Degrees of necessity and of sufficiency
We suggest measures to quantify the degrees of necessity and of sufficiency (DN and DS) of prognostic factors for dichotomous, survival, ordinal and nominal outcomes. A cause, represented by certain values of prognostic factors, is considered necessary for an event if, without the cause, the event cannot develop. It is considered sufficient for an event if the event is unavoidable in the presence of the cause. Necessity and sufficiency can be seen as the two faces of causation, and this symmetry and equal relevance are reflected by the suggested measures. The measures provide an approximate, in some cases an exact, multiplicative decomposition of explained variation as defined by Schemper for dichotomous outcomes.
SAS macros and R functions are provided for the following types of outcomes:
- NecSuff for dichotomous outcomes
- NecSuff_Surv for survival outcomes
- NecSuff_Ord for ordinal outcomes
- NecSuff_Nom0 for nominal outcomes with reference category
- NecSuff_CR for survival outcomes with competing risks
References
Gleiss, A, Schemper, M (2019):
"Quantifying degrees of necessity and of sufficiency in cause-effect relationships with dichotomous and survival outcomes.", Statistics in Medicine. 2019;38:4733–4748.
doi:10.1002/sim.8331
Gleiss, A, Henderson, R, Schemper, M (2021):
"Degrees of necessity and of sufficiency: further results and extensions, with an application to covid-19 mortality in Austria", Statistics in Medicine. 2021;40:3352-3366.
doi:10.1002/sim.8961
Gleiss, A, Gnant, M, Schemper, M:
"Explained variation and degrees of necessity and of sufficiency for competing risks survival data", submitted
SAS macros and R functions are provided at the github repository:
https://github.com/agleiss/NecSuff
For download from github select 'Code' and then 'Download ZIP'. Please report bugs or make suggestions for enhancements directly at this github repository by creating corresponding issues.