# Risk Difference Meta-analysis

Case-control studies of dichotomous outcomes (e.g. dead or alive) can by represented by arranging the observed counts into fourfold (2 by 2) tables. Meta-analysis may be used to investigate the combination or interaction of a group of independent studies, for example a series of fourfold tables from similar studies conducted at different centres. This StatsDirect function examines the risk difference within each stratum (a single fourfold table) and across all of the studies/strata.

For a single stratum risk difference is defined as follows:

 EXPOSURE Exposed Non-Exposed OUTCOME: Cases: a b Non-cases: c d

Risk difference = [a/(a+c)] - [b/(b+d)]

For each table the observed risk difference is displayed with a confidence interval. The ’near exact’ method of Miettinen and Nurminen is used to construct the confidence interval (Mee, 1984; Anbar, 1983; Gart and Nam, 1990; Miettinen and Nurminen, 1985; Sahai and Kurshid, 1991). If the ’try exact’ option is not selected then a normal approximation to the confidence interval is given instead.

The Mantel-Haenszel type method of Greenland and Robins (Greenland and Robins, 1985; Sahai and Kurshid, 1991) is used to estimate the pooled risk difference for all strata, assuming a fixed effects model: - where ni = ai+bi+ci+di.

A confidence interval for the pooled risk difference is calculated using the Greenland-Robins variance formula (Greenland and Robins, 1985). A chi-square test statistic is given with associated probability of the pooled risk difference being equal to zero. Note that some packages give a z statistic; this is equal to the square root of the chi-square statistic with one degree of freedom, i.e. it is equivalent.

The inconsistency of results across studies is summarised in the I² statistic, which is the percentage of variation across studies that is due to heterogeneity rather than chance – see the heterogeneity section for more information.

Note that the results from StatsDirect may differ slightly from other software or from those quoted in papers; this is due to differences in the variance formulae. StatsDirect employs the most robust practical approaches to variance according to accepted statistical literature.

DATA INPUT:

Observed frequencies should be entered in a workbook as follows:

 Exposed/Experimental Non-exposed/Non-experimental Total number Number of cases Total number Number of cases

...where total number = cases + non-cases

Example

Test workbook (Meta-analysis worksheet: Exposed total, Exposed cases, Non-exposed total, Non-exposed cases, Study).

The following data combine seven placebo-controlled randomized trials of the effect of aspirin in preventing death after myocardial infarction:

 Aspirin Placebo Trial patients deaths patients deaths MRC-1 615 49 624 67 CDP 758 44 771 64 MRC-2 832 102 850 126 GASP 317 32 309 38 PARIS 810 85 406 52 AMIS 2267 246 2257 219 ISIS-2 8587 1570 8600 1720

To analyse these data in StatsDirect first prepare them in four workbook columns and label these columns appropriately. Alternatively, open the test workbook using the file open function of the file menu. Then select risk difference from the meta-analysis section of the analysis menu. Select the columns marked "Exposed total", "Exposed cases", "Non-exposed total" and "Non-exposed cases" when prompted for data. Note that "exposed" and "experimental" groups are the same.

For this example:

 Study Risk difference 95% CI (Miettinen) % Weight (fixed, random) MRC-1 -0.0277 -0.0606 0.0048 4.4457 10.8419 CDP -0.025 -0.0511 0.0007 5.4861 14.7560 MRC-2 -0.0256 -0.0585 0.0071 6.0348 10.7025 GASP -0.022 -0.0726 0.0278 2.2459 5.5797 PARIS -0.0231 -0.0641 0.014 3.8817 8.2922 AMIS 0.0115 -0.0062 0.0292 16.2334 21.5868 ISIS-2 -0.0172 -0.0289 -0.0054 61.6722 28.2409

Fixed effects (Mantel-Haenszel, Greenland-Robins)

Pooled risk difference = -0.014263 (95% CI = -0.022765 to -0.005762)

Chi² (test risk difference differs from 0) = 10.812247 (df = 1) P = 0.001

Non-combinability of studies

Cochran Q = 10.461119 (df = 6) P = 0.1065

Moment-based estimate of between studies variance = 0.000112

I² (inconsistency) = 42.6% (95% CI = 0% to 74.4%)

Random effects (DerSimonian-Laird)

Pooled risk difference = -0.014947 (95% CI = -0.0276 to -0.002295)

Chi² (test risk difference differs from 0) = 5.361139 (df = 1) P = 0.0206

Bias indicators

Begg-Mazumdar: Kendall's tau = 0.333333 P = 0.3813 (low power)

Egger: bias = -0.804119 (95% CI = -3.724382 to 2.116144) P = 0.5107

Here we can say with 95% confidence, assuming a random effects model, that for those given aspirin the true population risk of dying in the specified interval after a heart attack is at least 0.003 less than the risk for those not given aspirin. Assuming a fixed effects model a stronger inference could be made about a risk difference of 0.006 (the lower absolute confidence limit) but the high inter-study variation makes the fixed effects model less appropriate.