A medical journal study is figuring prominently in a federal judge’s decision whether to delay a new requirement that drug companies include list prices in TV advertising.

Attorneys for Merck & Co., Eli Lilly and Co., and Amgen Inc. argued last week that the Department of Health and Human Services and the Centers for Medicare & Medicaid Services are violating their First Amendment rights; lack the statutory authority to impose such a requirement; and would only mislead the public about drug costs because few patients ever pay the wholesale, or “list,” price.

Judge Amit P. Mehta said he would...