Median CD4 count at diagnosis and proportion of late diagnoses are not good
indicators of HIV case finding
eMETHODS
CD4 count at diagnosis and proportion of late diagnoses measure the distribution of infection
among newly diagnosed, i.e., P(Duration|Diagnosis), but for HIV case finding, the quantify of
interest is the probability of diagnosis given an patient’s infection duration, i.e.,
P(Diagnosis|Duration). The relationship between the two probabilities can be expressed in the
below formula using Bayes Rule.
𝑃(𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛|𝐷𝑖𝑎𝑔𝑛𝑜𝑠𝑖𝑠) =
𝑃(𝐷𝑖𝑎𝑔𝑛𝑜𝑠𝑖𝑠|𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛)𝑃(𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛)
𝑃(𝐷𝑖𝑎𝑔𝑛𝑜𝑠𝑖𝑠)
As the formula demonstrates, the quantity that is simpler to observe in actual data,
P(Duration|Diagnosis) is proportional to the quantity of interest, P(Diagnosis|Duration), by a
factor of P(Duration)/P(Diagnosis). However, differences in P(Duration|Diagnosis) over time or
between populations do not correspond to proportional differences in P(Diagnosis|Duration),
because P(Duration)/P(Diagnosis) varies in a single population over time or between
populations in different stages of the epidemic.
To further illustrate the differences of these two probabilities, we use an example with
hypothetical data. CD4 count at diagnosis and proportion of late diagnoses are used to present
P(Duration|Diagnosis), and HIV case detection rate is used to present P(Diagnosis|Duration).
HIV case detection rate is the rate at which undiagnosed HIV infections are detected by HIV
case finding programs and can be measured as the number of new diagnoses in a year divided
by the sum of the number of undiagnosed HIV-infected individuals at the beginning of the year
and the number of new infections in the year. HIV case detection rate varies by duration of
infection that people in their early or late stage of infection are more likely to be diagnosed with
a higher HIV case detection rate because of a recent exposure or symptoms. We assume a
case detection rate of 25% among new infections, who have been infected for less than 1 year,
and 90% among persons infected for 9 or more years. For ease of presentation and
understanding, we assume an equal case detection rate of 8% among those infected for
between 1 year and less than 9 years.
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We present the number of undiagnosed and diagnosed infections by duration of infection in
three communities with an emerging epidemic, a stable epidemic, and a declining epidemic,
respectively. The number of undiagnosed persons by duration of infection in a stable epidemic
is estimated based on an incidence of 1,000 new infections every year in the last 10 years and
the above mentioned case detection rates; the number of undiagnosed persons in an emerging
epidemic is estimated based on an incidence of 1,000 new infections 10 years ago and a
steadily increasing incidence since with an incidence of 1,200 this year and the above
mentioned case detection rates; the number of undiagnosed persons in a declining epidemic is
estimated based on an incidence of 1,000 new infections 10 years ago and a steadily declining
incidence since with an incidence of 800 this year and the above mentioned case detection
rates.
Based on the previous study findings that among untreated HIV-infected persons, the average
time for HIV infection to progress to AIDS (CD4 < 200 cells/mm3) is 10 years and the average
loss of CD4 count is 50 cells/mm3 per year 1,2, we estimate the CD4 count at diagnosis to be
200 cells/mm3 at the end of the 9th year of infection and adding back 50 cells/mm3 per year, e.g.,
250 and 300 cells/mm3 at the end of the 8th and 7th year of infection, respectively. The
proportion of late diagnoses is the number of late diagnoses (≥9 years in duration of infection)
divided by the total number of new diagnoses. The crude case detection rate is the number of
new diagnoses in a year divided by the sum of the number of undiagnosed at the beginning of
the year and the number of new infections in the year. The adjusted case detection rate is a
weighted average of duration of infection-specific case detection rates, where the weights are
the proportions of persons in the corresponding groups of a standard population. In our
analysis, we use a direct standardization method by combining the undiagnosed HIV patient
populations in the three communities to create a standard population. The case detection rate
among new infections, i.e., the cumulative probability of diagnosis within 1 year of infection, is
the number of newly diagnosed new infections (<1 year in duration of infection) divided by the
total number of new infections. We performed all analyses with Microsoft Excel.
References
1.
Kuo JM, Taylor JM, Detels R. Estimating the AIDS incubation period from a prevalent cohort. Am
J Epidemiol. 1991;133(10):1050-1057.
2.
Rodriguez B, Sethi AK, Cheruvu VK, et al. Predictive value of plasma HIV RNA level on rate of CD4
T-cell decline in untreated HIV infection. JAMA. 2006;296(12):1498-1506.
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