dat.hasselblad1998.RdResults from 24 studies on the effectiveness of various counseling types for smoking cessation.
dat.hasselblad1998
The data frame contains the following columns:
| id | numeric | id number for each treatment arm |
| study | numeric | study id number |
| authors | character | study author(s) |
| year | numeric | publication year |
| trt | character | intervention group |
| xi | numeric | number of individuals abstinent |
| ni | numeric | number of individuals in group |
The dataset includes the results from 24 studies on the effectiveness of various counseling types for smoking cessation (i.e., self-help, individual counseling, group counseling, and no contact). The dataset indicates the total number of individuals within each study arm and the number that were abstinent from 6 to 12 months. The majority of the studies compared two interventions types against each other, while 2 studies compared three types against each other simultaneously.
The data can be used for a ‘network meta-analysis’ (also called ‘mixed treatment comparison meta-analysis’). The code below shows how such an analysis can be conducted using an arm-based and a contrast-based model (see Salanti et al., 2008, for more details).
Hasselblad, V. (1998). Meta-analysis of multitreatment studies. Medical Decision Making, 18(1), 37--43. https://doi.org/10.1177/0272989X9801800110
Gleser, L. J., & Olkin, I. (2009). Stochastically dependent effect sizes. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (2nd ed., pp. 357--376). New York: Russell Sage Foundation.
Law, M., Jackson, D., Turner, R., Rhodes, K., & Viechtbauer, W. (2016). Two new methods to fit models for network meta-analysis with random inconsistency effects. BMC Medical Research Methodology, 16, 87. https://doi.org/10.1186/s12874-016-0184-5
Salanti, G., Higgins, J. P. T., Ades, A. E., & Ioannidis, J. P. A. (2008). Evaluation of networks of randomized trials. Statistical Methods in Medical Research, 17(3), 279--301. https://doi.org/10.1177/0962280207080643
### copy data into 'dat' dat <- dat.hasselblad1998 dat#> id study authors year trt xi ni #> 1 1 1 Reid et al. 1974 no_contact 75 731 #> 2 2 1 Reid et al. 1974 ind_counseling 363 714 #> 3 3 2 Cottraux et al. 1983 no_contact 9 140 #> 4 4 2 Cottraux et al. 1983 ind_counseling 23 140 #> 5 5 2 Cottraux et al. 1983 grp_counseling 10 138 #> 6 6 3 Slama et al. 1990 no_contact 2 106 #> 7 7 3 Slama et al. 1990 ind_counseling 9 205 #> 8 8 4 Jamrozik et al. 1984 no_contact 58 549 #> 9 9 4 Jamrozik et al. 1984 ind_counseling 237 1561 #> 10 10 5 Rabkin et al. 1984 no_contact 0 33 #> 11 11 5 Rabkin et al. 1984 ind_counseling 9 48 #> 12 12 6 Decker and Evans 1989 self_help 20 49 #> 13 13 6 Decker and Evans 1989 ind_counseling 16 43 #> 14 14 7 Richmond et al. 1986 no_contact 3 100 #> 15 15 7 Richmond et al. 1986 ind_counseling 31 98 #> 16 16 8 Leung 1991 no_contact 1 31 #> 17 17 8 Leung 1991 ind_counseling 26 95 #> 18 18 9 Mothersill et al. 1988 self_help 11 78 #> 19 19 9 Mothersill et al. 1988 ind_counseling 12 85 #> 20 20 9 Mothersill et al. 1988 grp_counseling 29 170 #> 21 21 10 Langford et al. 1983 no_contact 6 39 #> 22 22 10 Langford et al. 1983 ind_counseling 17 77 #> 23 23 11 Gritz et al. 1992 no_contact 79 702 #> 24 24 11 Gritz et al. 1992 self_help 77 694 #> 25 25 12 Campbell et al. 1986 no_contact 18 671 #> 26 26 12 Campbell et al. 1986 self_help 21 535 #> 27 27 13 Sanders et al. 1989 no_contact 64 642 #> 28 28 13 Sanders et al. 1989 ind_counseling 107 761 #> 29 29 14 Hilleman et al. 1993 ind_counseling 12 76 #> 30 30 14 Hilleman et al. 1993 grp_counseling 20 74 #> 31 31 15 Gillams et al. 1984 ind_counseling 9 55 #> 32 32 15 Gillams et al. 1984 grp_counseling 3 26 #> 33 33 16 Mogielnicki et al. 1986 self_help 7 66 #> 34 34 16 Mogielnicki et al. 1986 grp_counseling 32 127 #> 35 35 17 Page et al. 1986 no_contact 5 62 #> 36 36 17 Page et al. 1986 ind_counseling 8 90 #> 37 37 18 Vetter and Ford 1990 no_contact 20 234 #> 38 38 18 Vetter and Ford 1990 ind_counseling 34 237 #> 39 39 19 Williams and Hall 1988 no_contact 0 20 #> 40 40 19 Williams and Hall 1988 grp_counseling 9 20 #> 41 41 20 Pallonen et al. 1994 no_contact 8 116 #> 42 42 20 Pallonen et al. 1994 self_help 19 149 #> 43 43 21 Russell et al. 1983 no_contact 95 1107 #> 44 44 21 Russell et al. 1983 ind_counseling 143 1031 #> 45 45 22 Stewart and Rosser 1982 no_contact 15 187 #> 46 46 22 Stewart and Rosser 1982 ind_counseling 36 504 #> 47 47 23 Russell et al. 1979 no_contact 78 584 #> 48 48 23 Russell et al. 1979 ind_counseling 73 675 #> 49 49 24 Kendrick et al. 1995 no_contact 69 1177 #> 50 50 24 Kendrick et al. 1995 ind_counseling 54 888### create network graph ('plyr' and 'igraph' packages must be installed) if (FALSE) { require(igraph) pairs <- data.frame(do.call(rbind, sapply(split(dat$trt, dat$study), function(x) t(combn(x,2)))), stringsAsFactors=FALSE) lvls <- c("no_contact", "self_help", "ind_counseling", "grp_counseling") pairs$X1 <- factor(pairs$X1, levels=lvls) pairs$X2 <- factor(pairs$X2, levels=lvls) tab <- table(pairs[,1], pairs[,2]) tab # adjacency matrix g <- graph_from_adjacency_matrix(tab, mode = "plus", weighted=TRUE, diag=FALSE) vertex_attr(g, "name") <- c("No Contact", "Self-Help", "Individual\nCounseling", "Group\nCounseling") plot(g, edge.curved=FALSE, edge.width=E(g)$weight, layout=layout_on_grid, vertex.size=35, vertex.color="lightgray", vertex.label.color="black", vertex.label.font=2)} ### calculate log odds for each study arm dat <- escalc(measure="PLO", xi=xi, ni=ni, add=1/2, to="all", data=dat) dat#> id study authors year trt xi ni yi vi #> 1 1 1 Reid et al. 1974 no_contact 75 731 -2.1628 0.0148 #> 2 2 1 Reid et al. 1974 ind_counseling 363 714 0.0336 0.0056 #> 3 3 2 Cottraux et al. 1983 no_contact 9 140 -2.6277 0.1129 #> 4 4 2 Cottraux et al. 1983 ind_counseling 23 140 -1.6094 0.0511 #> 5 5 2 Cottraux et al. 1983 grp_counseling 10 138 -2.5046 0.1030 #> 6 6 3 Slama et al. 1990 no_contact 2 106 -3.7329 0.4096 #> 7 7 3 Slama et al. 1990 ind_counseling 9 205 -3.0294 0.1104 #> 8 8 4 Jamrozik et al. 1984 no_contact 58 549 -2.1284 0.0191 #> 9 9 4 Jamrozik et al. 1984 ind_counseling 237 1561 -1.7186 0.0050 #> 10 10 5 Rabkin et al. 1984 no_contact 0 33 -4.2047 2.0299 #> 11 11 5 Rabkin et al. 1984 ind_counseling 9 48 -1.4250 0.1306 #> 12 12 6 Decker and Evans 1989 self_help 20 49 -0.3640 0.0827 #> 13 13 6 Decker and Evans 1989 ind_counseling 16 43 -0.5108 0.0970 #> 14 14 7 Richmond et al. 1986 no_contact 3 100 -3.3271 0.2960 #> 15 15 7 Richmond et al. 1986 ind_counseling 31 98 -0.7621 0.0466 #> 16 16 8 Leung 1991 no_contact 1 31 -3.0123 0.6995 #> 17 17 8 Leung 1991 ind_counseling 26 95 -0.9642 0.0521 #> 18 18 9 Mothersill et al. 1988 self_help 11 78 -1.7698 0.1018 #> 19 19 9 Mothersill et al. 1988 ind_counseling 12 85 -1.7716 0.0936 #> 20 20 9 Mothersill et al. 1988 grp_counseling 29 170 -1.5679 0.0410 #> 21 21 10 Langford et al. 1983 no_contact 6 39 -1.6397 0.1837 #> 22 22 10 Langford et al. 1983 ind_counseling 17 77 -1.2404 0.0737 #> 23 23 11 Gritz et al. 1992 no_contact 79 702 -2.0596 0.0142 #> 24 24 11 Gritz et al. 1992 self_help 77 694 -2.0754 0.0145 #> 25 25 12 Campbell et al. 1986 no_contact 18 671 -3.5646 0.0556 #> 26 26 12 Campbell et al. 1986 self_help 21 535 -3.1751 0.0485 #> 27 27 13 Sanders et al. 1989 no_contact 64 642 -2.1938 0.0172 #> 28 28 13 Sanders et al. 1989 ind_counseling 107 761 -1.8064 0.0108 #> 29 29 14 Hilleman et al. 1993 ind_counseling 12 76 -1.6409 0.0955 #> 30 30 14 Hilleman et al. 1993 grp_counseling 20 74 -0.9778 0.0671 #> 31 31 15 Gillams et al. 1984 ind_counseling 9 55 -1.5882 0.1268 #> 32 32 15 Gillams et al. 1984 grp_counseling 3 26 -1.9042 0.3283 #> 33 33 16 Mogielnicki et al. 1986 self_help 7 66 -2.0711 0.1501 #> 34 34 16 Mogielnicki et al. 1986 grp_counseling 32 127 -1.0779 0.0412 #> 35 35 17 Page et al. 1986 no_contact 5 62 -2.3470 0.1992 #> 36 36 17 Page et al. 1986 ind_counseling 8 90 -2.2727 0.1298 #> 37 37 18 Vetter and Ford 1990 no_contact 20 234 -2.3479 0.0534 #> 38 38 18 Vetter and Ford 1990 ind_counseling 34 237 -1.7747 0.0339 #> 39 39 19 Williams and Hall 1988 no_contact 0 20 -3.7136 2.0488 #> 40 40 19 Williams and Hall 1988 grp_counseling 9 20 -0.1911 0.1922 #> 41 41 20 Pallonen et al. 1994 no_contact 8 116 -2.5467 0.1269 #> 42 42 20 Pallonen et al. 1994 self_help 19 149 -1.9010 0.0589 #> 43 43 21 Russell et al. 1983 no_contact 95 1107 -2.3611 0.0115 #> 44 44 21 Russell et al. 1983 ind_counseling 143 1031 -1.8232 0.0081 #> 45 45 22 Stewart and Rosser 1982 no_contact 15 187 -2.4096 0.0703 #> 46 46 22 Stewart and Rosser 1982 ind_counseling 36 504 -2.5522 0.0295 #> 47 47 23 Russell et al. 1979 no_contact 78 584 -1.8644 0.0147 #> 48 48 23 Russell et al. 1979 ind_counseling 73 675 -2.1038 0.0153 #> 49 49 24 Kendrick et al. 1995 no_contact 69 1177 -2.7694 0.0153 #> 50 50 24 Kendrick et al. 1995 ind_counseling 54 888 -2.7286 0.0195### convert trt variable to factor with desired ordering of levels dat$trt <- factor(dat$trt, levels=c("no_contact", "self_help", "ind_counseling", "grp_counseling")) ### add a space before each level (this makes the output a bit more legible) levels(dat$trt) <- paste0(" ", levels(dat$trt)) ### network meta-analysis using an arm-based model with fixed study effects ### by setting rho=1/2, tau^2 reflects the amount of heterogeneity for all treatment comparisons res <- rma.mv(yi, vi, mods = ~ factor(study) + trt - 1, random = ~ trt | study, rho=1/2, data=dat, btt="trt") res#> #> Multivariate Meta-Analysis Model (k = 50; method: REML) #> #> Variance Components: #> #> outer factor: study (nlvls = 24) #> inner factor: trt (nlvls = 4) #> #> estim sqrt fixed #> tau^2 0.4324 0.6575 no #> rho 0.5000 yes #> #> Test for Residual Heterogeneity: #> QE(df = 23) = 202.3334, p-val < .0001 #> #> Test of Moderators (coefficients 25:27): #> QM(df = 3) = 14.2278, p-val = 0.0026 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub #> factor(study)1 -1.3925 0.5820 -2.3926 0.0167 -2.5333 -0.2518 * #> factor(study)2 -2.7302 0.5842 -4.6731 <.0001 -3.8753 -1.5851 *** #> factor(study)3 -3.7217 0.6681 -5.5703 <.0001 -5.0312 -2.4121 *** #> factor(study)4 -2.2710 0.5829 -3.8958 <.0001 -3.4136 -1.1285 *** #> factor(study)5 -2.3914 0.7374 -3.2430 0.0012 -3.8367 -0.9461 ** #> factor(study)6 -0.9698 0.6421 -1.5104 0.1309 -2.2284 0.2887 #> factor(study)7 -2.0855 0.6369 -3.2744 0.0011 -3.3339 -0.8372 ** #> factor(study)8 -1.9592 0.6674 -2.9357 0.0033 -3.2672 -0.6512 ** #> factor(study)9 -2.3487 0.6032 -3.8936 <.0001 -3.5310 -1.1664 *** #> factor(study)10 -1.8062 0.6296 -2.8688 0.0041 -3.0402 -0.5722 ** #> factor(study)11 -2.2618 0.5978 -3.7835 0.0002 -3.4334 -1.0901 *** #> factor(study)12 -3.5643 0.6139 -5.8058 <.0001 -4.7675 -2.3610 *** #> factor(study)13 -2.3454 0.5836 -4.0188 <.0001 -3.4892 -1.2015 *** #> factor(study)14 -2.0624 0.6492 -3.1767 0.0015 -3.3348 -0.7899 ** #> factor(study)15 -2.4575 0.6868 -3.5781 0.0003 -3.8037 -1.1114 *** #> factor(study)16 -2.1438 0.6707 -3.1964 0.0014 -3.4583 -0.8293 ** #> factor(study)17 -2.6810 0.6448 -4.1581 <.0001 -3.9447 -1.4173 *** #> factor(study)18 -2.4066 0.5964 -4.0353 <.0001 -3.5755 -1.2377 *** #> factor(study)19 -1.4441 0.8108 -1.7811 0.0749 -3.0331 0.1450 . #> factor(study)20 -2.4041 0.6331 -3.7974 0.0001 -3.6450 -1.1633 *** #> factor(study)21 -2.4359 0.5817 -4.1877 <.0001 -3.5760 -1.2958 *** #> factor(study)22 -2.8559 0.5991 -4.7667 <.0001 -4.0301 -1.6816 *** #> factor(study)23 -2.3268 0.5838 -3.9857 <.0001 -3.4710 -1.1826 *** #> factor(study)24 -3.0893 0.5847 -5.2836 <.0001 -4.2353 -1.9433 *** #> trt self_help 0.3888 0.3221 1.2070 0.2274 -0.2426 1.0202 #> trt ind_counseling 0.6864 0.1904 3.6055 0.0003 0.3133 1.0596 *** #> trt grp_counseling 0.8438 0.3641 2.3176 0.0205 0.1302 1.5574 * #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>### all pairwise odds ratios of interventions versus no contact predict(res, newmods=cbind(matrix(0, nrow=3, ncol=24), diag(3)), intercept=FALSE, transf=exp, digits=2)#> #> pred ci.lb ci.ub pi.lb pi.ub #> 1 1.48 0.78 2.77 0.35 6.20 #> 2 1.99 1.37 2.89 0.52 7.60 #> 3 2.33 1.14 4.75 0.53 10.14 #>### all pairwise odds ratios comparing interventions (ic vs sh, gc vs sh, and gc vs ic) predict(res, newmods=cbind(matrix(0, nrow=3, ncol=24), rbind(c(-1,1,0), c(-1,0,1), c(0,-1,1))), intercept=FALSE, transf=exp, digits=2)#> #> pred ci.lb ci.ub pi.lb pi.ub #> 1 1.35 0.70 2.58 0.32 5.71 #> 2 1.58 0.72 3.43 0.35 7.10 #> 3 1.17 0.59 2.30 0.27 5.02 #>### forest plot of ORs of interventions versus no contact dev.new(width=7, height=4) par(mar=c(5,4,1,2)) forest(c(0,res$beta[25:27]), sei=c(0,res$se[25:27]), psize=1, xlim=c(-3,4), digits=c(2,1), efac=2, slab=c("No Contact", "Self-Help", "Individual Counseling", "Group Counseling"), atransf=exp, at=log(c(.5, 1, 2, 4, 8)), xlab="Odds Ratio for Intervention vs. No Contact", header=c("Intervention", "Odds Ratio [95% CI]")) ############################################################################ ### restructure dataset to a contrast-based format dat <- to.wide(dat.hasselblad1998, study="study", grp="trt", ref="no_contact", grpvars=6:7) ### calculate log odds ratios for each treatment comparison dat <- escalc(measure="OR", ai=xi.1, n1i=ni.1, ci=xi.2, n2i=ni.2, add=1/2, to="all", data=dat) dat#> id study authors year trt.1 xi.1 ni.1 trt.2 #> 1 1 1 Reid et al. 1974 ind_counseling 363 714 no_contact #> 2 2 2 Cottraux et al. 1983 grp_counseling 10 138 no_contact #> 3 3 2 Cottraux et al. 1983 ind_counseling 23 140 no_contact #> 4 4 3 Slama et al. 1990 ind_counseling 9 205 no_contact #> 5 5 4 Jamrozik et al. 1984 ind_counseling 237 1561 no_contact #> 6 6 5 Rabkin et al. 1984 ind_counseling 9 48 no_contact #> 7 7 6 Decker and Evans 1989 ind_counseling 16 43 self_help #> 8 8 7 Richmond et al. 1986 ind_counseling 31 98 no_contact #> 9 9 8 Leung 1991 ind_counseling 26 95 no_contact #> 10 10 9 Mothersill et al. 1988 grp_counseling 29 170 self_help #> 11 11 9 Mothersill et al. 1988 ind_counseling 12 85 self_help #> 12 12 10 Langford et al. 1983 ind_counseling 17 77 no_contact #> 13 13 11 Gritz et al. 1992 self_help 77 694 no_contact #> 14 14 12 Campbell et al. 1986 self_help 21 535 no_contact #> 15 15 13 Sanders et al. 1989 ind_counseling 107 761 no_contact #> 16 16 14 Hilleman et al. 1993 grp_counseling 20 74 ind_counseling #> 17 17 15 Gillams et al. 1984 grp_counseling 3 26 ind_counseling #> 18 18 16 Mogielnicki et al. 1986 grp_counseling 32 127 self_help #> 19 19 17 Page et al. 1986 ind_counseling 8 90 no_contact #> 20 20 18 Vetter and Ford 1990 ind_counseling 34 237 no_contact #> 21 21 19 Williams and Hall 1988 grp_counseling 9 20 no_contact #> 22 22 20 Pallonen et al. 1994 self_help 19 149 no_contact #> 23 23 21 Russell et al. 1983 ind_counseling 143 1031 no_contact #> 24 24 22 Stewart and Rosser 1982 ind_counseling 36 504 no_contact #> 25 25 23 Russell et al. 1979 ind_counseling 73 675 no_contact #> 26 26 24 Kendrick et al. 1995 ind_counseling 54 888 no_contact #> xi.2 ni.2 comp design yi vi #> 1 75 731 in-no in-no 2.1964 0.0204 #> 2 9 140 gr-no gr-in-no 0.1232 0.2159 #> 3 9 140 in-no gr-in-no 1.0183 0.1639 #> 4 2 106 in-no in-no 0.7035 0.5199 #> 5 58 549 in-no in-no 0.4098 0.0241 #> 6 0 33 in-no in-no 2.7797 2.1604 #> 7 20 49 in-se in-se -0.1469 0.1796 #> 8 3 100 in-no in-no 2.5649 0.3425 #> 9 1 31 in-no in-no 2.0481 0.7516 #> 10 11 78 gr-se gr-in-se 0.2019 0.1427 #> 11 11 78 in-se gr-in-se -0.0018 0.1954 #> 12 6 39 in-no in-no 0.3993 0.2574 #> 13 79 702 se-no se-no -0.0158 0.0287 #> 14 18 671 se-no se-no 0.3894 0.1040 #> 15 64 642 in-no in-no 0.3874 0.0281 #> 16 12 76 gr-in gr-in 0.6632 0.1626 #> 17 9 55 gr-in gr-in -0.3161 0.4550 #> 18 7 66 gr-se gr-se 0.9932 0.1914 #> 19 5 62 in-no in-no 0.0743 0.3290 #> 20 20 234 in-no in-no 0.5732 0.0873 #> 21 0 20 gr-no gr-no 3.5225 2.2410 #> 22 8 116 se-no se-no 0.6457 0.1858 #> 23 95 1107 in-no in-no 0.5379 0.0196 #> 24 15 187 in-no in-no -0.1427 0.0998 #> 25 78 584 in-no in-no -0.2394 0.0300 #> 26 69 1177 in-no in-no 0.0408 0.0348### calculate the variance-covariance matrix of the log odds ratios for multitreatment studies ### see Gleser & Olkin (2009), equation (19.11), for the covariance equation calc.v <- function(x) { v <- matrix(1/(x$xi.2[1]+1/2) + 1/(x$ni.2[1] - x$xi.2[1] + 1/2), nrow=nrow(x), ncol=nrow(x)) diag(v) <- x$vi v } V <- bldiag(lapply(split(dat, dat$study), calc.v)) ### add contrast matrix to dataset dat <- contrmat(dat, grp1="trt.1", grp2="trt.2") dat#> id study authors year trt.1 xi.1 ni.1 trt.2 #> 1 1 1 Reid et al. 1974 ind_counseling 363 714 no_contact #> 2 2 2 Cottraux et al. 1983 grp_counseling 10 138 no_contact #> 3 3 2 Cottraux et al. 1983 ind_counseling 23 140 no_contact #> 4 4 3 Slama et al. 1990 ind_counseling 9 205 no_contact #> 5 5 4 Jamrozik et al. 1984 ind_counseling 237 1561 no_contact #> 6 6 5 Rabkin et al. 1984 ind_counseling 9 48 no_contact #> 7 7 6 Decker and Evans 1989 ind_counseling 16 43 self_help #> 8 8 7 Richmond et al. 1986 ind_counseling 31 98 no_contact #> 9 9 8 Leung 1991 ind_counseling 26 95 no_contact #> 10 10 9 Mothersill et al. 1988 grp_counseling 29 170 self_help #> 11 11 9 Mothersill et al. 1988 ind_counseling 12 85 self_help #> 12 12 10 Langford et al. 1983 ind_counseling 17 77 no_contact #> 13 13 11 Gritz et al. 1992 self_help 77 694 no_contact #> 14 14 12 Campbell et al. 1986 self_help 21 535 no_contact #> 15 15 13 Sanders et al. 1989 ind_counseling 107 761 no_contact #> 16 16 14 Hilleman et al. 1993 grp_counseling 20 74 ind_counseling #> 17 17 15 Gillams et al. 1984 grp_counseling 3 26 ind_counseling #> 18 18 16 Mogielnicki et al. 1986 grp_counseling 32 127 self_help #> 19 19 17 Page et al. 1986 ind_counseling 8 90 no_contact #> 20 20 18 Vetter and Ford 1990 ind_counseling 34 237 no_contact #> 21 21 19 Williams and Hall 1988 grp_counseling 9 20 no_contact #> 22 22 20 Pallonen et al. 1994 self_help 19 149 no_contact #> 23 23 21 Russell et al. 1983 ind_counseling 143 1031 no_contact #> 24 24 22 Stewart and Rosser 1982 ind_counseling 36 504 no_contact #> 25 25 23 Russell et al. 1979 ind_counseling 73 675 no_contact #> 26 26 24 Kendrick et al. 1995 ind_counseling 54 888 no_contact #> xi.2 ni.2 comp design yi vi grp_counseling ind_counseling #> 1 75 731 in-no in-no 2.1964 0.0204 0 1 #> 2 9 140 gr-no gr-in-no 0.1232 0.2159 1 0 #> 3 9 140 in-no gr-in-no 1.0183 0.1639 0 1 #> 4 2 106 in-no in-no 0.7035 0.5199 0 1 #> 5 58 549 in-no in-no 0.4098 0.0241 0 1 #> 6 0 33 in-no in-no 2.7797 2.1604 0 1 #> 7 20 49 in-se in-se -0.1469 0.1796 0 1 #> 8 3 100 in-no in-no 2.5649 0.3425 0 1 #> 9 1 31 in-no in-no 2.0481 0.7516 0 1 #> 10 11 78 gr-se gr-in-se 0.2019 0.1427 1 0 #> 11 11 78 in-se gr-in-se -0.0018 0.1954 0 1 #> 12 6 39 in-no in-no 0.3993 0.2574 0 1 #> 13 79 702 se-no se-no -0.0158 0.0287 0 0 #> 14 18 671 se-no se-no 0.3894 0.1040 0 0 #> 15 64 642 in-no in-no 0.3874 0.0281 0 1 #> 16 12 76 gr-in gr-in 0.6632 0.1626 1 -1 #> 17 9 55 gr-in gr-in -0.3161 0.4550 1 -1 #> 18 7 66 gr-se gr-se 0.9932 0.1914 1 0 #> 19 5 62 in-no in-no 0.0743 0.3290 0 1 #> 20 20 234 in-no in-no 0.5732 0.0873 0 1 #> 21 0 20 gr-no gr-no 3.5225 2.2410 1 0 #> 22 8 116 se-no se-no 0.6457 0.1858 0 0 #> 23 95 1107 in-no in-no 0.5379 0.0196 0 1 #> 24 15 187 in-no in-no -0.1427 0.0998 0 1 #> 25 78 584 in-no in-no -0.2394 0.0300 0 1 #> 26 69 1177 in-no in-no 0.0408 0.0348 0 1 #> self_help no_contact #> 1 0 -1 #> 2 0 -1 #> 3 0 -1 #> 4 0 -1 #> 5 0 -1 #> 6 0 -1 #> 7 -1 0 #> 8 0 -1 #> 9 0 -1 #> 10 -1 0 #> 11 -1 0 #> 12 0 -1 #> 13 1 -1 #> 14 1 -1 #> 15 0 -1 #> 16 0 0 #> 17 0 0 #> 18 -1 0 #> 19 0 -1 #> 20 0 -1 #> 21 0 -1 #> 22 1 -1 #> 23 0 -1 #> 24 0 -1 #> 25 0 -1 #> 26 0 -1### network meta-analysis using a contrast-based random-effects model ### by setting rho=1/2, tau^2 reflects the amount of heterogeneity for all treatment comparisons res <- rma.mv(yi, V, mods = ~ self_help + ind_counseling + grp_counseling - 1, random = ~ comp | study, rho=1/2, data=dat) res#> #> Multivariate Meta-Analysis Model (k = 26; method: REML) #> #> Variance Components: #> #> outer factor: study (nlvls = 24) #> inner factor: comp (nlvls = 6) #> #> estim sqrt fixed #> tau^2 0.4324 0.6575 no #> rho 0.5000 yes #> #> Test for Residual Heterogeneity: #> QE(df = 23) = 202.3334, p-val < .0001 #> #> Test of Moderators (coefficients 1:3): #> QM(df = 3) = 14.2278, p-val = 0.0026 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub #> self_help 0.3888 0.3221 1.2070 0.2274 -0.2426 1.0202 #> ind_counseling 0.6864 0.1904 3.6055 0.0003 0.3133 1.0596 *** #> grp_counseling 0.8438 0.3641 2.3176 0.0205 0.1302 1.5574 * #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>### predicted odds ratios of interventions versus no contact predict(res, newmods=diag(3), transf=exp, digits=2)#> #> pred ci.lb ci.ub pi.lb pi.ub #> 1 1.48 0.78 2.77 0.35 6.20 #> 2 1.99 1.37 2.89 0.52 7.60 #> 3 2.33 1.14 4.75 0.53 10.14 #>### fit random inconsistency effects model (see Law et al., 2016) res <- rma.mv(yi, V, mods = ~ self_help + ind_counseling + grp_counseling - 1, random = list(~ comp | study, ~ comp | design), rho=1/2, phi=1/2, data=dat) res#> #> Multivariate Meta-Analysis Model (k = 26; method: REML) #> #> Variance Components: #> #> outer factor: study (nlvls = 24) #> inner factor: comp (nlvls = 6) #> #> estim sqrt fixed #> tau^2 0.4324 0.6575 no #> rho 0.5000 yes #> #> outer factor: design (nlvls = 8) #> inner factor: comp (nlvls = 6) #> #> estim sqrt fixed #> gamma^2 0.0000 0.0000 no #> phi 0.5000 yes #> #> Test for Residual Heterogeneity: #> QE(df = 23) = 202.3334, p-val < .0001 #> #> Test of Moderators (coefficients 1:3): #> QM(df = 3) = 14.2278, p-val = 0.0026 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub #> self_help 0.3888 0.3221 1.2070 0.2274 -0.2426 1.0202 #> ind_counseling 0.6864 0.1904 3.6055 0.0003 0.3133 1.0596 *** #> grp_counseling 0.8438 0.3641 2.3176 0.0205 0.1302 1.5574 * #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>