The analysis in this article is based on previously conducted studies, and does not involve any new studies of human or animal subjects performed by any of the authors.
Literature Data
A systematic screening of clinical trials involving tramadol and/or tapentadol for the treatment of non-malignant pain was performed. Clinical trials published until November 2011, were considered. The search sources included PubMed®/MEDLINE™, European Medicines Agency, and Food and Drug Administration drug labeling information and additional sources were identified in clinical trial registries. Several combinations of key words were used (see the Electronic Supplementary Material for details). A total of 83 sources were identified. Leaving out the sources which did not report any data on pain intensity or adverse event frequency or drop-out rate, and after full-text examination, publications describing 45 unique double-blind Phase II or Phase III randomized clinical trials in adult patients with chronic non-malignant pain were retained in the meta-analysis. A list of the trials used in the analysis with key information is provided in Supplementary Table S1 in the Electronic Supplementary Material.
The majority of the trials were placebo-controlled. Six tapentadol trials [13–18] were active-controlled trials, using oxycodone as comparator. Because these trials were large in size, hence informative, it was important to keep them in the analysis. In case of active-controlled trials with a comparator other than tramadol or tapentadol, only the arm corresponding to one of these two treatments was retained in the analysis dataset. The list of studies retained in the analysis is presented in Supplementary Table S1 in the Electronic Supplementary Material. It is also worth mentioning that three studies (Adler et al. [19], Mongin et al. [20] and Beaulieu et al. [21]) considered tramadol at several therapeutic doses and in various formulations without a placebo arm. For each treatment arm, information about patient population, sample size, baseline and demographic characteristics were also available.
In addition to describing the treatment effect over time, other differences among trials and treatment arms due to intrinsic (e.g., disease severity, gender, age) or extrinsic factors (e.g., concomitant medication) were accounted for in the analysis. These factors are introduced in the model as covariates. However, because patient-specific covariates are in the form of summary statistics, their values cover a narrower range than the individual values. Consequently, they are less informative about their effects unless the data have been stratified based on them. Covariates of interest in the dataset included year of publication, baseline pain intensity, pain syndrome, and trial duration. The various pain syndromes were grouped into the following categories: osteoarthritis pain, back pain, neuropathic pain, and other chronic non-malignant pain.
Pain Intensity
Pain intensity was analyzed on a scale ranging from 0 to 10 (0 = no pain, 10 = worst imaginable pain). Where efficacy was reported only in terms of change from baseline, the absolute pain intensity score was derived from the difference between change from baseline and baseline values. Pain intensity data from papers which failed to report baseline pain were discarded. Because the scales used to measure pain intensity were very heterogeneous, two broad categories were considered to capture the residual variability in the model: visual analog scale (VAS; continuous) and categorical scales. The rules used to convert the raw data into a 0–10 range are presented in Table 1.
Table 1 Conversion rules for each pain intensity scale
Graphical exploration of the data revealed a marked placebo response across studies (Fig. 1). The placebo effect in pain treatment is a well-known phenomenon [22] which was taken into account in the model development by capturing not only the pain intensity time course in the active treatment groups, but also in the placebo group. Capturing the precise time dynamics in the placebo groups was also important because the indirect comparison of treatments relies on a common (exchangeable) placebo response.
The proposed structural model (1) for the kth pain intensity measured in the jth treatment arm of trial i, at time t included three components: (i) a baseline term (Base); (ii) the placebo and drug effects time courses, and (iii) the between-study random effects and residual error terms. The model was written as follows:
$$ \begin{aligned}{\text{PI}}_{ijk} &= g\left\{ {{\text{Base}}_{ij} + R_{ij} \times \left( {1 - {\text{e}}^{{\lambda \times t_{ijk} }} } \right) + \varepsilon_{ijk} } \right\}\\ g\left\{ x \right\} &= 10 \times \frac{{{ \exp }\left( x \right)}}{{1 + { \exp }\left( x \right)}}\end{aligned} $$
(1)
In this equation, Base
ij
is the baseline estimate (or intercept); R
ij
corresponds to the placebo or drug effect, reflecting the change from baseline; and ε
ijk
represents the residual (unexplained) variability. The exploratory graphical analysis showed a mono-exponential decrease of the response over time (in all treatment groups including placebo), which was parameterized in the model by the decay rate λ. In order to estimate the respective effect size and time course, separate R and separate λ parameters were introduced in the model for each drug (placebo, tramadol, and tapentadol). The decay rate was parameterized such that: λ
drug = λ
pbo + λ
Δdrug.
In order to estimate the between-study variability, random effects were associated additively with the Base parameter and exponentially with the R parameter:
$$ \begin{aligned} {\text{Base}}_{ij} &= {\text{Base}} + \eta_{{{\text{Base}}_{ij} }} {\text{ with }}\eta_{{{\text{Base}}_{ij} }} \sim N\left( {0, \omega_{\text{Base}}^{2} } \right)\\ R_{ij} &= R \times e^{{\eta_{{R_{ij} }} }} \,{\text{with}}\,\eta_{{R_{ij} }} \sim N\left( {0, \omega_{R}^{2} } \right)\end{aligned} $$
In order to acknowledge our confidence in trials executed in larger populations, the residual error was entered in the model as inversely proportional to the number of patients (N) contributing to each data point.
$$ \varepsilon_{ijk} \sim N\left( {0, \frac{{\sigma_{\text{res}}^{2} }}{{N_{ijk} }}} \right). $$
As mentioned above, the residual variance was different whether the scale used to measure pain intensity was continuous (VAS) or categorical. These variances are hereafter referred to as σ
21
and σ
22
, instead of a unique σ
2res
.
The model was coded in R using the nlme function of package nlme [23]. This function fitted the non-linear mixed-effect model by the method of maximum likelihood.
Adverse Events and Drop-outs
The tolerability-related events (adverse events and drop-outs) were analyzed in terms of number of patients experiencing the event (at least once) during the treatment period. Using the same notation as above, the number of patients experiencing event E (at least once) was assumed to follow a binomial distribution with a probability pE
ij
, and a sample size N
ij
, such that:
$$ E_{ij} \sim {\text{Bin}}\left( {pE_{ij} , N_{ij} } \right). $$
The probability of a patient having an event in treatment arm j of trial i was modeled using a logistic model, as afunction of the intercept (α
0) and the m covariates (X
mij
), including drug (parameterized either as a factor or as a dose–response relationship), and other covariates. A term for between-treatment variability (u
ij
), assumed to be normally distributed in the logit scale, was also introduced in the model.
$$ \begin{aligned}& \log \left( {\frac{{pE_{ij} }}{{1 - pE_{ij} }}} \right) = \alpha_{0} + \mathop \sum \limits_{m} \beta_{m} X_{mij} + u_{ij} \\ & u_{ij} \sim N\left( {0, \omega_{E}^{2} } \right).\end{aligned} $$
This model evaluates the log odds of the outcome (E) probability on various predictors. Hence, the parameter β
m
measures the effect of increasing X
mij
by one unit on the log odds ratio.
When enough data were available the dose–response relationship was investigated using linear model. Non-linear dose–response relationships were discarded a priori based on observed trends in exploratory graphics.
The potential for an increased risk of an adverse event under treatment seemed likely to be related to treatment duration; the alternative would be to hypothesize a one-off risk increase on treatment initiation, with no additional risk thereafter, however long the treatment was applied. Hence, treatment duration was always tested as a covariate in the tolerability events and drop-out rates meta-analyses.
The model was coded in R using the glmer function of package lme4 [24]. This function fitted the linear model by the method of maximum likelihood.
Model Selection
During the model development phase, a cut-off of 4-points in Akaike Information Criterion value was used to decide which model to retain. Goodness-of-fit plots and visual predicted checks (VPC) inform the decision of whether to consider the model appropriate for simulations or not. Goodness-of-fit plots included plots of observed versus predicted, and observed versus individual predicted values, stratified (as appropriate) by drug, to ensure adequacy of the fit across drugs.
To obtain a VPC, the observations of the analysis dataset are simulated 1,000 times using the fitted model (structure, parameter estimates, and associated uncertainty). The distribution of the model predictions are superimposed onto the actual trial data to obtain a visual display of the model ability to describe the data it is coming from.
Indirect Comparison of Tramadol and Tapentadol
Particular attention was devoted to the comparison of tramadol and tapentadol benefit–risk ratios. In absence of clinical trial results providing head-to-head comparison between these two compounds, an adjusted indirect comparison method is considered.
Given the non-linear form (in the parameters) of the pain intensity time course model, tramadol and tapentadol were compared by simulation of typical time profiles. For this purpose, the typical tramadol dose was considered to be 300 mg qd, and the typical duration of a trial, 12 weeks. A total of 2,000 treatment arms (1,000 per group) each containing 1,000 patients were simulated, with a baseline pain intensity of 7 out of 10. The predicted differences in mean pain intensity between tramadol and tapentadol group for each trial were then summarized by the median, and 95% predictive interval.
For the comparison of event proportion, the Butcher’s [25] indirect treatment comparison method was readily applied to derive the odds-ratio between tramadol and tapentadol, as associated confidence intervals.