MIX sugar, pumpkin pie spice and corn starch in a large bowl. Cut apples into 1/4-inch thick slices and place in a separate bowl. Sprinkle apples with lemon juice and rum; add to dry ingredients. Stir to combine. Place in pie crust. Dot with 2 tablespoons of butter. Drizzle with caramel sauce.
STIR flour and brown sugar together in small bowl. Cut in 1/4 cup butter until mixture resembles coarse meal. Sprinkle evenly over top of pie.
BAKE in a preheated 400°F oven for 10 minutes. Reduce heat to 350°F and bake an additional 40 to 50 minutes, until golden brown. Serve warm with vanilla ice cream, if desired.