Eligibility Criteria:
Inclusion Criteria:
* Ambulatory, postmenopausal women (no vaginal bleeding for at least 2 years prior to screening) with osteoporosis
* Bone mineral density (BMD) T-score of at least -2.5 at femoral neck (FN), total hip (TH), or lumbar spine (LS) (Lumbar vertebrae L1-L4, with at least 2 evaluable vertebrae), with or without atraumatic fracture after menopause, OR
* BMD T-score of at least -1.5 at FN, TH, or LS (L1-L4, with at least 2 evaluable vertebrae), and 1 or more atraumatic fractures after menopause (vertebral or nonvertebral). Nonvertebral fracture sites allowed are wrist, hip, pelvis, rib, humerus, clavicle, leg (femur, tibia, and fibula, excluding ankle)
* Laboratory values for serum calcium, parathyroid hormone (PTH), and alkaline phosphatase must be within the normal reference range
Exclusion Criteria:
* Has an increased risk of osteosarcoma (bone tumor); this includes Paget's disease of bone, a previous bone tumor, or radiation involving the skeleton
* Has an allergy or intolerance to teriparatide or denosumab and/or is a poor candidate for teriparatide or denosumab treatment (investigator should refer to local product prescribing information)
* Has a history of exposure to DEM or TET therapy in the 12 months prior to screening or a known allergy to DEM or TET
* Has a condition that could put the participant at additional risk of an adverse event (AE) due to the bone biopsy procedure (for example, bleeding disorder)
* Has undergone 2 previous iliac crest bone biopsies (1 in each iliac crest)
* Has a 25-hydroxyvitamin D concentration of \<10 nanograms per milliliter (ng/mL)
* Has currently active or suspected (within 1 year prior to enrollment) diseases that affect bone metabolism, other than osteoporosis (such as renal osteodystrophy, hyperthyroidism, osteomalacia, or hyperparathyroidism)
* Has a history of certain cancers within 5 years prior to trial entry
* Current or recent (within 1 year prior to enrollment) celiac disease, inflammatory bowel disease, gastric bypass, or other malabsorption syndrome
* Has significantly impaired hepatic or renal function
* Has had treatment with systemic glucocorticoids in doses ≥5 mg/day prednisone/day or equivalent in the 6 calendar months prior to screening
* Has taken any intravenous osteoporosis medication
* Has had prior treatment with other bisphosphonates and not been off of them for a specific period of time before trial entry
* Has participated in any other clinical trial studying teriparatide, PTH, PTH analog, or denosumab, or prior or current treatment with teriparatide, PTH, PTH analog, or denosumab