How likely is unmeasured confounding to explain meta-analysis-derived associations between alcohol, other substances, and mood-related conditions with HIV risk behaviors?

Table 3 Assessment of unmeasured confounding among meta-analyses assessed by Point Estimate and PMSE sensitivity analyses

Exposure	Outcome	Pooled RR (95% CI)¹	E-value² (95% CI LL)	Bias factor³	Bias-adjusted RR (95% CI)	p̂(q)⁴	\({\rm{\hat T}}\)(r, q)⁵	Ĝ(r, q)⁶
Opioids	Non-adherence	1.28 (1.16–1.42)	1.88 (1.60)	1.11	1.15 (1.05–1.28)	0.702	1.254	1.819
Alcohol	Unprotected sex	1.36 (1.26–1.46)	2.05 (1.83)	1.17	1.16 (1.07–1.25)	0.67	1.452	2.263
Tobacco	Unprotected sex	1.24 (1.12–1.37)	1.79 (1.48)	1.17	1.06 (0.96–1.17)	0.429	1.469	2.299
Opioids	Unprotected sex	1.10 (0.89–1.37)	1.44 (1.00)	1.17	0.94 (0.76–1.17)	0.315	1.315	1.959
Stimulants	Unprotected sex	1.44 (1.37–1.52)	2.24 (2.08)	1.17	1.23 (1.17–1.30)	0.786	1.569	2.514
Depression	Unprotected sex	1.24 (1.10–1.41)	1.80 (1.44)	1.01	1.23 (1.10–1.40)	0.769	1.279	1.875
Anxiety	Unprotected sex	1.19 (1.08–1.32)	1.67 (1.38)	1.01	1.18 (1.07–1.30)	0.688	1.294	1.912
Tobacco	Transactional sex	1.75 (1.32–2.3)	2.89 (1.98)	1.17	1.49 (1.13–1.97)	0.791	2.190	3.805
Opioids	Transactional sex	1.39 (1.1–1.76)	2.12 (1.43)	1.17	1.18 (0.94–1.51)	0.588	1.691	2.773
Alcohol	Multiple sexual partners	1.40 (1.27–1.53)	2.14 (1.86)	1.17	1.19 (1.09–1.31)	0.748	1.415	2.181
Stimulants	Multiple sexual partners	1.64 (1.43–1.89)	2.66 (2.21)	1.17	1.40 (1.22–1.61)	0.831	2.062	3.541
Depression	Multiple sexual partners	1.18 (1.07–1.31)	1.65 (1.34)	1.01	1.17 (1.06–1.30)	0.628	1.359	2.057

¹ Converted from pooled ORs of Fig. 3
² E-value: quantifies how strongly an unmeasured confounder would need to be associated with the exposure (minimum risk ratio RR_XU) and outcome (minimum risk ratio RR_UY) to fully explain the observed association (RR_XY)
³ Bias factor: quantifies the maximum amount by which an unmeasured confounder could alter RR^T_XY
⁴ \({\rm{\hat p}}\)(q): the proportion of studies in a meta-analysis likely to meet or exceed a user-specified threshold of meaningfully strong effect (q)
⁵ \({\rm{\hat T}}\)(r, q): the minimum bias capable of reducing \({\rm{\hat p}}\)(q) to less than r (analogous to the bias factor)
⁶ \({\rm{\hat G}}\)(r, q): the minimum values of RR_UY and RR_XU capable of reducing p\({\rm{\hat p}}\)(q) to less than r (analogous to the E-value)

ISSN: 1471-2288