How to calculate small signal parameter for a BJT when early voltage is taken into consideration?

I have proved one formula of

output impedance
ro = (Va+Vce)/Ic = Va/Ic’

where Ic is collector current and Ic’ is collector current neglecting early effect.

But reading from standard texts other formulas are diverging like for
gm{trans-conductance} = Ic/Vt

is formula given in Razavi, Neamen .

But I am getting

gm=β/rb = Ic’/Vt

where rb is base emitter resistance and β is common emitter current gain.

Am I doing some mistake or its rather approximation the books are taking and in later case plz comment if the approximation is rather universally valid.