This study finds little correlation between the two:
"We evaluated the association of circulating levels of total and free testosterone, and of sex hormone binding globulin (SHBG), with the risk of cancers of the pancreas, kidney, and brain, and of total and free estradiol with the risk of kidney cancer, in the UK Biobank cohort study (n=425,793; 225 pancreatic cancers, 749 kidney cancers, 467 brain cancers). Multivariable Cox proportional hazards models were used to estimate hazard ratios and 95% confidence intervals for the associations. Testosterone and SHBG levels were not associated with risk of pancreatic cancer. Most of the associations for the other two anatomic sites were null. There were inverse associations between total testosterone and brain cancer in men and between SHBG and risk of kidney cancer in the total sample and in women. Estradiol was not associated with the risk of kidney cancer. The results of this study provide little support for associations between sex hormones/SHBG and risk of cancers of the pancreas, kidney, and brain."
"We evaluated the association of circulating levels of total and free testosterone, and of sex hormone binding globulin (SHBG), with the risk of cancers of the pancreas, kidney, and brain, and of total and free estradiol with the risk of kidney cancer, in the UK Biobank cohort study (n=425,793; 225 pancreatic cancers, 749 kidney cancers, 467 brain cancers). Multivariable Cox proportional hazards models were used to estimate hazard ratios and 95% confidence intervals for the associations. Testosterone and SHBG levels were not associated with risk of pancreatic cancer. Most of the associations for the other two anatomic sites were null. There were inverse associations between total testosterone and brain cancer in men and between SHBG and risk of kidney cancer in the total sample and in women. Estradiol was not associated with the risk of kidney cancer. The results of this study provide little support for associations between sex hormones/SHBG and risk of cancers of the pancreas, kidney, and brain."