Z-test for comparing two estimator values?

#1
Dear statistics community,

My supervisor asked me to compare values of Pohar Perme estimator of net survival in two regions of the country using Z-test. Am I right that we cannot use Z-test for comparing these estimator values? Pohar Perme estimator of net survival is defined in the paper available here (page 7 in PDF file or 191 acc. to page count): https://www.researchgate.net/public...ting_and_Modelling_Relative_Survival/download
I argue that Z-test can be used only for comparing means and fractions. Pohar Perme estimator of net survival is, actually, a weighted fraction. Am I right?

Thank you in advance.