A worked example

References

Table A

Table B

Table C
 
 

Adjusted indirect comparison of competing interventions: method and worked example (posted as supplied by author)

Adjusted indirect comparison

Suppose T_BA is the result of direct comparison of intervention B versus A, and T_CA is the direct comparison of intervention C versus A. Then the estimate of the adjusted indirect comparison of intervention B versus C (T’_BC) is calculated by

T’_BC = T_BA - T_CA

and its standard error is

SE(T’_BC)=Ö (SE(T_BA)²+ SE(T_CA)²)

where SE(T_BA) and SE(T_CA) are the standard errors of T_BA and T_CA respectively.

A worked example

The comparison methods used in the paper are illustrated by an example of meta-analysis (table B on website), based on a collaborative overview of randomised trials of antiplatelet therapy for the prevention of vascular events in high risk patients.^w1

There are three trials that directly compared high doses (500-1500 mg/day) aspirin with medium doses (75-325 mg/day) aspirin. The results of the three trials can be quantitatively combined in a meta-analysis. By using a random effects model, the pooled relative risk is 0.96 (0.81 to 1.15), indicating there is no significant difference between the high doses and the medium doses aspirin for the prevention of vascular events.

In addition, there are many trials that compared high doses aspirin or medium doses aspirin with control interventions. These trials can be used to make the adjusted indirect comparison of high doses versus medium doses aspirin. First, we quantitatively combine results of trials that compared high doses aspirin with control, or medium doses aspirin with control. Table C on website shows the results of meta-analyses.

In this example, the common intervention (A) for the adjusted indirect comparison is any treatment without antiplatelet therapy. Calculations below use log relative risk for the estimated treatment effects. From table B we can see that the treatment effect of high doses aspirin versus control is T_BA =- 0.1776, and the treatment effect of medium doses aspirin versus control is T_CA =- 0.2915.[wt2] Then the adjusted indirect estimate is

T’_BC = T_BA - T_CA = - 0.1776 - (- 0.2915) = 0.1139

and its standard error is

SE(T’_BC)=Ö (SE(T_BA)²+ SE(T_CA)²)=Ö (0.0356²+0.0303²)=0.0467

According to the above adjusted indirect comparison, the 95% confidence interval of estimated log relative risk is 0.1139± 1.96´ 0.0467. After the anti-logarithmic transformation, the relative risk of high doses versus medium doses aspirin by the adjusted indirect comparison is 1.12 (1.02 to 1.23). The result of adjusted indirect comparison suggests that high doses aspirin is less effective than medium doses aspirin. This result should be interpreted with caution because the validity and similarity of all trials (in terms of interventions, patients, and outcomes) involved needs to be examined. Nevertheless, the result of this adjusted indirect comparison does provide further support to the conclusion in the original overview that antiplatelet therapy with aspirin 75-325 mg/day is effective in the prevention of vascular events among high risk patients.^w1

The discrepancy between the direct and the adjusted indirect comparison can be assessed by calculating the difference in estimated log relative risk:

X = T_BC - T’_BC = - 0.0385 - 0.1139 = - 0.1524

The standard error of X is

SE(X)=Ö (SE(T_BC)²+ SE(T’_BC)²)=Ö (0.0902²+0.0467²)=0.102

The 95% confidence interval of X can be calculated by - 0.1524± 1.96´ 0.102 (that is, - 0.352 to 0.048). Because the 95% confidence interval include zero, the discrepancy between the direct and the adjusted indirect estimate is not significant (P>0.05).
 

References

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w2 ATC(II). Antiplatelet Trialists’ Collaboration. Collaborative overview of randomised trials of antiplatelet therapy—II: maintenance of vascular graft or arterial patency by antiplatelet therapy. BMJ 1994;308:159-68.

w3 ATC(III). Antiplatelet Trialists’ Collaboration. Collaborative overview of randomised trials of antiplatelet therapy—III: reduction in venous thrombosis and pulmonary embolism by antiplatelet prophylaxis among surgical and medical patients. BMJ 1994;308:235-46.

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Table A Posted as supplied by author. Included meta-analyses for both direct and indirect comparisons—data table and references
 

OR=odds ratio; SMD=standardised mean difference; ATC=Antiplatelet Trialists’ Collaboration; 5-ASA=5-aminosalicylic acid; AP=aerosolised pentamidine; Daps=dapsone; Dex=dextropropoxyphene; H₂RA=H₂ receptor antagonists; LMW heparin=low molecular weight heparin; NRT=nicotine replacement therapy; PPI=proton pump inhibitors; Pyri=pyrimethamine; SMX=sulfamethoxazole; TMP=trimethoprim; U heparin=unfractionated heparin.

*Numbers in brackets refer to number of meta-analyses from the same systematic review.
 
 

Table B Posted as supplied by author. Results of trials that evaluated high dose or medium dose aspirin for preventing vascular event

TIA=transient ischaemic attack. CABG=coronary artery bypass graft. PTCA=percutaneoustransluminal coronary angioplasty. CHD=coronary heart disease.
 
 

Table C Posted as supplied by author. Results of head-to-head comparisons