Type 1 diabetes is an autoimmune disease affecting 5-10\% of diabetic people worldwide. It is mediated by T cells that destroy pancreatic beta cells that secrete insulin responsible for regulating glucose homeostasis. The disease is associated with a series of conventional and novel anti-islet autoantibodies that may be present for years in high-risk subjects prior to the onset of hyperglycemia. Experimental evidence revealed that patients that tested positive for conventional autoantibodies take longer on average to develop the disease (up to 15 years) than those that tested positive for novel autoantibodies (less than 10 years). We test the hypothesis that T-cell receptor binding affinity (T-cell avidity) and killing efficacy are responsible for the difference between fast and slow progressors by building a series of mathematical models. The models reveal that low-avidity, low-efficacy T-cell clones can compete with high-avidity, high-efficacy clones to confer a degree of protection. We assume that T-cell avidity is correlated with the binding affinity of autoantibodies to the same peptide and use antibody level as a read-out that can be compared to experiments and ultimately used to develop better methods of predicting patient outcomes.