We used the Civil Registration System to identify 855,654 males born in Denmark (excluding Greenland and the Faroe Islands) between January 1, 1977 and December 31, 2003 . By means of a demographic algorithm that we used in two previous studies on possible outcomes of non-therapeutic circumcision [28, 29], we excluded 44,935 males with at least one parent or grandparent born in one of the following 17 predominantly Muslim countries: Turkey, Iraq, Pakistan, Iran, Somalia, Lebanon, Afghanistan, Morocco, Egypt, Syria, Indonesia, Algeria, Jordan, Bangladesh, Kuwait, Tunisia and Kosovo. No other predominantly Muslim country accounts for more than 0.1% of all non-Danish born citizens. The remaining 810,719 males constituted our study cohort of Danish-born non-Muslim males, whom we followed for the occurrence of HIV infection and other STIs over the age span 0–36 years between January 1, 1977 and November 30, 2013.
Cohort members who underwent non-therapeutic circumcision in a hospital setting were identified in the National Patient Register under surgery codes 55620 (period 1977–1995) or KKGV20 (since 1996) . Non-therapeutic circumcisions performed in private clinics by surgeons or gynecologists and subsidized by the national healthcare system were identified under disbursement code 5301 in the National Health Service Register (since 1994) . From 2004 onwards, non-therapeutic circumcision was gradually removed from regional lists of publicly subsidized surgical procedures, thus resulting in incomplete records for non-therapeutic circumcisions performed after 2003.
We also searched the files of these registries for all recorded cases of foreskin surgery other than non-therapeutic circumcision (e.g., phimosis surgery), using National Patient Register surgery codes 56640, 56680, 56700, 56720, or 56760 (period 1977–1995) and KKGH10, KKGV10, KKGV00, KKGH80, or KKGH80A (since 1996), and disbursement codes 3101, 3132, 3201, 3232, 4132, 4154, 4232, or 6422 in the National Health Service Register (since 1994) . We used this information to enable clean comparisons of rates of HIV infection and other STIs in males undergoing non-therapeutic circumcision v intact males by censoring cohort members on the date of such other foreskin surgery, as explained below.
Specific diagnostic codes according to the International Classification of Diseases, 8th (ICD-8, 1977–1993) and 10th edition (ICD-10, 1994–2013) were used to identify cohort members treated in Danish hospitals for HIV (ICD-8: 07983; ICD-10: B20-B24), syphilis (ICD-8: 091xx-097xx; ICD-10: A51-A53), gonorrhea (ICD-8: 098xx; ICD-10: A54), genital herpes (ICD-8: 05402; ICD-10: A60), anogenital warts (ICD-8: 09990; ICD-10: A630-A630D), or other STIs, including chlamydia, chancroid, granuloma inguinale and trichomoniasis (ICD-8: 07984, 099xx (except 09990), 131xx; ICD-10: A55-A59, A63-A64 (except A630-A630D)) between January 1, 1977 and November 30, 2013.
In separate analyses for each STI, we followed cohort members from their date of birth until the date of first recorded STI diagnosis, emigration, death or end of follow-up on November 30, 2013, which was the date of complete registry records at the time of data extraction for this and a previous study , whichever came first. All statistical analyses of the association of foreskin status with risk of HIV infection and other STIs during 1977–2013 were carried out as Cox proportional hazards regression analyses with age as the underlying time scale, stratifying the baseline hazard rates for birth year . Specifically, hazard ratios (HRs) with 95% confidence intervals (CIs) compared the hazard rates of each outcome between the reference group of intact males and males undergoing non-therapeutic circumcision. Each cohort member’s foreskin status was treated as a time-dependent variable being intact from birth and, when relevant, shifting to circumcised on the recorded date of non-therapeutic circumcision. Boys and men undergoing other foreskin surgery as described above were censored on the date of such surgery.
In a subsequent analysis, we examined the extent to which observed associations for any STI and for anogenital warts depended on the age when the non-therapeutic circumcision took place. Specifically, we calculated HRs comparing rates of any STI and of anogenital warts among males who underwent non-therapeutic circumcision at or before the age of 24 months and those who had this surgery after that age with corresponding rates in the reference category of intact males.
To compare observed rates of HIV acquisition among intact and circumcised males, we undertook a simulation study. Specifically, we conducted a series of 100,000 simulations to establish the probability distribution of anticipated numbers of cases of HIV infection among circumcised males in the cohort assuming no association between foreskin status and HIV risk. Such an approach was appropriate because the average periods of follow-up were almost identical in the compared groups, being 21.8 years among intact males and 21.6 years among circumcised males. Among international organizations and stakeholders arguing in favor of circumcision in the fight against HIV in Africa, the expectation is that infant or childhood circumcision will provide the same, or an even higher, degree of HIV protection compared to what has been reported for adult male circumcision [14, 22,23,24,25]. Consequently, we tested the directional (one-sided) null hypothesis of equal or higher rates of HIV acquisition in circumcised males against the alternative hypothesis that the rate is lower among circumcised males.
In one robustness analysis aimed to address the potential impact of socioeconomic confounding, we repeated the main analysis outlined above, this time stratifying for a variable capturing municipality-based average disposable household income level in quintiles (273,760–305,458, 305,742–322,403, 323,556–339,384, 340,184–358,568 and 359,050–599,126 Danish Kroner) (Statistics Denmark, www.statistikbanken.dk). Specifically, we treated this municipality-based socioeconomic variable as a time-dependent stratification variable, whose value depended on each cohort member’s actual day-to-day place of residence during follow-up.
In a second robustness analysis, we ended follow-up for HIV and other STIs on December 31, 2003 to eliminate any exposure misclassification due to incomplete data on non-therapeutic circumcisions performed after 2003.
By restricting our cohort to non-Muslims, using birth year as a stratification variable for the baseline hazard rates, using age as the underlying time scale in all analyses, and censoring on the date of other foreskin surgery, we ensured that all HRs were based on culturally comparable, same-aged strata of circumcised and intact males observed during comparable calendar years.
All Cox proportional hazards regression analyses were carried out using the PHREG procedure in SAS, version 9.4 (SAS Institute, Cary, NC, USA).