Computing Covariance between Log Risk Ratio and Risk Difference

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

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

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

lgrr	Log risk ratio for outcome 1.
rd	Risk difference for outcome 1.
v	Computed 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

## simple example
lgrr_rd(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)
#> $lgrr
#> [1] 0.5389965
#> 
#> $rd
#> [1] 0.1071429
#> 
#> $v
#> [1] 0.06519134
#> 
## calculate covariances for variable D and DD in Geeganage2010 data
attach(Geeganage2010)
#> The following objects are masked from Geeganage2010 (pos = 3):
#> 
#>     MD_DBP, MD_SBP, nc_D, nc_DBP, nc_DD, nc_SBP, nt_D, nt_DBP, nt_DD,
#>     nt_SBP, OR_D, OR_DD, sc_D, sc_DD, sdc_DBP, sdc_SBP, sdt_DBP,
#>     sdt_SBP, SMD_DBP, SMD_SBP, st_D, st_DD, studyID
#> The following objects are masked from Geeganage2010 (pos = 4):
#> 
#>     MD_DBP, MD_SBP, nc_D, nc_DBP, nc_DD, nc_SBP, nt_D, nt_DBP, nt_DD,
#>     nt_SBP, OR_D, OR_DD, sc_D, sc_DD, sdc_DBP, sdc_SBP, sdt_DBP,
#>     sdt_SBP, SMD_DBP, SMD_SBP, st_D, st_DD, studyID
D_DD <- unlist(lapply(1:nrow(Geeganage2010), function(i){lgrr_rd(r = 0.71,
        n1c = nc_SBP[i], n2c = nc_DD[i],
        n1t = nt_SBP[i], n2t = nt_DD[i], s2t = st_DD[i], s2c = sc_DD[i],
        f2c = nc_DD[i] - sc_DD[i], f2t = nt_DD[i] - st_DD[i],
        s1t = st_D[i], s1c = sc_D[i], f1c = nc_D[i] - sc_D[i], f1t = nt_D[i] - st_D[i])$v}))
D_DD
#>  [1] 0.113754126 0.069951058 0.019822129 0.019411371 0.016294904 0.110879932
#>  [7] 0.012470649 0.015732444 0.023476587 0.022617358 0.011670078 0.069015301
#> [13] 0.058873019 0.099649645 0.004440245 0.010741449 0.209557853
## the function mix.vcov() should be used for dataset