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Current status data arise when the exact timing of an event is unobserved, and it is only known at a given point in time whether or not the event has occurred. Recently Lin et al. (1998) studied the additive semiparametric hazards model for current status data. They showed that the analysis of current status data under the additive hazards model reduces to ordinary Cox regression under the assumption that a proportional hazards model may be used to describe the monitoring intensity. This analysis does not make efficient use of data, and in some cases it may not be appropriate to assume a proportional hazards model for the monitoring times. We study the semiparametric hazards model for current status data but make use of the semiparametric efficient score function. The suggested approach has the advantages that it is efficient in that it reaches the semiparametric information bound, and it does not involve any modelling of the monitoring times.