Abstract:
:We suggest measures to quantify the degrees of necessity and of sufficiency of prognostic factors for dichotomous and for survival 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 and Henderson for censored survival and for dichotomous outcomes. The measures, ranging from zero to one, are simple, intuitive functions of unconditional and conditional probabilities of an event such as disease or death. These probabilities often will be derived from logistic or Cox regression models; the measures, however, do not require any particular model. The measures of the degree of necessity implicitly generalize the established attributable fraction or risk for dichotomous prognostic factors and dichotomous outcomes to continuous prognostic factors and to survival outcomes. In a setting with multiple prognostic factors, they provide marginal and partial results akin to marginal and partial odds and hazard ratios from multiple logistic and Cox regression. Properties of the measures are explored by an extensive simulation study. Their application is demonstrated by three typical real data examples.
journal_name
Stat Medjournal_title
Statistics in medicineauthors
Gleiss A,Schemper Mdoi
10.1002/sim.8331subject
Has Abstractpub_date
2019-10-15 00:00:00pages
4733-4748issue
23eissn
0277-6715issn
1097-0258journal_volume
38pub_type
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