Response adaptive randomization methods that skew allocation towards the superior treatment arm in clinical trials have been shown to maintain power and maximize total expected response. These methods assume patients that withdraw from the study have outcomes similar to those that complete the study. However, if the consequence of withdrawal is the discontinuation from treatment, this assumption may not be valid, leading to allocation that has less than optimal characteristics. The flaws of this method are particularly prevalent if dropout rates differ between the treatment arms. We propose a response adaptive allocation ratio that adjusts for dropout, unrelated to unobserved treatment response, and factors in losses associated with discontinuation of treatment. When there is no dropout, our allocation ratio reduces to previously published response adaptive allocation ratios. We evaluate the features of our novel allocation ratio using traditional clinical trial operating characteristics.