Results from 31 studies examining differences in planning performance in schizophrenia patients versus healthy controls.

dat.knapp2017

## Format

The data frame contains the following columns:

 author character study author(s) year numeric publication year study numeric study id number task character type of task difficulty numeric task difficulty group1 character identifier for patient group within studies group2 character identifier for control group within studies comp numeric identifier for comparisons within studies yi numeric standardized mean difference for planning performance vi numeric corresponding sampling variance n_sz numeric number of schizophrenic patients n_hc numeric number of healthy controls yi numeric standardized mean difference for IQ vi numeric corresponding sampling variance

## Details

The studies included in this dataset examined differences between schizophrenia patients and healthy controls with respect to their performance on the tower of London test (https://en.wikipedia.org/wiki/Tower_of_London_test) or a similar cognitive tasks measuring planning ability. The outcome measure for this meta-analysis was the standardized mean difference (with positive values indicating better performance in the healthy controls compared to the schizophrenia patients).

The dataset has a more complex structure for several reasons:

1. Studies 2, 3, 9, and 20 included more than one schizophrenia patient group and the standardized mean differences were computed by comparing these groups against a single healthy control group.

2. Studies 6, 12, 14, 15, 18, 19, 22, and 26 had the patients and controls complete different tasks of varying complexity (essentially the average number of moves required to complete a task). Study 6 also included two different task types.

3. Study 24 provides two standardized mean differences, one for men and the other for women.

4. Study 29 provides three standardized mean differences, corresponding to the three different COMT Val158Met genotypes (val/val, val/met, and met/met).

All 4 issues described above lead to a multilevel structure in the dataset, with multiple standardized mean differences nested within some of the studies. Issues 1. and 2. also lead to correlated sampling errors.

## Source

Knapp, F., Viechtbauer, W., Leonhart, R., Nitschke, K., & Kaller, C. P. (2017). Planning performance in schizophrenia patients: A meta-analysis of the influence of task difficulty and clinical and sociodemographic variables. Psychological Medicine, 47(11), 2002–2016. https://doi.org/10.1017/S0033291717000459

## Author

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

## Concepts

psychology, standardized mean differences, multilevel models, multivariate models, cluster-robust inference, meta-regression

## Examples

### copy data into 'dat' and examine data
dat <- dat.knapp2017
dat[-c(1:2)]
#>    study            task difficulty group1 group2 comp    yi    vi n_sz n_hc yi_iq vi_iq
#> 1      1    SOC (CANTAB)       3.83     SZ     HC    1  0.62 0.075   24   33  0.72 0.076
#> 2      2    SOC (CANTAB)       3.83    SZ1     HC    1  0.46 0.047   44   44    NA    NA
#> 3      2    SOC (CANTAB)       3.83    SZ2     HC    2  0.73 0.052   38   44    NA    NA
#> 4      3    SOC (CANTAB)       3.83    SZ1     HC    1  1.18 0.062   39   37    NA    NA
#> 5      3    SOC (CANTAB)       3.83    SZ2     HC    2  1.09 0.073   27   37    NA    NA
#> 6      3    SOC (CANTAB)       3.83    SZ3     HC    3  0.91 0.102   15   37    NA    NA
#> 7      3    SOC (CANTAB)       3.83    SZ4     HC    4  0.91 0.084   20   37    NA    NA
#> 8      4             TOH         NA     SZ     HC    1  0.57 0.074   28   28    NA    NA
#> 9      5             TOL         NA     SZ     HC    1  0.40 0.180   13   10    NA    NA
#> 10     6    SOC (CANTAB)       2.00     SZ     HC    1  0.43 0.170   12   12  0.12 0.167
#> 11     6    SOC (CANTAB)       3.00     SZ     HC    2  1.37 0.206   12   12  0.12 0.167
#> 12     6    SOC (CANTAB)       4.00     SZ     HC    3  0.23 0.168   12   12  0.12 0.167
#> 13     6    SOC (CANTAB)       5.00     SZ     HC    4  0.97 0.186   12   12  0.12 0.167
#> 14     6 SOC (one-touch)       2.00     SZ     HC    5  0.56 0.173   12   12  0.12 0.167
#> 15     6 SOC (one-touch)       3.00     SZ     HC    6  0.79 0.180   12   12  0.12 0.167
#> 16     6 SOC (one-touch)       4.00     SZ     HC    7  1.19 0.196   12   12  0.12 0.167
#> 17     6 SOC (one-touch)       5.00     SZ     HC    8  0.92 0.184   12   12  0.12 0.167
#> 18     7             SOC       3.50     SZ     HC    1  0.20 0.096   22   20  0.62 0.100
#> 19     8             TOH         NA     SZ     HC    1  1.42 0.180   13   15    NA    NA
#> 20     9             TOL       4.00    SZ1     HC    1  0.35 0.074   27   28  1.21 0.086
#> 21     9             TOL       4.00    SZ2     HC    2  0.88 0.078   28   28  1.26 0.086
#> 22    10    SOC (CANTAB)       3.83     SZ     HC    1  1.08 0.079   26   33  0.76 0.074
#> 23    11    SOC (CANTAB)       3.83     SZ     HC    1  0.94 0.111   20   20  0.42 0.102
#> 24    12    SOC (CANTAB)       2.00     SZ     HC    1  0.44 0.020  135   81  0.49 0.020
#> 25    12    SOC (CANTAB)       3.00     SZ     HC    2  0.63 0.021  135   81  0.49 0.020
#> 26    12    SOC (CANTAB)       4.00     SZ     HC    3  0.38 0.020  135   81  0.49 0.020
#> 27    12    SOC (CANTAB)       5.00     SZ     HC    4  0.93 0.022  135   81  0.49 0.020
#> 28    13             TOL         NA     SZ     HC    1  0.33 0.102   24   17    NA    NA
#> 29    14             TOL       2.00     SZ     HC    1  0.00 0.073   32   24    NA    NA
#> 30    14             TOL       3.00     SZ     HC    2 -0.06 0.073   32   24    NA    NA
#> 31    14             TOL       4.00     SZ     HC    3  0.73 0.078   32   24    NA    NA
#> 32    14             TOL       5.00     SZ     HC    4  0.48 0.075   32   24    NA    NA
#> 33    15             TOL       2.00     SZ     HC    1  0.43 0.092   25   20    NA    NA
#> 34    15             TOL       3.00     SZ     HC    2  0.72 0.096   25   20    NA    NA
#> 35    15             TOL       4.00     SZ     HC    3  0.80 0.097   25   20    NA    NA
#> 36    15             TOL       5.00     SZ     HC    4  1.30 0.109   25   20    NA    NA
#> 37    16             TOL       4.67     SZ     HC    1  1.84 0.190   15   15    NA    NA
#> 38    17             TOL       3.50     SZ     HC    1  2.58 0.216   17   17  0.58 0.123
#> 39    18             TOL       3.00     SZ     HC    1  0.25 0.071   30   27  0.18 0.071
#> 40    18             TOL       4.00     SZ     HC    2  0.86 0.077   30   27  0.18 0.071
#> 41    18             TOL       5.00     SZ     HC    3  0.68 0.074   30   27  0.18 0.071
#> 42    19    SOC (CANTAB)       2.00     SZ     HC    1  0.21 0.060   36   31  0.48 0.062
#> 43    19    SOC (CANTAB)       3.00     SZ     HC    2  0.65 0.063   36   31  0.48 0.062
#> 44    19    SOC (CANTAB)       4.00     SZ     HC    3  0.30 0.061   36   31  0.48 0.062
#> 45    19    SOC (CANTAB)       5.00     SZ     HC    4  0.45 0.062   36   31  0.48 0.062
#> 46    20          BACS-J         NA    SZ1     HC    1  1.03 0.054   20  340    NA    NA
#> 47    20          BACS-J         NA    SZ2     HC    2  0.92 0.104   10  340    NA    NA
#> 48    21    SOC (CANTAB)       3.83     SZ     HC    1  1.12 0.108   28   17    NA    NA
#> 49    22             TOL       2.00     SZ     HC    1  0.52 0.052   40   40    NA    NA
#> 50    22             TOL       3.00     SZ     HC    2  0.50 0.052   40   40    NA    NA
#> 51    22             TOL       4.00     SZ     HC    3  0.49 0.051   40   40    NA    NA
#> 52    23             SOC       3.83     SZ     HC    1  0.30 0.042   48   48    NA    NA
#> 53    24      TOL-Drexel       5.50    SZ1    HC1    1  0.36 0.022   86   97  0.47 0.023
#> 54    24      TOL-Drexel       5.50    SZ2    HC2    2  0.41 0.030   75   62  0.10 0.030
#> 55    25             SOC       3.83     SZ     HC    1  0.79 0.086   25   25    NA    NA
#> 56    26             SOC       2.00     SZ     HC    1  0.23 0.031   77   55    NA    NA
#> 57    26             SOC       3.00     SZ     HC    2  0.58 0.032   77   55    NA    NA
#> 58    26             SOC       4.00     SZ     HC    3  0.57 0.032   77   55    NA    NA
#> 59    26             SOC       5.00     SZ     HC    4  0.79 0.034   77   55    NA    NA
#> 60    27      TOL-Drexel       5.50     SZ     HC    1  0.70 0.071   30   30    NA    NA
#> 61    28             SOC       3.83     SZ     HC    1  1.16 0.136   20   15  0.23 0.117
#> 62    29          BACS-J         NA    SZ1    HC1    1  1.29 0.039   56   68  0.37 0.033
#> 63    29          BACS-J         NA    SZ2    HC2    2  0.63 0.039   47   62  0.43 0.038
#> 64    29          BACS-J         NA    SZ3    HC3    3  0.31 0.121   15   19  1.00 0.134
#> 65    30             TOL       3.83     SZ     HC    1  0.11 0.070   30   27    NA    NA
#> 66    31 TOL (four-disk)       5.60     SZ     HC    1  0.87 0.036   60   60    NA    NA

# \dontrun{

library(metafor)

### fit a standard random-effects model ignoring the issues described above
res <- rma(yi, vi, data=dat)
res
#>
#> Random-Effects Model (k = 66; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of total heterogeneity): 0.0551 (SE = 0.0212)
#> tau (square root of estimated tau^2 value):      0.2348
#> I^2 (total heterogeneity / total variability):   47.74%
#> H^2 (total variability / sampling variability):  1.91
#>
#> Test for Heterogeneity:
#> Q(df = 65) = 129.0088, p-val < .0001
#>
#> Model Results:
#>
#> estimate      se     zval    pval   ci.lb   ci.ub     ​
#>   0.6557  0.0439  14.9521  <.0001  0.5698  0.7417  ***
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>

### fit a multilevel model with random effects for studies and comparisons within studies
### (but this ignored the correlation in the sampling errors)
res <- rma.mv(yi, vi, random = ~ 1 | study/comp, data=dat)
res
#>
#> Multivariate Meta-Analysis Model (k = 66; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0383  0.1958     31     no       study
#> sigma^2.2  0.0263  0.1621     66     no  study/comp
#>
#> Test for Heterogeneity:
#> Q(df = 65) = 129.0088, p-val < .0001
#>
#> Model Results:
#>
#> estimate      se     zval    pval   ci.lb   ci.ub     ​
#>   0.6801  0.0560  12.1513  <.0001  0.5704  0.7898  ***
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>

### create variable that indicates the task and difficulty combination as increasing integers
dat$task.diff <- unlist(lapply(split(dat, dat$study), function(x) {
task.int <- as.integer(factor(x$task)) diff.int <- as.integer(factor(x$difficulty))
diff.int[is.na(diff.int)] <- 1

### construct correlation matrix for two tasks with four different difficulties where the
### correlation is 0.4 for different difficulties of the same task, 0.7 for the same
### difficulty of different tasks, and 0.28 for different difficulties of different tasks
R <- matrix(0.4, nrow=8, ncol=8)
R[5:8,1:4] <- R[1:4,5:8] <- 0.28
diag(R[1:4,5:8]) <- 0.7
diag(R[5:8,1:4]) <- 0.7
diag(R) <- 1
rownames(R) <- colnames(R) <- paste0(rep(1:2, each=4), ".", 1:4)
R
#>      1.1  1.2  1.3  1.4  2.1  2.2  2.3  2.4
#> 1.1 1.00 0.40 0.40 0.40 0.70 0.28 0.28 0.28
#> 1.2 0.40 1.00 0.40 0.40 0.28 0.70 0.28 0.28
#> 1.3 0.40 0.40 1.00 0.40 0.28 0.28 0.70 0.28
#> 1.4 0.40 0.40 0.40 1.00 0.28 0.28 0.28 0.70
#> 2.1 0.70 0.28 0.28 0.28 1.00 0.40 0.40 0.40
#> 2.2 0.28 0.70 0.28 0.28 0.40 1.00 0.40 0.40
#> 2.3 0.28 0.28 0.70 0.28 0.40 0.40 1.00 0.40
#> 2.4 0.28 0.28 0.28 0.70 0.40 0.40 0.40 1.00

### construct an approximate V matrix accounting for the use of shared groups and
### for correlations among tasks/difficulties as specified in the R matrix above
V <- vcalc(vi, cluster=study, grp1=group1, grp2=group2, w1=n_sz, w2=n_hc,

### correlation matrix for study 3 with four patient groups and a single control group
round(cov2cor(V[dat$study == 3, dat$study == 3]), 2)
#>      [,1] [,2] [,3] [,4]
#> [1,] 1.00 0.47 0.38 0.42
#> [2,] 0.47 1.00 0.35 0.38
#> [3,] 0.38 0.35 1.00 0.32
#> [4,] 0.42 0.38 0.32 1.00

### correlation matrix for study 6 with two tasks with four difficulties
cov2cor(V[dat$study == 6, dat$study == 6])
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1.00 0.40 0.40 0.40 0.70 0.28 0.28 0.28
#> [2,] 0.40 1.00 0.40 0.40 0.28 0.70 0.28 0.28
#> [3,] 0.40 0.40 1.00 0.40 0.28 0.28 0.70 0.28
#> [4,] 0.40 0.40 0.40 1.00 0.28 0.28 0.28 0.70
#> [5,] 0.70 0.28 0.28 0.28 1.00 0.40 0.40 0.40
#> [6,] 0.28 0.70 0.28 0.28 0.40 1.00 0.40 0.40
#> [7,] 0.28 0.28 0.70 0.28 0.40 0.40 1.00 0.40
#> [8,] 0.28 0.28 0.28 0.70 0.40 0.40 0.40 1.00

### correlation matrix for study 24 with two independent groups
cov2cor(V[dat$study == 24, dat$study == 24])
#>      [,1] [,2]
#> [1,]    1    0
#> [2,]    0    1

### correlation matrix for study 29 with three independent groups
cov2cor(V[dat$study == 29, dat$study == 29])
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    1    0
#> [3,]    0    0    1

### fit multilevel model as above, but now use this V matrix in the model
res <- rma.mv(yi, V, random = ~ 1 | study/comp, data=dat)
res
#>
#> Multivariate Meta-Analysis Model (k = 66; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0102  0.1009     31     no       study
#> sigma^2.2  0.0557  0.2360     66     no  study/comp
#>
#> Test for Heterogeneity:
#> Q(df = 65) = 152.4935, p-val < .0001
#>
#> Model Results:
#>
#> estimate      se     zval    pval   ci.lb   ci.ub     ​
#>   0.6696  0.0546  12.2735  <.0001  0.5626  0.7765  ***
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
predict(res, digits=2)
#>
#>  pred   se ci.lb ci.ub pi.lb pi.ub
#>  0.67 0.05  0.56  0.78  0.16  1.18
#>

### use cluster-robust inference methods based on this model
robust(res, cluster=study)
#>
#> Multivariate Meta-Analysis Model (k = 66; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0102  0.1009     31     no       study
#> sigma^2.2  0.0557  0.2360     66     no  study/comp
#>
#> Test for Heterogeneity:
#> Q(df = 65) = 152.4935, p-val < .0001
#>
#> Number of estimates:   66
#> Number of clusters:    31
#> Estimates per cluster: 1-8 (mean: 2.13, median: 1)
#>
#> Model Results:
#>
#> estimate     se¹    tval¹  df¹   pval¹  ci.lb¹  ci.ub¹     ​
#>   0.6696  0.0543  12.3418   30  <.0001  0.5588  0.7804  ***
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> 1) results based on cluster-robust inference (var-cov estimator: CR1,
#>    approx. t-test and confidence interval, dfs = residual method)
#>

### use methods from clubSandwich package
robust(res, cluster=study, clubSandwich=TRUE)
#>
#> Multivariate Meta-Analysis Model (k = 66; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0102  0.1009     31     no       study
#> sigma^2.2  0.0557  0.2360     66     no  study/comp
#>
#> Test for Heterogeneity:
#> Q(df = 65) = 152.4935, p-val < .0001
#>
#> Number of estimates:   66
#> Number of clusters:    31
#> Estimates per cluster: 1-8 (mean: 2.13, median: 1)
#>
#> Model Results:
#>
#> estimate     se¹    tval¹   df¹   pval¹  ci.lb¹  ci.ub¹     ​
#>   0.6696  0.0543  12.3260  22.3  <.0001  0.5570  0.7821  ***
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> 1) results based on cluster-robust inference (var-cov estimator: CR2,
#>    approx. t-test and confidence interval, dfs = Satterthwaite method)
#>

### examine if task difficulty is a potential moderator of the effect
res <- rma.mv(yi, V, mods = ~ difficulty, random = ~ 1 | study/comp, data=dat)
#> Warning: Rows with NAs omitted from model fitting.
res
#>
#> Multivariate Meta-Analysis Model (k = 57; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0465  0.2156     25     no       study
#> sigma^2.2  0.0275  0.1659     57     no  study/comp
#>
#> Test for Residual Heterogeneity:
#> QE(df = 55) = 115.9211, p-val < .0001
#>
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 10.0201, p-val = 0.0015
#>
#> Model Results:
#>
#>             estimate      se    zval    pval    ci.lb   ci.ub    ​
#> intrcpt       0.1803  0.1682  1.0717  0.2838  -0.1494  0.5100
#> difficulty    0.1241  0.0392  3.1655  0.0015   0.0472  0.2009  **
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
sav <- robust(res, cluster=study)
sav
#>
#> Multivariate Meta-Analysis Model (k = 57; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0465  0.2156     25     no       study
#> sigma^2.2  0.0275  0.1659     57     no  study/comp
#>
#> Test for Residual Heterogeneity:
#> QE(df = 55) = 115.9211, p-val < .0001
#>
#> Number of estimates:   57
#> Number of clusters:    25
#> Estimates per cluster: 1-8 (mean: 2.28, median: 1)
#>
#> Test of Moderators (coefficient 2):¹
#> F(df1 = 1, df2 = 23) = 17.7635, p-val = 0.0003
#>
#> Model Results:
#>
#>             estimate     se¹   tval¹  df¹   pval¹   ci.lb¹  ci.ub¹     ​
#> intrcpt       0.1803  0.1239  1.4547   23  0.1593  -0.0761  0.4367
#> difficulty    0.1241  0.0294  4.2147   23  0.0003   0.0632  0.1850  ***
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> 1) results based on cluster-robust inference (var-cov estimator: CR1,
#>    approx. t/F-tests and confidence intervals, dfs = residual method)
#>
sav <- robust(res, cluster=study, clubSandwich=TRUE)
sav
#>
#> Multivariate Meta-Analysis Model (k = 57; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0465  0.2156     25     no       study
#> sigma^2.2  0.0275  0.1659     57     no  study/comp
#>
#> Test for Residual Heterogeneity:
#> QE(df = 55) = 115.9211, p-val < .0001
#>
#> Number of estimates:   57
#> Number of clusters:    25
#> Estimates per cluster: 1-8 (mean: 2.28, median: 1)
#>
#> Test of Moderators (coefficient 2):¹
#> F(df1 = 1, df2 = 7.39) = 17.2483, p-val = 0.0038
#>
#> Model Results:
#>
#>             estimate     se¹   tval¹   df¹   pval¹   ci.lb¹  ci.ub¹    ​
#> intrcpt       0.1803  0.1244  1.4499  7.77  0.1862  -0.1079  0.4685
#> difficulty    0.1241  0.0299  4.1531  7.39  0.0038   0.0542  0.1940  **
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> 1) results based on cluster-robust inference (var-cov estimator: CR2,
#>    approx. t/F-tests and confidence intervals, dfs = Satterthwaite method)
#>

### draw bubble plot
regplot(sav, xlab="Task Difficulty", ylab="Standardized Mean Difference", las=1, digits=1, bty="l")

# }