Amide-linked conjugate compounds and uses thereof

A compound, or a pharmaceutically acceptable salt thereof, the compound comprising at least one EP4 agonist linked to an amide linker through an ester bond and an amino bisphosphonate linked to the amide linker through an amide bond,

• wherein the EP4 agonist is
• wherein:
• X is —CH2—, —S—, —O—, or —NH—;
• Y is COOR′, optionally substituted tetrazole, or C(O)NHSO2R;
• R is optionally substituted alkyl with one to ten carbon atoms or optionally substituted aryl;
• n is 1, 2, or 3;
• R1 is independently H or halogen;
• Ar is aryl, substituted aryl, or heteroaryl;
• R′ is H or alkyl with one to ten carbon atoms, and
• is a double or single bond;
• and wherein the amide linker is
• wherein
• R3 is each independently H, OR′, halogen, CN, or C(O)R′,
• R′ is each independently H or alkyl with one to ten carbon atoms, or the two R's form a ring of up to 6 carbons,
• NHR″, if present, is the amino group of the amino bisphosphonate,
• q, if present, is 1 or 2,
• n, if present, is 1, 2 or 3,
• and
• wherein one or more of the aliphatic carboxylic acid groups can react with the C-15 hydroxyl group of the EP4 agonist to form the ester bond and the remaining carboxylic acid group can react with the amino group of the amino bisphosphonate to form the amide bond.