In MathiasHarrer/metapsyTools: Several R Helper Functions For The "Metapsy" Database

Introducing metapsyTools

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The metapsyTools package facilitates the calculation of effect sizes (i.e. Hedges' $g$) and meta-analyses based on the Metapsy database (or databases adhering to the same format).

The package consists of two modules:

1. A module to check the data format and calculate effect sizes for all possible study comparisons (preparation module);
2. A module to select relevant comparisons for a specific meta-analysis, calculate the results (including subgroup analyses), and generate tables (analysis module).

The idea is to use the two modules in different contexts. For example, the preparation module can be used every time the database is updated to gather all information, calculate effect sizes, and bring the data into a format suitable for further analyses.

This final dataset then builds the basis for the analysis module. Researchers simply have to filter out the comparisons that are relevant for their investigation, and can then use functions of the package to run a full meta-analysis, including sensitivity and subgroup analyses.

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Important: The preparation module requires a familiarity with the general structure of the database, as well as intermediate-level knowledge of R and the `metapsyTools` package itself, in order to diagnose (potential) issues. We advise that the preparation step (i.e. checking the data format, expanding multiarm trials, and calculating effect sizes each time the database is updated) should be conducted by a person with some proficiency in R & data wrangling. The analysis module, on the other hand, should be usable by all researchers.

The Preparation Module

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The preparation module in metapsyTools allows to:

• check if the classes of variables in the imported data set are as required, using checkDataFormat
• check for formatting conflicts which have to be resolved prior to any further steps, using checkConflicts
• expand multiarm trials, thereby creating two rows in the data set for each possible treatment arm combination in each multiarm trial, using expandMultiarmTrials
• calculate Hedges' $g$ for each comparison, provided suitable data is available, and generate a data set ready for meta-analyses, using calculateEffectSizes.

Required Structure of the Database

For your own convenience, it is highly advised to strictly follow some data formatting rules prior to importing the dataset for effect size calculation. If all of these rules are followed closely, it minimizes the risk of receiving error messages, producing conflicts, etc.

The package can handle both data in the "long" and "wide" format. In the long format, each row represents a specific result of one trial arm (e.g. the measured self-reported depression severity in the control group at post-test in some study x). In the wide format, each row represents a specific comparison of two trial arms.

Long Format

If the database is in the long format, the dataset must contain these columns, with exactly this variable name:

• study. The name and year of the study the result was extracted from, as a character variable, e.g. "Cuijpers, 2019". This variable should not differ between study arms, measurement points, etc.
• condition. A character variable, representing if the trial arm served as the control group ("cg") or intervention group ("ig") in this specific trial. Overall, condition must only contain "cg" or "ig" values.
• Cond_spec. A character variable, representing the "condition specification". This variable encodes the type of intervention/control group employed in the trial arm (e.g. "cau" for care as usual, or "pst" for problem-solving therapy). NOTE: for multiarm trials, this variable encodes the different treatment in each trial arm. In multiarm trials, Cond_spec must have different values in differing treatment arms. Say, e.g., that one trial consisted of conditions PST online, PST face-to-face, and a wait-list. Here, we still use "pst" to specify that Problem-Solving Therapy was employed; but in brackets, we add the "special" subtype of PST to uniquely identify the two intervention arms. In sum, the values for this trial in Cond_spec would therefore be "pst (online)", "pst (f2f)" and "wl".
• multiple_arms. A character variable. This variable should be NA when a trial arm is not part of a multiarm study. When the arm is part of a multiarm trial, this variable should have the same value as in Cond_spec.
• is.multiarm. A numeric variable which indicates if a trial arm is not part of a multiarm study (0, i.e. the study only has one intervention and one control group) or is part of a multiarm study (1).
• no.arms. A numeric variable, indicating the number of arms in one trial. In non-multiarm trials, this should be 2.
• Outc_measure. A character variable, indicating the type of instrument used to measure the results (e.g. "phq-9"). If the same instrument was used to measure several quantities in one study, the type of outcome must be added in brackets, for example "hdrs (response)" and "hdrs (remission)".
• Time. A character variable, indicating the assessment point (e.g. "baseline" or "post").
• Time_weeks. A character variable, indicating the assessment point in time units (e.g. "2 month" or "0"). Can be NA in case no information was reported.
• primary. A numeric variable, indicating if the row contains results of the trial's primary outcome (1) or not (0).
• sr_clinician. A character variable, representing if an outcome was self-reported (e.g. "self-reported"), or assessed in some other way (e.g. "clinician"-rated).
• rob. A variable indicating how many risk of bias criteria were fulfilled. This variable is not essential but expected by default in, for example, runMetaAnalysis.
• ... Further variables to be used (among other things) for subgroup analyses, study details in the meta-analysis publication, meta-regression, or to define treatment types analyzed in network meta-analyses, and so forth.

The following variables have to be added to calculate effect sizes (all of class numeric):

• Mean, SD and N:
• Post_M. The mean of the measured outcome in the trial arm, if applicable. Otherwise, leave as NA.
• Post_SD. The sample standard deviation of the measured outcome in the trial arm, if applicable. Otherwise, leave as NA.
• Post_N. The sample size of the trial arm, if applicable. Otherwise, leave as NA.
• Change Scores:
• Change_m (note the lowercase "m"!). The mean pre-post change in the trial arm, if applicable. Otherwise, leave as NA.
• Change_SD. The sample standard deviation of the change scores in the trial arm, if applicable. Otherwise, leave as NA.
• Change_N. The sample size of the trial arm, if change scores are used. Otherwise, leave as NA, particularly when data for Post_M and Post_SD are available in the same row.
• Response, Remission, ...
• Improved_N. The number of individuals in the trial arm who have improved. It is crucial that the outcome should be positive/desired (i.e. remission, response, but not e.g. deterioration) to ensure that the calculated effect sizes have the correct sign in the end!
• Rand_N. If the row contains improvement data: the number of individuals in the trial arm. Otherwise, leave as NA, particularly when data for Post_M and Post_SD, or Change_m and Change_SD are available in the same row.

The psyCtrSubset dataset an example of a correctly formatted database in the "long" format. You can run data("psyCtrSubset") after metapsyTools has been loaded to inspect it.

Wide Format

If the database is in the wide format, the dataset must contain these columns, with exactly this variable name:

• study. The name and year of the study the result was extracted from, as a character variable, e.g. "Cuijpers, 2019". This variable should not differ between study arms, measurement points, etc.
• Cond_spec_trt1 and Cond_spec_trt2. A character variable, representing the "condition specification" in the trial arms that are being compared. This variable encodes the type of intervention/control group employed in the trial arm (e.g. "cau" for care as usual, or "pst" for problem-solving therapy). NOTE: in multiarm trials, Cond_spec_trt... must have different values in differing treatment arms. Say, e.g., that one trial consisted of conditions PST online, PST face-to-face, and a wait-list. Here, we still use "pst" to specify that Problem-Solving Therapy was employed; but in brackets, we add the "special" subtype of PST to uniquely identify the two intervention arms. In sum, the values for this trial in Cond_spec_trt... would therefore be "pst (online)", "pst (f2f)" and "wl".
• multiple_arms_trt1 and multiple_arms_trt2. A character variable. This variable should be NA when a trial arm is not part of a multiarm study. When the arm is part of a multiarm trial, this variable should have the same value as in Cond_spec_trt....
• is.multiarm. A numeric variable which indicates if a comparison is not part of a multiarm study (0, i.e. the study only has one intervention and one control group) or is part of a multiarm study (1).
• no.arms. A numeric variable, indicating the number of arms in one trial. In non-multiarm trials, this should be 2.
• Outc_measure. A character variable, indicating the type of instrument used to measure the results (e.g. "phq-9"). If the same instrument was used to measure several quantities in one study, the type of outcome must be added in brackets, for example "hdrs (response)" and "hdrs (remission)".
• Time. A character variable, indicating the assessment point (e.g. "baseline" or "post").
• Time_weeks. A character variable, indicating the assessment point in time units (e.g. "2 month" or "0"). Can be NA in case no information was reported.
• primary. A numeric variable, indicating if the row contains results of the trial's primary outcome (1) or not (0).
• sr_clinician. A character variable, representing if an outcome was self-reported (e.g. "self-reported"), or assessed in some other way (e.g. "clinician"-rated).
• rob. A variable indicating how many risk of bias criteria were fulfilled. This variable is not essential but expected by default in, for example, runMetaAnalysis.
• ... Further variables to be used (among other things) for subgroup analyses, study details in the meta-analysis publication, meta-regression, or to define treatment types analyzed in network meta-analyses, and so forth.

The following variables have to be added to calculate effect sizes (all of class numeric):

• Mean, SD and N:
• Post_M_trt1 and Post_M_trt2. The mean of the measured outcome in both trial arms that are being compared, if applicable. Otherwise, leave as NA.
• Post_SD_trt1 and Post_SD_trt2. The sample standard deviations of the measured outcome in the two trial arms that are being compared, if applicable. Otherwise, leave as NA.
• Post_N_trt1 and Post_N_trt2. The sample sizes of the two trial arms that are being compared, if applicable. Otherwise, leave as NA.
• Change Scores:
• Change_m_trt1 and Change_m_trt2 (note the lowercase "m"!). The mean pre-post change scores in the two trial arms that are being compared, if applicable. Otherwise, leave as NA.
• Change_SD_trt1 and Change_SD_trt2. The sample standard deviations of the change scores in the two trial arms that are being compared, if applicable. Otherwise, leave as NA.
• Change_N_trt1 and Change_N_trt2. The sample sizes of the two trial arms that are being compared, if change scores are used. Otherwise, leave as NA, particularly when data for Post_M_trt.. and Post_SD_trt... are available in the same row.
• Response, Remission, ...
• Improved_N_trt1 and Improved_N_trt2. The number of individuals in the two trial arms who have improved. It is crucial that the outcome should be positive/desired (i.e. remission, response, but not e.g. deterioration) to ensure that the calculated effect sizes have the correct sign in the end!
• Rand_N_trt1 and Rand_N_trt2. If the comparison contains improvement data: the number of individuals in the two trial arms that are being compared. Otherwise, leave as NA, particularly when data for Post_M and Post_SD, or Change_m and Change_SD are available in the same row.

The psyCtrSubsetWide dataset an example of a correctly formatted database in the "wide" format. You can run data("psyCtrSubsetWide") after metapsyTools has been loaded to inspect it.

Additional Considerations

Further remarks concerning the required data structure:

• Often, it will not be possible to calculate the effect size data for all comparisons (e.g. because they reported their results in an "exotic" format, or because only the calculated value of $d$ or $g$ was reported). In this case, leave all effect size data variables in the dataset as NA. After using calculateEffectSizes, these comparisons will simply be forwarded without any calculations, and have NA in the calculated effect size and standard error columns. These gaps can then be filled manually by simply inserting the calculated $g$ and $\sqrt{V_g}$ values in the es and se columns generated by calculatedEffectSizes to "fill the gaps". When the database is updated the next time, this leads to a temporary loss of the manually calculated effect sizes (the rows with manually calculated effect sizes will again be NA if the functions are used on the entire updated database). However, this should not be a large issue. The calculateEffectSizes function creates a unique id variable in the final dataset for each comparison. This ID can be used to match comparisons with their manually calculated effect sizes from the last update again.
• The study variable should be identical for all arms (and outcomes measured in that arm) provided by the same study. However, there is one exception. When results are consistently reported separately for subgroups within the trial (e.g. M, SD and N for patients with and without a clinical diagnosis, for all trial arms), these subgroups should be treated as independent studies (or alternatively, the results can be pooled to obtain overall data). This means that the study variable has to be adapted in this very special case to differentiate between the subgroups. This can be done by adding the subgroup in brackets, e.g. "Dimidjan, 2005 (no diagnosis)" and "Dimidjan, 2005 (diagnosis)".
• Each comparison/row can only contain effect size data for one effect size data type as declared above (Mean, SD, N or Change Scores or Response/Remission), but for the selected effect size data type, all required data must be available (e.g. if Post_M and Post_N are provided, one must also provide data for Post_SD).
• If the data is in the long format, effect size data should only be added if this specific outcome (e.g. PHQ-9 at post-test) was assessed in all trial arms. It is not possible to add effect size data that was only measured in some arms within one trial, but not all.
• Please do not include a variable with the name "id", "es", or "se" in the original data file, because these are added later. See "Calculation of Hedges' $g$" for more information.

Data Format & Conflict Check

Once the data set has been pre-structured correctly, metapsyTools allows you to check the required variable format and control for potential formatting conflicts.

If the formatting rules above are followed, none of the default behavior of the preparation module has to be changed. At first, one can run checkDataFormat. As an illustration, we will use the database2021Subset data frame, which is directly available after installing metapsyTools.

library(metapsyTools)
data("database2021Subset")
database2021Subset <- checkDataFormat(database2021Subset)

The function will then show a prompt, asking you to specify the the format of the dataset:

Enter: Is the data set in long [l] or wide [w] format? 

In this case, the dataset is in the "long" format, so l should be entered in the console. This gives the following output:

## - [OK] data set contains all variables in 'must.contain'.
## - [OK] variables contain only the values specified in 'variable.contains'.
## - [OK] 'study' has desired class character.
## - [OK] 'condition' has desired class character.
## - [OK] 'Cond_spec' has desired class character.
## - [OK] 'is.multiarm' has been converted to class numeric.
## - [OK] 'no.arms' has desired class numeric.
## - [OK] 'multiple_arms' has desired class character.
## - [OK] 'primary' has desired class numeric.
## - [OK] 'Time' has desired class character.
## - [OK] 'Time_weeks' has desired class character.
## - [OK] 'sr_clinician' has desired class character.
## - [OK] 'Post_M' has desired class numeric.
## - [OK] 'Post_SD' has desired class numeric.
## - [OK] 'Post_N' has desired class numeric.
## - [OK] 'Rand_N' has desired class numeric.
## - [OK] 'Improved_N' has desired class numeric.
## - [OK] 'Change_m' has desired class numeric.
## - [OK] 'Change_SD' has desired class numeric.
## - [OK] 'Change_N' has desired class numeric.

We see that the function has checked the required variables and their class. If divergent, the function will also try to convert the variable to the desired format.

You can avoid the prompt asking for the database format if you specify the data.format argument directly in the function:

database2021Subset <- checkDataFormat(database2021Subset,
                                      data.format = "long")

Required variables for unique IDs: To function properly, the `metapsyTools` functions must be able to generate a _unique_ ID for each comparison. By default, this is achieved by combining information of the `study`, `condition`, `Cond_spec`, `is.multiarm`, `no.arms`, `multiple_arms`, `Outc_measure`, `Time`, `primary`, `Time_weeks`, and `sr_clinician` variables. These variables are included by default in the `must.contain` argument in the `checkDataFormat` function. If all required variables are detected, an `OK` message is returned; as is the case in our example.

We can also check the data for potential formatting issues, using the checkConflicts function.

database2021Subset <- checkConflicts(database2021Subset) 

## - [OK] No data format conflicts detected

In our case, no data format conflicts were detected. This is because all the data were pre-structured correctly. If data conflicts exist, the output looks similar to this:

## - [!] Data format conflicts detected!
## ID conflicts 
## - check if the specified number of arms is correct 
## - check if selected variables really create unique assessment point IDs 
## - check if 'Cond_spec' uniquely identifies all trial arms in multiarm trials 
## --------------------
## Ammerman, 2013
## Arean, 1993
## Bedard, 2014
## Burns, 2013
## Carr, 2017
## Choi, 2012
## Ebert, 2018
## Freedland, 2015
## Hautzinger, 2004
## Hummel, 2017
## Johansson, 2012a
## 
## Trials with 2+ control groups 
## - NOTE: As of version 0.2.0, 'metapsyTools' can handle 2+ control groups! 
## --------------------
## Ammerman, 2013
## Arean, 1993
## Bedard, 2014
## Burns, 2013
## Carr, 2017
## Choi, 2012
## Ebert, 2018
## Freedland, 2015
## Hautzinger, 2004
## Hummel, 2017
## Johansson, 2012a

Note: Since version 0.2.0 the Trials with 2+ control groups section studies are not regarded as data conflicts anymore, because the functionality can now handle 2+ control groups. ID conflicts, however, will always have to be fixed before proceeding. ID conflicts indicate that unique comparison IDs could not be created for all results.

Expanding Multiarm Trials

After all data format conflicts are resolved, one can process to expand multiarm trials. This means that for each possible comparison within a multiarm trial, there will be two rows in the data set, representing the two arms that are being compared. This is a prerequisite to calculate all possible between-group effect sizes later on.

Imagine that one multiarm study compared CBT, PST, CAU and a waitlist (i.e. a four-arm trial). Under these conditions, there are $\binom{4}{2} = \frac{4!}{2!(4-2)!} = 6$ distinct arm combinations. We can represent this as a graph with 6 distinct arrows; each double arrow stands for one possible combination:

library(igraph)
vertex = c("CBT","PST", "CBT","CAU", "CBT","WL", "PST","CBT", "PST","CAU", "PST","WL", "CAU","CBT", "CAU","PST", "CAU","WL", "WL","CBT", "WL","PST", "WL","CAU")
g1 <- graph(edges=vertex, n=4, directed=TRUE) 
plot(g1, vertex.size = 35, vertex.color = "lightblue",
     vertex.label.family="Helvetica")

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In this example, 12 rows would be included after running expandMultiarmTrials, with 6 row pairs each corresponding with one of the 6 unique combinations.

We can try this out with our database2021Subset data set, saving the result as database2021SubsetExpanded, and exploring the number of added rows after expansion.

database2021SubsetExpanded <- expandMultiarmTrials(database2021Subset)
nrow(database2021SubsetExpanded) - nrow(database2021Subset)

## - [OK] Multiarm trial expansion successful
## [1] 169

We see that the expansion was successful, and that 169 rows were added in the process.

Calculation of Hedges' $g$

After the multiarm expansion, the effect size ($g$) and its variance can be calculated for all comparisons, using calculateEffectSizes. When applying calculateEffectSizes, the effect size functions specified in the funcs argument are applied by default, which means that effect sizes based on Mean, SD and N, Change Scores and binary outcomes can be calculated.

The function also transforms the provided data set from the "longer" format (one row per arm) to a "wider" format, in which each comparison corresponds with one row. Sometimes, however, information may differ between trial arms (e.g. the proportion of women included in each arm, or the overall treatment type). The calculateEffectSizes function handles this by automatically generating two columns with suffixes _trt1 and _trt2 for each variable with differing values within one comparison. This means that no information that differs between comparison arms is lost.

The data set returned by calculateEffectSizes also includes a new variable id (Note: therefore, please do not include a variable with the name "id" in the original data file, because this is added later). This ID uniquely identifies each comparison.

The calculated effect size, Hedges' $g$ and its standard error, are saved in columns es and se, respectively, in the data frame returned by calculateEffectSizes. Therefore, please do not include a variable with the name "es" or "se" in the original data file.

When the data are pre-structured as described above, no further specifications are needed to use calculateEffectSizes; only the expanded (!) dataset has to be provided. We save the result as data.

data <- calculateEffectSizes(database2021SubsetExpanded)
data[,c("id", "es", "se")]

## - Calculating effect sizes...
## - [OK] Effect sizes calculated successfully
##                                                   id      es     se
## 1                         Aagaard_2017_1_bdi-1_ba... -0.1939 0.2244
## 2                         Aagaard_2017_1_bdi-1_po...  0.0000 0.2314
## 3                             Abas_2018_0_dssq_ba... -0.5054 0.3621
## 4                                Abas_2018_0_dssq... -0.5516 0.3864
## 5                            Abas_2018_1_phq-9_ba...  1.5594 0.4086
## 6                               Abas_2018_1_phq-9... -0.7104 0.3913
## 7   Ahmadpanah_2016_1_bdi-1_baseline_0_self-repor...  0.7715 0.3792
## 8         Ahmadpanah_2016_1_bdi-1_baseline_0_self...  0.4126 0.3692
## 9        Ahmadpanah_2016_1_bdi-1_baseline_0_self-... -0.3286 0.3677
## 10 Ahmadpanah_2016_1_bdi-1_post_2month_self-repor...  0.3182 0.3675
## 11       Ahmadpanah_2016_1_bdi-1_post_2month_self... -1.5681 0.4202
## 12      Ahmadpanah_2016_1_bdi-1_post_2month_self-... -1.7788 0.4347
## 13                         Alexopoulos_2016_1_hdr...      NA     NA
## 14              Alexopoulos_2016_1_hdrs(remission...  0.1700 0.1782

Looking at the column names, we also see that variables that differ between trial arms within one comparison have been split into two variables with suffixes _treat1 and _treat2, where _treat1 represents the reference treatment.

colnames(data)

##  [1] "study"                              "id"                                
##  [3] "id_study_condition_instrument_trt1" "id_study_condition_instrument_trt2"
##  [5] "condition_trt1"                     "condition_trt2"                    
##  [7] "arm_format_trt1"                    "arm_format_trt2"                   
##  [9] "outcome_type"                       "outc_instrument"                   
## [11] "sr_clinician"                       "dich"                              
## [13] "dich_type"                          "change"                            
## [15] "other_statistic_trt1"               "other_statistic_trt2"              
## [...]                          
## [71] "Post_N_trt2"                        "Post_SD_trt1"                      
## [73] "Post_SD_trt2"                       "Post_M_trt1"                       
## [75] "Post_M_trt2"                        "type_trt1"                         
## [77] "type_trt2"                          "Time_weeks"                        
## [79] "Time"                               "Outc_measure"                      
## [81] "no.arms"                            "is.multiarm"                       
## [83] "Cond_spec_trt1"                     "Cond_spec_trt2"                    
## [85] "es"                                 "se" 

Please note that the current version of the data set only includes all unique treatment arm combinations, not all unique comparisons. Let us use the four-arm trial example (CBT, PST, CAU and a wait-list) again. While this trial provides 6 unique trial arm combinations, the number of unique comparisons is higher: $\frac{n!}{(n-k)!} = \frac{4!}{2!} = 12$.

This is because the sign of the calculated effect size depends on which treatment serves as the reference. The effect of CBT vs. PST, for example, depends on which arm serves as the reference group (i.e. CBT-PST or PST-CBT). Depending on which arm is chosen (and assuming non-zero mean differences), the calculated Hedges' $g$ value will either be negative (e.g. $g$=-0.31) or positive ($g$=0.31). We see this visualized in the graph below. There are now two directed arrows for each comparison (12 in total), and each arrow reads as "is compared to":

{width=200px}

To truly calculate all unique comparisons, we have to set the include.switched.arms argument to TRUE when running calculateEffectSizes.

data <- calculateEffectSizes(database2021SubsetExpanded,
                             include.switched.arms = TRUE)
data[1:10, c("id", "Cond_spec_trt1", "Cond_spec_trt2", "es")]

##                                              id Cond_spec_trt1 Cond_spec_trt2      es
## 1               Aagaard_201...e_0_self-reported            cbt            cau  -0.193
## 2  Aagaard_2017_1_bdi-1_bas...rted_arm_switched            cau            cbt   0.193
## 3               Aagaard_201...ear_self-reported            cbt            cau   0.000
## 4  Aagaard_2017_1_bdi-1_pos...rted_arm_switched            cau            cbt   0.000
## 5                   Abas_20...e_0_self-reported            pst            cau  -0.505
## 6      Abas_2018_0_dssq_bas...rted_arm_switched            cau            pst   0.505
## 7                      Abas..._NA_self-reported            pst            cau  -0.551
## 8         Abas_2018_0_dssq_...rted_arm_switched            cau            pst   0.551
## 9                  Abas_201...e_0_self-reported            pst            cau   1.559
## 10    Abas_2018_1_phq-9_bas...rted_arm_switched            cau            pst  -1.559

The resulting data frame data now follows a "wider" format and includes all effect sizes that can theoretically be calculated. As a last step, one has to manually add the effect sizes and standard errors of comparisons for which calculateEffectSizes returned NA. This leads to a final data set which can be used with the analysis module, which will be described next.

Should I use `include.switched.arms`? It is not essential to calculate all possible arm comparisons, because, for Hedges' $g$, reference groups can always be "switched" by multiplying the calculated effect size by -1. However, having all possible comparisons in your data set is convenient, because all required comparisons pertaining to a particular research question (e.g. "how effective is PST when CBT is the reference group?") can directly be filtered out; there is typically no need for further data manipulation steps.

The Analysis Module

---

The analysis module in metapsyTools allows to run different kinds of meta-analyses based on the final data set created by the preparation module. It is designed to also be usable by researchers who were not directly involved in the preparation step, and is less demanding in terms of required background knowledge.

The analysis module allows to:

• Filter data using strict rules, fuzzy string matching, or by implementing prioritization rules (filterPoolingData and filterPriorityRule).
• Run conventional (random-effects) meta-analysis models as well as commonly reported sensitivity analyses (runMetaAnalysis)
• Run subgroup analyses based on the fitted model (subgroupAnalysis)
• Create study information tables (createStudyTable).

Filtering Relevant Comparisons

The metapsyTools package contains functions which allow to flexibly filter out comparisons that are relevant for a particular meta-analysis.

The filterPoolingData function is the main function for filtering. We simply have to provide the final data set with calculated effect sizes (see preparation module), as well as one or several filtering criteria pertaining to our specific research question.

Say that we want to run a meta-analysis of all studies in which CBT was compared to wait-lists, with the BDI-II at post-test being the analyzed outcome. We can filter out the relevant comparisons like this:

data %>% 
  filterPoolingData(Cond_spec_trt1 == "cbt",
                    Cond_spec_trt2 == "wl",
                    outc_instrument == "bdi-1",
                    Time == "post") %>% nrow()

## [1] 6

We see that $k$=6 comparisons fulfill these criteria. Note, however, that this will only select comparisons for which Cond_spec was exactly defined as "cbt". For multiarm trials, it is necessary to add specifications in brackets (e.g. "cbt (online)") to make the conditions in each arm unique. To filter out all comparisons which applied some form of CBT, we need to apply fuzzy matching. This can be achieved by using the Detect function within filterPoolingData:

data %>% 
  filterPoolingData(Detect(Cond_spec_trt1, "cbt"),
                    Detect(Cond_spec_trt2, "wl"),
                    outc_instrument == "bdi-1",
                    Time == "post") %>% nrow()

## [1] 11

We see that now, $k$=11 CBT vs. wait-list comparisons were detected.

We can create even more complex filters. Say that we want to examine the effect, as measured by the BDI-I at post-test, of CBT, PST, and BAT compared to either CAU or wait-lists. We can visualize this with a graph again:

library(igraph)
vertex = c("CBT", "CAU", "CBT", "WL", "PST", "CAU", "PST", "WL", "BAT", "CAU", "BAT", "WL")
g1 <- graph(edges=vertex, directed=TRUE) 
plot(g1, vertex.size = 35, vertex.color = "lightblue",
     vertex.label.family="Helvetica", layout=layout.circle)

{width=200px}

We can use the OR-Operator | within filterPoolingData for such filter types. Again, we use the Detect function to allow for fuzzy matching:

data %>% 
  filterPoolingData(Detect(Cond_spec_trt1, "cbt|pst|bat"),
                    Detect(Cond_spec_trt2, "cau|wl"),
                    outc_instrument == "bdi-1",
                    Time == "post") -> ma.data

ma.data %>% select(study, Cond_spec_trt1, Cond_spec_trt2)

                  study Cond_spec_trt1 Cond_spec_trt2
1         Aagaard, 2017            cbt            cau
2  Allart van Dam, 2003            cbt            cau
3           Arean, 1993            pst             wl
4            Ayen, 2004            cbt           wl A
5            Ayen, 2004            cbt           wl B
6         Barrera, 1979            bat             wl
7           Beach, 1992      cbt (bmt)             wl
8           Beach, 1992            cbt             wl
9      Boeschoten, 2017            pst             wl
10         Bowman, 1995            cbt             wl
11         Bowman, 1995            pst             wl
12          Brown, 1984    cbt (group)             wl
13          Brown, 1984    cbt (phone)             wl
14          Brown, 1984            cbt             wl
15          Carta, 2012            cbt            cau
16        Casanas, 2012            cbt            cau
17        Casanas, 2012            cbt            cau
18        Casanas, 2012            cbt            cau
19     Castonguay, 2004            cbt             wl
20     Castonguay, 2004            cbt             wl
21            Cho, 2008            cbt            cau
22            Cho, 2008            cbt            cau
23           Choi, 2012            cbt             wl
24      Chowdhary, 2016            bat            cau
25      Chowdhary, 2016            bat            cau
26      Chowdhary, 2016            bat            cau

Lastly, one can also filter data according to a specified priority rule, using the filterPriorityRule function. This is particularly helpful to select instruments. Say, for example, that we ordered certain instruments based on their known reliability. Now, for each study, we only want to select the comparison in which the most reliable instrument was used. It is possible that, for some studies, all used instruments are relatively unreliable. However, given our priority rule, we can still extract the comparison with a relatively high reliability, and discard all the other measurements within one study that are even less reliable.

Assume that our priority rule for the employed instrument is "hdrs" (priority 1), "bdi-2" (priority 2), "phq-9" (priority 3) and "bdi-1" (priority 4). We can implement the rule like this:

data %>% 
  # First, filter all other relevant characteristics
  filterPoolingData(Detect(Cond_spec_trt1, "cbt|pst|bat"),
                    Detect(Cond_spec_trt2, "cau|wl"),
                    Time == "post") %>% 
  # Now, implement the priority rule for the outcome instrument
  filterPriorityRule(outc_instrument = c("hdrs", "bdi-2", "phq-9", "bdi-1")) %>% 
  # Show filter results
  select(study, Cond_spec_trt1, Cond_spec_trt2, outc_instrument)

##                   study Cond_spec_trt1 Cond_spec_trt2 outc_instrument
## 1         Aagaard, 2017            cbt            cau           bdi-1
## 2            Abas, 2018            pst            cau           phq-9
## 3  Allart van Dam, 2003            cbt            cau           bdi-1
## 4        Ammerman, 2013            cbt            cau            hdrs
## 5           Arean, 1993            pst             wl            hdrs
## 6           Arean, 1993            pst             wl            hdrs
## 7            Ayen, 2004            cbt           wl A           bdi-1
## 8            Ayen, 2004            cbt           wl B           bdi-1
## 9         Barrera, 1979            bat             wl           bdi-1
## 10          Beach, 1992      cbt (bmt)             wl           bdi-1
## 11          Beach, 1992            cbt             wl           bdi-1
## 12         Berger, 2011   cbt (guided)             wl           bdi-2
## 13         Berger, 2011 cbt (unguided)             wl           bdi-2
## 14     Boeschoten, 2017            pst             wl           bdi-2
## 15     Boeschoten, 2017            pst             wl           bdi-2
## 16         Bowman, 1995            cbt             wl            hdrs
## 17         Bowman, 1995            pst             wl            hdrs
## 18         Bowman, 1995            cbt             wl            hdrs
## 19         Bowman, 1995            pst             wl            hdrs
## 20          Brown, 1984    cbt (group)             wl           bdi-1
## 21          Brown, 1984    cbt (phone)             wl           bdi-1
## 22          Brown, 1984            cbt             wl           bdi-1
## 23          Burns, 2013            cbt            cau           phq-9
## 24           Carr, 2017            cbt            cau            hdrs
## 25          Carta, 2012            cbt            cau           bdi-1
## 26        Casanas, 2012            cbt            cau           bdi-1
## 27        Casanas, 2012            cbt            cau           bdi-1
## [...]

Pooling Effects

After all relevant rows have been filtered out (in our case, these relevant comparisons are the ones we saved in ma.data previously), we can start to pool the effect sizes. The runMetaAnalysis function serves as a wrapper for several commonly used meta-analytic approaches, and, by default, applies them all at once to our data:

• "overall". Runs a generic inverse-variance (random-effects) model. All included effect sizes are treated as independent.
• "combined". Pools all effect sizes within one study before calculating the overall effect. This ensures that all effect sizes are independent (i.e., unit-of-analysis error & double-counting is avoided). To combine the effects, one has to assume a correlation of effect sizes within studies, empirical estimates of which are typically not available. By default, runMetaAnalysis assumes that $\rho$=0.5.
• "lowest.highest". Runs a meta-analysis, but with only (i) the lowest and (ii) highest effect size within each study included.
• "outlier". Runs a meta-analysis without statistical outliers (i.e. effect sizes for which the confidence interval does not overlap with the confidence interval of the overall effect).
• "influence". Runs a meta-analysis without influential cases (see influence.rma.uni for details).
• "rob". Runs a meta-analysis with only low-RoB studies included. By default, only studies with a value > 2 in the rob variable are considered for this analysis.
• "threelevel". Runs a multilevel (three-level) meta-analysis model, with effect sizes nested in studies.
• "threelevel.che". Runs a multilevel (three-level) "correlated and hierarchical effects" (CHE) meta-analysis model. In this model, effect sizes are nested in studies, and effects within studies are assumed to be correlated. This will typically be a plausible modeling assumption in most real-world use cases.

res <- runMetaAnalysis(ma.data)

## - Pooling the data...
## - [OK] Calculated overall effect size
## - [OK] Calculated effect size using only lowest effect
## - [OK] Calculated effect size using only highest effect
## - [OK] Calculated effect size using combined effects (rho=0.5)
## - [OK] Calculated effect size with outliers removed
## - [OK] Calculated effect size with influential cases removed
## - [OK] Calculated effect size using only low RoB information
## - [OK] Calculated effect size using three-level MA model
## - [OK] Robust variance estimation (RVE) used for three-level MA model
## - [OK] Calculated effect size using three-level CHE model (rho=0.5)
## - [OK] Robust variance estimation (RVE) used for three-level CHE model
## - [OK] Done!

We can inspect the results by calling the created res object in the console. By default, an HTML table should pop up along with the console output. These pre-formatted HTML results tables can easily be transferred to, for example, MS Word using copy & paste.

res

## Model results ---------------------- 
##   model                      k     g g.ci           p         i2 i2.ci          prediction.ci    nnt
## 1 Overall                   25 -0.73 [-1.06; -0.39] <0.001  80.3 [71.61; 86.29] [-2.06; 0.61]   7.06
## 2 Combined                  14 -0.74 [-1.19; -0.28] 0.004   80.6 [68.31; 88.08] [-2.2; 0.72]    7   
## 3 One ES/study (lowest)     14 -0.76 [-1.17; -0.35] 0.001   67.6 [43.34; 81.45] [-1.9; 0.38]    6.87
## 4 One ES/study (highest)    14 -0.62 [-1.09; -0.15] 0.014   84.0 [74.51; 89.92] [-2.11; 0.87]   7.81
## 5 Outliers removed          22 -0.56 [-0.74; -0.37] <0.001  41.9 [3.57; 65.02]  [-1.04; -0.07]  8.4 
## 6 Influence Analysis        23 -0.54 [-0.77; -0.31] <0.001  73.8 [60.43; 82.58] [-1.42; 0.33]   8.56
## 7 Only rob > 2               9 -0.28 [-0.59; 0.03]  0.074   80.8 [64.49; 89.63] [-1.19; 0.63]   14.6 
## 8 Three-Level Model         25 -0.8  [-1.23; -0.37] <0.001  88.2 -              [-2.4; 0.81]    6.69
## 9 Three-Level Model (CHE)   25 -0.75 [-1.16; -0.34] 0.002   84.9 -              [-2.14; 0.65]   6.95 
##
## Variance components (three-level model) ---------------------- 
##                   tau2   i2
## Between Studies 0.4767 75.1
## Within Studies  0.0830 13.1
## Total           0.5597 88.2
##
## Variance components (three-level CHE model) ------------------ 
##                   tau2   i2
## Between Studies 0.3406 68.5
## Within Studies  0.0818 16.4
## Total           0.4224 84.9

Using the summary method, details of the analysis settings can be printed. This function also returns recommended citations for the applied methods and/or packages.

summary(res)

Analysis settings ---------------------------------------------------------- 

✓ [Overall] Random effects model assumed. 
✓ [Overall] Heterogeneity variance (tau2) calculated using restricted 
  maximum-likelihood estimator.
✓ [Overall] Test statistic and CI of the pooled effect calculated using 
  the Knapp-Hartung adjustment. 
✓ [Outliers removed] ES removed as outliers if the CI did not overlap 
  with pooled effect CI. 
✓ [Influence Analysis] Influential cases determined using diagnostics 
  of Viechtbauer and Cheung (2010). 
✓ [Combined] 'Combined' analysis: ES combined on study level assuming 
  a correlation of rho = 0.5. 
✓ [Three-Level Model] Three-level model estimated via restricted maximum 
  likelihood, using the 'rma.mv' function in {metafor}. 
✓ [Three-Level Model] Test statistics and CIs of the three-level model 
  calculated based on a t-distribution. 
✓ [Robust Variance Estimation] Robust variance estimation was used to 
  guard the three-level model(s) from misspecification. This was done 
  using functions of the {clubSandwich} package.


Cite the following packages/methods: ---------------------------------------

 - {meta}: Balduzzi S, Rücker G, Schwarzer G (2019),
          How to perform a meta-analysis with R: a practical tutorial,
          Evidence-Based Mental Health; 22: 153-160. 
 - {metafor}: Viechtbauer, W. (2010). Conducting meta-analyses in R
          with the metafor package. Journal of Statistical Software, 36(3), 1-48.
          https://doi.org/10.18637/jss.v036.i03. 
 - {dmetar}: Harrer, M., Cuijpers, P., Furukawa, T.A., & Ebert, D.D. (2021).
          Doing Meta-Analysis with R: A Hands-On Guide. Boca Raton, FL and London:
          Chapman & Hall/CRC Press. ISBN 978-0-367-61007-4. 
 - R: R Core Team (2021). R: A language and environment for statistical computing.
          R Foundation for Statistical Computing, Vienna, Austria.
          URL https://www.R-project.org/.
 - Influential cases: Viechtbauer, W., & Cheung, M. W.-L. (2010). Outlier and influence
          diagnostics for meta-analysis. Research Synthesis Methods, 1(2), 112–125.
          https://doi.org/10.1002/jrsm.11 
 - tau2 estimator: Viechtbauer W. (2005): Bias and efficiency of meta-analytic variance
          estimators in the random-effects model.Journal of Educational and
          Behavioral Statistics, 30, 261–93 
 - Knapp-Hartung: Hartung J, Knapp G (2001a): On tests of the overall treatment
          effect in meta-analysis with normally distributed responses.
          Statistics in Medicine, 20, 1771–82
 - Three-level CHE model: Pustejovsky, J.E., Tipton, E. Meta-analysis with Robust
          Variance Estimation: Expanding the Range of Working Models. Prevention
          Science (2021). https://doi.org/10.1007/s11121-021-01246-3 
 - Robust variance estimation: Pustejovsky, J.E., Tipton, E. Meta-analysis with Robust
          Variance Estimation: Expanding the Range of Working Models. Prevention
          Science (2021). https://doi.org/10.1007/s11121-021-01246-3 

The runMetaAnalysis function allows to tweak many, many details of the specific meta-analysis models (run ?runMetaAnalysis to see the entire documentation). The most important arguments one may want to specify are:

• method.tau. This argument controls the method to be used for estimating the between-study heterogeneity variance $\tau^2$. The default is "REML" (restricted maximum likelihood), but other options such as the DerSimonian-Laird estimator ("DL") are also available (see the runMetaAnalysis function documentation for more details). Note that three-level meta-analysis models can only be fitted using (restricted) maximum likelihood.
• nnt.cer. The runMetaAnalysis function uses the method by Furukawa and Leucht to calculate the Number Needed to Treat (NNT) for each pooled effect size. This method needs an estimate of the control group event rate (CER). By default, nnt.cer = 0.2 is used, but you can set this to another value if desired.
• rho.within.study. To combine effect sizes on a study level before pooling (Combined model), one has to assume a within-study correlation of effects. By default, rho.within.study = 0.5 is assumed, but this value can and should be changed based on better approximations. This value also controls the assumed within-study correlation in the multilevel CHE mdoel.
• low.rob.filter. By default, the function uses all comparisons for which the risk of bias rating in the rob variable has a value greater 2 (low.rob.filter = "rob > 2"). If your risk of bias rating is in another variable, or if another threshold should be used, you can change this argument accordingly.

Here is an example of a runMetaAnalysis call with non-default settings:

runMetaAnalysis(ma.data,
                method.tau = "DL",
                nnt.cer = 0.4,
                rho.within.study = 0.8,
                low.rob.filter = "rob >= 4")

It is also possible to directly extract each calculated model from the runMetaAnalysis results object. Each of these models are identical to the ones one would receive by running metagen or rma.mv directly.

res$model.overall
res$model.combined
res$model.lowest
res$model.highest
res$model.outliers
res$model.influence
res$model.rob
res$model.threelevel
res$model.threelevel.che

This means that any kind of operation available for metagen or rma models is also available for the models created by runMetaAnalysis. For example, we can generate a funnel plot for our "overall" model like this:

library(meta)
funnel(res$model.overall, 
       studlab = TRUE, 
       contour = c(0.9, 0.95, 0.99),
       col.contour = c("darkgreen", "green", "lightgreen"))

{width=400px}

It is also possible to generate forest plots of all the calculated models. We only have to plug the results object into plot, and specify the name of the model for which the forest plot should be retrieved:

plot(res, "overall")        # Overall model (all ES assumed to be independent)
plot(res, "combined")       # ES combined within studies before pooling
plot(res, "lowest.highest") # Lowest and highest ES removed (creates 2 plots)
plot(res, "outliers")       # Outliers-removed model
plot(res, "influence")      # Influential cases-removed model
plot(res, "threelevel")     # Three-level model
plot(res, "threelevel.che") # Three-level CHE model

This is what the "overall" model forest plot looks like in our example:

plot(res, "overall")

{width=400px}

Note that the plot function is simply a wrapper for the forest.meta function in the meta package. Therefore, all the advanced styling options are also available using extra arguments.

plot(res, "overall", 
     col.predict = "lightgreen", 
     col.square = "lightblue",
     fontfamily = "Palatino")

{width=400px}

It is also possible to generate Baujat and Leave-One-Out Plots (not displayed here).

plot(res, "baujat")
plot(res, "loo-es")
plot(res, "loo-i2")

Subgroup Analysis

The subgroupAnalysis function can be used to perform subgroup analyses. Every column included in the data set initially supplied to runMetaAnalysis can be used as a subgroup variable.

For example, we might want to check if effects differ by country (country) or intervention type (arm_format_trt1):

sg <- subgroupAnalysis(res, country, arm_format_trt1)
sg

## - [OK] 'model.overall' used for subgroup analyses.
## 
## Subgroup analysis results ---------------------- 
##   variable        group n.comp     g g.ci           i2    i2.ci        nnt   p    
## 1 country         3          9 -0.76 [-1.79; 0.26]  89.7  [82.6; 93.9] 6.88  0.037
## 2 country         1         10 -0.92 [-1.33; -0.52] 39.6  [0; 71.2]    6.21  0.037
## 3 country         6          2 -0.79 [-4.76; 3.17]  0     -            6.73  0.037
## 4 country         5          1 -0.89 [-1.41; -0.37] -     -            6.32  0.037
## 5 country         7          3 -0.46 [-0.62; -0.3]  0     [0; 89.6]    9.66  0.037
## 6 arm_format_trt1 cbt       19 -0.81 [-1.27; -0.35] 84.2  [76.6; 89.3] 6.64  0.191
## 7 arm_format_trt1 pst        3 -0.75 [-2.13; 0.64]  64.8  [0; 89.9]    6.93  0.191
## 8 arm_format_trt1 bat        3 -0.46 [-0.62; -0.3]  0     [0; 89.6]    9.66  0.191

We are informed that the "overall" model has been used for the subgroup analyses. By default, an HTML table should also pop up. The p column to the right represents the significance of the overall subgroup effect (e.g. there is a significant moderator effect of country).

It is also possible to conduct subgroup analyses using another model, say, the three-level model. We only have to specify .which.run:

sg <- subgroupAnalysis(res, 
                       country, arm_format_trt1,
                       .which.run = "threelevel")
sg

## - [OK] 'model.threelevel' used for subgroup analyses.
## 
## Subgroup analysis results ---------------------- 
##   variable        group n.comp     g g.ci           i2    i2.ci nnt   p    
## 1 country         1         10 -1.05 [-2.99; -1.22] -     -     5.86  0.960
## 2 country         3          9 -0.68 [-1.88; 0.51]  -     -     7.36  0.960
## 3 country         5          1 -0.89 [-3.06; 1.28]  -     -     6.32  0.960
## 4 country         6          2 -0.78 [-2.96; 1.41]  -     -     6.78  0.960
## 5 country         7          3 -0.46 [-2.53; 1.61]  -     -     9.66  0.960
## 6 arm_format_trt1 bat        3 -0.46 [-2.58; 0.75]  -     -     9.66  0.892
## 7 arm_format_trt1 cbt       19 -0.82 [-2.57; 0.92]  -     -     6.59  0.892
## 8 arm_format_trt1 pst        3 -0.9  [-2.84; 1.03]  -     -     6.28  0.892

When the number of studies in subgroups are small, it is sensible to use a common estimate of the between-study heterogeneity variance $\tau^2$ (in lieu of subgroup-specific estimates). This can be done by setting the .tau.common argument to TRUE in the function:

sg <- subgroupAnalysis(res, 
                       country, arm_format_trt1,
                       .which.run = "threelevel",
                       .tau.common = TRUE)

Meta-Regression

Since the runMetaAnalysis function saves all fitted models internally, it is also possible to extract each of them individually to do further computations. Say, for example, that we want to do a multiple meta-regression using our threelevel model. We want to use the risk of bias rating, as well as the scaled study year as predictors. This can be achieved by extracting the model to be analyzed using the $ operator, and then using metaRegression to fit the model.

metaRegression(res$model.threelevel, 
               ~ scale(as.numeric(rob)) + scale(year))

Multivariate Meta-Analysis Model (k = 25; method: REML)

Variance Components:

            estim    sqrt  nlvls  fixed       factor 
sigma^2.1  0.4118  0.6417     14     no        study 
sigma^2.2  0.0845  0.2906     25     no  study/es.id 

Test for Residual Heterogeneity:
QE(df = 22) = 85.9318, p-val < .0001

Test of Moderators (coefficients 2:3):
F(df1 = 2, df2 = 22) = 1.6824, p-val = 0.2090

Model Results:

                        estimate      se     tval  df    pval    ci.lb    ci.ub 
intrcpt                  -0.8063  0.1996  -4.0389  22  0.0005  -1.2203  -0.3923  *** 
scale(as.numeric(rob))    0.4249  0.2805   1.5148  22  0.1441  -0.1568   1.0066      
scale(year)              -0.0990  0.2965  -0.3338  22  0.7417  -0.7138   0.5159      

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Study Tables

---

The createStudyTable function allows to create an overview table for the included studies/comparisons. One only has to supply the filtered data set first, and then the names of the desired variables in the order in which they should appear in the table. It is also possible to rename factor labels directly in the function, determine how far values should be rounded, and if variable names should be changed:

createStudyTable(ma.data,

                 ## COLUMNS --------------------------------------
                 # Simply add columns in the order in which
                 # they should appear in the table
                 study, age_group, mean_age_trt1, percent_women_trt1,

                 # You can directly recode values within a variable
                 arm_format_trt1 = c("CBT" = "cbt", 
                                     "PST" = "pst",
                                     "BA" = "bat"),
                 arm_format_trt2 = c("Wait-List" = "wl", 
                                     "Care-As-Usual" = "cau"),
                 n_sessions_trt1, Post_N_trt1, Post_N_trt2, 
                 country = c("Europe" = "3", "USA" = "1",
                             "Asia" = "6", "Middle East" = "7", 
                             "Australia" = "5"),
                 sg, ac, ba, itt,


                 ## SPECIFICATIONS -------------------------------
                 # .round.by.digits controls the number of rounded digits for
                 # specified columns
                 .round.by.digits = list(mean_age_trt1 = 0, 
                                         Post_N_trt1 = 0,
                                         Post_N_trt2 = 0),

                 # .column.names allows to rename columns
                 .column.names = list(age_group = "age group",
                                      mean_age_trt1 = "mean age",
                                      percent_women_trt1 = "% female",
                                      arm_format_trt1 = "Intervention",
                                      arm_format_trt2 = "Control",
                                      n_sessions_trt1 = "Sessions",
                                      Post_N_trt1 = "N_ig", 
                                      Post_N_trt2 = "N_cg"))

## - Creating HTML table...
## - [OK] Study table created successfully
## 
##                   study age group mean age % female Intervention       Control Sessions ...
## 1         Aagaard, 2017         4       48     0.71          CBT Care-As-Usual        8 ...
## 2  Allart van Dam, 2003         4       46     0.62          CBT Care-As-Usual       12 ...
## 3           Arean, 1993         5       66     0.75          PST     Wait-List       12 ...
## 4            Ayen, 2004         4       51     1.00          CBT     Wait-List       12 ...
## 5         Barrera, 1979         4       36     0.50           BA     Wait-List        8 ...
## 6           Beach, 1992         4       39     1.00          CBT     Wait-List       18 ...
## 7      Boeschoten, 2017         4       49     0.80          PST     Wait-List        5 ...
## 8          Bowman, 1995         4       36     0.63          CBT     Wait-List        4 ...
## 9          Bowman, 1995         4       36     0.63          PST     Wait-List        4 ...
## 10          Brown, 1984         4       36     0.70          CBT     Wait-List       12 ...
## 11          Brown, 1984         4       36     0.70          CBT     Wait-List       12 ...
## 12          Brown, 1984         4       36     0.70          CBT     Wait-List       12 ...
## 13          Carta, 2012         4       42     0.66          CBT Care-As-Usual       12 ...
## 14        Casanas, 2012         4       53     0.89          CBT Care-As-Usual        9 ...
## 15        Casanas, 2012         4       53     0.89          CBT Care-As-Usual        9 ...
## 16     Castonguay, 2004         4       39     0.75          CBT     Wait-List       16 ...
## 17     Castonguay, 2004         4       39     0.75          CBT     Wait-List       16 ...
## 18            Cho, 2008         4       30     1.00          CBT Care-As-Usual        9 ...
## 19            Cho, 2008         4       30     1.00          CBT Care-As-Usual        9 ...
## 20           Choi, 2012         4       39     0.80          CBT     Wait-List        6 ...
## 21      Chowdhary, 2016         4       41     0.69           BA Care-As-Usual        7 ...
## 22      Chowdhary, 2016         4       41     0.69           BA Care-As-Usual        7 ...

By default, createStudyTable also returns an HTML table that one can copy & paste in MS Word.

Still have questions? This vignette only provides a superficial overview of `metapsyTools`' functionality. Every function also comes with a detailed documentation, which you may consult to learn more about available options and covered use cases. Please note that `metapsyTools` is still at an early development stage, which means that errors or other problems may still occur under some circumstances. To report an issue or ask for help, you can contact **Mathias** ([e-mail]).

MathiasHarrer/metapsyTools documentation built on May 1, 2022, 5:14 p.m.