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In large cohort studies it can be impractical to report individual data that only summary or aggregated data are available. Using aggregated data from Bernoulli trials is expected to result in overdispersion so that a quasi-binomial approach would seem feasible. We show that when applied to aggregated data arising from cohorts of individuals according to a chain binomial model, the quasi-binomial model results in biased estimates. We propose an alternate calibration estimator and demonstrate its improved performance by simulations. The calibration method is then applied to model the probability of leaving a personal emergency link service in Hong Kong. [ABSTRACT FROM AUTHOR]