Both groups received identical-looking pills. Is that allocation concealment?

Identical-looking pills are good, but they are about blinding, not allocation concealment. Allocation concealment means that the people enrolling patients cannot know the next assignment until the patient has been enrolled, for example with sequentially numbered, opaque, sealed envelopes, or with central randomization, where an office or computer system away from the clinic reveals the assignment only after enrollment.

Block randomization is an accepted and well-regarded method of random allocation. Filling the blocks in order of enrollment within each clinic is simply how blocked randomization by clinic works: the sequence is prepared in advance, and each new patient receives the next assignment on the list. What makes it random is that the order of assignments within each block was generated by chance, for example by computer. It would not be random if the order of enrollment itself decided the group, as in alternation, or if assignment followed date of birth.

Please read the methods again and check two things. First, does the paper say the order within the blocks was random? If it only says that blocks were used, the RoB 2 guidance answers the question about a random sequence with "no information". Second, how was the allocation concealed? With small blocks of a fixed size, a recruiter who sees each assignment may be able to predict the last ones in a block. If the paper does not say how allocation was concealed, the randomization domain will usually be rated "some concerns".

References

• Higgins JPT, Savović J, Page MJ, Elbers RG, Sterne JAC. Chapter 8: Assessing risk of bias in a randomized trial (last updated October 2019), Sections 8.3.1 and 8.3.2. In: Cochrane Handbook for Systematic Reviews of Interventions, version 6.5. Cochrane, 2024.
• Higgins JPT, Savović J, Page MJ, Sterne JAC (editors). Revised Cochrane risk-of-bias tool for randomized trials (RoB 2): full guidance document, 22 August 2019. https://www.riskofbias.info