R a single coefficient to model the general correlation,O. EFTHIMIOU AND OTHERSan amalgam of the correlations within and between studies. Rather than modeling and separately, they assume an general variance ovariance matrix, so that Y X + with N (, ). This matrix is again block diagol with every block corresponding to a study, to ensure that Diag(,., N S ) To get a study i, R + i,R D + i,D ih R + i,R. i R + i,R D + i,D D + i,D ih The ih coefficient in is definitely the overall correlation in study i, a hybrid on the inside and betweenstudy correlation coefficients. We can again model the different ih inside a wide variety of strategies, based around the PubMed ID:http://jpet.aspetjournals.org/content/153/3/412 ture on the data, e.g. ih i. The parameters model for the variation additiol towards the sampling error that enters because of heterogeneity, and they’re comparable for the parameters of , but not straight equivalent unless the withinstudy variances are compact relative for the betweenstudy variances in model. The clear advantage of model is that the withinstudy correlations are no longer required. NMA for two correlated outcomes The two models described in the earlier section is often easily extended to execute a metaalysis for any network of treatments, if all included research have just two therapies arms. These models, even so, can’t manage the case of Taprenepag web studies comparing more than two therapies. In this section, we present two models for performing an NMA of research with a number of arms reporting on two correlated outcomes, generalizing the models presented in Section The outcomes might be biry (and relative treatment impact is usually measured as log odds ratios or log threat ratios), continuous (effects measured as mean differences or standardized mean variations) or time to event (effects measured as log hazard ratios). Note that in order to use the standardized imply distinction to get a continuous outcome a large sample approximation is needed. For additional information, see Section of supplementary material accessible at Biostatistics RC160 web on-line. Inside the acute mania example, the outcomes are identified as the biry response towards the therapy (R) and dropout price (D). We exemplify the methodology for the case of networks containing studies with a maximum of three arms. We assume a random effects model and that the consistency equations (XY,R XZ,R YZ,R ) hold for all treatments X, Y and Z; similarly for outcome D Model : Simplifying the variance ovariance matrices. The very first system is primarily based on simplifying the inside and betweenstudy variance ovariance matrices in order that the amount of parameters needed is minimized, eases computatiol burden and potential estimation difficulties. Let us start by thinking about a network of research reporting around the correlated outcomes R and D to get a network of N T different treatments The model is Y X + + with Y the vector in the observed effects, X the design and style matrix, the vector of the fundamental parameters, i.e. the N T 
parameters for the comparison of every remedy versus the reference (Lu and Ades,; Salanti and others, ), the vector of random effects, along with the vector of random errors (Dias and other individuals,; Salanti and others, ). The style matrix X describes the structure on the network and embeds the consistency equations (Salanti and others, ); it maps the observed comparisons in to the basic parameters. By way of example, if A is selected to be the reference remedy, a study comparing B to C for outcome R provides information to get a linear combition of two basic parameters as BC,R AC,R AB,R. To get a twoarm study i that compares treatments.R a single coefficient to model the overall correlation,O. EFTHIMIOU AND OTHERSan amalgam on the correlations within and amongst research. Rather than modeling and separately, they assume an overall variance ovariance matrix, to ensure that Y X + with N (, ). This matrix is again block diagol with each block corresponding to a study, to ensure that Diag(,., N S ) To get a study i, R + i,R D + i,D ih R + i,R. i R + i,R D + i,D D + i,D ih The ih coefficient in will be the overall correlation in study i, a hybrid of the within and betweenstudy correlation coefficients. We are able to once again model the distinctive ih inside a wide variety of techniques, based on the PubMed ID:http://jpet.aspetjournals.org/content/153/3/412 ture on the data, e.g. ih i. The parameters model for the variation additiol to the sampling error that enters due to heterogeneity, and they’re comparable for the parameters of , but not straight equivalent unless the withinstudy variances are smaller relative for the betweenstudy variances in model. The clear benefit of model is the fact that the withinstudy correlations are no longer needed. NMA for two correlated outcomes The two models described within the preceding section is often conveniently extended to carry out a metaalysis for a network of treatment options, if all incorporated research have just two treatment options arms. These models, however, cannot manage the case of research comparing greater than two treatment options. In this section, we present two models for performing an NMA of research with numerous arms reporting on two correlated outcomes, generalizing the models presented in Section The outcomes can be biry (and relative treatment impact could be measured as log odds ratios or log risk ratios), continuous (effects measured as mean differences or standardized imply differences) or time for you to event (effects measured as log hazard ratios). Note that in order to make use of the standardized imply difference for any continuous outcome a sizable sample approximation is necessary. For 
additional facts, see Section of supplementary material offered at Biostatistics on the web. In the acute mania example, the outcomes are identified because the biry response to the treatment (R) and dropout price (D). We exemplify the methodology for the case of networks containing studies having a maximum of three arms. We assume a random effects model and that the consistency equations (XY,R XZ,R YZ,R ) hold for all remedies X, Y and Z; similarly for outcome D Model : Simplifying the variance ovariance matrices. The initial strategy is primarily based on simplifying the within and betweenstudy variance ovariance matrices in order that the amount of parameters needed is minimized, eases computatiol burden and possible estimation difficulties. Let us start by considering a network of studies reporting on the correlated outcomes R and D to get a network of N T different treatments The model is Y X + + with Y the vector from the observed effects, X the style matrix, the vector in the standard parameters, i.e. the N T parameters for the comparison of each therapy versus the reference (Lu and Ades,; Salanti and other folks, ), the vector of random effects, and also the vector of random errors (Dias and others,; Salanti and others, ). The style matrix X describes the structure with the network and embeds the consistency equations (Salanti and other folks, ); it maps the observed comparisons in to the standard parameters. By way of example, if A is chosen to become the reference treatment, a study comparing B to C for outcome R gives details for any linear combition of two standard parameters as BC,R AC,R AB,R. For any twoarm study i that compares treatment options.
