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Using <strong>the</strong> method proposed by Bucher and<br />

colleagues. 63 and adapted from Song and<br />

colleagues, 62 an adjusted indirect comparison was<br />

undertaken to estimate <strong>the</strong> efficacy <strong>of</strong> docetaxel<br />

plus <strong>prednisone</strong> versus <strong>prednisone</strong> alone in<br />

improving overall survival f<strong>or</strong> men <strong>with</strong> HRPC.<br />

Using <strong>the</strong> adjusted indirect method means that<br />

<strong>the</strong> power <strong>of</strong> randomisation in <strong>the</strong> <strong>or</strong>iginal studies<br />

is maintained. However, this method is only valid<br />

when <strong>the</strong> magnitude <strong>of</strong> <strong>the</strong> <strong>treatment</strong> effect is<br />

consistent between <strong>the</strong> different studies being<br />

compared.<br />

The estimate <strong>of</strong> <strong>the</strong> adjusted indirect comparison<br />

is given by<br />

T BC = T BA – T CA<br />

where T BA is <strong>the</strong> <strong>treatment</strong> effect f<strong>or</strong> intervention<br />

B versus intervention A, T CA is <strong>the</strong> <strong>treatment</strong> effect<br />

f<strong>or</strong> intervention C versus intervention A and T BC is<br />

<strong>the</strong> indirect comparison <strong>of</strong> interest, <strong>the</strong> estimate <strong>of</strong><br />

<strong>the</strong> <strong>treatment</strong> effect <strong>of</strong> intervention B versus<br />

intervention C.<br />

The estimate <strong>of</strong> <strong>the</strong> standard err<strong>or</strong> <strong>of</strong> <strong>the</strong> estimate<br />

<strong>of</strong> <strong>the</strong> indirect <strong>treatment</strong> effect, T BC, is given by<br />

SE(TBC) = √ ––––––––––<br />

SE(TBA) 2 + SE(TCA) 2<br />

–––––––––––<br />

where SE(T BA) and SE(T CA) are <strong>the</strong> standard err<strong>or</strong>s<br />

<strong>of</strong> T BA and T CA, respectively.<br />

W<strong>or</strong>ked example: docetaxel plus<br />

<strong>prednisone</strong> versus <strong>prednisone</strong><br />

(overall survival)<br />

Using <strong>the</strong> adjusted method, <strong>the</strong> <strong>treatment</strong> effect<br />

(T BC) <strong>of</strong> overall survival f<strong>or</strong> docetaxel plus<br />

<strong>prednisone</strong> versus <strong>prednisone</strong> can be calculated<br />

using mitoxantrone plus <strong>prednisone</strong> as a<br />

common comparat<strong>or</strong> between trials. In this<br />

example:<br />

Interventions:<br />

A = mitoxantrone plus <strong>prednisone</strong><br />

B = docetaxel plus <strong>prednisone</strong> (3-weekly)<br />

C = <strong>prednisone</strong><br />

Appendix 8<br />

Health Technology Assessment 2007; Vol. 11: No. 2<br />

Adjusted indirect comparisons<br />

© Queen’s Printer and Controller <strong>of</strong> HMSO 2007. All rights reserved.<br />

Treatment effects:<br />

T BA = HR f<strong>or</strong> death; docetaxel plus <strong>prednisone</strong><br />

versus mitoxantrone plus <strong>prednisone</strong><br />

T CA = HR f<strong>or</strong> death; <strong>prednisone</strong> versus<br />

mitoxantrone plus <strong>prednisone</strong><br />

There is an estimate from TAX 327 27 <strong>of</strong> T BA =<br />

0.76 (95% CI: 0.62 to 0.94). Using <strong>the</strong> random<br />

effects pooled estimate calculated in <strong>the</strong> section<br />

‘Pooled estimate <strong>of</strong> effectiveness <strong>of</strong> mitoxantrone<br />

plus a c<strong>or</strong>ticosteroid versus a c<strong>or</strong>ticosteroid’ (p. 34)<br />

an HR f<strong>or</strong> death = 0.99 (95% CI: 0.82 to 1.20) f<strong>or</strong><br />

mitoxantrone plus <strong>prednisone</strong> versus <strong>prednisone</strong>.<br />

However in <strong>or</strong>der to perf<strong>or</strong>m <strong>the</strong> adjusted indirect<br />

comparison, mitoxantrone plus <strong>prednisone</strong> is<br />

used as <strong>the</strong> common comparat<strong>or</strong>, so this figure<br />

must be inverted to give an estimate <strong>of</strong> <strong>prednisone</strong><br />

versus mitoxantrone plus <strong>prednisone</strong>; T CA = 1.01<br />

(95% CI: 0.83 to 1.22).<br />

In <strong>or</strong>der to use <strong>the</strong> adjusted indirect comparison<br />

technique, <strong>the</strong> ln (HR)s and c<strong>or</strong>responding<br />

standard err<strong>or</strong>s must be used in <strong>the</strong> calculations.<br />

The results <strong>of</strong> <strong>the</strong>se calculations can <strong>the</strong>n be<br />

converted back to HRs and standard err<strong>or</strong>s (using<br />

antilog transf<strong>or</strong>mations), f<strong>or</strong> ease <strong>of</strong><br />

interpretation.<br />

Theref<strong>or</strong>e, using <strong>the</strong> adjusted method and <strong>the</strong><br />

ln(HR)s and standard err<strong>or</strong>s, <strong>the</strong> <strong>treatment</strong> effect<br />

f<strong>or</strong> docetaxel plus <strong>prednisone</strong> versus <strong>prednisone</strong><br />

f<strong>or</strong> overall survival is given by<br />

lnT BC = lnT BA – lnT CA = –0.274 – 0.01 = –0.284<br />

The standard err<strong>or</strong> is<br />

SE(lnT BC) = √ –––––––––––––––––––––––––<br />

SE(lnT BA) 2 + SE(lnT CA) 2<br />

= √ –––––––––––––––––––––––<br />

0.106 2 + 0.321 2 = 0.338<br />

Acc<strong>or</strong>ding to this estimate, <strong>the</strong> 95% CI f<strong>or</strong> lnT BC<br />

is:<br />

–0.284 ± (1.96 × 0.338) = –0.568 to –0.0009<br />

After anti-log transf<strong>or</strong>mations, we have a<br />

<strong>treatment</strong> effect <strong>of</strong> overall survival f<strong>or</strong> docetaxel<br />

plus <strong>prednisone</strong> versus <strong>prednisone</strong>; HR f<strong>or</strong> death<br />

= 0.752 (95% CI: 0.567 to 0.999).<br />

159

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