A systematic review published by the Campbell Collaboration summarises the research on the correlation between reading-related preschool predictors, such as code-related skills  and linguistic comprehension, and later reading comprehension skills.

Sixty-four longitudinal studies met the eligibility criteria for the review. These studies spanned 1986 to 2016 and were mostly carried out in the US, Europe and Australia. Overall, the findings of the review found that:

• Code-related skills (rhyme awareness, phoneme awareness, letter knowledge and rapid automatised naming) are most important for reading comprehension in beginning readers.
• However, linguistic comprehension (grammar and vocabulary) gradually takes over as children become older.
• All predictors, except for non-word repetition, were moderately to strongly correlated with later reading comprehension.
• Non-word repetition had only a weak to moderate correlation to later reading comprehension ability.

These results suggest a need for a broad focus on language skills in preschool-age children in order to establish a strong foundation for reading comprehension.

Source: Hjetland, H. N., Brinchmann, E.l., Scherer, R., & Melby-Lervåg, M. (2017). Preschool predictors of later reading comprehension ability: a systematic review. Oslo, Norway: Campbell Systematic Reviews.