The Neyman-Pearson lemma, i.e., the likelihood ratio test and its generalized version, have been used for the development of the synthetic aperture radar (SAR) change detection methods. For detecting changes caused by targets on the ground such as vehicles, a target model, or at least certain assumptions concerning the targets, are always required for deriving a statistical hypothesis test. Without the prior knowledge on targets, it is difficult to make any assumption. An inappropriate assumption can degrade change detection performance significantly. To avoid this technical issue, the new forms of likelihood ratio test for SAR change detection are introduced in this paper. The proposed forms are shown to be very flexible. They can be utilized to develop change detection methods for different types of data, e.g., data in scalar form, data in vector form, data represented in complex number, and data represented in real number. The flexibility of the proposed forms is also shown by the the capability to implement change detection methods in the iterative and non-iterative ways. For the illustration purpose, a new change detection method is developed on one of the introduced forms and tested using TanDEM-X data measured in Karlshamn, Sweden in 2016. Author