Appendix Table 1.

Notational glossary.

N1	Number of cases, some living some deceased
N̂1j	Estimated number of cases with genotype j
N0	Number of controls, all genotyped
N̂0j	Estimated number of controls with genotype j
n1	Number of surviving cases
m	number of deceased cases (=N1−n1)
nij	Number with case status i and genotype j
mjk	Number of deceased cases with offspring genotype j and spouse genotype k
mjc	Number of deceased cases with offspring genotype j and no spouse genotype
mjp	Number of deceased cases with spouse genotype j
mO	Number of deceased cases with no offspring genotype information
m1A, m1a	Number of deceased case for whom we have a genotyped child and who must have passed allele A (a) to the child m1A = m00 + m01 + m12 + m0c = m0+ + m12; m1a = m10 + m21 + m22 + m2c = m10 + m2+
m1Aa	Number of deceased cases for whom we have a genotyped child and the child has genotype Aa; m1Aa = m1c
m1*	Number of deceased cases whose family members’ genotypes provide no information in predicting cases’ genotype; m1* = m11 + mO
Nijk	Number of subjects with case status i, genotype j, and environmental exposure k
Y	Disease status flag (1 if case)
G	Genotype of study participant
Gf, Gc, Gp	Genotype of deceased case’s family member(s)
Gc	Genotype of deceased case’s offspring
Gp	Genotype of deceased case’s spouse (the other parent of that offspring)
S	Survival status flag (1 if alive)
R, Rc, Rp	Flag for recruitability of family members, offspring and spouse for deceased case (1 if recruitable)
f(G)	Function of G for logistic association with disease
h(G)	Function of G for logistic association with death, given disease
β	Genetic association parameter for disease association model
ρ	Proportion of deceased cases whose death is unrelated to G
α	Genetic association parameter for death model that conditions on disease
pa	MAF in the control population
${\widehat{p}}_a^{\ast }$	Consistent estimator for the MAF in the case population
${\widehat{p}}_a^{\ast \ast }$	Consistent estimator for the proportion of subjects with a allele in the case population
γ	Proportion of family members who are not recruitable.