In early May, the Oklahoma Medical Board suspended a Midwest City doctor’s license for six months after an investigation connected two prescription overdose deaths to his prescribing practices.

But it took four weeks before Dr. Dwayne Roush’s suspension became official.

In mid-January, the medical board barred Dr. H. Peter Koenen-Myers Jr. from reapplying for his lapsed medical license after determining he had overprescribed opioids to a patient who later died of an overdose.

It took 10 weeks before the suspension went into effect, board records show.

Since 2015, some state licensure boards fo...