Table 4.

Fully-Adjusted Association between High Adherence to Hormone Therapy and Hip Fracture after External Adjustment for Low Adherence Behaviors

Formula	RRplacebo	RRfull
$R{R}_{\mathit{\text{full}}}=R{R}_{\mathit{\text{adj}}}\times \frac{P_l(R{R}_{\mathit{\text{placebo}}}-1)+1}{P_h(R{R}_{\mathit{\text{placebo}}}-1)+1}$	1 / 0.50 = 2.0	0.62*
	1 / 0.33 = 3.03	0.68
	1 / 0.78 = 1.28	0.57

^*example calculation per (28), $R{R}_{\mathit{\text{full}}}=0.54\times \frac{0.50(2.0-1)+1}{0.30(2.0-1)+1}=0.62$

RR_adj=0.54 (observed adjusted association between high adherence to HT and hip fracture)

P_h=0.30 (prevalence of poor adherence behavior among women with high adherence to placebo, i.e., prevalence of low/missing persistence with osteoporosis medications from table 3)

P_l=0.50 (prevalence of poor adherence behavior among women with low adherence to placebo, i.e., prevalence of low/missing persistence with osteoporosis medications from table 3)

RR_placebo=0.50 (95%CI=0.33–0.78), inverted observed adjusted association between poor adherence to placebo and hip fracture, observed in Table 2

RR_full=fully adjusted association between HT and hip fracture, after controlling for residual confounding (adherence behavior identified by adherence to osteoporosis pharmacotherapy).

Applying differential adherence to statins identifies similar externally-adjusted results, i.e., RR=0.63, with point estimates for the RR ranging from 0.57 to 0.69 depending on the true value of RR_placebo