Non-parametric statistical test for testing exponentiality with applications in medical research.

The aim of designing the non-parametric statistical test in this paper is to assess some treatment methods by studying the failure behavior of the observed survival data. A treatment method represents the application of different healthcare interventions for the cure or reduction of disease-related symptoms. The survival times of patients are registered after applying the proposed treatment method. The behavior of the observed data in this paper is assumed to enjoy an increasing failure rate or constant failure rate (exponential case) property. If the survival data have increasing failure rate property, then the proposed treatment method is useless (has negative influence on patients) and another method should be recommended, while if the collected data have exponential property, then the proposed treatment method has no positive or negative influence on patients. To guarantee a right assessment using the proposed statistical test, its efficiency and power are calculated and compared with other tests. The proposed statistical test is applied in case of some cancer treatments.