The Hanford Thyroid Disease Study (HTDS) is one of the largest and most complex epidemiologic studies of the relation between environmental exposures to I and thyroid disease. The study detected no dose-response relation using a 0.05 level for statistical significance. The results for thyroid cancer appear inconsistent with those from other studies of populations with similar exposures, and either reflect inadequate statistical power, bias, or unique relations between exposure and disease risk. In this paper, we explore these possibilities, and present evidence that the HTDS statistical power was inadequate due to complex uncertainties associated with the mathematical models and assumptions used to reconstruct individual doses. We conclude that, at the very least, the confidence intervals reported by the HTDS for thyroid cancer and other thyroid diseases are too narrow because they fail to reflect key uncertainties in the measurement-error structure. We recommend that the HTDS results be interpreted as inconclusive rather than as evidence for little or no disease risk from Hanford exposures.