It's pretty hard to definitely prove individual occurence medical issues. For example, exposure to arsenic is known to increase risk of cancers. Even if you biopsy the tissue and find arsenic, you can't say for certain that is the cause - look at how some tobacco users live to 90 and never develop cancer, even if it's rare. It would probably be enough evidence in a court of law.
Large scale case studies can be good evidence depending on the nature of the particles being studied and how easy it is to control for other variables.