Repeated ordinal outcomes capture how treatment benefits and harms evolve over time. We develop doubly robust estimation and inference for visit-specific win probabilities and their prespecified weighted summaries, with Desirability of Outcome Ranking as a motivating example. Baseline confounding is addressed through augmented inverse-probability weighting (AIPW) of treatment-specific marginal category probabilities or joint multinomial targeted maximum likelihood estimation (TMLE). We consider fold-specific and pooled targeting and establish conditions for double-robust consistency and semiparametric efficiency under participant-level cross-fitting. When only one nuisance model is correctly specified, inference based only on the efficient influence function may be invalid. For smooth parametric nuisance models, we derive covariance corrections from the complete estimating procedure, including targeting. When a correctly specified propensity model is estimated by maximum likelihood, a simplified score correction accommodates convergent flexible outcome learners without requiring their derivatives. The corrected covariance estimators retain within-participant dependence and support visit-specific, weighted-summary, and joint inference across repeated assessments. Simulations supported double robustness, demonstrated the importance of cross-fitting with overfit learners, and showed improved marginal and joint confidence coverage with the proposed corrections. TMLE, particularly with pooled targeting, often had lower root mean squared error under adequate treatment overlap, whereas AIPW was more stable under weak overlap. An electronic health record study of hospitalized adults with an acute respiratory illness illustrates how the trajectory and weighted summary reveal complementary aspects of the treatment comparison.

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