HIV Infection in hemophiliacsThe data for this lab are from the Multicenter Hemophilia Cohort Study,which is sponsored by the U.S. National Cancer Institute (NCI). The studyfollowed over 1600 hemophilia patients at 16 treatment centers (12 in theU.S. and 4 in western Europe) during the period from January 1, 1978 toDecember 31, 1995. The MHCS is one of the two large U.S. epidemiologicalstudies of hemophiliacs, the other being the Transfusion Safety Study Groupof the University of Southern California.Patients in the MHCS are classified according to age, HIV status, andseverity of hemophilia. To determine severity of hemophilia, on each annualquestionnaire patients indicate the amount of clotting-factor concentrate theyhave received in that year. The severity of hemophilia reported here is cal-culated from the average annual clotting-factor concentrate received in the1978–84 period.Each record in the data set corresponds to one stratum of hemophiliacsin one calendar year of the study. For example, one row in the data providesinformation on all severe hemophiliacs in 1983 who were HIV-negative andbetween the ages of 10 and 14 inclusive. In this group in 1983, the patientscontributed 6.84 person years to the study, and none of them died. In general,a subject’s person years are calculated from the beginning of the s tudy, ortheir birth date if they were born after January 1, 1978, until the time of lastcontact or the end of the study, whichever is earlier. When a subject diesor drops out before the end of the study, then the last contact occurs at thetime of death or withdrawal.Variable DescriptionYear Calendar year: 78; ... ;95.HIV HIV status: 1=negative; 2=positive.Severity Average annual dose of clotting-factor concentrate:1= over 50,000 units; 2= 20,001–50,000 units;3= 1–20,000 units; 4=unknown; 5=none.Age Age in 5-year intervals:1= under 5; 2= 5 to 9;... ; 14= 65 and over.Person years Total amount of time during the calendar year that thepeople in the stratum were alive and part of the study.Deaths Number of deaths in the calendar year for the stratum.• Begin by comparing the age distribution of person years for the HIV-1negative and HIV-positive groups. Is the HIV-negative populationyounger or older than the HIV-positive population?• From 1980 to 1985, the c lotting-factor concentrates were contaminatedwith HIV, and it was during this time period that the hemophiliacswho received contaminated transfusions were infected. By 1985, meth-ods were available for screening blood supplies, and HIV was virtuallyeliminated from blood products. How might this window of exposureaffect the age distribution of the HIV-infected hemophiliacs over time?Is calendar year a potential confounder?• According to Duesberg, it is not HIV that has caused AIDS amonghemophiliacs, but the “other junk” in the transfusions the patient re-ceives. Duesberg claims that these other contaminants are the realcause of AIDS, and that it is critical to take into account the quanti-ties of clotting-factor concentrate that people with hemophilia receivein their lifetime for a fair comparison of mortality rates of seropositiveand seronegative patients. Do you find evidence in the MHCS study tosupport Duesberg’s claim?• Combine the HIV-positive mortality rates for each age group using aweighted average, where the weights reflect the relative size of each agegroup in some standard population. Use the s ame age adjustment forthe HIV-negative rates.• Use a simulation method to create confidence intervals for the differencein mortality rates between HIV-positive and HIV-negative hemophiliacsaccording to severity of hemophilia and calendar year. Present yourresults