Rapidly progressive glomerulonephritis (RPGN) is a life-theatening nephritis with a rapid decline in renal function. In this paper, we examine the three alternative treatments relative to the most commonly-used oral steroid for the two prevalent forms of RPGN, called PautiCrGN and MPA, in Japan. The response “Exitus” is potentially non-ignorably missing because the data were reported by those who administered the treatment. We use the method proposed in Ibrahim (1996) for estimating parameters in binomial logistic model when the missing response is potentially nonignorable. For PautiCrGN patients, we found that the three alternative treatments did not seem to affect the survival of the patients. MPA patients who underwent the steroidpulse or the cyclophosphamide with the oral steroid, seemed less likely to have survived compared with those who received the oral steroid only. For PautiCrGN patients, their exitus was not non-ignorably missing at first sight, and its missingness increased when the patients received the combined treatment. If, however, steroidpulse and/ or cyclophosphamide were additionally prescribed as the patients' conditions deteriorated, then the observed correlation above may prove the existence of non-ignorably missing exitus instead, because the exitus of serious patients might have been under-reported precisely because of their conditions.