Computing Covariance between Log Odds Ratio and Log Risk Ratio

The function lgor_lgrr computes covariance between log odds ratio and log risk ratio, when the two outcomes are binary. See mix.vcov for effect sizes of the same or different types.

lgor_lgrr(r, n1c, n2c, n1t, n2t,
          n12c = min(n1c, n2c),
          n12t = min(n1t, n2t),
          s2c, s2t, f2c, f2t, s1c, s1t, f1t, f1c)

Arguments

r

Correlation coefficient of the two outcomes.
n1c

Number of participants reporting outcome 1 in the control group.
n2c

Number of participants reporting outcome 2 in the control group.
n1t

Number of participants reporting outcome 1 in the treatment group.
n2t

Number of participants reporting outcome 2 in the treatment group.
n12c

Number of participants reporting both outcome 1 and outcome 2 in the control group. By default, it is equal to the smaller number between n1c and n2c.
n12t

Defined in a similar way as n12c for the treatment group.
s2c

Number of participants with event for outcome 2 (dichotomous) in the control group.
s2t

Defined in a similar way as s2c for the treatment group.
f2c

Number of participants without event for outcome 2 (dichotomous) in the control group.
f2t

Defined in a similar way as f2c for the treatment group.
s1c

Number of participants with event for outcome 1 (dichotomous) in the control group.
s1t

Defined in a similar way as s1c for the treatment group.
f1c

Number of participants without event for outcome 1 (dichotomous) in the control group.
f1t

Defined in a similar way as f1c for the treatment group.

Author

Min Lu

Value

lgorLog odds ratio for outcome 1.
lgrrLog risk ratio for outcome 2.
vComputed covariance.

References

Ahn, S., Lu, M., Lefevor, G.T., Fedewa, A. & Celimli, S. (2016). Application of meta-analysis in sport and exercise science. In N. Ntoumanis, & N. Myers (Eds.), An Introduction to Intermediate and Advanced Statistical Analyses for Sport and Exercise Scientists (pp.233-253). Hoboken, NJ: John Wiley and Sons, Ltd.

Wei, Y., & Higgins, J. (2013). Estimating within study covariances in multivariate meta-analysis with multiple outcomes. Statistics in Medicine, 32(7), 119-1205.

Examples

lgor_lgrr(r = 0.71,
          n1c = 30, n2c = 35, n1t = 28, n2t = 32,
          s2c = 5, s2t = 8, f2c = 30, f2t = 24,
          s1c = 5, s1t = 8, f1c = 25, f1t = 20)

#> $lgor
#> [1] 0.6931472
#> 
#> $lgrr
#> [1] 0.5596158
#> 
#> $v
#> [1] 0.2183995
#> 
## calculate covariances for variable D and DD in Geeganage2010 data
attach(Geeganage2010)
D_DD <- unlist(lapply(1:nrow(Geeganage2010),
              function(i){lgor_lgrr(r = 0.71, n1c = nc_SBP[i], n2c = nc_DD[i],
                 n1t = nt_SBP[i], n2t = nt_DD[i], s2t = st_DD[i], s2c = sc_DD[i],
                 f2c = nc_DD[i] - sc_DD[i], f2t = nt_DD[i] - st_DD[i],
                 s1t = st_D[i], s1c = sc_D[i],
                 f1c = nc_D[i] - sc_D[i], f1t = nt_D[i] - st_D[i])$v}))
D_DD

#>  [1] 0.27751337 0.20339717 0.05362256 0.05223042 0.03794159 0.28533503
#>  [7] 0.03410108 0.04363094 0.06182834 0.05156606 0.02965997 0.16734183
#> [13] 0.14830118 0.24652916 0.01068699 0.03391899 0.65302306
## the function mix.vcov() should be used for dataset