The N.F.L. and its doctors have consistently dismissed independent studies showing unusual cognitive decline in former players. They insist that a long-term study by the league’s committee on concussions, expected to be published in several years, will be the authoritative analysis.

But that study is fraught with statistical, systemic and conflict-of-interest problems that make it inappropriate to examine the issue, according to many experts in epidemiology, dementia and health policy who assessed the study’s design. Another voice belonged to a member of the House Judiciary Committee, which will hold a hearing on football brain injuries Wednesday.

“Hey, why don’t we let tobacco companies determine whether smoking is bad for your health or not?” said Representative Linda T. Sanchez, Democrat of California and a member of the Judiciary Committee. “It’s a very appropriate metaphor.”

Every independent expert in epidemiology and neurology contacted by The New York Times cited at least one of the following issues: that the study’s paucity of subjects will leave it unable to find any statistically significant difference in dementia rates; that a study financed by the N.F.L. and run by its committee doctors cannot be considered trustworthy; and that Dr. Ira Casson, the league’s primary voice in discrediting all outside evidence, should not personally be conducting all of the neurological examinations.