). Standard errors for phase-shift and amplitude were estimated as sums of standard errors for each model coefficient minus covariance. We evaluated the correlation between phase and amplitude terms for influenza A and B (combined), influenza A, and influenza B and pneumococcal sine waves, by year, by calculating Spearman correlation coefficients. Heterogeneity of phase and amplitude terms for S. pneumoniae, influenza A and B (combined), influenza A, and influenza B was assessed through meta-analysis using Cochran's Q test, and quantified using I 2 statistics. Differences in the magnitude of heterogeneity of amplitude or phase by pathogen was assessed using Knepp and Entwisle's method for assessing difference between chisquared statistics [12] . As the 2003/2004 and 2008/2009 influenza seasons were outliers with respect to timing and amplitude, and we also performed sensitivity analyses in which these years were excluded.