In clinical medicine, due to some accidents will inevitably produce the situation of missing data, this study for its with missing and truncated data, the use of mathematical statistics methods for inference supplement. After classifying the types of incomplete data, the article utilizes the great likelihood and empirical likelihood to form a linear statistical model to infer such data. It verifies it through simulation experiments and example analysis. In the simulation experiment, for the case of the same missing probability, as the number of samples increases from 150 to 300, the bias, variance, and mean square error of this paper’s algorithm in parameter β1 are reduced to 0.0122, 0.1435, and 0.1441, respectively. In the actual statistical inference analysis of cardiac disease and heart transplantation, the standard error of this paper’s method reduces by 0.0576 compared with that of CAA, and the inference The results are by the reality. In clinical medicine, this study proposes a practical statistical extrapolation method and a realization path for objective interpretation when incomplete data is present.