Effectiveness of Couple-Based HIV Counseling and Testing for Women Substance Users and Their Primary Male Partners: A Randomized Trial

Table 1

Bernoulli formula, estimated risk parameters, and self-reported behaviors used to create composite HIV risk outcome measure (HIVRISK).

Bernoulli mathematical formula
HIVRISK = 1−(1−A)(1−B)(1−C)
A=𝜋1[1−1−𝛼𝑣^mvu1−𝜀𝛼𝑣^mvp1−𝛼𝑎^mau1−𝜀𝛼𝑎^map1−𝛼𝑗^mij]
B=𝜋2[1−1−𝛼𝑣^svu1−𝜀𝛼𝑣^svpsv1−𝛼𝑎^sau1−𝜀𝛼𝑎^sapsa]
C=𝜋3[1−1−𝛼𝑗^sijsj]
Estimated HIV risk parameters	Base estimates	Source
𝜋1: probability that primary male sex partner is HIV infected	1.0∣.15∣.05	^†
𝜋2: probability that a secondary sex partner is HIV infected	0.15	^‡
𝜋3: probability that an injection partner is HIV infected	0.25	^‡
𝛼𝑎: per contact probability of HIV transmission (infectivity) for anal sex	.017	[43, 44]
𝛼𝑣: per contact HIV transmission for male-to-female vaginal sex	.0008	[43]
𝛼𝑗: per act HIV transmission for receptive syringe sharing	.0074	[45, 46]
𝜀: condom failure rate	.10	[44]
Measured self-reported risk behaviors
mvu: number of acts of condom unprotected vaginal intercourse with primary male partner
mvp: number of acts of condom protected vaginal intercourse with primary male partner
mau: number of acts of condom unprotected anal intercourse with primary male partner
map: number of acts of condom protected anal intercourse with primary male partner
mij: number of times receptive syringe sharing with primary male partner
svu: number of acts of condom unprotected vaginal intercourse with secondary sex partner
svp: number of acts of condom protected vaginal intercourse with secondary sex partner
sau: number of acts of condom unprotected anal intercourse with secondary sex partner
sap: number of acts of condom protected anal intercourse with secondary sex partner
sij: number of times receptive syringe sharing with secondary partner
sv: number of secondary vaginal sex partners
sa: number of secondary anal sex partners
sj: number of secondary injection partners

A represents HIV risk from a primary male partner; B is HIV risk from a secondary sex partner; C is HIV risk from a secondary injection partner.
^†Based on self-reported HIV status of male partner: self-reported HIV positive = 1.0; self-reported HIV negative/unaware and IDU = 0.15; self-reported HIV negative/unaware and non-IDU = .05.
^‡Based on unpublished data on HIV prevalence among IDU and non-IDU men in Harlem and South Bronx, NY, USA.