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For the situation, in addition to competing risk and interval censoring, another feature that makes the analysis difficult is that the failure cause may be unknown or missing. Most existing methods for addressing these challenges rely on two-stage estimation procedures, which could suffer efficiency loss and high computational cost. To overcome these, we propose a direct likelihood approach based on a mixture model framework. The proposed method accounts for both competing risks and missingness of event types directly in a likelihood function and facilitates estimation through a sieve maximum likelihood estimation, simplifying the estimation procedure and thus enhancing the estimation efficiency. The consistency and asymptotic normality of the resulting estimators are established, and the idea behind the proposed approach can be extended to other competing risks model frameworks. 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