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Organ-transplanted patients typically receive high amounts of immunosuppressive drugs (e.g., tacrolimus) as a mechanism to reduce their risk of organ rejection. However, due to the diabetogenic effect of these drugs, this practice exposes them to greater risk of New-Onset Diabetes After Trans-plant (NODAT), and hence, becoming insulin-dependent. This common conundrum of balancing the risk of organ rejection versus that of NODAT is further complicated due to various factors that create ambiguity in quantifying risks: (1) false-positive and false-negative errors of medical tests,(2) inevitable estimation errors when data sets are used, (3) variability among physicians’ attitudes towards ambiguous outcomes, and (4) dynamic and patient risk-profile dependent progression of health conditions. To address these challenges, we propose an ambiguous partially observable Markov decision process (APOMDP) framework, where dynamic optimization with respect to a “cloud” of possible models allows us to make decisions that are robust to misspecifications of risks. We first provide various structural results that facilitate characterizing the optimal policy. Using a clinical data set, we then compare the optimal policy to the current practice as well as some other bench-marks, and discuss various implications for both policy makers and physicians. In particular, our results show that substantial improvements are achievable in two important dimensions: (a) the quality-adjusted life expectancy (QALE) of patients, and (b) medical expenditures.