Preventive Human Papillomavirus (HPV) Vaccine Trial in Kidney Transplant Recipients

Inclusion Criteria:

* Candidate for renal transplant, expected to undergo transplant surgery \>= 30 days and =\< 12 months after enrollment

  * For potential participants on the institutional waiting list for deceased donor transplant, a study clinician confirms the candidate is likely to receive a transplant within the next 12 months, taking into account the candidate's priority on the waiting list, age, medical status, institutional policies, and scores like the Estimated Post-Transplant Survival (EPTS) Score and Calculated Panel Reactive Antibody (CPRA) percentage, etc
  * For potential participants expected to undergo a living donor transplant, one or more donor(s) have been identified and is/are in work-up (even though all work-up status may or may not be complete); a study clinician confirms the living donor transplant is likely to be scheduled within the next twelve months after taking into account donor work-up progress, age and medical status, and institutional policies
  * Notes:

    * Living and deceased donor transplant recipients: The study was originally restricted to participants who were expecting to receive only living donor renal transplants; however, less than a third of kidney transplants in the United States occur with kidneys from living donors; a majority of transplants are in the setting of donation of kidneys from deceased donors; to permit efficiencies in accrual, the study is amended (from version 3.5) to also open enrollment to recipients of deceased donor kidneys
    * Transplant recipients of both genders: The study was originally designed to be conducted only among women; however, in October 2018, the Food and Drug Administration (FDA) approved an age expansion indication for the Gardasil 9 HPV vaccine for both women and men up to 45 years (from the originally approved upper age limit of 26 years), thus opening a new clinical cancer preventative option for middle-age adults of both genders; the primary endpoint for the study is HPV-vaccine-type-specific seroconversion rates, which are not expected to be differential by gender, based on extrapolating from the uniformly high (\> 99%) seroconversion rates observed regardless of gender in studies among immunocompetent individuals; however, HPV vaccine-type-specific titer levels (GMT) differences by gender will be analyzed as a secondary endpoint, given variability in immune response titer levels observed between males and females in immunocompetent individuals (related to the differences in body mass index or hitherto unproven factors related to hormone-immune interactions); another advantage of expanding this study to males will be to facilitate efficiencies in accrual, since men constitute the majority (55%-65%) of all kidney transplant recipients in the United States; although a majority of current HPV-associated cancers among solid organ transplant recipients occur among women, there is increasing evidence of the link between HPV infection and oropharyngeal cancers that disproportionately affect men; HPV-related oropharyngeal cancers are now the most common HPV-related cancers in the United States, surpassing even the incidence of cervical cancer; the expansion of enrollment to men will also allow this study to look at the effect of HPV vaccination on persistence of oral HPV infection as a secondary/exploratory endpoint in the context of transplant-related immunosuppression
* Age 18-49 years. We have chosen to focus on adults aged 18-49 for this initial study in transplant recipients for a few reasons. Prior data for HPV vaccine response exists for adults up to 49 years of age, providing an important external comparison group for our study. Immune response and exposure wane as age increases and we want to minimize the potential for age-related confounding of our study outcome. For this initial trial, we thought it best to maintain homogeneity in the study population to the extent possible. Finally, given that about half of renal transplant recipients in the United States (U.S.) are between the ages of 18-49 years, selecting this age range permits efficiency in study accrual
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%)
* The effects of the Gardasil 9 HPV vaccine on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because there have been no adequate and well-controlled studies of Gardasil 9 in pregnant women, women who are able to become pregnant must have a confirmed negative pregnancy test result within the past 28 days prior to enrollment and must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; women who have had a both ovaries removed or a tubal ligation will not be required to have a pregnancy test; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately
* Ability to understand and the willingness to sign a written informed consent document and medical release form
* Willing and able to comply with trial protocol and follow-up

Exclusion Criteria:

* Previous prophylactic HPV vaccination
* Prior organ transplant
* Anticipated desensitization treatment; this decision to exclude a participant who may need desensitization will be based on the site clinician's judgement; desensitization procedures vary somewhat among the five participating transplant centers, which does not permit proposing uniform criteria across all study sites for determining exclusion due to desensitization; in general, women who have received a prior transplant, have unsuitable scores on Calculated Panel Reactive Antibody (PRA) percentage (institution-specific thresholds), or an ABO incompatible donor are likely to undergo desensitization at one or more of the study centers; these factors, among others, will be used by the study clinician to determine exclusion due to anticipated desensitization is warranted for a particular participant in the study
* Current use of any other investigational agents
* History of allergic reactions to yeast or attributed to compounds of similar chemical or biologic composition to Gardasil 9 HPV vaccine
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* For female participants: Pregnant or intention to get pregnant, or breastfeeding; pregnant women are excluded from this study because the safety and effectiveness of Gardasil 9 HPV vaccine have not been established in pregnant women; it is not known whether Gardasil 9 is excreted in human milk; because many drugs are excreted in human milk, caution should be exercised when Gardasil 9 is administered to a nursing woman; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Gardasil 9, women who are breastfeeding will be excluded
* History of cervical cancer or anal cancer
* History of active malignancy, including basal/squamous cell skin cancer
* Concurrent illness, such as known psychiatric disorders or substance abuse (i.e., average alcohol consumption of more than 3 drinks per day), which in the opinion of the investigators would compromise either the patient or the integrity of the data
* Patients on anticoagulation or with bleeding disorders should be evaluated by a physician for risk/benefit of bleeding disorders with intramuscular injections prior to study enrollment; patients determined to be at high risk for bleeding with intramuscular injections will be excluded