All of the following are methods of survival analysis except: (DNB Dec 12)
Ref: Basic & Clinical Biostatistics, by Dawson – Saunders & Trapp, Pg 191-193
a. Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, and duration analysis or duration modeling in economics or sociology.
b. More generally, survival analysis involves the modelling of time to event data; in this context, death or failure is considered an "event" in the survival analysis literature.
c. Another example of time to event modeling could be the rate or time to which former convicts commit a crime again after they've been released. In this case, the 'event' of interest would be committing a crime.
d. Many concepts in Survival analysis have been explained by the Counting Process Theory, which has emerged more recently.
e. The flexibility of a counting process is that it allows modeling multiple (or recurrent) events.
f. This type of modeling fits very well in many situations (e.g. people can go to jail multiple times, alcoholics can start and stop drinking multiple times, people can get married and get a divorce many times).
g. Survival analysis attempts to answer questions such as: what is the fraction of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the odds of survival?
h. To answer such questions, it is necessary to define "lifetime". In the case of biological survival, death is unambiguous, but for mechanical reliability, failure may not be well-defined, for there may well be mechanical systems in which failure is partial, a matter of degree, or not otherwise localized in time.
i. Even in biological problems, some events (for example, heart attack or other organ failure) may have the same ambiguity. The theory outlined below assumes well-defined events at specific times; other cases may be better treated by models which explicitly account for ambiguous events.
j. The theory of survival presented here also assumes that death or failure happens just once for each subject. Recurring event or repeated event models relax that assumption. The study of recurring events is relevant in systems reliability, and in many areas of social sciences and medical research.
Kruskal–Wallis one-way analysis of variance
a. In statistics, the Kruskal–Wallis one-way analysis of variance by ranks is a non-parametric method for testing equality of population medians among groups. It is identical to a one-way analysis of variance with the data replaced by their ranks.
b. It is an extension of the Mann–Whitney U test to 3 or more groups.
c. Since it is a non-parametric method, the Kruskal–Wallis test does not assume a normal population, unlike the analogous one-way analysis of variance. However, the test does assume an identically-shaped and scaled distribution for each group, except for any difference in medians.