Mixed treatment comparisons (MTCs) are meta-analytic statistical techniques that incorporate the findings from several studies, where in most cases none of the studies compared all the treatments at one time, to address the comparative effectiveness and safety of interventions accounting for all sources of data. In the MTC data framework, since few head-to-head comparisons are available, we must rely on indirect comparisons, typically each investigated treatment against a control or a standard treatment. The biggest assumption in MTCs is exchangeability among studies; that is, any ordering of the true treatment effects across studies is equally likely a priori. In addition, populations in selected studies should be similar to the target population for valid clinical interpretation. Bayesian hierarchical statistical meta-analysis for MTCs with a single binary outcome has been investigated actively since the 1980s. However, compared with the binary outcome setting, there has been comparatively little development in Bayesian MTCs for continuous outcomes. Our interest in Bayesian MTC methods for multiple continuous outcomes is motivated by a systematic literature review at the Minnesota Evidence-based Practice Center (EPC) that investigated the effectiveness of physical therapies on chronic pain secondary to knee osteoarthritis (OA) for community-dwelling adults. OA treatments aim to reduce or control pain, improve physical function, prevent disability, and enhance quality of life. We recorded means of measured pain, disability, function, and quality of life scores associated with various physical therapy interventions from randomized studies. As our OA data contain many studies reporting multiple outcomes, and measured on the same subjects, correlations across arms and outcomes are likely, but this case has not been discussed much in the literature. For example, similar types of drugs or physical therapies may tend to behave similarly inducing correlated results, and multiple outcomes also can induce correlations (e.g., subjects with severe pain would be more likely to have disability). Most randomized controlled trials (RCTs) include only two or three treatment arms, including a control group, due to limited resources. This results in extremely sparse data for MTCs when used across all possible treatments. Suppose that we can calculate the missingness rate as the summation of the ratio of the number of missing arms to the total number of treatments across all studies. Then, the missingness rate is 40 to 60 percent when we compare 5 treatments, and the rate could increase up to about 70 percent if 10 treatments are considered. Lu and Ades's approach, a standard MTC model, uses only the observed data. However, we can borrow strength from those missing data after imputing them in a Bayesian hierarchical model that accounts for between-treatment and between-outcome correlations using Markov chain Monte Carlo (MCMC) algorithms. Especially when the missingness does not occur randomly but depends on some observed or unobserved information, ignoring such missing data can cause biased estimators. In this report we review existing MTC models and propose novel Bayesian missing data approaches to combine multiple continuous outcomes. The main objectives are to (1) impute unobserved arms by considering them as unknown parameters which can be modeled along with the other unknown, (2) incorporate between-treatment or between-outcome correlations, and (3) introduce an arm-based approach that features fewer constraints than standard contrast-based methods. We also rank the treatments with a sensible scoring system incorporating such multiple outcomes. We apply our models to the OA data and interpret our findings. Finally, we include a simulation study to investigate the performance of our methods in terms of Type I error, power, and the probability of incorrectly selecting the best treatment.