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Two highly publicized studies applied different analytical approaches, a dynamic marginal structural model and a multiple imputation method, to different observational databases and came up with different conclusions. Discrepancies between the two studies' results could be due to differences between patient populations, fundamental differences between statistical methods, or differences between implementation details. For example, the two studies adjusted for different covariates, compared different thresholds, and had different criteria for qualifying measurements. If both analytical approaches were applied to the same cohort holding technical details constant, would their results be similar? In this study, we applied both statistical approaches using observational data from 12,708 HIV\u2010infected persons throughout the USA. We held technical details constant between the two methods and then repeated analyses varying technical details to understand what impact they had on findings. We also present results applying both approaches to simulated data. Results were similar, although not identical, when technical details were held constant between the two statistical methods. Confidence intervals for the dynamic marginal structural model tended to be wider than those from the imputation approach, although this may have been due in part to additional external data used in the imputation analysis. We also consider differences in the estimands, required data, and assumptions of the two statistical methods. Our study provides insights into assessing optimal dynamic treatment regimes in the context of starting antiretroviral therapy and in more general settings. 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