Ritonavir-boosted protease inhibitor-based versus non-nucleoside reverse transcriptase inhibitor-based highly active antiretroviral therapy regimens: a systematic review and individual patient data me

Data analysis

Individual patient data analysis (IPD)
We will contact trial authors in order to obtain protocols and individual patient data from each trial. Trial authors will be offered co-authorship, with one author per trial for small trials and two authors for large trials.

IPD meta-analysis uses the original ‘‘raw'' data from each participant in the included trials. The data are centrally collected, checked, re-analysed and combined (Stewart & Parmar, 1993; Stewart & Clarke, 1995). An advantage of IPD analysis over the conventional aggregate data meta-analysis approach is that it allows detailed participant-level exploration of treatment effectiveness in relation to individuals' characteristics such as age or stage of disease (Stewart & Clarke, 1995; Riley et al., 2010).
With the introduction of IPD that differentiates clearly at least two levels of analysis, the individual and the study. There are two different approaches that can be followed 1) two-stage analysis, which produce first aggregate data for each study and then these data are synthesized in the second step using a suitable model for aggregated-data meta-analysis. And 2) one-stage analysis that allows to model the data as a unique database accounting for the study as a cluster effect and model that way the individual- and group-level possible covariates.

The IPD will be analyzed under the one-stage approach, which allows to model individual effect clustered within study. A nonlinear mixed model by maximizing an approximation to the likelihood integrated over the random-effects will be undertaken using xtmelogit in STATA or PROC NLMIXED in SAS for the binary outcome (Sutton et al., 2007; Riley et al. 2008), . A linear mixed model will be used for continuous outcome. Finally, covariate interactions will be evaluated separating within-trial and across-trial information (Riley et al., 2008).

Network meta-analysis: For a connected network diagram a random-effects network meta-analysis (NMA) will be employed accounting properly for correlations induced by multi-arm studies (studies that compare more than two treatments) (White 2012, Franchini 2012). NMA is the statistical methodology developed to combine information across a network of trials that address the same question but involve different interventions. It is common, though, that an active treatment is compared to a placebo or a non-active control, rather than another active treatment. Decision-makers often have to deal with such lack of data and subsequently cannot make judgements. When direct comparative data are not available, but the treatments of interest are compared to a common intervention, e.g. placebo, the indirect comparison can provide important information. Consider for example the network of A, B and C treatments with A vs. B and A vs. C available comparisons. To infer on the efficacy of B and C treatments the indirect comparison can be employed by analysing A vs. B and A vs. C studies jointly (Bucher et al 1997). NMA synthesises both direct and indirect estimates to make inference on all treatments included in a network of trials. The method provides more precise estimates than conducting indirect comparisons or including all comparisons as separate studies, as it ‘borrows strength' from all the available evidence in the network (Higgins and Whitehead 1996).
Lack of transitivity in network meta-analysis can question the consistency of the underlying estimates and the validity of the results. It is therefore important to statistically evaluate the consistency between direct and indirect evidence, as the joint analysis of treatments can be misleading if the network is inconsistent. The assumption of consistency will be evaluated using two different approaches. First, we will examine for any material differences within each closed loop (treatment pairs that form ‘evidence cycles') of the network separately using the loop-specific method (Bucher et al 1997). Then the assumption in the entire network will be evaluated using the design-by-treatment interaction model (White 2012). In case of important inconsistency possible sources of it will be investigated.
The between-study heterogeneity will be assumed to be common across comparisons (Lu and Ades 2004) and an estimate of it will be reported. Under the key assumption of consistency, treatments are going to be ranked according to their efficacy providing the probability for each intervention of being the most effective (first-best), second-best, third-best, and so on.


Dealing with missing data
For trials where individual patient data cannot be obtained we will contact corresponding authors to obtain missing outcome data. For unpublished trials we will try to obtain copies of protocols and clinical study reports and contact authors for additional information. In addition we will search the FDA website for FDA reviews of the corresponding trials (Hart et al., 2012).

Multiple imputation techniques (Burgess et al., 2013) will be used to impute missing data in outcomes and also for missing covariates (Resche-Rigon et al., 2013). Rubin's rules will be applied at the study level prior to the pooling of study-specific estimates, and a within-study imputation model will be used.


Assessment of heterogeneity
We will describe heterogeneity using I2 and its confidence interval (Huedo-Medina, 2006)

Assessment of reporting biases
We will use a funnel plot for our primary outcome to discuss publication bias.

Handling of data
For the outcomes mortality or disease progression, severe toxicity, treatment discontinuation and mortality, our main analyses will be based on time-to-event data. We will also report the analysis of available risk data using the latest follow-up. If more than one cut-off of HIV-RNA to define virological suppression is reported in a trial we will use the lowest cut-off.

Statistical analysis

Due to variations in backbone therapy, disease severity at treatment initiation and clinical setting, we assume that individual trials are not all estimating the same intervention effect and we will therefore use a random-effects model.

Using Stata and other statistical softwares (i.e., R and SAS), for mixed models with IPD, we will estimate adjusted odds ratios for the nonlinear mixed models and regression beta coefficients for the linear ones when the outcome is continuous, both with estimated 95% confidence intervals using a random-effects model using full maximum information to estimate the variance.

For risk data we will analyse patients according to intention to treat using complete case analysis (Akl et al., 2013) where patients with missing data are excluded. We will calculate pooled risk ratios and estimated 95% confidence intervals using the random-effects model with the Mantel-Haenszel method for dichotomous data.

For continuous outcomes we will calculate pooled mean differences and estimated 95% confidence intervals using the random-effects model with the inverse variance method.

For multi-arm trials or trials of factorial design we will combine trial arms based on whether the third drug is a ritonavir-boosted PI or NNRTI.

Subgroup analysis and investigation of heterogeneity
We will explore treatment regimes using metaregression analyses according to:
•   Type of boosted PI (that is, atazanavir, darunavir, fosamprenavir, lopinavir, tipranavir or saquinavir).
•   Type of NNRTI (that is, efavirenz, nevirapine, etravirine or rilpivirine).
•   Type of NRTI backbone therapy (that is, containing either tenofovir or abacavir and either zidovudine or stavudine).
•   Previous exposure to single dose nevirapine to prevent mother-to-child transmission.
•   Gender
•   Patients with viral load above or below 100,000 copies/mL.
•   Patients with CD4+ counts above or below 200 cells/mm3.
•   Trials conducted in developing countries or in affluent settings. Individual risk of bias domains (low versus high/unclear risk of selection, performance, detection and attrition bias.

Sensitivity analysis

We will conduct an as-treated sensitivity analysis and compare the results against an intention-to-treat analysis.

We will conduct a sensitivity analysis of HIV-RNA by using the highest cut-off in trials reporting more than one cut-off.

We will conduct a sensitivity analysis by excluding trials where we have used indirect methods to estimate data (e.g. estimated means, standard deviations or hazard ratios).

We will conduct a sensitivity analysis using log transformed CD4+ counts.

We will conduct sensitivity analysis using the fixed effect for the analyses of our primary outcome and mortality.

We will conduct sensitivity analysis imputing missing outcome data using the approach described by Akl (Akl et al., 2013) for binary data and Ebrahim (Ebrahim et al., 2013) for continuous data.