How can two biological variables have opposing secular trends, yet be positively related? A demonstration using timing of puberty and adult height.

Timing of puberty and adult height have opposing secular trends yet are positively associated in individuals. We demonstrate this using data from a single sample and discuss possible statistical and epidemiological reasons behind it. The sample comprised 365 females from Fels Longitudinal Study born 1929-1992. We used Super-Imposition by Translation and Rotation (SITAR) to estimate individual age at peak height velocity (PHV) and PHV from serial height data (8149 observations between 5 and 24 years). General linear regression was used to investigate the association between height and age at PHV, and secular trends in height, age at PHV and PHV. Although adult height increased 0.42 (95% CI: 0.08, 0.77) cm per decade, and age at PHV decreased 1.14 (-3.74, 1.45) weeks per decade, adult height increased by 2.44 (1.78, 3.10) cm per year higher age at PHV. We found tentative evidence of the positive association between age at PHV and adult height strengthened 0.25 (-0.09, 0.59) cm each decade. Secular trends in related variables may differ if the between-individual and between-cohort associations are different. To understand if a secular trend in one variable has contributed to a trend in another, each needs to be modelled over time, together with the changing association between them.