- Email: [email protected]
DESCRIBING THE AIDS EPIDEMIC
98
falling after transurethral resection to 124/80 mm Hg. One patient, with mean blood pressure 180/110 mm Hg at age 48, had not been treated with drugs. His plasma renin activity was 5 67 pmol h-1 ml-l (recumbent) and 9-18 (ambulant). Postoperatively his blood pressure fell to 120/80 mm Hg and his plasma renin activity was reduced to 3-07 pmol h-1 ml-l (recumbent) and 3 97 (ambulant) (normal ranges 1-2-2-4 and 30-43, respectively). The hypertension in these cases may result from increased sodium retention, high renin secretion, or decreased activity of renomedullary vasodepressor substances. Jones et al provide suggestive evidence of sodium retention, indicating volume overload, but this may be linked with high renin secretion. High renin hypertension has been described in unilateral obstruction of the urinary tract with raised renin concentration within renal vein blood derived from the obstructed kidney.2-4 Relief of obstruction restored blood pressure and renal vein renin concentration to nonnal.2 Apart from correcting hypertension, which was present in 52% of Jones and colleagues’ patients, surgery is necessary to restore renal function. Initial glomerular filtration rate ranged from 20 to 25 (mean 23) ml per min per 1 -73 m2 in my four patients, and recovery took many months and in one case years. Inappropriate hypertensive drug treatment could mask this decline in renal function. Singleton Hospital, Sketty, Swansea SA2 8QA
R. R. GHOSE
1. Ghose RR, Birks JL. Secondary hypertension accompanying high pressure chronic retention. Postgrad Med J 1985; 61: 167-69. 2. Belman AB, Kopp KA, Simon NM. Renal-pressor hypertension secondary to unilateral hydronephrosis. N Engl J Med 1968; 278: 1133-36. 3. Nemoy NJ, Fichman MP, Sellars A. Unilateral ureteral obstruction: a cause of reversible high renin content hypertension. JAMA 1973; 225: 512-13. 4. Squiteri AP, Ceccarelli FE, Wurster JC. Hypertension with elevated renal vein renins secondary to ureto-pelvic junction obstruction. J Urol 1974; iii: 284-87.
SEX RATIO IN OUTBREAKS OF PARVOVIRUS B19 INFECTION
SiR,—Amside is a village of about 2300 people on the estuary of the River Kent in south Cumbria. From the middle of October to the end of December, 1986, an epidemic of erythema infectiosum occurred in the primary school of 165 children ; 101 children and 5 of the 8 female teachers fell ill with a rash. Only 2 children were tested but both were positive for parvovirus B 19-specific IgM. 22 adults in the village had a rash during this time; 11 were tested and B19 infection was demonstrated in 10. The remaining adult had no evidence of recent B 19 infection, and no cases had evidence of recent rubella. 21 of the 22 adult cases were in females and all had arthralgia. It has been suggested that the female preponderance of clinically apparent laboratory-diagnosed B19 infections may be a consequence of females being more likely to attend general practitioners and have investigations done because of an awareness of the dangers of a rash in pregnancy. However, in this village community, questioning of many residents and the diagnosed cases failed to reveal any further cases in men. One possibility is that males are less likely to have a clinically apparent illness. Another is that adult infection is most likely to result from contact with infected children, and females would have more prolonged contact; this possibility is suggested by the age and sex linked seroepidemiological study from West Germany presented in abstract by T. F. Schwartz, M. Roggendorf, and F. Deinhardt at the Third European Congress of Clinical Microbiology (The
Hague, 1987). The adult male case was of interest because B19 DNA was present in the first serum collected 3 days after the onset of pruritus and mild erythema followed by arthralgia. B19-specific IgM was not detected in this serum although it was present in a sample collected 11 days later. It is usually thought that in B 19 infection the viraemia precedes the rash so that sera taken soon after the onset of a rash would be expected to have detectable specific IgM.l At the time of the epidemic there were 5 pregnant women in the village and all were tested. One woman had a subclinical B19 infection at about 35 weeks’ gestation and the pregnancy proceeded uneventfully to term. Twins were delivered and seem normal. The
4
remaining
women
were
detected) but none had
a
susceptible (B19-specific IgG not or serological evidence of
clinical illness
infection. Several B19 outbreaks in villages or schools have been reported but there has been little information on the sex ratio in adults. B19 diagnostic services report a higher frequency of symptomatic illness in femalesand this outbreak suggests that the sex difference is real and not a reflection of bias in cases being selected for investigation.
recent
Department of Virology, Preston Infirmary, Preston PR1 6PS The
Surgery, Arnside
Joint Department of Medical Microbiology, University College London and Middlesex Hospital Medical School, London
P. MORGAN-CAPNER J. WRIGHT
J. P. LONGLEY M.
J. ANDERSON
1. Anderson
MJ, Higgins PG, Davis LR, et al. Experimental parvoviral infection in humans. JInf Dis 1985; 152: 257-65. 2. Cohen BJ. Human parvovirus B19 and fifth disease. In: Mortimer PP, ed. Public health virology, 12 reports. London: Public Health Laboratory Service, 1986. 130-43.
UNUSUAL REACTION TO MORPHINE
SiR,—Isaw an unusual drug reaction in a 68-year-old man who had a terminal carcinoma of the prostate with spinal secondaries. He became depressed and was started on dothiepin, 75 mg at night, in addition to sustained-release morphine, 30 mg a day. His pain was controlled on this regimen for a week, then his morphine dose was increased to 60 mg daily. Within 24 h he had a bizarre psychotic reaction which started with paranoid delusions and anxiety, and worsened into stupor within hours. He was admitted with a presumptive diagnosis of malignant meningitis. However, all tests were negative and, on withdrawal of the morphine and the antidepressant, and with a single injection of 40 mg flupenthixol, his condition resolved. Interestingly, he was free of pain during this episode. About 6 weeks later he was again in sufficient pain to need opioids, and tentative administration of a single tablet of 30 mg sustained-release morphine produced, within a few hours, a recurrence of his psychosis, although in a milder form consisting only of disordered thought. This episode was relieved by flupenthixol within a day. I had initially assumed that it was the combination of the tricyclic antidepressant and morphine that had caused this reaction, but I now realise that it was the morphine alone. Fortunately, in this patient’s case, phenazocine was adequate in controlling pain and did not cause any unusual symptoms to return. Canbury Medical Centre, 1 Elm Road, Kingston upon Thames, Surrey KT2 6HR
MICHAEL D’SOUZA
DESCRIBING THE AIDS EPIDEMIC
SIR,-Professor Anderson and his colleagues (May 9, p 1073) say of my Nature paper1 that I used an inappropriate probability distribution and parameters for the incubation period of AIDS. This view seems inconsistent with their criticism of Brookmeyer and Gail’s2 attempt to establish a minimum size of the AIDS epidemic in the United States on the grounds that "many combinations of different values of the epidemiological parameters" appear to fit in with what we know of the epidemic so far. I used the normal distribution to model the probability of AIDS in time following infection (the AIDS density function) but also suggested that the log-normal form might eventually prove to be more appropriate. The normal distribution which appeared to give the best fit with transfusion cases, and also described the growth of HIV infection in the US and UK, had a mean of 14 or 15 years andaa standard deviation of about 5 years. Besides normal and log-normal distributions several othef might be suitable for the AIDS density function. The Weibutt distribution, used by Lui et al3 and by Anderson and colleagues,has the advantage that it can produce a wide variety of possible shape but without the two long "tails" that characterise normal distribn’ tions. This distribution is widely used in the modelling of epidemic* =
=
99 but in typical epidemics we are interested in new infections while in predicting AIDS cases the emphasis at present should be on the probability of disease developing, over time, in someone who is already infected. Failure to appreciate this has, I believe, adversely affected epidemiological research on AIDS. Lui et aP used transfusion data to estimate an AIDS density function for Weibull distribution, and found a mean of 4-5 years. This is much too low and Anderson et al seem to recognise this when they choose 8 years on the grounds that this "mirrors the widely held belief that the current estimate is bound to rise as the duration of observation of patients infected by blood transfusion increases". If an estimate provided by the Weibull distribution is so far out would it not be better to question whether the distribution itself is the appropriate one before making such modifications? I suggested a mean incubation of 14-15 years. Anderson et al seem to favour 8 years but take out insurance by remarking that 30-50 years of longitudinal study may be required to fmd out what proportion of HIV-infected people will proceed to AIDS and after how long. Their outright rejection of a 15 year mean is therefore strange. Anderson et al, by setting the mean for sexual activity at 10 per year and the variance at 200, make no allowance for changes in sexual practices or for changes in infectivity in those infected. We know from the Middlesex Hospital study4 that there seem to have been hardly any new infections after mid-1984 in male homosexuals presenting at a sexually transmitted disease clinic. A similar picture of low recent growth in infection is suggested from the infection statistics on recruits to the US armed forces. My model (normal, mean 15 years) produces just this pattern while figure 2 in Anderson’s (Weibull, 8 years) does not. Anderson et al claim that their model produces seropositivity rates for highly active male homosexuals that are in line with the Middlesex Hospital figures. This may be true for 1986 but for 1984 the difference was large (21-6% infected in the Middlesex study versus 3-5% in the Anderson model). Middlesex figures suggest that most infections occurred before 1984; the Anderson figures suggest that most infections occurred later, and mainly in 1986. 1 suggested! that AIDS will develop in almost every HIVinfected individual unless a treatment is forthcoming. Total numbers infected to date in the UK according to Anderson’s p = 1, mean =4year model would be 5822 people, and for the p = 1, mean =8 year model would be 20 084 (p is the proportion infected who will acquire AIDS). Known HIV seropositives in the UK already exceed 5822, and even 20 084 is well below current estimates. This implies that for an 8 year mean Weibull model to be correct p would have to be 0’3-0’5, not 1.00-there seems little reason for such optimism. Their emphasis on the transmission of the disease may have caused Anderson et al to underestimate the importance of the AID S density function. Most of the growth in AIDS numbers is being produced from the increasing probability through time of HIVinfected persons contracting AIDS, and little of it through the current spread of infection. Predicting AIDS cases over the next 5-10 years will depend mainly on our understanding of the AIDS density function, rather than on accurate predictions of the spread of
infection. St Stephen’s Hospital,
MALCOLM REES
London SW10 9TH
1 Rees M. The sombre view of AIDS. Nature 1987; 326: 343-45. 2. Brookmeyer R, Gail MH. Minimumsize of theacquiredimmunodeficiencysyndrome (AIDS) epidemic in the United States. Lancet 1986; ii: 1320-22. 3 Lui KJ, Lawrence DN, Morgan WM A model-based approach for mean incubation period oftransfusion-associated acquired immunodeficiency syndrome. Proc Natl Acad Sci USA 1986, 83: 3051-55. 4. Came CA, Weller IVD, Johnson AM, et al. Prevalence of antibodies to human immunodeficiency virus, gonorrhoea rates, and changes in sexual behaviour in homosexual men in London. Lancet 1987; i: 656-58.
transmission and natural history of HI V infection, much of which is still unknown. Anderson et al remark that "30-50 years of longitudinal study may be required" to gather the data needed for classical models of epidemic spread. In contrast, we proposed a method for estimating the minimum size of the epidemic by projecting AIDS cases from among those already infected.l The method depends only on counts of AIDS cases in previous years and an estimate of the incubation distribution. We stressed the importance of the incubation distribution and reported on the sensitivity of our projections to variations in this distribution. The method essentially consists of estimating infection times by back-calculating from observed AID S incidence data via use of the incubation distribution. Anderson et al challenge us "both on technical grounds and because [we] ignore the number and dynamics of the seropositive individuals in the population". This number and dynamics are a strength not a weakness in predicting the minimum size of the epidemic. As for technical grounds, the integral we used is exact, not an approximation as stated by Anderson et al, and follows from the definition of a cumulative distribution function. Anderson et al cite no other technical defects in our work nor can we find any on the basis of their criticisms. Anderson et al’s table illustrates that the main variable influencing AIDS projections is the incubation distribution, as previously discussed by us. We have found our methods are also useful for obtaining short-term projections, which are not nearly as sensitive to the assumed incubation period distribution as are long-term projections. Although these short-term projections do not account for new infections, they may be accurate because of the relatively long incubation period of HIV infection. Indeed, using only 1985 data, our projections of the number of AIDS cases diagnosed in the USA in 1986 was 15 100. The actual number diagnosed in 1986 after adjustment for reporting delays (as of May 18, 1987) was 14 682. Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205, USA
RON BROOKMEYER
National Cancer Institute,
Bethesda, Maryland
MITCHELL H. GAIL
1. Brookmeyer R, Gail MH. Minimum size of the acquired immunodeficiency syndrome (AIDS) epidemic in the United States. Lancet 1986; ii: 1320-22.
AIDS DEFINITION FOR AFRICA
SiR,—The article by Colebunders and co-workers1 should encourage clinicians and epidemiologists working in Africa to adopt the World Health Organisation’s provisional clinical case-definition of AIDS. The Rwandese Ministry of Public Health adopted this definition for a surveillance programme that began in June, 1986. All cases meeting the clinical definition were tested for HIV antibodies
by enzyme immunoassay (’Vironostika’; Organon Tekinka) and by indirect immunofluorescence assay (IFA) using uninfected cells as internal control (JLC, Allaman). The table compares the positive predictive value for HIV seropositivity of the WHO case-definition in the first 117 patients diagnosed in various regions of Rwanda. This predictive value for HIV seropositivity calculated in urban-based adults compares favourably with that calculated in 95 patients meeting the Centers for Disease Control case-definition of AIDS and diagnosed during the same period. However, when compared with its value in urban adults the predictive value of the WHO definition for HIV POSITIVE PREDICTIVE VALUE FOR HIV SEROPOSITIVITY OF WHO AND OF CDC CLINICAL CASE-DEFINITION OF AIDS IN RWANDA
METHODS FOR PROJECTING THE AIDS EPIDEMIC
S!R,—The calculations by Professor Anderson and colleagues
(May 9, p 1073) illustrate the difficulties
in
projecting the AIDS
epidemic with classical models and methods for the spread of an epidemic. The models require accurate information on the
*% of total
meeting WHO (or CDC) cntena who were found HIV antibody positive by
enzyme unmunoassay and I FA
falling after transurethral resection to 124/80 mm Hg. One patient, with mean blood pressure 180/110 mm Hg at age 48, had not been treated with drugs. His plasma renin activity was 5 67 pmol h-1 ml-l (recumbent) and 9-18 (ambulant). Postoperatively his blood pressure fell to 120/80 mm Hg and his plasma renin activity was reduced to 3-07 pmol h-1 ml-l (recumbent) and 3 97 (ambulant) (normal ranges 1-2-2-4 and 30-43, respectively). The hypertension in these cases may result from increased sodium retention, high renin secretion, or decreased activity of renomedullary vasodepressor substances. Jones et al provide suggestive evidence of sodium retention, indicating volume overload, but this may be linked with high renin secretion. High renin hypertension has been described in unilateral obstruction of the urinary tract with raised renin concentration within renal vein blood derived from the obstructed kidney.2-4 Relief of obstruction restored blood pressure and renal vein renin concentration to nonnal.2 Apart from correcting hypertension, which was present in 52% of Jones and colleagues’ patients, surgery is necessary to restore renal function. Initial glomerular filtration rate ranged from 20 to 25 (mean 23) ml per min per 1 -73 m2 in my four patients, and recovery took many months and in one case years. Inappropriate hypertensive drug treatment could mask this decline in renal function. Singleton Hospital, Sketty, Swansea SA2 8QA
R. R. GHOSE
1. Ghose RR, Birks JL. Secondary hypertension accompanying high pressure chronic retention. Postgrad Med J 1985; 61: 167-69. 2. Belman AB, Kopp KA, Simon NM. Renal-pressor hypertension secondary to unilateral hydronephrosis. N Engl J Med 1968; 278: 1133-36. 3. Nemoy NJ, Fichman MP, Sellars A. Unilateral ureteral obstruction: a cause of reversible high renin content hypertension. JAMA 1973; 225: 512-13. 4. Squiteri AP, Ceccarelli FE, Wurster JC. Hypertension with elevated renal vein renins secondary to ureto-pelvic junction obstruction. J Urol 1974; iii: 284-87.
SEX RATIO IN OUTBREAKS OF PARVOVIRUS B19 INFECTION
SiR,—Amside is a village of about 2300 people on the estuary of the River Kent in south Cumbria. From the middle of October to the end of December, 1986, an epidemic of erythema infectiosum occurred in the primary school of 165 children ; 101 children and 5 of the 8 female teachers fell ill with a rash. Only 2 children were tested but both were positive for parvovirus B 19-specific IgM. 22 adults in the village had a rash during this time; 11 were tested and B19 infection was demonstrated in 10. The remaining adult had no evidence of recent B 19 infection, and no cases had evidence of recent rubella. 21 of the 22 adult cases were in females and all had arthralgia. It has been suggested that the female preponderance of clinically apparent laboratory-diagnosed B19 infections may be a consequence of females being more likely to attend general practitioners and have investigations done because of an awareness of the dangers of a rash in pregnancy. However, in this village community, questioning of many residents and the diagnosed cases failed to reveal any further cases in men. One possibility is that males are less likely to have a clinically apparent illness. Another is that adult infection is most likely to result from contact with infected children, and females would have more prolonged contact; this possibility is suggested by the age and sex linked seroepidemiological study from West Germany presented in abstract by T. F. Schwartz, M. Roggendorf, and F. Deinhardt at the Third European Congress of Clinical Microbiology (The
Hague, 1987). The adult male case was of interest because B19 DNA was present in the first serum collected 3 days after the onset of pruritus and mild erythema followed by arthralgia. B19-specific IgM was not detected in this serum although it was present in a sample collected 11 days later. It is usually thought that in B 19 infection the viraemia precedes the rash so that sera taken soon after the onset of a rash would be expected to have detectable specific IgM.l At the time of the epidemic there were 5 pregnant women in the village and all were tested. One woman had a subclinical B19 infection at about 35 weeks’ gestation and the pregnancy proceeded uneventfully to term. Twins were delivered and seem normal. The
4
remaining
women
were
detected) but none had
a
susceptible (B19-specific IgG not or serological evidence of
clinical illness
infection. Several B19 outbreaks in villages or schools have been reported but there has been little information on the sex ratio in adults. B19 diagnostic services report a higher frequency of symptomatic illness in femalesand this outbreak suggests that the sex difference is real and not a reflection of bias in cases being selected for investigation.
recent
Department of Virology, Preston Infirmary, Preston PR1 6PS The
Surgery, Arnside
Joint Department of Medical Microbiology, University College London and Middlesex Hospital Medical School, London
P. MORGAN-CAPNER J. WRIGHT
J. P. LONGLEY M.
J. ANDERSON
1. Anderson
MJ, Higgins PG, Davis LR, et al. Experimental parvoviral infection in humans. JInf Dis 1985; 152: 257-65. 2. Cohen BJ. Human parvovirus B19 and fifth disease. In: Mortimer PP, ed. Public health virology, 12 reports. London: Public Health Laboratory Service, 1986. 130-43.
UNUSUAL REACTION TO MORPHINE
SiR,—Isaw an unusual drug reaction in a 68-year-old man who had a terminal carcinoma of the prostate with spinal secondaries. He became depressed and was started on dothiepin, 75 mg at night, in addition to sustained-release morphine, 30 mg a day. His pain was controlled on this regimen for a week, then his morphine dose was increased to 60 mg daily. Within 24 h he had a bizarre psychotic reaction which started with paranoid delusions and anxiety, and worsened into stupor within hours. He was admitted with a presumptive diagnosis of malignant meningitis. However, all tests were negative and, on withdrawal of the morphine and the antidepressant, and with a single injection of 40 mg flupenthixol, his condition resolved. Interestingly, he was free of pain during this episode. About 6 weeks later he was again in sufficient pain to need opioids, and tentative administration of a single tablet of 30 mg sustained-release morphine produced, within a few hours, a recurrence of his psychosis, although in a milder form consisting only of disordered thought. This episode was relieved by flupenthixol within a day. I had initially assumed that it was the combination of the tricyclic antidepressant and morphine that had caused this reaction, but I now realise that it was the morphine alone. Fortunately, in this patient’s case, phenazocine was adequate in controlling pain and did not cause any unusual symptoms to return. Canbury Medical Centre, 1 Elm Road, Kingston upon Thames, Surrey KT2 6HR
MICHAEL D’SOUZA
DESCRIBING THE AIDS EPIDEMIC
SIR,-Professor Anderson and his colleagues (May 9, p 1073) say of my Nature paper1 that I used an inappropriate probability distribution and parameters for the incubation period of AIDS. This view seems inconsistent with their criticism of Brookmeyer and Gail’s2 attempt to establish a minimum size of the AIDS epidemic in the United States on the grounds that "many combinations of different values of the epidemiological parameters" appear to fit in with what we know of the epidemic so far. I used the normal distribution to model the probability of AIDS in time following infection (the AIDS density function) but also suggested that the log-normal form might eventually prove to be more appropriate. The normal distribution which appeared to give the best fit with transfusion cases, and also described the growth of HIV infection in the US and UK, had a mean of 14 or 15 years andaa standard deviation of about 5 years. Besides normal and log-normal distributions several othef might be suitable for the AIDS density function. The Weibutt distribution, used by Lui et al3 and by Anderson and colleagues,has the advantage that it can produce a wide variety of possible shape but without the two long "tails" that characterise normal distribn’ tions. This distribution is widely used in the modelling of epidemic* =
=
99 but in typical epidemics we are interested in new infections while in predicting AIDS cases the emphasis at present should be on the probability of disease developing, over time, in someone who is already infected. Failure to appreciate this has, I believe, adversely affected epidemiological research on AIDS. Lui et aP used transfusion data to estimate an AIDS density function for Weibull distribution, and found a mean of 4-5 years. This is much too low and Anderson et al seem to recognise this when they choose 8 years on the grounds that this "mirrors the widely held belief that the current estimate is bound to rise as the duration of observation of patients infected by blood transfusion increases". If an estimate provided by the Weibull distribution is so far out would it not be better to question whether the distribution itself is the appropriate one before making such modifications? I suggested a mean incubation of 14-15 years. Anderson et al seem to favour 8 years but take out insurance by remarking that 30-50 years of longitudinal study may be required to fmd out what proportion of HIV-infected people will proceed to AIDS and after how long. Their outright rejection of a 15 year mean is therefore strange. Anderson et al, by setting the mean for sexual activity at 10 per year and the variance at 200, make no allowance for changes in sexual practices or for changes in infectivity in those infected. We know from the Middlesex Hospital study4 that there seem to have been hardly any new infections after mid-1984 in male homosexuals presenting at a sexually transmitted disease clinic. A similar picture of low recent growth in infection is suggested from the infection statistics on recruits to the US armed forces. My model (normal, mean 15 years) produces just this pattern while figure 2 in Anderson’s (Weibull, 8 years) does not. Anderson et al claim that their model produces seropositivity rates for highly active male homosexuals that are in line with the Middlesex Hospital figures. This may be true for 1986 but for 1984 the difference was large (21-6% infected in the Middlesex study versus 3-5% in the Anderson model). Middlesex figures suggest that most infections occurred before 1984; the Anderson figures suggest that most infections occurred later, and mainly in 1986. 1 suggested! that AIDS will develop in almost every HIVinfected individual unless a treatment is forthcoming. Total numbers infected to date in the UK according to Anderson’s p = 1, mean =4year model would be 5822 people, and for the p = 1, mean =8 year model would be 20 084 (p is the proportion infected who will acquire AIDS). Known HIV seropositives in the UK already exceed 5822, and even 20 084 is well below current estimates. This implies that for an 8 year mean Weibull model to be correct p would have to be 0’3-0’5, not 1.00-there seems little reason for such optimism. Their emphasis on the transmission of the disease may have caused Anderson et al to underestimate the importance of the AID S density function. Most of the growth in AIDS numbers is being produced from the increasing probability through time of HIVinfected persons contracting AIDS, and little of it through the current spread of infection. Predicting AIDS cases over the next 5-10 years will depend mainly on our understanding of the AIDS density function, rather than on accurate predictions of the spread of
infection. St Stephen’s Hospital,
MALCOLM REES
London SW10 9TH
1 Rees M. The sombre view of AIDS. Nature 1987; 326: 343-45. 2. Brookmeyer R, Gail MH. Minimumsize of theacquiredimmunodeficiencysyndrome (AIDS) epidemic in the United States. Lancet 1986; ii: 1320-22. 3 Lui KJ, Lawrence DN, Morgan WM A model-based approach for mean incubation period oftransfusion-associated acquired immunodeficiency syndrome. Proc Natl Acad Sci USA 1986, 83: 3051-55. 4. Came CA, Weller IVD, Johnson AM, et al. Prevalence of antibodies to human immunodeficiency virus, gonorrhoea rates, and changes in sexual behaviour in homosexual men in London. Lancet 1987; i: 656-58.
transmission and natural history of HI V infection, much of which is still unknown. Anderson et al remark that "30-50 years of longitudinal study may be required" to gather the data needed for classical models of epidemic spread. In contrast, we proposed a method for estimating the minimum size of the epidemic by projecting AIDS cases from among those already infected.l The method depends only on counts of AIDS cases in previous years and an estimate of the incubation distribution. We stressed the importance of the incubation distribution and reported on the sensitivity of our projections to variations in this distribution. The method essentially consists of estimating infection times by back-calculating from observed AID S incidence data via use of the incubation distribution. Anderson et al challenge us "both on technical grounds and because [we] ignore the number and dynamics of the seropositive individuals in the population". This number and dynamics are a strength not a weakness in predicting the minimum size of the epidemic. As for technical grounds, the integral we used is exact, not an approximation as stated by Anderson et al, and follows from the definition of a cumulative distribution function. Anderson et al cite no other technical defects in our work nor can we find any on the basis of their criticisms. Anderson et al’s table illustrates that the main variable influencing AIDS projections is the incubation distribution, as previously discussed by us. We have found our methods are also useful for obtaining short-term projections, which are not nearly as sensitive to the assumed incubation period distribution as are long-term projections. Although these short-term projections do not account for new infections, they may be accurate because of the relatively long incubation period of HIV infection. Indeed, using only 1985 data, our projections of the number of AIDS cases diagnosed in the USA in 1986 was 15 100. The actual number diagnosed in 1986 after adjustment for reporting delays (as of May 18, 1987) was 14 682. Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205, USA
RON BROOKMEYER
National Cancer Institute,
Bethesda, Maryland
MITCHELL H. GAIL
1. Brookmeyer R, Gail MH. Minimum size of the acquired immunodeficiency syndrome (AIDS) epidemic in the United States. Lancet 1986; ii: 1320-22.
AIDS DEFINITION FOR AFRICA
SiR,—The article by Colebunders and co-workers1 should encourage clinicians and epidemiologists working in Africa to adopt the World Health Organisation’s provisional clinical case-definition of AIDS. The Rwandese Ministry of Public Health adopted this definition for a surveillance programme that began in June, 1986. All cases meeting the clinical definition were tested for HIV antibodies
by enzyme immunoassay (’Vironostika’; Organon Tekinka) and by indirect immunofluorescence assay (IFA) using uninfected cells as internal control (JLC, Allaman). The table compares the positive predictive value for HIV seropositivity of the WHO case-definition in the first 117 patients diagnosed in various regions of Rwanda. This predictive value for HIV seropositivity calculated in urban-based adults compares favourably with that calculated in 95 patients meeting the Centers for Disease Control case-definition of AIDS and diagnosed during the same period. However, when compared with its value in urban adults the predictive value of the WHO definition for HIV POSITIVE PREDICTIVE VALUE FOR HIV SEROPOSITIVITY OF WHO AND OF CDC CLINICAL CASE-DEFINITION OF AIDS IN RWANDA
METHODS FOR PROJECTING THE AIDS EPIDEMIC
S!R,—The calculations by Professor Anderson and colleagues
(May 9, p 1073) illustrate the difficulties
in
projecting the AIDS
epidemic with classical models and methods for the spread of an epidemic. The models require accurate information on the
*% of total
meeting WHO (or CDC) cntena who were found HIV antibody positive by
enzyme unmunoassay and I FA