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I'm trying to use GeMTC (a package for Bayesian Network Meta Analysis) for an analysis that mixes contrast-based data (Hazard Ratio;HR) with arm-based data (event counts). The documentation specifies that this is possible, but requires the standard error of the log-hazard in the baseline arm for mutli-arm trials.

Relative effect data. A data frame defining the arms of each study, containing the columns ‘study’ and ‘treatment’, where ‘treatment’ must refer to an existing treatment ID if treatments were specified. The column ‘diff’ specifies the mean difference between the current arm and the baseline arm; set ‘diff=NA’ for the baseline arm. The column ‘std.err’ specifies the standard error of the mean difference (for non-baseline arms). For trials with more than two arms, specify the standard error of the mean of the baseline arm in ‘std.err’, as this determines the covariance of the differences"

(from the mtc.network manual

Unfortunately, this data is not available. However, a paper by Woods et.al. specifies that it is possible to compute/approximate.

The variance for a log hazard ratio is the sum of the variances for the individual log hazards. Standard errors of the log hazards for each trial arm can therefore be estimated by solving simultaneous equations based on the standard errors for the set of log-hazard ratios. For example: \begin{equation} se_b = \sqrt{((se^2_{k_1,b} + se^2_{k_2,b} - se^2_{k_1,k_2} )/2)} \end{equation} Where $se^2_{i,j}$ is the variance of the log hazard ratio comparing arm $i$ to arm $j$ and $se_i$ is the standard error of the log hazard for arm $i$. The standard errors of the log hazards for the other treatment arms are then estimated as: \begin{equation} se_k=\sqrt{se^2_{k,b} - se^2_b} \end{equation}

The paper then goes on outlining how to compute $se_{k_1,k_2}$ in formula 9.

In order to estimate standard errors of the log hazards for each treatment, we required estimates of the uncertainty associated with four treatment contrasts. In some cases this data may not be available and thus the methods presented in equations 7 and 8 may not be feasible. For example, hazard ratios and associated measures of uncertainty may only be available for each active treatment relative to a single common comparator (e.g. placebo) as is commonly reported in the published literature.

However I am at a loss on how to apply these formulas correctly in GeMTC.

Replicating the data from Woods I have the following code:

data.ab <- read.table(textConnection(' study treatment responders sampleSize 01 Salmeterol 1 229 01 Placebo 1 227 02 Fluticasone 4 374 02 Salmeterol 3 372 02 SFC 2 358 02 Placebo 7 361 03 Salmeterol 1 554 03 Placebo 2 270'), header=T) data.re <- read.table(textConnection(' study treatment diff std.err 04 Placebo NA NA 04 Fluticasone -0.276 0.203 05 Placebo NA 0.066 05 SFC -0.209 0.098 05 Salmeterol -0.154 0.096 05 Fluticasone 0.055 0.092 '), header=T) network <- mtc.network(data.ab=data.ab, data.re=data.re) model <- mtc.model(network, link="cloglog", likelihood="binom", linearModel="fixed") mtc.run(model) -> results forest(relative.effect(results, t1="Placebo"))

I used their value from Table 3 (0.66) as the value for the log-hazard standard error of Placebo. The results are similar. But, I cannot compute this value in the general case of > 2-arm studies when data comes in as Table 2.

Help would be much appreciated!

(Github issue)