Crude rate and ASR in research

#1
Hello! New here. I am not a native english speaker so I’m sorry in advance if I make a mistake.

I need clarification for Crude rate and ASR (age standardized raze) equasions.

Part of my research is looking at trends in cancer and comparing incidence and morality rates country wide and state wide (this is the best explanation I can give).

I made an Excel database with all of the relevant data - frequencies of cancer patients divided by year and gender (age is not a variable that is important in this research) both for the country (population around 4 milion) and state in county (population around 110 thousand). I searched the equastions and calculated the crude rates and ASR from the data and I want to do charts that represent the trends in that type of cancer through the years. But I have a feeling (looking at other research) that I have made a mistake somewhere in the calculations.

So I have a question:

When I am calculating the crude rate and ASR for the state do I use the population and stand. population of the state (110 thousand) people or do I still use the population od the country (4 milion)?

Example:

For the country:

Number of xy cancer type male patients in 2015 was 1890 for the whole country population 4 milion. The crude rate (looking at the world stand) is 1890/4 000 000*100 000. And the ASR is crude rate*stand popl where stand popul is number od males that year/4 000 000.

For the state:
Number of xy cancer type male patients in 2015 was 55 in the state population 110 thousand. The crude rate (looking at the world stand) is then 55/110 000*100 000 or is it 55/4 000 000*100 000?

And the ASR is crude rate*stand popl where stand popul is number od males that year/4 000 000 or numer of males that year/110 000????

I am really confused since I researched everything before I started and the math seemd not so bad so when I was done I was happy and now I see that other researches have extremly different ASR figures (smaller numbers) that I have, and they have similar raw score numbers to mine (same county population, similar state population, similar number of cancer patients).

Can somebody please help me to confirm or dispute my math?

Thank you in advance!