Final answer:
The question appears to pertain to fertility treatment methods with the lowest complication rate, yet the provided options, in vitro fertilization and surgical ligation or re-ligation of the fallopian tubes, are treatments for infertility rather than being ranked by complication rates.
Step-by-step explanation:
The blank in question seems to refer to a method or process related to fertility treatment with the lowest complication rate. However, it's not clear what specific term is expected to fill the blank as the provided context refers to treatment options rather than a particular method with the lowest complication rate. Treatment options such as in vitro fertilization are available for individuals facing fertility challenges. This method involves fertilizing an egg outside of the body and then implanting it into the uterus. Another surgical option for overcoming certain types of infertility issues is the surgical ligation of fallopian tubes, which intentionally seals the tubes, or surgical removal of an obstruction followed by the re-ligation of the fallopian tubes.