How to Properly Set Up If in While Loop

I'm going to add the rest of the functionality to the program later it's still in it's early stages, but I cant seem to get out of the while loop for some reason even though the if statement is within it and under the menu. Here's the code so far.

continue="true"

#while loop to keep the code running till the user inputs Q
while [ $continue = "true" ] 

#loop start
do
        #clearing screen before showing the menu
        clear
        echo "A to Create a user account"
        echo "B to Delete a user account"
        echo "C to Change Supplementary Group for a user account"
        echo "D to Create a user account"
        echo "E to Delete a user account"
        echo "F to Change Supplementary Group for a user account"
        echo "Q to Quit"
        read -p "What would you like to do?:" choice

        #Test to end the program
        if [ $choice = 'Q' ] || [ $choice = 'q']
                then
                $continue="false"
        fi
#loop end
done```