Leuprolide Acetate or Goserelin Acetate Compared With Observation in Treating Patients With High-Risk Prostate Cancer Who Have Undergone Radical Prostatectomy

Inclusion Criteria:

* PRE-REGISTRATION:
* Informed consent explained and signed prior to any study related procedures
* Patients with any one of the following "high risk" criteria:

  * Clinical or pathological Gleason score 8-10
  * Prostate-specific antigen (PSA) \> 20 ng/ml at initial presentation prior to radical prostatectomy
* Willingness to provide mandatory tissue for research purposes
* Willingness to provide mandatory blood for research purposes
* Has no history of androgen deprivation therapy within the past 6 months or has been treated neoadjuvantly up to 6 months prior to radical prostatectomy with the following agents; luteinizing hormone-releasing hormone (LHRH) agonists, anti-androgens, 5 alpha-reductase inhibitors, and peripheral anti-androgens
* REGISTRATION:
* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2; or Karnofsky performance of \> 60%
* Patients with any one of the following "high risk" criteria:

  * Gleason, prostate specific antigen, seminal vesicle and margin status (GPSM) score \>= 10 \[GS + 1\*(PSA 4-10)+2\*(PSA 10.1-20)+3\*(PSA \> 20)+2\*(seminal vesicular or nodal involvement) +2\*(margin)\](determined post radical prostatectomy)
  * Post prostatectomy seminal vesicle invasion (pT3b) or pT4
  * Two or less microscopic lymph nodal metastasis determined at the time of prostatectomy OR
  * Gleason 4+3 at the time of prostatectomy with margin positivity
* Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) =\< 2 x institutional upper limit of normal (ULN)
* Total bilirubin =\< 2 x institutional ULN
* For patients identified as high-risk on the basis of pathological criteria after undergoing radical prostatectomy: interval time for study enrollment after radical prostatectomy will be =\< 28 days of the prostatectomy
* For patients identified as high-risk prior to undergoing radical prostatectomy: patients presenting with a high Gleason score (8-10) and/or a PSA \> 20 ng/ml are deemed eligible for study participation and study registration as long as the eligibility criteria is reconfirmed post radical prostatectomy; these patient groups may choose to register prior to or after prostatectomy
* Study randomization must occur =\< 28 days of radical prostatectomy; all patients consented on the trial, whether consented in the pre-prostatectomy or post-prostatectomy period, will be randomized to study treatments =\< 28 days of prostatectomy
* Ability to complete questionnaire(s) by themselves or with assistance

Exclusion Criteria:

* PRE-REGISTRATION
* Transitional cell, small cell, or squamous cell carcinoma of the prostate; NOTE: patients consented for participation prior to prostatectomy, if detected to have above listed histo-pathologies after prostatectomy will be deemed ineligible and not proceed to study randomization
* History of primary prostate cancer treatment
* Evidence of clinical nodal disease (N1) or grossly evident metastasis at the time of enrollment
* History of bilateral orchiectomy; unilateral orchiectomy with normal range serum testosterone levels will be allowed for enrollment
* Evidence of metastasis on radiographic metastatic workup within a preceding period of 4 months from the time of study entry, including whole body radionuclide bone scan, computed tomography (CT) and/or magnetic resonance (MR) scan of the pelvis and abdomen; otherwise will perform at the time of the baseline tests and result must be normal to continue on study; results of ProstaScint or other radionuclide scans, excluding radionuclide bone scans, will NOT be used to establish metastatic disease if all other studies are negative
* Receiving other experimental drugs =\< 4 weeks prior to consenting
* Uncontrolled infection
* History of other cancer, excluding squamous cell and basal cell skin cancers, within the preceding 2 years
* Documented history of human immunodeficiency virus (HIV) positivity or other acquired immunodeficiency disorder, congenital immunodeficiency disorder, or history of organ transplantation
* Unable to follow up every three months for the first year to Mayo Clinic, Rochester for receiving LHRH analogues or study monitoring
* REGISTRATION:
* Uncontrolled infection
* Unable to follow up every three months for the first year to Mayo Clinic, Rochester for receiving LHRH analogues or study monitoring