Truncated binary data occurs when a group of individuals, who each have a binary response, are observed only if one or more of the individuals has a positive response. In this paper the group will be taken to be a motor vehicle accident and the binary response taken to be survival or death. We compare two regression techniques that can be used for truncated binary data. The first procedure, conditional logistic regression (Breslow and Day, 1980, Statistical Methods in Cancer Research. 1: The Analysis of Case-Control Studies. No. 32. Lyon: IARC) conditions on the actual number of deaths, and has been previously used for this type of data. The second procedure, truncated logistic regression, conditions on there being at least one death. It is computationally simpler than conditional logistic for groups of size greater than two and can be considerably more efficient. A major difference between the two methods is that only truncated logistic regression requires a knowledge of group level covariates and allows estimation of group level effects.