Background The log-binomial model has been suggested as the gold standard for estimation of relative risks (RRs) in epidemiological studies. However, it often fails to converge. Previous studies have explored alternative approaches, but the problem has received little attention where data are clustered.

Methods Using clustered data from the CUPID study, we compared the magnitude and precision of risk estimates when different analytical approaches were applied to assess associations of risk factors with low back and elbow pain. The analytical models were: Zang&Yu and modified Zang&Yu random-intercept (RI) logistic regression, RI Poisson regression (without and with robust standard errors (SEs)), the frailty model, and complementary log-log regression (with robust SEs and RI). Estimates from these methods and their calculated precision were compared to those from RI log-binomial models. The measure of comparison for RRs was defined as

Difference = [RR from method – RR from log-binomial method]/average of the two RRs.

Results RRs from the RI Poisson and frailty models were very similar to those from the RI log-binomial model (all differences <10%). Estimates from other approaches deviated from the RI log-binomial estimates. Unlike estimates from the Zang&Yu method, those from the modified Zang&Yu method performed poorly, with a tendency to overestimate RRs, particularly in adjusted models. Precision of RRs from the RI Poisson model with robust SEs was very similar to that from the RI log-binomial model. The frailty, RI Poisson (without robust SEs), and RI complementary log-log models indicated precision for RRs that was slightly greater than but comparable to that from the RI log-binomial model.

Conclusions These results support the use of RI Poisson regression with robust SEs for estimating RRs when the RI log-binomial fails to converge. Alternative models may be used when the focus is more on point estimates of RRs than their precision.