Gurprit Grover and Dulumoni Das* Department of Statistics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India.

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1 Journal of AIDS and HIV Research Vol. 3(), pp. -9, January 20 Avalable onlne academcjournals.org/jahr ISSN Academc Journals Full Length Research Paper Decrement table and the estmaton of human mmunodefcency vrus (HIV) mortalty rate wth an applcaton to hemophla-assocated acqured mmune defcency syndrome (AIDS) Gurprt Grover and Dulumon Das* Department of Statstcs, Faculty of Mathematcal Scences, Unversty of Delh, Delh, Inda. Accepted 30 December, 200 The human mmunodefcency vrus/ acqured mmune defcency syndrome (HIV/AIDS) epdemc represents the most serous publc health problem n Inda. There s no denal of the enormty of the problem. The avalable survellance data clearly ndcates that HIV s prevalent n almost all parts of the country. Hence, knowledge of HIV ncdence s mportant to formulate sensble strateges amed at controllng the HIV/AIDS epdemc. The objectve of ths paper s to estmate the probablty of dyng n the stage of HIV (Grover and Das, 2005) n a year wthout passng to the state of AIDS (HIV mortalty rate). Secondly, a double decrement lfe table approach (Bswas et al., 2006) has been followed for a cohort of hemophlacs who were at rsk of nfecton wth the AIDS vrus. Ths devce conssts essentally of two decrements: HIV postve hemophlacs ether depart from the AIDS-free group by eventually developng AIDS or by dyng from other causes; those who eventually develop AIDS ether reman alve wth t untl they de from t or de from other causes. The dstrbuton of ncubaton perod of AIDS s based on a two-stage parametrc regresson model (Brookmeyer and Goedert, 989), proposed for the analyss of cohort of hemophlacs. Key words: HIV mortalty rate, ncubaton perod, two-stage parametrc regresson model, double decrement lfe table, sero-postvty. INTRODUCTION The human mmunodefcency vrus (HIV), whch causes acqured mmunodefcency syndrome (AIDS), s the leadng nfectous cause of adult deaths n the world. Gven the scale of the epdemc, HIV/AIDS s now consdered not only a health problem, but also a developmental and securty threat. Even f a cure s found tomorrow, the toll of death and sufferng by 20 wll far exceed any other recorded human catastrophe, any other prevous epdemc, natural dsaster, war, or ncdent of genocdal volence. The frst case was reported among homosexual men n the USA n 98 (Avert: It has reached pandemc *Correspondng author. E-mal: dasdulumon@gmal.com. proportons, as no country n the world s free from HIV/AIDS. It ranks as one of the most destructve mcrobal scourges n human hstory and poses a formdable challenge to the bomedcal research and publc health communtes of the world. AIDS and ts related syndromes have changed vrtually every aspect of medcne and socety at large. AIDS s a condton n whch the nbult mmune mechansm of the human body breaks down completely. The process s gradual but ultmately suppresses the mmunty of the ndvduals. Accordng to estmates from the UNAIDS (2009) Report on the global AIDS epdemc, around 3.3 mllon adults (aged 5 or above) and 2. mllon chldren (younger than 5) were lvng wth HIV by the end of More than 25 mllon people have ded of AIDS snce 98. At the end of 2008, women accounted for 50% (5.7 mllon) of all

2 2 J. AIDS HIV Res. adults lvng wth HIV worldwde. The epdemc had left behnd 5 mllon AIDS orphans defned as those aged under 8 who have lost one or both parents to AIDS. Durng 2008, some 2.7 mllon people became nfected wth HIV. Around half of the people who acqure HIV became nfected before they turn 25 and typcally de of the lfe-threatenng llnesses called AIDS before ther 35th brthday. Around 430,000 chldren aged 4 or younger became nfected wth HIV. Over 90% of newly nfected chldren are babes born to women wth HIV. The year also saw 2 mllon deaths from AIDS - a hgh global total, despte antretrovral therapy, whch reduced AIDSrelated deaths among those who receved t. Of the 2 mllon people who ded of AIDS durng 2008, more than one n seven was chld. Every hour, around 3 chldren de as a result of AIDS. The number of deaths probably peaked around 2005, and has snce declned only slghtly (UNAIDS, 2009). It s establshed (Dwyer, 995) that HIV klls the most mportant or pvotal cells wthn the mmune system, CD-4 lymphocytes, t compromses the mmune system s ablty to fght nfecton. The 992 survellance defnton by Center for Dsease Control (renamed as the Center for Dsease Control and Preventon n 993) for AIDS defned AIDS as ncludng people wth CD-4 counts of less than 200 cells per cubc mllmetre (or a CD-4 person less than 4%) (Smth, 996). No evdence exsts to date to suggest that anybody nfected wth HIV has successfully elmnated the vrus or produced an mmunologcal response that would make one confdent that AIDS wll never develop, whle 67% of patents nfected wth HIV wll have developed AIDS wthn ten years of nfecton (Dwyer, 995), those that stay well longer are currently beng nvestgated to determne f they make a more effectve mmune response to HIV than those who are ll at the end of ten years of nfecton. Ths data suggest that not all HIV postve people are lkely to develop AIDS. Prelmnary evdence suggests that 5% of HIV postve ndvduals may never develop AIDS. It follows that a sero-postve person s dffcult to be dentfed (unless clncally declared as sero-postve) and thus most of the sero-postve ndvduals reman undentfed n the populaton. There are frequent deaths of sero-postve ndvduals reported as due to other vsbly apparent causes. As HIV patents cannot be dentfed n general, therefore, the death of HIV s mstaken as beng the death due to other dseases wth related symptoms (lke darrhoea, tuberculoss, cardac falure etc.). Hence, knowledge of HIV mortalty rate can probably help n the adjustment of mortalty rates due to other causes whch are generally ascrbed as apparently the causes for HIV mortalty. Agan, studes show that the hazard rate of an HIV ndvdual at a gven pont of tme remans the same rrespectve of the fact that whether he s dagnosed as an AIDS patent or not. Ths s because of the complete lack of prognoss n the treatment of AIDS. Thus, nether the number of actual sero-postve persons nor ther deaths over tme are avalable for the estmaton of HIV mortalty rates. Hence, an approach of double decrement lfe table wth two decremented forces of HIV, vz., mortalty and converson to AIDS, has been followed for estmatng HIV mortalty rates. Hemophla (heem-o-fill-ee-ah) s a rare bleedng dsorder n whch blood does not clot normally. People havng hemophla, may bleed for a longer tme than others after an njury. They also may bleed nternally, especally n knees, ankles, and elbows. Ths bleedng can damage body organs or tssues and may be lfe threatenng ( The frst cases of AIDS n persons wth hemophla were reported n 98. In the early and md-980s, as many as two-thrds of all Amercans wth hemophla became nfected wth HIV. The Natonal Hemophla Foundaton reports that by June of 992, 2,248 cases of AIDS had been confrmed among persons wth hemophla and an estmated,500 people wth hemophla had ded from the dsease. Ironcally, use of the plasma concentrates that had ushered n hemophla's "golden age" had become one of the most perlous rsk factors for the dsease ( Hemophla-AIDS statstcs from Germany reports that about 50% of the 6,000 German hemophlacs are HIV-postve (Koerper, 989). A key epdemologc descrptor of nfectous dsease s the tme t takes from nfecton to the dagnoss of the dsease or the ncubaton perod (Sratwell, 950). In the context of AIDS, we refer to the ncubaton perod as the tme elapsed from HIV seroconverson (that s detecton of antbodes by serologcal tests) to the onset of a clncal condton defnng the AIDS (Centers for Dsease Control, 987). Estmatng the progresson from HIV nfecton to fullblown AIDS s of partcular mportance for patent counsellng, for decdng f and when to admnster treatment, for montorng the success of therapy, and for health plannng (Charott, 994). Estmates of progresson to AIDS among haemophlacs have recently been produced both n Italy and n other countres based on data from natonal or multnatonal cohort studes (Goedert et al., 989; Darby, 990). Charott et al. (992) has presented and dscussed the effects of some parametrc estmaton procedures of seroconverson tme on the analyss of progresson to AIDS, usng data for Italan haemophlacs. Charott et al. (994) estmated the medan ncubaton tme between human mmunodefcency vrus (HIV) nfecton and onset of acqured mmunodefcency syndrome (AIDS), usng three parametrc models and sx estmates of seroconverson tme for 732 HIV-postve haemophlacs enrolled n the Italan regstry of patents wth congental coagulaton dsorders. Papadopulos-Eleopulos et al. (995) carefully examned the assocaton between the acqured mmune defcency syndrome (AIDS) and haemophla and found that many patents wth haemophla have become HIV

3 Grover and Das. 3 nfected and/or developed the AID clncal syndrome as a drect result of the transfuson of factor VIII preparatons contamnated wth ths partcular vrus. But despte the many clams that HIV causes AIDS n hemophlacs (Centers for Dsease Control, 986; Insttute of Medcne, 988; Wess and Jaffe, 990; Chorba, 994) not much work has been done on the morbdty or mortalty of HIVpostve hemophlacs. The present study has therefore focused on the estmaton of mortalty of HIV patents and the progresson from HIV nfecton to full-blown AIDS for a cohort of hemophla patents. In epdemologc studes of an nfectous dsease, two mportant objectves are to dentfy rsk factors for nfecton and rsk factors for progresson to clncal dsease once nfected. Brookmeyer et al. (989) developed analytc methods for dentfyng rsk factors both for nfecton and for onset of clncal dsease once nfected, when the tme of nfecton can be determned wthn an nterval. Here, a two-stage parametrc regresson model was proposed for jontly estmatng the effects of covarates on rsk of nfecton as well as rsk of progresson to clncal dsease once nfected, where the two stages refer to nfecton (Stage ) followed by onset of clncal dsease (Stage 2). There are two types of covarates: X, whch modfy rsk of nfecton, and X 2, whch modfy rsk of dsease once nfected; some covarates may be ncluded n both X and X 2. The rsk of AIDS depends on two types of covarates. The frst type ( X ) are covarates that modfy rsk of HIV nfecton. The hemophlacs were at the rsk of HIV nfecton because some lots of replacement clottng factor had been nfected. Covarates that could affect rsk of nfecton among haemophlacs nclude the hemophla treatment centre or geographc regon because some regons may have receved nfected lots earler than others, and the amount and type of clottng factor receved. The second type of covarates, X 2, whch are sometmes called cofactors, are those that modfy rsk of onset of clncal AIDS followng nfecton. These covarates may nclude age, pror health status, and possbly dose of noculum receved. Some covarates may be common to both X and X 2. The objectve of ths paper s to estmate the probablty of dyng n the stage of HIV n a year wthout passng to the state of AIDS (that s, HIV mortalty rate). Secondly, a double decrement lfe table has been constructed. Ths devce conssts essentally of two decrements: HIV postve hemophlacs ether depart from the AIDS-free group by eventually developng AIDS or by dyng from other causes; those who eventually develop AIDS ether reman alve wth t untl they de from t or de from other causes. The dstrbuton of ncubaton perod of AIDS s based on a two-stage parametrc regresson model proposed by Brookmeyer et al. (989). An applcaton has been presented for a cohort of hemophlacs n USA who were nfected wth the AIDS vrus. METHODOLOGY Computaton of probablty of dyng n HIV The latest statstcs of the global HIV and AIDS were publshed by UNAIDS n November 2009, and refer to the end of The newly nfected populaton wth HIV of the world s 2.7 mllon (UNAIDS, 2009) and the number of deaths due to HIV/AIDS s 2 mllon by the end of Therefore, the death rate due to HIV (Grover and Das, 2005) can be taken as Total number of death cases due to HIV Death rate = Total Populaton lvng wth HIV 2, 000, 000 = = , 000, 000 per person per year whch roughly gves the mean hazard rate ( λ) due to HIV as λ = log ( death rate ) = ( log ) = Defnng the random varable X as the age of death due to HIV counted from the date of nfecton wth HIV, the densty functon of X s gven by f ( x) = λ ( T x) λ e e λt for 0 x T and λ > 0 where f ( x ) s a proper probablty densty. f ( x ) s chosen as a truncated exponental dstrbuton truncated at T (the upper lmt of the tme of death due to HIV) wth the property of ncreasng probablty of deaths wth advancng x. The proporton of deaths denoted by durng to (+) year due to HIV s gven by e e λt λ ( + ) λ = e e λt Puttng λ = , 3 (Becker et al., 99) s usually abnormally long even to the extent () (2) T = (the ncubaton perod of AIDS of 30 years or even more) and takng = (0,, 2,..., 30) n (2), we can obtan the HIV mortalty rate denoted by ( = 0,,2,...,30) between to ( + ) year of age from the date of nfecton of HIV, whch are presented n Table (Probablty of dyng n the stage of HIV by years). Incubaton perod dstrbuton from a cohort study of hemophlacs Brookmeyer et al. (989) developed a two stage model for AIDS and appled t to a study of hemophla-assocated AIDS. Ths Natonal Cancer Insttute Multcenter Hemophla Cohort Study conssted of a cohort of hemophlacs who were actve patents on January, 978, at one of the three treatment centers (Hershey, New York, and Pttsburgh) n the Unted States. In the cohort, there

4 4 J. AIDS HIV Res. Table. Probablty of dyng n the stage of HIV by years. Age nterval from the date of nfecton of HIV ( to +) were 458 hemophlacs. Of these, only 296 were nfected wth HIV after January, 978. No nformaton on the date of nfecton was avalable for the remanng 62 hemophla patents. The analyss produced an estmate of the ncubaton perod dstrbuton, S(t; X, β ) 2, defned as the cumulatve probablty of developng AIDS at or before t years from seroconverson. The estmated cumulatve dstrbuton of ncubaton perod for hemophlacs s gven by: 2.56 S( t; X 2, β ) = exp( t ) (t measured n years), and the ncubaton perod dstrbuton s obtaned as shown n Table 2 (Incubaton Perod Dstrbuton). A double decrement lfe table of HIV hemophla populaton A double decrement lfe table (Fgure.Double decrement table for the ncdence of AIDS) has been prepared for a cohort of 296 hemophlacs (Brookmeyer and Goedert, 989) wth the followng two decrement states: () Due to death n the HIV state wthout passng to the state of AIDS (State ) (2) Transton from HIV to the state of AIDS (State 2) Computaton of HIV Hemophla Populaton The lfe table starts wth a cohort of l 0 = 296 seropostve hemophlacs. Let be the probablty of dyng for an HIV hemophla patent durng to + years followng the onset of seropostvty wthout passng to the state of AIDS and P = be the complementary probablty of survval. Smlarly, p be the probablty that an HIV hemophla patent wll pass to the state of AIDS durng to + year. Then q = p

5 Grover and Das. 5 Table 2. Incubaton perod dstrbuton. Age nterval from the date of nfecton of HIV ( to +) Incubaton perod (p ) q = (-p ) be the probablty that an HIV hemophla patent wll not pass to the state of AIDS durng to + year. Then, the HIV hemophla populaton at age n s gven by: n { }. for n (3) l = l q n 0 = 0 Now from (3), we obtan the successve values of HIV hemophla populaton{ l n } by usng HIV mortalty rate ( values) from Table (Probablty of dyng n the stage of HIV by years) and the probablty of an HIV hemophla patent not passng to the state of AIDS ( q values) from Table 2 (Incubaton Perod Dstrbuton). These are presented n Table 3 (HIV hemophla populaton at the begnnng of a year startng wth a cohort of 296 newly nfected hemophla HIV patents). Decrements n the cohort of HIV hemophla patents Usng the lfe table, an alternatve estmate of the probablty of hemophla HIV between to (+) year can be obtaned by the formula gven as l l + Y = l p + Agan, we can see that (I=,2, ). Y and (4) values are almost the same

6 6 J. AIDS HIV Res. Fgure. Double decrement table for the ncdence of AIDS. Table 3. HIV Hemophla populaton at the begnnng of a year startng wth a cohort of 296 newly nfected hemophla HIV patents. No. of year of age from the date of nfecton of HIV () HIV Hemophla populaton

7 Grover and Das. 7 We can also obtan: () The number of hemophla deaths n HIV durng to (+) years ( l l ) = + p + () The number of brths of hemophla AIDS from HIVs durng to (+) year = ( l l+ ) ( l l ) p p + = + p + The resultng double decrement of hemophla HIV patents wth ncreasng age s shown n Table 4 (Decomposton of the decrement n the cohort of hemophla HIV patents by ther deaths and the brths of AIDS). RESULTS Table 3 (HIV Hemophla populaton at the begnnng of a year startng wth a cohort of 296 newly nfected hemophla HIV patents) gves the HIV hemophla populaton at dfferent ages.table 4 (Decomposton of the decrement n the cohort of hemophla HIV patents by ther deaths and the brths of AIDS) shows the resultng double decrements of hemophla HIV patents wth ncreasng age. The analyss shows that the decrement n hemophla HIV populaton s ncreasng ntally and s hghest n the 7 th and 8 th ntervals. After that a decreasng trend s observed as age ncreases and from the end of the 8 th nterval, the loss n the cohort of hemophla HIVs remans relatvely constant, fluctuatng between 3 and 4. A smlar constant trend s observed by examnng the number of deaths n the cohort of hemophla HIV patents. The hghest proporton (00%) of the decrement n the cohort s due to State and occurs after the completon of 2 years from the date of nfecton wth HIV to the end. However, the brths of hemophla AIDS patents ncrease monotoncally wth the advancement of age n the begnnng after nfecton wth HIV. It reaches a peak at the 7 th and 8 th ntervals and then decreases. Fgure 2 (Composton of 296 HIV hemophlacs to AIDS double decrement table) shows the changng proportons n States and 2 for ths example. DISCUSSION The natural hstory of human mmunodefcency vrus (HIV) nfecton n persons wth haemophla s not well (5) (6) establshed and may dffer from that n other acqured mmunodefcency syndrome (AIDS) rsk groups (Goedert et al., 986; Ekert, 987; Turner, 987). Dfferences n the route and frequency of exposure to HIV, dfferences n the prevalence of potental cofactors for the development of AIDS (e.g., coexstent nfectons), and dfferences n routne medcal care could lead to a varaton n dsease progresson and ultmate outcome, such as death. For some tme, scentsts had known that hemophlacs were at hgh rsk of hepatts, a group of vral dseases that can be transmtted by contamnated blood and blood products. Though, not usually fatal, hepatts s serous. In 982, food and drug admnstraton (FDA) lcensed a vaccne to protect aganst hepatts B. But for AIDS, there s no cure and no vaccne. People lvng wth hemophla are at enormously hgh rsk of HIV nfecton, because they requre regular transfusons of clottng factors n order to mantan a normal blood clottng system. From the late 970s to the md-980s, about half of all people wth hemophla became nfected wth HIV through blood products. Many of these people have developed AIDS. Currently, 0 to 5% of persons wth hemophla are nfected wth HIV. The AIDS epdemc has placed great health, economc, ethcal and emotonal burdens on affected famles and the wder bleedng dsorders communty ( Hence, ths study s motvated by the most perlous rsk factor for HIV nfecton and the dsease AIDS of hemophla patents. Also, the estmates of HIV deaths and AIDS brths for ths communty, obtaned n ths chapter, are of great practcal mportance and can lead to great benefts to the socety by helpng the scentsts to explot new technques and dscoveres for reducng the rsk of AIDS nfecton among hemophlacs. A methodology has been developed here to estmate HIV mortalty rate and then a double decrement lfe table analyss wth two decremental forces of HIV patents, vz., mortalty due to HIV and converson to AIDS has been constructed for a cohort of hemophla patents. The ncubaton perod dstrbuton s based on the jont analyss of the effect of covarates on both rsk of nfecton and rsk of AIDS once nfected (Brookmeyer and Goedert, 989). Jont estmaton s needed because the tme nterval n whch seroconverson occurred was wde for a large number of hemophlacs. Usng the data from Natonal Cancer Insttute Multcenter Hemophla Cohort study for hemophla-assocated AIDS, we obtaned the brth of AIDS patent followng the dagnoss of HIV nfected hemophla and the death of hemophla patent followng the nfecton of HIV n the Unted States. In the present study, t s showed that the hghest decrement (20 cases) n the cohort s observed durng 7 th to 8 th year from the date of nfecton wth HIV. The largest death of hemophla HIV (4 cases) occurred n 26 th and 30 th ntervals. The brth of hemophla AIDS attaned the peak (7 cases) n absolute terms at the 7 th and 8 th

8 8 J. AIDS HIV Res. Table 4. Decomposton of the decrement n the cohort of hemophla HIV patents by ther deaths and the brths of AIDS. Age nterval from the date of nfecton of HIV ( to +) Decrement n hemophla HIV populaton No. of deaths of hemophla HIV No. of brths of hemophla AIDS ntervals and then decreases. From Fgure 2 (Composton of 296 HIV hemophlacs to AIDS double decrement table) the trends of hemophla HIV deaths and hemophla AIDS brths exhbt that the decrement of the cohort of hemophla HIVs s more affected by State 2 n the begnnng then decreases, but after reachng the22 nd nterval, hemophla patents co nfected wth HIV are not convertng to the stage of AIDS. Thus, a careful examnaton reveals that the HIVpostve hemophlacs were at hgher rsk of onset of clncal AIDS than the rsks of death due to other causes n the state of HIV for the frst 7 years from nfecton wth HIV. Wth progresson of tme the loss n the populaton of HIV postve haemophla was controlled because more severe cases of hemophla could receve more frequent and larger doses of replacement clottng factors. Furthermore, the progresson to AIDS occurred n the begnnng due to severe condton of hemophla at the entry of the cohort. Agan towards the end of the study perod, HIV nfected hemophlacs ded of a cause other than gong to the stage of AIDS. Thus, our fndngs provde a novel mechansm for understandng the deaths of HIV hemophlacs wthout gong to the stage of full blown AIDS. It also provdes mportant nformaton on the brths of AIDS patents from a cohort of HIV nfected hemophlacs, thus, tryng to gve a better pcture to dentfy the hemophla AIDS populaton. Many real-lfe data-analytc problems nvolve modellng complexphenomena. In ths paper, we present qute smple model of an essentally complex phenomenon: the spread of HIV nfectons and the development of AIDS amongst hemophlacs n USA. Our purpose n ths work

9 Grover and Das. 9 Fgure 2. Composton of 296 HIV hemophlacs to AIDS double decrement table. s to present an llustraton and dscusson of ths methodology, to demonstrate ts power for the analyss of complex data. We also focus on the applcaton of the concepts by the researchers for the analyss of data relatng to other countres. REFERENCES Becker NG, Watson LF, Carln JB (99). A method of non parametrc back projecton and ts applcaton to AIDS data. Stat. Med., 0: Bswas S, Grover G, Gurung AB (2006). On the estmaton of mortalty and dstrbuton of ncubaton perod of AIDS. Bostat. Aspects Health Popul., pp Brookmeyer R, Goedert JJ (989). Censorng n an epdemc wth an applcaton to hemophla-assocated AIDS. Bometrcs, 45: Centers for Dsease Control (eds) (986). Reports on AIDS publshed n the morbdty and mortalty weekly report. June 98 through February 986. Centers for Dsease Control (987). Revson of the CDC survellance case defnton for Acqured Immunodefcency Syndrome. MMWR, 36: s-5s. Charott F, Palomb M, Schnaa N, Ghrardn A, Prospero, L (992). Effects of dfferent parametrc estmates of seroconverson tme on analyss of progresson to AIDS among Italan HIV-postve haemophlacs. Stat. Med., : Charott F, Palomb M, Schnaa N, Ghrardn A, Bellocco R (994). Medan tme from seroconverson to AIDS n Italan HIV-postve haemophlacs: dfferent parametrc estmates. Stat. Med., 3: Chorba TL, Holman RC, Strne TW, Clarke MJ, Evatt BL (994). Changes n longevty and causes of death among persons wth hemophla. Am. J. Hematol., 45: 2-2. Darby SC, Doll R, Thakrar B, Rzza CR, Cox DR (990). Tme from nfecton wth HIV to onset of AIDS n patents wth haemophla n the UK. Stat. Med., 9: Dwyer JM (995). Bomedcal aspects of HIV and AIDS. Curr. Sc., 59: 0: Ekert H (987). AIDS ncubaton perod. Nature, 329: 494. Goedert JJ, Bggar RJ, Wess SH (986). Three-year ncdence of AIDS n fve cohorts of HTLV-III-nfected rsk group members. Scence, 23: Goedert JJ, Kessler CM, Aledort LM, Bggar RJ, Andes WA, Whm II GC, Drummond JE, Vadya K, Mann DL, Eyster ME, Ragn MV, Lederman MM, Cohen AR, Bray GL, Rosenberg ES, Fredman RM, Hlgartner MW, Blattner WA, Kroner B, Gal MH (989). A prospectve study of human mmunodefcency vrus type nfecton and the development of AIDS n subjects wth hemophla. New Engl. J. Med., 32: Grover G, Das D (2005). On the constructon of clncal lfe table for studyng the survvablty of AIDS cases. J. Commun. Ds., 37(3): Hemophla and HIV. 3 rd August, HIV/AIDS, 3 rd August, December, at.html,3rd December, 200. Insttute of Medcne (988). Confrontng AIDS-Update 988. Natonal Academy Press. Washngton DC. Koerper MA (989). AIDS and hemophla, In: AIDS: Pathogeness and treatment, JA Levy (ed.) Marcel Dekker. Inc. New York. pp Papadopulos-Eleopulos E, Turner VF, Papadmtrou JM, Causer, D (995). Factor VIII, HIV and AIDS n haemophlacs: An analyss of ther relatonshp. Genetca, 95: Smth JM (996). AIDS and socety. Upper Saddle Rver NJ: Prentce Hall. 370+xv. Paperback. Sratwell PE (950). The dstrbuton of ncubaton perods of nfectous dsease. Am. J. Hyg., 5: Turner MJ, Whte JO, Soutter WP (987). AIDS ncubaton perod n male hemophlacs. Nature, 330: 702. UNAIDS (2009). Report. Wess R, Jaffe H (990). Duesberg, HIV and AIDS. Nature (London), 345: