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Comparison of Bayesian survival analysis and Cox regression analysis in simulated and breast cancer data sets

Survival analysis is a statistical method where the outcome variable that is considered is the time until the occurrence of an event or called an event. Survival analysis in the medical world can be used to test the survival of patients suffering from a disease, one of which is kidney failure. Based on the results of the 2013 Basic Health Research, 0.2% of the total population of Indonesia, namely 499,800 people, experienced kidney failure. Kidney failure is a process of decreasing kidney function that requires renal replacement therapy, in the form of hemodialysis or kidney transplantation. If the survival data involve independent variables that are thought to affect the survival time, then the Cox Proportional Hazard (PH) regression approach can be developed which can be developed for the Multivariate Adaptive Regression Spline (MARS) approach. The MARS approach is a nonparametric regression approach with high-dimensional data, namely data with an independent variable of 3≤𝑝≤20 and a data sample of 50≤N≤1000. This study aims to describe the characteristics of patients with kidney failure, identify the factors that affect the survival time of patients with kidney failure and determine the MARS model. The MARS approach is obtained from a combination of functional basis, maximum interaction, and minimum observation by trial and error. Based on the model that has been formed using the MARS approach, it is found that the most influential variables on the survival time of patients with kidney failure are age, urea levels, and creatine levels.
 Key words: Renal failure, hemodialysis, survival analysis, nonparametric, MARS

This article employs Multivariate Adaptive Regression Spline (MARS) for determination of friction capacity of driven piles in clay. MARS is non-parametric adaptive regression procedure. Pile length, pile diameter, effective vertical stress, and undrained shear strength are considered as input of MARS and the output of MARS is friction capacity. The developed MARS gives an equation for determination of <TEX>$f_s$</TEX> of driven piles in clay. The results of the developed MARS have been compared with the Artificial Neural Network. This study shows that the developed MARS is a robust model for prediction of <TEX>$f_s$</TEX> of driven piles in clay.

PurposeThe purpose of this paper is to investigate proprietary data from customers of a Southern Louisiana credit union. It analyzes the factors that contribute to an accelerated failure time (AFT) using information from customers’ credit applications as well as information provided in their credit report.Design/methodology/approachThis paper investigates the factors that affect credit risk using survival analysis by employing two primary models – the AFT model and the Cox proportional hazard (PH) model. While several studies employ the Cox PH model, few use the AFT model. However, this paper concludes that the AFT model has superior predictive qualities.FindingsThis paper finds that the factors specific to borrowers and local factors play an important role in the duration of a loan.Practical implicationsThis paper offers an easily interpretable model for determining the duration of a potential borrower. The marketing department of credit unions can then use this information to predict when a customer will default, thus allowing the credit union to intervene in a timely manner to prevent defaults. Further, the credit union can use this information to seek out customers who are less likely to default.Originality/valueThis study is different from the previous research due to its focus on credit unions, which have distinct characteristics. Compared to similar lending institutions, the charter of the credit union does not allow management to sell off loans to other investors.

In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it would be controversial to suggest a general guideline to construct an optimal time partition. While a great deal of research has been done to relax the assumption of the fixed split times for other non-parametric processes, to our knowledge, no methods have been developed for a gamma process prior, which is one of the most widely used in Bayesian survival analysis. In this paper, we propose a new Bayesian framework for proportional hazards models where the cumulative baseline hazard function is modelled a priori by a gamma process. A key feature of the proposed framework is that the number and position of interval cutpoints are treated as random and estimated based on their posterior distributions.

The concept of orthometric heights system determination plays a major key role in geodesy, and it has broad applications in various fields and activities. In geodesy, one significant quantity is the orthometric height, the height above or below the geoid along the gravity plumbline. Conventionally, the orthometric height is determined by gravimetry and levelling techniques. However, the aforementioned techniques has its own demerits. Thus, the error is accumulated with the increase of the propagation measurement line, it is difficult to convert two separated points which is located in two continents or islands separated by sea. These techniques are tedious, time consuming and expensive. In order to resolve this challenge, many researchers resort to various techniques and approaches of obtaining orthometric heights for an area using various mathematical models. It is in this quest that, this study seek to estimate orthometric heights of a mine by utilizing plausible alternative techniques based on artificial neural networks (ANN), multivariate adaptive regression splines (MARS), polynomial regression models and multiple linear regression (MLR). The working efficiency and performance of each model has been assessed based on statistical indicators of Mean (M), Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Bias Error (MBE), Mean Absolute Error (MAE), Standard Deviation (SD), Correlation coefficient (R), Correction of determination (R2), and Signal to Noise Ratio (SNR). The statistical findings reveal that all the models produce satisfactory results in estimating the orthometric heights in the mine. MARS and ANN models compare to the MLR and polynomial models achieved higher results in terms of accuracy with mean and standard deviation of -0.000001888 m, +2.24736 m, and +0.005835 m and 0.095063 m respectively. This study will create the opportunity for geospatial practitioners to recognize the significant of ANN, MARS, MLR, and Polynomial model in solving some of the problems in geoscientific community.

Multivariate adaptive regression splines (MARS) technique is an adaptive non-parametric regression approach which has been used for various forecasting and data mining applications in recent years. This technique is more useful when a large number of explanatory variable candidates need to be considered. In this paper, the MARS technique is applied to forecast the hourly Ontario energy price (HOEP). The MARS models are developed in this work considering two scenarios for the explanatory variables. In the first scenario, the model is build based solely on the lagged values of the HOEP. In the second scenario, current and lagged values of the latest predispatch price and demand information, made available by the Ontario Independent Electricity System Operator (IESO), are also considered as explanatory variables. The forecasts generated by the developed models for high and low demand periods are significantly more accurate than the currently available forecasts for HOEP, demonstrating the MARS capability for electricity market price forecasting.

The survival analysis can be used in time to event data, this one of the tools to estimate the probability of survival in patients. To estimate the patient's survivorship based on time-independent variable this called nonparametric model. Acceleration failure model is considered the parametric model, it takes covariate and multiple effects of survivorship, is measured through a log-linear model taking the logarithm of survival time and the outcomes of the dependent variable. The model assumes that follow survival function is known as assuming the effect of a covariate is to accelerate or decelerate the life of patients by important constant. Hence the AFT model is alternative to proportional hazard models because in this model analysis the effect of a covariate to multiply the hazard by the constant. This study discusses the survival time of patients by acceleration failure time model in TB patients, like the variable is age, Regimen, sex, and weight are considered. We have been check the model fit from the failure distribution, whether it is fitting for the model in that distribution based on deviation method (-2LL) using partial log-likelihood functions.

Major specialization at High School is aimed to gives opened opportunity for students to choose subject that are interest and develop their potential in accordance with the abilities, interests, talents, and personality. Major specialization at High school is influenced by some factors. To detect those factors, used biner logistic regression method and Multivariate Adaptive Regression Spline (MARS). Biner Logistic Regression is method that describes relationship between dependent variable and some independent variable, with independent variable has been coded 1 as representing the presence of the characteristic, and 0 as representing the absence of the characteristic. MARS is multivariate nonparametric regression method that development of Recursive Partitioning Regression (RPR) method and Spline method for high dimensional data that produces accurate prediction and continuous models on knots. Both of the methods are compared to know the best method used in research. From the result of analysis using biner logistic regression method and MARS, concluded that major specialization has been influenced by mathematic score, science score and relationship between students and friends. From proportion test, concluded classification that formed by regression logistic is as good as by MARS. Keywords : Major specialization at High School, Biner Logistic Regression, Mutlivariate Adaptive Regression Spline (MARS), Clasification

Analyzing angle crashes at unsignalized intersections using machine learning techniques

Application of Multivariate Adaptive Regression Splines (MARS) approach in prediction of compressive strength of eco-friendly concrete

Studies have shown that interactions of single nucleotide polymorphisms (SNPs) may play an important role in understanding the causes of complex disease. We have proposed an integrated machine learning method that combines two machine-learning methods-Random Forests (RF) and Multivariate Adaptive Regression Splines (MARS)-to identify a subset of important SNPs and detect interaction patterns more effectively and efficiently. In this two-stage RF-MARS (TRM) approach, RF is first applied to detect a predictive subset of SNPs, and then MARS is used to identify the interaction patterns. We evaluated the TRM performances in four models. RF variable selection was based on out-of-bag classification error rate (OOB) and variable important spectrum (IS). Our results support that RF(OOB) had better performance than MARS and RF(IS) in detecting important variables. This study demonstrates that TRM(OOB) , which is RF(OOB) plus MARS, has combined the strengths of RF and MARS in identifying SNP-SNP interactions in a scenario of 100 candidate SNPs. TRM(OOB) had greater true positive rate and lower false positive rate compared with MARS, particularly for searching interactions with a strong association with the outcome. Therefore, the use of TRM(OOB) is favored for exploring SNP-SNP interactions in a large-scale genetic variation study.

Through a threshold equation, we propose a time-transformed accelerated failure time (AFT) model with time-dependent covariate history in survival analysis. This model contains a general class of semiparametric lifetime regression models, including AFT with identical time-scale and a wide spectrum of Cox’s hazard regression models and their frailty variants. We first construct the semiparametric efficient statistical inferences on the AFT model with identical time-scale. The theoretical semiparametric Fisher information bound is explicitly derived under right-censored data setting. And the overidentified estimating equation (OEE) approach based on two martingale processes is shown to achieve this semiparametric efficiency bound. Extensions of the semiparametric efficient statistical inferences to the time-transformed AFT versions are also discussed. We also conclude that most log-rank estimating equations would suffer severe information loss primarily caused by wiggling pattern of the baseline hazard function, while the OEE approach can alleviate the damaging effects. A simulated biological life history example is numerically studied.

An efficient Bayesian inversion method for seepage parameters using a data-driven error model and an ensemble of surrogates considering the interactions between prediction performance indicators

The protein tyrosine phosphatase, receptor type, N polypeptide 2 (PTPRN2) gene may play a role in cancer; however, no study has focused on the associations of genetic variants within the PTPRN2 gene with age at onset (AAO) of cancer.