# Transform meta-analysis data from two arm-based formats into contrast-based format This function transforms data that are given in wide or long arm-based format (e.g. input format for WinBUGS) to a contrast-based format that is needed as input to R function `netmeta`. The function can transform data with binary, continuous, or generic outcomes as well as incidence rates from arm-based to contrast-based format. ```r pairwise( treat, event, n, mean, sd, TE, seTE, time, data = NULL, studlab, incr = gs("incr"), allincr = gs("allincr"), addincr = gs("addincr"), allstudies = gs("allstudies"), reference.group, keep.all.comparisons, append = !is.null(data), warn = FALSE, ... ) ``` ## Arguments - `treat`: A list or vector with treatment information for individual treatment arms (see Details). - `event`: A list or vector with information on number of events for individual treatment arms (see Details). - `n`: A list or vector with information on number of observations for individual treatment arms (see Details). - `mean`: A list or vector with estimated means for individual treatment arms (see Details). - `sd`: A list or vector with information on the standard deviation for individual treatment arms (see Details). - `TE`: A list or vector with estimated treatment effects for individual treatment arms (see Details). - `seTE`: A list or vector with standard errors of estimated treatment effect for individual treatment arms (see Details). - `time`: A list or vector with information on person time at risk for individual treatment arms (see Details). - `data`: An optional data frame containing the study information. - `studlab`: A vector with study labels (optional). - `incr`: A numerical value which is added to cell frequencies for studies with a zero cell count, see Details. - `allincr`: A logical indicating if `incr` is added to cell frequencies of all studies if at least one study has a zero cell count. If FALSE (default), `incr` is added only to cell frequencies of studies with a zero cell count. - `addincr`: A logical indicating if `incr` is added to cell frequencies of all studies irrespective of zero cell counts. - `allstudies`: A logical indicating if studies with zero or all events in two treatment arms are to be included in the meta-analysis (applies only if `sm` is equal to `"RR"` or `"OR"`). - `reference.group`: Reference treatment (first treatment is used if argument is missing). - `keep.all.comparisons`: A logical indicating whether all pairwise comparisons or only comparisons with the study-specific reference group should be kept ('basic parameters'). - `append`: A logical indicating whether variables from data set provided in argument `data` are appended to data set with pairwise comparisons. - `warn`: A logical indicating whether warnings should be printed (e.g., if studies are excluded due to only providing a single treatment arm). - ``...``: Additional arguments passed-through to the functions to calculate effects. ## Returns A data frame with the following columns: - **TE**: Treatment estimate comparing treatment 'treat1' and 'treat2'. - **seTE**: Standard error of treatment estimate. - **studlab**: Study labels. - **treat1**: First treatment in comparison. - **treat2**: Second treatment in comparison. - **event1**: Number of events for first treatment arm (for metabin and metainc). - **event2**: Number of events for second treatment arm (for metabin and metainc). - **n1**: Number of observations for first treatment arm (for metabin and metacont). - **n2**: Number of observations for second treatment arm (for metabin and metacont). - **mean1**: Estimated mean for first treatment arm (for metacont). - **mean2**: Estimated mean for second treatment arm (for metacont). - **sd1**: Standard deviation for first treatment arm (for metacont). - **sd2**: Standard deviation for second treatment arm (for metacont). - **TE1**: Estimated treatment effect for first treatment arm (for metagen). - **TE2**: Estimated treatment effect for second treatment arm (for metagen). - **seTE1**: Standard error of estimated treatment effect for first treatment arm (for metagen). - **seTE2**: Standard error of estimated treatment effect for second treatment arm (for metagen). - **time1**: Person time at risk for first treatment arm (for metainc). - **time2**: Person time at risk for second treatment arm (for metainc). All variables from the original dataset are also part of the output dataset; see Details. ## Details R function `netmeta` expects data in a contrast-based format , where each row corresponds to a comparison of two treatments and contains a measure of the treatment effect comparing two treatments with standard error, labels for the two treatments and an optional study label. In contrast-based format, a three-arm study contributes three rows with treatment comparison and corresponding standard error for pairwise comparison **A** vs **B**, **A** vs **C**, and **B** vs **C** whereas a four-arm study contributes six rows / pairwise comparisons: **A** vs **B**, **A** vs **C**, `...`, **C** vs **D**. Other programs for network meta-analysis in WinBUGS and Stata require data in an **arm-based** format, i.e. treatment estimate for each treatment arm instead of a difference of two treatments. A common (wide) arm-based format consists of one data row per study, containing treatment and other necessary information for all study arms. For example, a four-arm study contributes one row with four treatment estimates and corresponding standard errors for treatments **A**, **B**, **C**, and **D**. Another possible arm-based format is a long format where each row corresponds to a single study arm. Accordingly, in the long arm-based format a study contributes as many rows as treatments considered in the study. The pairwise function transforms data given in (wide or long) arm-based format into the contrast-based format which consists of **pairwise** comparisons and is needed as input to the `netmeta` function. The pairwise function can transform data with binary outcomes (using the `metabin` function from R package meta), continuous outcomes (`metacont` function), incidence rates (`metainc` function), and generic outcomes (`metagen` function). Depending on the outcome, the following arguments are mandatory: * treat, event, n (see `metabin`); * treat, n, mean, sd (see `metacont`); * treat, event, time (see `metainc`); * treat, TE, seTE (see `metagen`). Argument `treat` is mandatory to identify the individual treatments. The other arguments contain outcome specific data. These arguments must be either lists (wide arm-based format, i.e., one row per study) or vectors (long arm-based format, i.e., multiple rows per study) of the same length. For the wide arm-based format, each list consists of as many vectors of the same length as the multi-arm study with the largest number of treatments. If a single multi-arm study has five arms, five vectors have to be provided for each lists. Two-arm studies have entries with `NA` for the third and subsequent vectors. Each list entry is a vector with information for each individual study; i.e., the length of this vector corresponds to the total number of studies incorporated in the network meta-analysis. Typically, list elements are part of a data frame (argument `data`, optional); see Examples. An optional vector with study labels can be provided which can be part of the data frame. In the long arm-based format, argument `studlab` is mandatory to identify rows contributing to individual studies. Additional arguments for meta-analysis functions can be provided using argument '`...`'. The most important argument is `sm` defining the summary measure. More information on this and other arguments is given in the help pages of R functions `metabin`, `metacont`, `metainc`, and `metagen`, respectively. For standardised mean differences (argument `sm = "SMD"`), equations (4) and (5) in Crippa & Orsini (2016) are used to calculated SMDs and standard errors. These equations guarantee consistent SMDs and standard errors for multi-arm studies. Note, the summary measure is actually Cohen's d as Hedges' g is not consistent in multi-arm studies. For binary outcomes, 0.5 is added to all cell frequencies (odds ratio) or only the number of events (risk ratio) for studies with a zero cell count. For odds ratio and risk ratio, treatment estimates and standard errors are only calculated for studies with zero or all events in both groups if `allstudies` is `TRUE`. This continuity correction is used both to calculate individual study results with confidence limits and to conduct meta-analysis based on the inverse variance method. For the risk difference, 0.5 is only added to all cell frequencies to calculate the standard error. For incidence rates, 0.5 is added to all cell frequencies for the incidence rate ratio as summary measure. For the incidence risk difference, 0.5 is only added to all cell frequencies to calculate the standard error. The value of pairwise is a data frame with as many rows as there are pairwise comparisons. For each study with **p** treatments, **p*(p-1) / 2** contrasts are generated. Each row contains the treatment effect (`TE`), its standard error (`seTE`), the treatments compared ((`treat1`), (`treat2`)) and the study label ((`studlab`)). Further columns are added according to type of data. All variables from the original dataset are also part of the output dataset. If data are provided in the long arm-based format, the value of a variable can differ between treatment arms; for example, the mean age or percentage of women in the treatment arm. In this situation, two variables instead of one variable will be included in the output dataset. The values "1" and "2" are added to the names for these variables, e.g. "mean.age1" and "mean.age2" for the mean age. In general, any variable names in the original dataset that are identical to the main variable names (i.e., "TE", "seTE", ...) will be renamed to variable names with ending ".orig". A reduced data set with basic comparisons (Rücker & Schwarzer, 2014) can be generated using argument `keep.all.comparisons = FALSE`. Furthermore, the reference group for the basic comparisons can be specified with argument `reference.group`. ## Note This function must not be confused with `netpairwise` which can be used to conduct pairwise meta-analyses for all comparisons with direct evidence in a network meta-analysis. ## Examples ```r # Example using continuous outcomes (internal call of function # metacont) # data(Franchini2012) # Transform data from arm-based format to contrast-based format p1 <- pairwise(list(Treatment1, Treatment2, Treatment3), n = list(n1, n2, n3), mean = list(y1, y2, y3), sd = list(sd1, sd2, sd3), data = Franchini2012, studlab = Study) p1 ## Not run: # Conduct network meta-analysis # net1 <- netmeta(p1) net1 # Draw network graphs # netgraph(net1, points = TRUE, cex.points = 3, cex = 1.5, thickness = "se.common") netgraph(net1, points = TRUE, cex.points = 3, cex = 1.5, plastic = TRUE, thickness = "se.common", iterate = TRUE) netgraph(net1, points = TRUE, cex.points = 3, cex = 1.5, plastic = TRUE, thickness = "se.common", iterate = TRUE, start = "eigen") # Example using generic outcomes (internal call of function # metagen) # # Calculate standard error for means y1, y2, y3 Franchini2012$se1 <- with(Franchini2012, sqrt(sd1^2 / n1)) Franchini2012$se2 <- with(Franchini2012, sqrt(sd2^2 / n2)) Franchini2012$se3 <- with(Franchini2012, sqrt(sd3^2 / n3)) # Transform data from arm-based format to contrast-based format # using means and standard errors (note, argument 'sm' has to be # used to specify that argument 'TE' is a mean difference) p2 <- pairwise(list(Treatment1, Treatment2, Treatment3), TE = list(y1, y2, y3), seTE = list(se1, se2, se3), n = list(n1, n2, n3), data = Franchini2012, studlab = Study, sm = "MD") p2 # Compare pairwise objects p1 (based on continuous outcomes) and p2 # (based on generic outcomes) # all.equal(p1[, c("TE", "seTE", "studlab", "treat1", "treat2")], p2[, c("TE", "seTE", "studlab", "treat1", "treat2")]) # Same result as network meta-analysis based on continuous outcomes # (object net1) net2 <- netmeta(p2) net2 # Example with binary data # data(smokingcessation) # Transform data from arm-based format to contrast-based format # (interal call of metabin function). Argument 'sm' has to be used # for odds ratio as risk ratio (sm = "RR") is default of metabin # function. # p3 <- pairwise(list(treat1, treat2, treat3), list(event1, event2, event3), list(n1, n2, n3), data = smokingcessation, sm = "OR") p3 # Conduct network meta-analysis # net3 <- netmeta(p3) net3 # Example with incidence rates # data(dietaryfat) # Transform data from arm-based format to contrast-based format # p4 <- pairwise(list(treat1, treat2, treat3), list(d1, d2, d3), time = list(years1, years2, years3), studlab = ID, data = dietaryfat) p4 # Conduct network meta-analysis using incidence rate ratios (sm = # "IRR"). Note, the argument 'sm' is not necessary as this is the # default in R function metainc called internally. # net4 <- netmeta(p4, sm = "IRR") summary(net4) # Example with long data format # data(Woods2010) # Transform data from long arm-based format to contrast-based # format Argument 'sm' has to be used for odds ratio as summary # measure; by default the risk ratio is used in the metabin # function called internally. # p5 <- pairwise(treatment, event = r, n = N, studlab = author, data = Woods2010, sm = "OR") p5 # Conduct network meta-analysis net5 <- netmeta(p5) net5 ## End(Not run) ``` ## References Crippa A, Orsini N (2016): Dose-response meta-analysis of differences in means. **BMC Medical Research Methodology**, 16 :91. ## See Also `netmeta`, `metacont`, `metagen`, `metabin`, `metainc`, `netgraph.netmeta`, `pairwise` ## Author(s) Gerta Rückergerta.ruecker@uniklinik-freiburg.de , Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de