Efforts by health insurers to stem the opioid crisis appear to be making some headway. For instance, Philadelphia-based Independence Blue Cross has been making inroads, and took credit for helping decrease the number of overdose deaths in the city in the first quarter of 2018.

The death rate in Philadelphia declined in the first quarter of 2018, when there were 50 fewer deaths than the previous period of 2017, according to Independence Blue Cross, a 2.5-million member insurer that serves...