Stochastic Frontier Analysis and Cancer Survivability

Introduction

In this globalized and highly competitive, industries are successful and profitable when their operations are technically efficient. The managers and applied economists are periodically checking the pertinent data to confirm that the production in their industry is technically efficient and cost effective. The stochastic frontier analysis (SFA) is a statistical approach to make an assessment of the technical efficiency of chosen industries in the comparison pool. The SFA is based on a linear model connecting the observed production or cost variable, a bunch covariates to predict the prediction or cost using regression concepts and two error components. What is error component? The discrepancy between an observed and its prediction is defined the error. The usual regression methodology involves just one error component to indicate the random noises which influence the observable.

The SFA is a generalization of the regression methodology because of the two error components. In SFA, the second error is accommodated to portray the technical inefficiency (TE) of the production operation and it could have an impact on the observable. These two error components, namely the random noise and the technical inefficiency do not have to be statistically independent but are assumed to be independent in SFA. The expected values of the observable in the presence and in the absence of the technical inefficiency are involved to make an efficiency score of the operation of each industry in the comparison pool. This wonderful seminal thinking was promoted first by Meeusen et al. (1977) and independently by Aigner et al. (1977) within a month. The details are explained and illustrated later in the chapter.

The SFA is not the only methodology available to compare units. There is an alternate but nonparametric methodology to SFA and it is called Data Envelopment Analysis (DEA). Later, this chapter investigates the advantages versus disadvantages of SFA and DEA in order to compare a decision making units (DMUs) with an example about survivability from the melanoma cancer in nations around the world. The chapter briefly describes the differences between the DEA and SFA. The study of the melanoma cancer data is interesting from the point of view of learning SFA and DEA as well. The healthcare researchers are so far not fond of these two powerful methodologies. The SFA methodology is formally introduced, explained and then used to comprehend the survival chance without melanoma cancer due to ultra violet radiation for residents in 45 nations around the world. In contrast to the DEA which is a deterministic methodology, the SFA is a stochastic methodology. The SFA is a powerful, parametric methodology and it is valuable to sort out big data, to bring forth essential information and to contrast DMUs.

The basis of the comparison in SFA is called technical efficiency. This is done using an underlying statistical distribution for the given data. As demonstrated in this article, most often the given data follows normal distribution and it is confirmed using what is known as Box plot. The technical efficiency of the SFA is comparable to the relative efficiency of the DEA which makes use of the mathematical programming concept. Both SFA and DEA have advantages versus disadvantages though they are alternate to each other. In the application of SFA, the data are required to have stochastic components. In the application of DEA, the data are assumed to be deterministic type. The SFA is explained and is illustrated using a stochastic data of 45 nations with their latitude, amount of falling ultra violet, survival rate among men and women from melanoma cancer around the world in 2003.