Table.

Weighting schemes for case–cohort designs.

Type of case–cohort design		Cases not in sub-cohort		Non-cases in sub-cohort	Cases in sub-cohort
Simple All cases selected; Selection probability of sub-cohort = x%
			TY-ε to TY: w=1.0	w= 1/x%		T0 to TY-ε: w= 1/x% TY-ε to TY: w=1.0
Covariate-stratified All cases selected; Sub-cohort selection probabilities of xA% (Group A) and xB% (Group B)
	Group A		TY-ε to TY: w=1.0	w= 1/xA%		T0 to TY-ε: w= 1/xA% TY-ε to TY: w=1.0
	Group B		TY-ε to TY: w=1.0	w= 1/xB%		T0 to TY-ε: w= 1/xB% TY-ε to TY: w=1.0
Outcome-stratified 100% of type I and y% of type II cases selected; Sub-cohort selection probability x% for all
		Type I: TY-ε to TY: w=1.0	Type II: TY-ε to TY: $\text{w}=\frac{1}{y\%+x\%-(x\%*y\%)}$	w= 1/x%	Type I: T0 to TY-ε: w= 1/x% TY-ε to TY: w=1.0	Type II: T0 to TY-ε: w= 1/x% TY-ε to TY: $\text{w}=\frac{1}{y\%+x\%-(x\%*y\%)}$
Covariate- and Outcome-stratified 100% of type I and y% of type II cases selected; Sub-cohort selection probabilities of xA% (Group A) and xB% (Group B)a
	Group A	Type I: TY-ε to TY: w=1.0	Type II: TY-ε to TY: $\text{w}=\frac{1}{y\%+x_A\%-\left(x_A\%*y\%\right)}$	w= 1/xA%	Type I: T0 to TY-ε: w= 1/xA% TY-ε to TY: w=1.0	Type II: T0 to TY-ε: w= 1/xA% TY-ε to TY: $\text{w}=\frac{1}{y\%+x_A\%-\left(x_A\%*y\%\right)}$
	Group B	Type I: TY-ε to TY: w=1.0	Type II: TY-ε to TY: $\text{w}=\frac{1}{y\%+x_B\%-\left(x_B\%*y\%\right)}$	w= 1/xB%	Type I: T0 to TY-ε: w= 1/xB% TY-ε to TY: w=1.0	Type II: T0 to TY-ε: w= 1/xB% TY-ε to TY: $\text{w}=\frac{1}{y\%+x_B\%-\left(x_B\%*y\%\right)}$
Case-independent designs Selection probability of cases = v%; Selection probability of non-cases = z%
			w=1/v%	w= 1/z%		w=1/v%

W = weight;T₀ = Start of follow-up; T_Y = Event time, ε= a very small number (less than a unit increase on your time scale)

^aAssumes case selection independent of group selection, but if this is not the case the weights can be calculated separately for each group/subtype combination (e.g. selecting y_A% of type II cases in group A but y_B% of type II cases in group B)