In 2016, a researcher at the European Centre for Disease Prevention and Control published "Safety of human papillomavirus vaccines: a review", which concluded
"several SAEs allegedly reported as caused by HPV vaccines have been shown to be only temporarily associated, but not causally associated, with the vaccination... Both HPV vaccines available are generally safe and well tolerated. Efforts should be made to increase the vaccination coverage of these vaccines as an important tool to decrease the disease burden of HPV."
The FDA reviewed the clinical trial results for safety and efficacy, and approved Gardasil for use against cervical cancer and genital warts in women in 2006, and against anal cancer in anyone aged 9 through 26 in 2010.
"Pooled analysis of large and long-term safety data from the human papillomavirus-16/18-AS04-adjuvanted vaccine clinical trial programme" summarizes the safety data from clinical trials of Cervarix.
Among 2,252,716 girls, 37% received HPV vaccine and 4,096 AID occurred during a mean follow-up time of 33 months. The incidence of AID was not increased after exposure to HPV vaccination, except for Guillain-Barre syndrome (GBS) ... Under the hypothesis of a causal relationship, this would result in 1-2 GBS cases attributable to HPV vaccine per 100,000 girls vaccinated.
In this large, nationwide study including the first six birth cohorts of girls offered quadrivalent HPV vaccine through the national immunisation programme in Norway, no association between HPV vaccination and risk of CFS/ME was observed. Medical history was associated with both increased risk of CFS/ME and lower uptake of HPV vaccine. The current findings support the favourable safety profile of quadrivalent HPV vaccine reported from other pre- and post-licensure studies.
We found no evidence of an increased risk of GBS following HPV vaccination in England and, based on the upper end of the 95% CI for the RI and the number of HPV vaccine doses given in England, can exclude a risk of about 1 per million doses.
"no evidence of an increased risk of AD in women aged 9 to 25 years after AS04-HPV-16/18 vaccination."
"Rates of AEFI [within 42 days] after HPV immunization in Alberta are low and consistent with types of events seen elsewhere."
"Taking into account the totality of the available information the PRAC concluded that the evidence does not support that HPV vaccines (Cervarix, Gardasil, Gardasil 9, Silgard) cause CRPS or POTS. The benefits of HPV vaccines continue to outweigh their risks."
"The study included 3,983,824 females, among whom 789,082 received a total of 1,927,581 qHPV vaccine doses... there was no increased risk of multiple sclerosis (crude incidence rates, 6.12 events/100,000 person-years [95% CI, 4.86-7.69] and 21.54 events/100,000 person-years [95% CI, 20.90-22.20] for the vaccinated and unvaccinated periods; adjusted rate ratio, 0.90 [95% CI, 0.70-1.15]) or other demyelinating diseases (crude incidence rates, 7.54 events/100,000 person-years [95% CI, 6.13-9.27] and 16.14 events/100,000 person-years [95% CI, 15.58-16.71]; adjusted rate ratio, 1.00 [95% CI, 0.80-1.26]) associated with qHPV vaccination... These findings do not support concerns about a causal relationship between qHPV vaccination and demyelinating diseases."
"[Among] all Danish women aged 10 through 44 years from October 1 2006 through July 31, 2013... [totaling] 1,613,798 women, including 500,345 (31%) who received the quadrivalent vaccine, we identified 4376 incident cases of VTE. Of these, 889 women (20%) were vaccinated during the study period. There was no association between the quadrivalent vaccine and VTE during the 42 days following vaccination..."
"Rates of spontaneous abortions and major birth defects were not greater than the Metro Atlanta Congenital Defects Program unexposed population rates. Analysis of 6 years of pregnancy registry data shows no adverse signals."
A total of 113 specialised centres recruited (from December 2007 to April 2011) females aged 14-26 years with incident cases of six types of ADs: idiopathic thrombocytopenic purpura (ITP), central demyelination/multiple sclerosis (MS), Guillain-Barre syndrome, connective tissue disorders (systemic lupus erythematosus, rheumatoid arthritis/juvenile arthritis), type 1 diabetes mellitus and autoimmune thyroiditis. Control subjects matched to cases were recruited from general practice. ... 211 definite cases of ADs were matched to 875 controls. The adjusted odds ratio (OR) for any quadrivalent HPV vaccine use was 0.9 [95% confidence interval (CI) 0.5-1.5]. The individual ORs were 1.0 (95% CI 0.4-2.6) for ITP, 0.3 (95% CI 0.1-0.9) for MS, 0.8 (95% CI 0.3-2.4) for connective disorders and 1.2 (95% CI 0.4-3.6) for type 1 diabetes. No exposure to HPV vaccine was observed in cases with either Guillain-Barre syndrome or thyroiditis.
CONCLUSIONS: No evidence of an increase in the risk of the studied ADs was observable following vaccination with Gardasil within the time periods studied. There was insufficient statistical power to allow conclusions to be drawn regarding individual ADs.
"This cohort study of about one million adolescent girls aged 10 to 17 years utilised routine healthcare data from two Scandinavian countries to identify potential serious adverse events during the first four years after the qHPV vaccine was marketed. ... Although significantly increased rate ratios were initially observed for three outcomes, further assessment showed no consistent evidence for a plausible association; firstly, these risk signals were relatively weak, as assessed by prespecified criteria, and, secondly, no temporal relation between vaccine exposure and outcome was evident. Thus, this study identified no safety signals with respect to autoimmune, neurological, and venous thromboembolic events after the qHPV vaccine had been administered."
See also " Evaluation of autoimmune safety signal in observational vaccine safety studies", in which the authors of the study describe some of their methods.
VAERS can't really measure probabilities, since it lacks any way to track everyone who was vaccinated. It's more meant to point out things to look for in more rigorous studies.
The Clinical Consult Case Review Working Group reviews individual cases of adverse events following immunizations. During 2004-2009, it identified 76 cases from VAERS and pubmed searches. About half of the cases were neurological in nature. The group concluded that 3 of the 76 cases were definitely related to vaccine administration, and 12 were probably related.
In "Postlicensure safety surveillance for quadrivalent human papillomavirus recombinant vaccine", VAERS data was found to indicate an incidence per 100,000 doses of 8.2 for syncope; 7.5 for local site reactions; 6.8 for dizziness; 5.0 for nausea; 4.1 for headache; 3.1 for hypersensitivity reactions; 2.6 for urticari.
According to "Reports of Health Concerns Following HPV Vaccination",
As of September 15, 2011, approximately 40 million doses of Gardasil were distributed in the U.S. and VAERS received a total of 20,096 reports of adverse events ... 92% were considered to be non-serious, and 8% were considered serious. [Of these, there were] 71 VAERS reports of death. ... Thirty four of the total death reports have been confirmed and 37 remain unconfirmed due to no identifiable patient information in the report such as a name and contact information to confirm the report. A death report is confirmed (verified) after a medical doctor reviews the report and any associated records. In the 34 reports confirmed, there was no unusual pattern or clustering to the deaths that would suggest that they were caused by the vaccine and some reports indicated a cause of death unrelated to vaccination.i.e. the 34 death reports, while confirmed to have good contact info etc., are not confirmed to be from Gardasil.
You can review the 34 reports yourself; here is a table listing each one, with links to the full records. 23 of them aren't easily explained by pre-existing conditions.
Even assuming all 23 deaths were caused by VAERS, and the data from VAERS were suitable for measuring risk, that would still only mean the additional risk of death due to three doses of Gardasil in a lifetime is very roughly 2 in a million, or 0.0002%. For comparison, the lifetime risk of dying of cervical cancer is 0.24%. So taking Gardasil is about 1000 times safer than not taking it!
In "Anaphylaxis as an adverse event following immunisation in the UK and Ireland" (full text), researchers looked at anaphalaxis from all vaccines administered to children under 16 in the UK and Ireland September 2008 and October 2009, and found 7 cases, six of which required treatment with adrenalin. They estimated this represented 12.0 per 100 000 dose for single component measles vaccine, and 1.4 cases per million doses for Cervarix.
"The clinical symptoms most frequently reported were dizziness, headache, and syncope. Reporting rates of syncope or loss of consciousness and seizures with qHPV vaccine were 17 and 3.2 per 100,000 doses administered, respectively, and 15 and 1.6 for syncope or loss of consciousness and syncopal seizures occurred on the day of vaccination. The reporting rates of syncope or loss of consciousness and seizures were 6.4 and 0.4, for the other vaccines."
"Between 2007 and 2011, 133 confirmed AEFIs were reported while 691,994 HPV4 vaccine doses were distributed in the school-based program. ... Ten serious AEFIs were reported (7.5% of reports) including 2 anaphylaxis, 2 seizures, 1 thrombocytopenia and 1 death. Further review found that the reports of anaphylaxis did not meet the Brighton anaphylaxis definition and the death was attributed to a preexisting cardiac condition... No new safety signals were identified, especially no reports of VTE in this younger female population."
"The reporting rate after 4vHPV vaccine for syncope and syncopal seizures was 7.8/100,000 and 2.6/100,000 doses distributed, respectively."
"The most often reported systemic AEs were myalgia (64%), fatigue (24%) and headache (21%; Figure 4.2). ... no unexpected AEs after vaccination were found".
This paper has detailed data on how long various local and systemic reactions last, it's worth a read.
"We estimated background rates of neurological and allergic events in adolescent boys to be 252.9 and 175.2 per 100 000 person-years, respectively. Assuming an 80% vaccination rate with three doses per person -- which equates to 1 440 000 doses administered nationally per year in the first 2 years of the program -- about 2.4 episodes of Guillain-Barre syndrome would be expected to occur in the 6 weeks following vaccination. Within 1 day of vaccination, about 3.9 seizures, 0.3 episodes of anaphylaxis and 6.5 acute allergy presentations would be expected."In "Human papilloma virus immunization in adolescent and young adults: a cohort study to illustrate what events might be mistaken for adverse reactions", researchers looked at the background rate of health problems before HPV vaccination was introduced, and found
"If HPV immunization had been used with 80% coverage, 3 per 100,000 adolescents would have required emergency care for asthma/allergy within 24 hours and 2 per 100,000 for diabetes within 1 week of an injection."
Syncope (vasovagal or vasodepressor reaction) can occur after vaccination, most commonly among adolescents and young adults. During 1990--2004, a total of 3,168 reports to Vaccine Adverse Event Reporting System (VAERS) were coded as syncope; 35% of these episodes were reported among persons aged 10--18 years (CDC, unpublished data, 2005). Approximately 14% of reported syncopal episodes resulted in hospitalization because of injury or medical evaluation. Serious injury, including skull fracture and cerebral hemorrhage, has resulted from syncopal episodes after vaccination (92). A review of syncope after vaccination indicated that 63% of syncopal episodes occurred <5 minutes after vaccination, and 89% occurred within 15 minutes after vaccination (93). Although syncopal episodes are uncommon and severe allergic reactions are rare, vaccine providers should strongly consider observing patients for 15 minutes after they are vaccinated (94). If syncope develops, patients should be observed until the symptoms resolve.This does not seem to be specific to the HPV vaccine.
You could look at Gardasil as an HPV with all of the L2 and E1 through E7 genes, and most copies of the L1 genes, removed. Without those E genes, it's not going to be infectious or carcinogenic.