Children when they are in the 18 month age range don't have the words yet to respond to others at their level (other children). Here is a list of things that work with this age range.
1. When you see a child looking frustrated and in a situation where biting is likely get there quickly and calmly. Use words to fill in what you think the child would say to the other child and use hand signals to help send the message. Direct the child to hold up their hand and say "Stop."
2. If you have a child that just appears to like biting things then it is helpful to give the child a biting cloth (small knotted washcloth) that they can pull out and chew on when they are stressed (For the old folks think of Jerry Tarkanian).
3. Sometimes biting is a reflection of a child having tooth issues. Remember the earlier years when the child was teething. They got relief from chewing on one of those cool biting things.
4. So what if you have a child that seems to bite others around the same time of day? I had a boy named David that would bite someone just before snack every day (okay he didn't bite every day, but when he did bite that was when it was). We learned to make him the first one in to wash his hands and head to the snack table and the problem disappeared.
5. With the example of Caroline and Patrick, it was a rare occurance. Biting for that age should be thought of as an aggressive act that can fit easily into one of the four types of aggression. In his case it was instrumental aggression. What he wanted was to get her to stop. After he bit, she stopped.
6. I have only had two children that would look at you and tell you they were going to hurt a specific person or tell that child themself that they were about to get hurt prior to launching an attack. Both cases were children with multiple other issues that they were dealing with and it was important to deal with the individual behaviors while also searching for a more global understanding of what would work. One of these children is now graduating from college with a degree in special education and he wants to work with young children with emotional problems. In his case I had him for two years and the consistency of the methods used to help him made the most difference in his progress.
7. I just thought of another child. This had more to do with the child who was the victim than the biter. She had three different children bite her over a period of a few weeks. They were all about 30 months old and they really thought she was the most wonderful child in the room and they couldn't get enough of her. This was of great concern to her mother who worried that her daughter from an early age had "victim" pinned on her. In that case where we focused on was making her more assertive and developing play skills. That made the difference.
When looking at biting it is important to consider all of the factors and make a judgment. Think about age, developmental abilities and inabilities, situation, who was involved, time of day, location where it happened, where did the bite take place, was it in response to anything or apparently isolated, etc.