Forecasting Pediatric Aids

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In this section, we review some methodological approaches for assessing the scope of the pediatric AIDS epidemic. The incubation period of perinatally transmitted HIV infection is somewhat shorter than for other transmission modes (Auger, Thomas, De Gruttola, 1988). Furthermore, in some settings one has access to nearly exhaustive HIV seroprevalence surveys among newborns. Thus, the preferred methodological approaches for assessing the scope of pediatric AIDS are different than for adult AIDS. Predictions for pediatric AIDS are best obtained by using several methodologies and data sources. We propose an approach for assessing the pediatric epidemic that combines empirical extrapolations, back-calculations, and HIV seroprevalence survey data. The methods are illustrated on the New York City pediatric AIDS epidemic.

Table 10.2 lists the various modes of transmission for pediatric AIDS cases in the United States. The vast majority (84%) of cases result from perinatal transmission (mother to child). Because of the shorter incubation period of pediatric AIDS, short-term forecasts of pediatric AIDS strongly depend not only on the numbers of newborns infected years ago but also on the current and future perinatal infection rates. In contrast, short-term projections of adult AIDS incidence depend

Table 10.2 Classifications of Pediatric AIDS by Risk Group in the United States

1. Mother at risk for AIDS/HIV infection a. Mother is IVDU

b. Mother had sex with IVDU

c. Mother had sex with bisexual male d. Mother born in pattern II country c. Mother was transfusion recipient d. Mother with other or unspecified risk

2. Child was recipient of blood transfusion, component or tissue

3. Child with hemophilia/coagulation disorder

4. Undetermined

Source: HIV/AIDS Surveillance Report, Centers for Disease Control, January 1991. Based on cases reported through December 1990.

primarily on the number of people infected several years earlier, because the risk of developing AIDS in the first few years following infection is small in adults. The annual number of perinatally infected newborns is given by (Chin, 1990),

i where jV( is the number of infected women at age i; is the proportion of women at age i who give birth in the year (i.e., the age specific fertility rate); and/» is the probability of transmission from an infected mother to child. A number of different epidemiological studies have suggested that the transmission probability, p, is approximately one-third (Section 2.4.3).

A hybrid approach to forecasting AIDS in New York City, using pediatric AIDS incidence data through 1986, is summarized in four steps as follows:

1. Use pediatric AIDS incidence data through 1986, together with an estimate of the pediatric incubation period, to reconstruct perinatal infection rates for the period 1981-6, using back-calculation methods.

2. Use seroprevalence surveys among newborns in New York to estimate the perinatal infection rate in 1988.

3. Use simple regression methods to obtain a smoothed reconstruction of the perinatal infection curve for the period 1981-8. Use simple extrapolation to forecast perinatal infection rates in the short-term.

4. Propagate forward the perinatal infection rates derived in step 3 by using the incubation period to obtain projections of pediatric AIDS incidence.

Step 1. Table 10.3 is a crossclassification of pediatric (perinatal) AIDS cases in New York City by birth year and incubation period. The incubation period for perinatally transmitted AIDS is defined as the age of AIDS diagnosis. The data in Table 10.3 are right truncated because AIDS cases with long incubation periods may not yet be diagnosed. The data structure of Table 10.3 is the same as the transfusion-associated AIDS data considered in Section 4.3 and the reporting delay data considered in Section 7.3. Methods for right truncated data outlined in Chapter 7 could be used to estimate both the incubation period distribution and the number of infected newborns by birth year.

Auger, Thomas, and De Gruttola (1988) give an estimate of the incubation period for pediatric AIDS (Table 10.4); we use this estimate to reconstruct the number of infected newborns. For example, by the end of 1987 there were 54 diagnosed AIDS cases who were born in 1986

Table 10.3 New York City Pediatric AIDS Incidence Data Crossclassified by Birth Year and Incubation Period (cases diagnosed by end of 1987)

Birth Year

Incubation Period (Years)

Cumulative Cases Diagnosed

Number Infected

0-1

1-2

2-3

3-4

4-5 5-6

6-7

1981

1

2

3

0

5 4

0

15

23

1982

1

4

3

1

1 0

10

18

1983

20

8

1

4

2 —

35

74

1984

20

2

3

4

— —

29

75

1985

27

7

14

— —

48

148

1986

42

12

— —

54

225

Notes: Data adapted from Auger, et al. (1988). Cases include only those from perinatal transmission (i.e., mother at risk of HIV infection). Number infected is obtained by dividing cumulative cases by F(T) where T is the truncation time, and F is the incubation distribution.

NJ M

Table 10.4 Incubation Period for Pediatric AIDS

F( 6) = .60 F( 7) = .70 F( 8) = .85 F(9) = .92 F(10) ss 1.00

Source: Based on Auger, Thomas, and De Gruttola (1988). Notes: F{t) is the cumulative probability of AIDS diagnosis within t years of birth. Incubation distribution is the conditional distribution given diagnosis within 10 years. It is assumed ^(10) = 1.0, which may be a reasonable assumption. Auger, Thomas, and De Gruttola estimate F*(t), the conditional distribution given diagnosis within 10 years. In this table it is assumed F = F*, that is, F( 10) = 1.0.

(for simplicity we assume they were all born in the middle of the year). The probability the incubation period is less than 1.5 years is approximately F( 1.5) = [F(2) + F(l)]/2 = .24 (from Table 10.4). Thus, the estimated number of infected children born in 1986 is 54/.24 = 225. The estimated numbers of infected children by year of birth is given in the last column of Table 10.3.

Step 2. Novick, Berns, Stricof, et al. (1989) reported the results of an ongoing newborn seroprevalence study in New York state in the one-year period from November 30, 1987, to November 30, 1988. Blood was collected from every infant using heel-prick techniques as part of a mandatory program for the detection of hereditary disorders. Assays were performed on anonymous samples, and no identifying information was abstracted. During this period in New York City, 125,120 newborns were tested, of whom 1570 were HIV positive (1.25% HIV seropositive). Assuming a perinatal transmission rate ofp = 1/3, one estimates 1570 x 1/3 = 523 perinatally transmitted infections in 1988.

Step 3. In order to piece together the infection rates based on back-calculation (1981-6) and seroprevalence surveys (1988), the infection rates were graphically smoothed by eye (Figure 10.3). A more sophisticated analysis would regress the log infection rates on a polynomial in time, using a weighted least squares approach that accounts for the variance and covariances of the estimated infection rates. It was necessary to extrapolate Figure 10.3 to obtain future perinatal infection rates. The working assumption was that rates remained constant, at least for the very short term. Thus it was assumed there were about 523 new perinatal infections per year in 1988 and thereafter. In fact, more recent work of Novick, Glebatis, and Stricof (1991) has shown that the numbers of new seronegative infants

1981 1982 1983 1984 1985 1986 1987 1988 Calendar year

Figure 10.3 New York City pediatric (perinatal) infection rates. Estimates for 1981-86 based on back-calculation; estimate for 1988 based on seroprevalence surveys among newborns.

1981 1982 1983 1984 1985 1986 1987 1988 Calendar year

Figure 10.3 New York City pediatric (perinatal) infection rates. Estimates for 1981-86 based on back-calculation; estimate for 1988 based on seroprevalence surveys among newborns.

born each year in New York City has remained constant from November 30, 1987, to March 31, 1990.

Step 4. The rates in Figure 10.3 were propagated forward using the incubation distribution to obtain AIDS incidence projections. For example, from the estimated 523 infections occurring in 1988 there are an expected 523 x (.085) = 44 AIDS cases diagnosed in 1990. The factor .085 arises by assuming that all 523 infections occurred in the middle of 1988. The probability an infant infected in the middle of 1988 would be diagnosed in 1990 is F{2.5) - F{1.5), which is [F(3) — F(l)]/2 = .085 by linear interpolation. The results of these sorts of calculations are given in Table 10.5.

A more formal modeling approach for combining AIDS surveillance with HIV seroprevalence surveys of newborns for assessing the scope of the pediatric epidemic was described by De Gruttola, Tu, and Pagano (1992). By combining these two data sources, they estimated that approximately 10.0-12.0% of children born to infected mothers will develop AIDS by age 6. They concluded that pediatric AIDS incidence in New York City will continue to rise, but at rates smaller than those in Table 10.5, perhaps because their data suggest longer incubation periods than in Table 10.4. Their analysis suggested that the median age at diagnosis of a pediatric AIDS case will increase over the next several years.

To accurately forecast health care needs it is important to consider not only AIDS incidence but also AIDS prevalence. AIDS prevalence refers to the numbers of individuals who are alive with an AIDS diagnosis. In order to forecast AIDS prevalence, AIDS incidence would be "forward calculated" using the survival function for AIDS. Scott, Hutto, Makuch, et al. (1989) report a median survival of pediatric AIDS (time from AIDS diagnosis to death) of 38 months. Assuming an exponential survival distribution, this suggests that 80.3% of the cases that survive through the end of the current year would survive to the end of the next year. For each cohort of new AIDS cases, the factor 80.3% is successively applied to estimate the numbers of survivors by year following diagnosis. Applying such calculations to the annual AIDS incidence data in Table 10.5, one projects sharp increases in the prevalence of pediatric AIDS in New York City from fewer than 100 cases in 1985 to over 1500 cases in 1995.

This method of forecasting pediatric AIDS depends on a number of data sources and methods. The results are therefore subject to several sources of uncertainty. The results are sensitive to the estimated recent perinatal infection rate based on seroprevalence surveys (e.g., the estimated number of 523 perinatally transmitted infections in 1988 in New York City) and to the assumption that this rate persists. Second, the incubation period of perinatally transmitted HIV infection is uncertain. The results of Auger, Thomas, and De Gruttola (1988) were based on right truncated data and do not account for incubation periods associated with perinatal transmission longer than 10 years (see

Table 10.5 Forward Calculation of Perinatal Infection Rates to Obtain Pediatric AIDS Incidence

Year of Infection

Yearly Number Infected

Expected Yearly Number of AIDS Diagnoses

1987

1988

1989

1990

1991

1992

1993

1994

1995

1981

16

1.4

2.0

1.8

1.2

0

0

0

0

0

1982

35

3.2

3.2

4.4

3.9

2.6

0

0

0

0

1983

60

5.1

5.4

5.4

7.5

6.6

4.5

0

0

0

1984

95

5.7

8.1

8.6

8.6

11.9

10.5

7.1

0

0

1985

148

12.6

8.9

12.6

13.3

13.3

18.5

16.3

11.1

0

1986

225

33.8

19.4

13.5

19.1

20.3

20.3

28.1

24.8

16.9

1987

343

30.9

51.5

29.2

20.6

29.2

30.9

30.9

42.9

37.7

1988

523

47.1

78.5

44.5

31.4

44.5

47.1

47.1

65.4

1989

523

47.1

78.5

44.5

31.4

44.5

47.1

47.1

1990

523

47.1

78.5

44.5

31.4

44.5

47.1

1991

523

47.1

78.5

44.5

31.4

44.5

1992

523

47.1

78.5

44.5

31.4

1993

523

47.1

78.5

44.5

1994

523

47.1

78.5

1995

523

47.1

Totals

93

146

201

244

285

331

376

419

460

Note: Yearly number infected is obtained from Figure 10.3.

Note: Yearly number infected is obtained from Figure 10.3.

SI SI

Table 10.4). The results also depend on the assumption that about one third of initially seropositive newborns are, in fact, infected with HIV (Section 2.4.3).

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