A study of the efficacy of pneumococcal vaccination in the elderly was described as follows22:

We conducted a 2-year retrospective cohort study among all elderly members of a staff-model managed care organization who had a baseline diagnosis of chronic lung disease. The study outcomes were assessed over 2 years, from November 15, 1993, through November 14, 1995, and included hospitalizations for pneumonia and influenza.

Of 1898 subjects, 1280 (67%) had received pneumococcal vaccination. This included 843 (44%) who were vaccinated prior to November 15, 1993 and an additional 437 (23%) vaccinated after that date. During the follow-up period there were 174 hospitalizations for pneumonia and influenza. The observed cumulative incidence was 138 per 1000 in the 618 unvaccinated persons and 70 per 1000 in the 1280 persons following their receipt of vaccination. This represents a 49% reduction in hospitalization for pneumonia and influenza.

Even if there were neither misclassification nor confounding in this study, the estimate of benefit associated with pneumococcal vaccination in elderly patients with chronic lung disease must be biased.

a. Why? In which direction?

b. How could the analysis be conducted to remove this source of bias?