In this paper, we propose EDA methodologies for efficient, datapath-wide reliability analysis under Bias Temperature Instability (BTI). The proposed EDA flow combines the efficiency of atomistic, pseudo-transient BTI modeling with the accuracy of commercial Static Timing Analysis (STA) tools. In order to reduce the transistor inventory that needs to be tracked by the STA solver, we develop a thresholdpruning methodology to identify the variation-critical part of a design. That way, we accelerate variation-aware STA iterations, with a maximum speedup of 6.82x achieved for representative benchmark circuits. We substantiate the efficiency of the proposed framework for realistic designs. For a CPU datapath, our threshold-pruning technique outperforms built-in pruning commands of the STA solver by 16.87% in terms of runtime improvement. We demonstrate the impact of BTI after three years of operation, with clock frequency degradation up to 24% and functional yield reduction below 90% for higher frequencies.