Summary

Data consist of the mean VAS at various time points throughout a period of stable pain (after the treatment effect is assumed to have operated), from 4.35 to 156.54 weeks.

A simple analysis of the mean difference in VAS scores over this period was carried out, where the data inputs are the averages of the means reported at all time points and their variances. However, the averaging needs to account for the correlation in the observations at different time points. This correlation was assumed to be 0.87 and constant over time. If other sources of information on the within-study correlation at different time points become available, the calculations can easily be redone.

We describe the method used to impute the within-trial correlations at different time points within the same trial, and for calculating the average and variance of correlated outcomes. The resulting averages and variances are used as data inputs into a standard MTC model in WinBUGS. Results from fixed effects (FE) and random effects (RE) models are described and the FE model is recommended.

There is potential for inconsistency in one loop in this network, but no evidence of inconsistency was found.

Data

Data on mean VAS score are available from eight trials, comparing four treatments.

Treatments were coded 1 to 4 (Table 142), the data available are described in table and the network diagram is presented in Figure 81 . OPM was chosen as the overall baseline, or reference treatment.

TABLE 142

Treatment Codes. Treatment 1 is assumed to be the baseline reference treatment with which all others are compared

FIGURE 81

Treatment network for mean VAS score in stable period.

Methods

Calculating the mean and variance of all means in stable period

For each arm of each study in Table 143 , let y _j be the mean VAS score at time point j and s _j the standard error of the observations at time point j. For a given study, reporting at J time points (J ≥ 1), we have a vector of observations Y, such that,

TABLE 143

Data available for stable period

$$\mathbf{Y}=\left(\begin{array}{c}{y}_1\\ y_2\\ \mathrm{⋮}\\ y_J\end{array}\right)\sim N_J(\mathbf{m}\text{,}\mathbf{V})$$

(1)

where m is a vector of unknown means and V is the variance–covariance matrix, assumed known. Letting Z represent a linear combination of the elements of Y, such that,

$$Z=\frac{y_1+y_2+\dots +y_J}{J}=\mathbf{BY}$$

(2)

where

$$\mathbf{B}=\frac{1}{J}\left[\begin{array}{cccc}1& 1& \mathrm{\dots }& 1\end{array}\right]$$

(3)

we have,

$$Var(Z)={\mathbf{BVB}}^{\text{′}}$$

(4)

For each arm of each study, V has in its diagonal the variances of the mean at each time point, $S_j^2$ , and the off-diagonal elements in row i, column j, will hold ρs _j s _i , where ρρ = 0.87 and independent of the time lag between observations i and j.

Repeating this method for all arms of each study, we get $Z=y_{i\text{,}k}^{*}$ the average of the mean VAS score in arm k of study i, (i = 1,. . .,16, k = 1,2) with variances calculated using equation (4).

The transformed data, on which the MTC will be carried out, are given in Table 144 .

TABLE 144

Transformed means and variances for mean VAS score for input into WinBUGS

Results

Model fit statistics for the FE and RE models are given in Table 145 . Although the RE model has a slightly better fit, this is at the expense of more parameters, and the DIC does not favour any of the models. We will, therefore, prefer the FE model, owing to its simplicity and easier interpretation. However, a re-examination of the Blasco study (study 1) is recommended as it is showing a relatively poor fit – this appears to be because it is the only study comparing OPM with vertebroplasty and (marginally) favouring OPM, while all other trials favour vertebroplasty.

TABLE 145

Model fit statistics for MTC analyses

A plot of the effects (mean differences) of all treatments relative to each other is given in Figure 82 . Differences > 0 favour the lowest numbered treatment.

FIGURE 82

Plot of mean differences of all treatments relative to each other. Values to the right of the vertical (green) line favour the lowest numbered treatment. Treatment codes are given in Table 142 .

Vertebroplasty and kyphoplasty (treatments 2 and 3) appear to be the best treatments, although the differences are small (about 1 point) and may not be clinically significant.

Consistency

There is only one evidence loop in this network (see Figure 81 ) formed by treatments 1, 2 and 3. Consistency was checked by comparing the treatment effects obtained from separate pairwise meta-analysis for each pair of treatments using the Bucher approach as recommended in Dias et al. ⁴⁰⁴ No evidence of inconsistency was found (Bayesian p-value > 0.8).