' medical records that underwent modified radical mastectomy or breast saving. These patients were admitted to Besat and Chamran Hospitals, Tehran, Iran, during 2010–2015 and followed until 2017. The Aalen's and Lin and Ying's AH models and also traditional Cox model were applied for analysis of time to death of BC patients using R 3.5.1 software.Results:In Aalen's and also Lin and Ying's AH models, age at diagnosis, history of disease, number of lymph nodes, metastasis, hormonal therapy, and evacuation lymph nodes were prognostic factors for the survival of BC patients (P < 0.05). In addition, in the Lin and Ying's AH model tumor size (P = 0.048) was also identified as a significant factor. According to Aalen's plot, metastasis, age at diagnosis, and number of lymph nodes had a time-varying effect on survival time. These variables had a different slope as the times go on.Conclusion:AH model may yield new insights in prognostic studies of survival time of patients with BC over time. Because of the positive slope of estimated cumulative regression function in Aalen's plot, metastasis, higher age at diagnosis, and high number of lymph nodes are important factors in reducing the survival BC, and then based on these factors, the therapists should consider a special therapeutic protocol for BC patients.

Competing Risks Data Analysis with High-dimensional Covariates: An Application in Bladder Cancer

Additive time-dependent hazard model with doubly truncated data

Mediation analysis plays an increasingly crucial role in identifying potential causal pathways between exposures and outcomes. However, there is currently a lack of developed mediation approaches for high-dimensional survival data, particularly when considering additive hazard models. The present study introduces two novel approaches for identifying statistically significant mediators in high-dimensional additive hazard models, including the multiple testing-based mediator selection method and knockoff filter procedure. The simulation results demonstrate the outstanding performance of these two proposed methods. Finally, we employ the proposed methodology to analyze the Cancer Genome Atlas (TCGA) cohort in order to identify DNA methylation markers that mediate the association between smoking and survival time among lung cancer patients.

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.

When describing the influence of equipment state to failure rate, traditional additive hazard model (AHM) has certain defects. Therefore, an improved AHM with equipment age and health index (HI) as variables is established, in which HI is used to describe the equipment state. In order to fit out the model's five parameters, a nonlinear constrained optimization problem was posed. A sampling algorithm based on Monte Carlo method was also proposed to obtain parameter ranges and initial values. When the sample data are complete, the parameters can be fitted out by Trust Region algorithm. Historical data of most equipment lack HI time series at present, so non-sequential Monte Carlo method is applied in the section of example analysis to obtain approximate solution of parameters. Fitting results of the example show that an AHM with practical significance can be acquired through the parameter fitting method. Compared with the results of two models with age as the only variable, sum of squares due to error (SSE) of the AHM decreases by at least 10%.

In the disciplines of medicine, biology and social science, causal mediation analysis is widely used to examine the effect of an exposure on an outcome through different causal pathways. Recently, there is rapid development of mediation analysis with survival data. An early work of Lange and Hansen proposed to identify the direct and indirect causal effects under the additive hazards model with a single mediator. However, inaccurate measurements of mediators and confounders may lead to biased causal effect estimation. We propose a measurement error correction approach to tackle measurement error in the mediators and confounders under the additive hazards model where multiple mediators are present. We apply the proposed corrected method to the ACTG175 Study data set, and uncover interesting findings.

Background: Bladder cancer is the ninth most commonly diagnosed malignancy worldwide. The trend of bladder cancer incidence and mortality is rising in Iran. This study was aimed to evaluate the survival rate of patients with bladder cancer in Yazd province, Iran. Methods: In this retrospective cohort study, data were collected from 340 patients suffering from bladder cancer referred to Shahid Rahnemon and Shohada-Kargar Hospitals in Yazd province, Iran between April, 2001 and March, 2012. Variables included age, gender, stage of cancer, place of residence and type of treatment. The Kaplan-Meier and Cox regression analyses were used to evaluate the relationship between each variable and survival time. A P value less than 0.05 was considered significant. Results: The mean age of total patients was 65.8 ± 13.6 years, and their mean survival time was 68.55 ± 6.05 months. Cumulative survival rates at the end of 1, 3, and 5 years in bladder cancer patients were 91%, 58%, and 51.4%, respectively. A statistically significant association was found between age (P = 0.005), stage of disease (P = 0.0003), type of treatment (P = 0.0003) and survival time of patients. Data showed no significant correlation between age, gender, place of residence and patients’ survival. Conclusions: The survival of patients suffering from bladder cancer in this study was less than other reports. Patients’age and cancer stage were the effective factors in survival time. Continuous screening of older people for cancer diagnosis in early stages is seemed to improve survival in patients. Keywords: Bladder; Cancer; Survival Rate; Iran

BackgroundTumor microenvironment is composed of tumor cells, fibroblasts, endothelial cells, and infiltrating immune cells. Tumor-associated immune cells may inhibit or promote tumor growth and progression. This study was conducted to determine whether the number and microlocalization of macrophages, mature dendritic cells and cytotoxic T cells in non-small cell lung cancer are associated with patient's survival time.MethodsNinety-nine patients with non-small cell lung cancer (NSCLC) were included in this retrospective study. Paraffin-embedded NSCLC specimens and their clinicopathological data including up to 8-year follow-up information were used. Immunohistochemical staining for CD68 (marker for macrophages), CD83 (marker for mature dendritic cells), and CD8 (marker for cytotoxic T cells) was performed and evaluated in a blinded fashion. The numbers of immune cells in tumor islets and stroma, tumor islets, or tumor stroma were counted under a microscope. Correlation of the cell numbers and patient's survival time was analyzed using the Statistical Package for the Social Sciences (version 13.0).ResultsThe numbers of macrophages, mature dendritic cells and cytotoxic T cells were significantly more in the tumor stroma than in the tumor islets. The number of macrophages in the tumor islets was positively associated with patient's survival time, whereas the number of macrophages in the tumor stroma was negatively associated with patient's survival time in both univariate and multivariate analyses. The number of mature dendritic cells in the tumor islets and stroma, tumor islets only, or tumor stroma only was positively associated with patient's survival time in a univariate analysis but not in a multivariate analysis. The number of cytotoxic T cells in the tumor islets and stroma was positively associated with patient's survival time in a univariate analysis but not in a multivariate analysis. The number of cytotoxic T cells in the tumor islets only or stroma only was not associated with patient's survival time.ConclusionsThe number of macrophages in the tumor islets or stroma is an independent predictor of survival time in NSCLC patients. Counting macrophages in the tumor islets or stroma is more useful in predicting patient's survival time than counting mature dendritic cells or cytotoxic T cells.

BackgroundTranscriptome data generates massive amounts of information that can be used for characterization and prognosis of patient outcomes for many diseases. The goal of our research is to predict the survival time of lung adenocarcinoma patients and improve the accuracy of classifying the long-survival cohort and short-survival cohort.MethodsWe filtered prognostic features related with survival time of lung adenocarcinoma patients by the method of Relief and predicted whether survival time of the patient is >3 years or not—using eight machine learning algorithms (Support Vector Machines, Random Forests, Logistic Regression, Naïve Bayes, Linear Regression, Support Vector Regression (kernel Poly), Support Vector Regression (kernel Linear), and Ridge Regression). Then the best-performed algorithm was chosen to build a predictive model of survival time of lung adenocarcinoma patients. Further, another dataset was used to verify the stability and suitability of this model. We explored the underlying mechanisms of RNA expression changes with the corresponding DNA mutations and DNA methylation patterns in the 22 selected genetic features.ResultsThe best machine learning algorithm was Naïve Bayes (accuracy=75%, AUC =0.81) using the top 22 genetic features, and this algorithm had the stable and great performance on another dataset as well. The coupled mutation number of the long-survival group (>6 years) was less than the short-survival group (<1 year) in 22 genes (P=0.031).ConclusionsThe expression of gene panel can predict the survival time of lung adenocarcinoma patients using Naïve Bayes. These 22 genes do affect the survival time of lung adenocarcinoma.

Goodness-of-fit tests for Cox's proportional hazards model and Aalen's additive risk model, in which each model is compared on an equal footing with the best fitting fully nonparametric model, are developed. The goodness-of-fit statistics are based on differences each model, with a fully nonparametric estimator of d recently introduced by the authors. Here A( , z) denotes the conditional hazard function of the survival time of an individual with covariate vector z. Comparison of the results of the tests makes it possible to decide whether Cox's proportional hazards or Aalen's additive risk model gives a better fit to the data. In addition, a goodness-of-fit test for Cox's model within the family of all proportional hazards models A(t, z) = AO(t)r(z), where AO is a baseline hazard function and r is a general relative risk function, is developed. Additive hazards and proportional hazards regression models used in the analysis of censored survival data can give substantially different results. For instance, in connection with a study of cancer mortality among Japanese atomic bomb survivors, Muirhead & Darby (1987) have noted that the two models give substantially different estimates of the age-spe- cific probability that an individual will develop radiation induced cancer. Muirhead & Darby (see also Aranda-Ordaz, 1983) introduced a generalized parametric model which contains parametric additive hazards and proportional hazards models as special cases. The goodness- of-fit of each model is then obtained by comparing with the best fitting model within the generalized family, allowing the two special models to be treated on an equal footing. Beyond the parametric setting, much effort has been devoted to the development of goodness-of-fit tests for Cox's (1972) proportional hazards model

Gap times between recurrent events are often of primary interest in medical and observational studies. The additive hazards model, focusing on risk differences rather than risk ratios, has been widely used in practice. However, the marginal additive hazards model does not take the dependence among gap times into account. In this paper, we propose an additive mixed effect model to analyze gap time data, and the proposed model includes a subject-specific random effect to account for the dependence among the gap times. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The finite sample behavior of the proposed methods is evaluated through simulation studies, and an application to a data set from a clinic study on chronic granulomatous disease is provided.

Survival models allowing for random effects (e.g., frailty models) have been widely used for analyzing clustered time‐to‐event data. Accelerated failure time (AFT) models with random effects are useful alternatives to frailty models. Because survival times are directly modeled, interpretation of the fixed and random effects is straightforward. Moreover, the fixed effect estimates are robust against various violations of the assumed model. In this paper, we propose a penalized h‐likelihood (HL) procedure for variable selection of fixed effects in the AFT random‐effect models. For the purpose of variable selection, we consider three penalty functions, namely, least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and HL. We demonstrate via simulation studies that the proposed variable selection procedure is robust against the misspecification of the assumed model. The proposed method is illustrated using data from a bladder cancer clinical trial.

For determining a manageable set of covariates potentially influential with respect to a time-to-event endpoint, Cox proportional hazards models can be combined with variable selection techniques, such as stepwise forward selection or backward elimination based on p-values, or regularized regression techniques such as component-wise boosting. Cox regression models have also been adapted for dealing with more complex event patterns, for example, for competing risks settings with separate, cause-specific hazard models for each event type, or for determining the prognostic effect pattern of a variable over different landmark times, with one conditional survival model for each landmark. Motivated by a clinical cancer registry application, where complex event patterns have to be dealt with and variable selection is needed at the same time, we propose a general approach for linking variable selection between several Cox models. Specifically, we combine score statistics for each covariate across models by Fisher's method as a basis for variable selection. This principle is implemented for a stepwise forward selection approach as well as for a regularized regression technique. In an application to data from hepatocellular carcinoma patients, the coupled stepwise approach is seen to facilitate joint interpretation of the different cause-specific Cox models. In conditional survival models at landmark times, which address updates of prediction as time progresses and both treatment and other potential explanatory variables may change, the coupled regularized regression approach identifies potentially important, stably selected covariates together with their effect time pattern, despite having only a small number of events. These results highlight the promise of the proposed approach for coupling variable selection between Cox models, which is particularly relevant for modeling for clinical cancer registries with their complex event patterns.

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.