Adherence to the intervention?

Does " Adherence to the intervention was high" mean "the number of the people who insisted daily taking multivitamin was high"?

Context:

Second, Grodstein and coworkers evaluated the efficacy of a daily multivitamin to prevent cognitive decline among 5947 men aged 65 years or older participating in the Physicians' Health Study II. After 12 years of follow-up, there were no differences between the multivitamin and placebo groups in overall cognitive performance or verbal memory. Adherence to the intervention was high, and the large sample size resulted in precise estimates showing that use of a multivitamin supplement in a well-nourished elderly population did not prevent cognitive decline.