Computing Covariance between Mean Difference and Risk Difference

The function lgor_rd computes covariance between mean difference and risk difference. See mix.vcov for effect sizes of the same or different types.

md_rd(r, n1c, n2c, n1t, n2t,
      n12c = min(n1c, n2c), n12t = min(n1t, n2t),
      s2c, s2t, f2c, f2t, sd1c, sd1t)

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	Number 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.
sd1c	Sample standard deviation of outcome 1 for the control group.
sd1t	Defined in a similar way as sd1c for the treatment group.

Author

Min Lu

Value

rd	Computed risk difference for outcome 2.
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

## a simple example
md_rd(r = 0.71, n1c = 34, n2c = 35, n1t = 25, n2t = 32,
      s2c = 5, s2t = 8, f2c = 30, f2t = 24, sd1t = 0.4, sd1c = 8)
#> $rd
#> [1] 0.1071429
#> 
#> $v
#> [1] 0.06063116
#> 
## calculate covariances for variable SBP and DD in Geeganage2010 data
attach(Geeganage2010)
#> The following objects are masked from Geeganage2010 (pos = 3):
#> 
#>     MD_DBP, MD_SBP, nc_D, nc_DBP, nc_DD, nc_SBP, nt_D, nt_DBP, nt_DD,
#>     nt_SBP, OR_D, OR_DD, sc_D, sc_DD, sdc_DBP, sdc_SBP, sdt_DBP,
#>     sdt_SBP, SMD_DBP, SMD_SBP, st_D, st_DD, studyID
#> The following objects are masked from Geeganage2010 (pos = 4):
#> 
#>     MD_DBP, MD_SBP, nc_D, nc_DBP, nc_DD, nc_SBP, nt_D, nt_DBP, nt_DD,
#>     nt_SBP, OR_D, OR_DD, sc_D, sc_DD, sdc_DBP, sdc_SBP, sdt_DBP,
#>     sdt_SBP, SMD_DBP, SMD_SBP, st_D, st_DD, studyID
#> The following objects are masked from Geeganage2010 (pos = 5):
#> 
#>     MD_DBP, MD_SBP, nc_D, nc_DBP, nc_DD, nc_SBP, nt_D, nt_DBP, nt_DD,
#>     nt_SBP, OR_D, OR_DD, sc_D, sc_DD, sdc_DBP, sdc_SBP, sdt_DBP,
#>     sdt_SBP, SMD_DBP, SMD_SBP, st_D, st_DD, studyID
#> The following objects are masked from Geeganage2010 (pos = 6):
#> 
#>     MD_DBP, MD_SBP, nc_D, nc_DBP, nc_DD, nc_SBP, nt_D, nt_DBP, nt_DD,
#>     nt_SBP, OR_D, OR_DD, sc_D, sc_DD, sdc_DBP, sdc_SBP, sdt_DBP,
#>     sdt_SBP, SMD_DBP, SMD_SBP, st_D, st_DD, studyID
#> The following objects are masked from Geeganage2010 (pos = 7):
#> 
#>     MD_DBP, MD_SBP, nc_D, nc_DBP, nc_DD, nc_SBP, nt_D, nt_DBP, nt_DD,
#>     nt_SBP, OR_D, OR_DD, sc_D, sc_DD, sdc_DBP, sdc_SBP, sdt_DBP,
#>     sdt_SBP, SMD_DBP, SMD_SBP, st_D, st_DD, studyID
SBP_DD <- unlist(lapply(1:nrow(Geeganage2010), function(i){md_rd(r = 0.71,
               n1c = nc_SBP[i], n2c = nc_DD[i], n1t = nt_SBP[i], n2t = nt_DD[i],
               sd1t = sdt_SBP[i], s2t = st_DD[i], sd1c = sdc_SBP[i], s2c = sc_DD[i],
               f2c = nc_DD[i] - sc_DD[i], f2t = nt_DD[i] - st_DD[i])$v}))
SBP_DD
#>  [1] 1.31282944 1.46226447 0.24609036 0.24375926 0.14406999 1.30604939
#>  [7] 0.17628538 0.08638135 0.30057845 0.23916473 0.07264930 0.62377857
#> [13] 0.58277535 1.43662352 0.05570118 0.30224261 1.02877434
## the function mix.vcov() should be used for dataset