Doubling Time

Serum PSA is measured using the Hybritech assay (San Diego, CA). The PSA doubling time (DT) is calculated assuming that PSA changes over time in an exponential fashion (Patel 1997):
(1)

where PSA(t) is the PSA level at time t after study enrolment, PSA(0) is the PSA level at baseline, λ and γ are linear and quadratic rates. Taking a natural logarithms of both side of equation 1 yields:
(2)

and this is the equation of a quadratic line with intercept lnPSA(0), linear slope λ and curvature γ. When PSA level increases twice (t = DT), the equation 2 is changed into . Therefore, the corresponding PSA DT is then:
(3)

If we simply consider the linear slope (γ = 0), the equation 2 becomes and the PSA DT is defined as ln2/λ (Pound 1999).