-A1-
Modeling the Declining Positivity Rates for Human Immunodeficiency Virus
Testing in New York State
TECHNICAL APPENDIX
This appendix supplements the manuscript text by representing the stock-and-flow
diagram as a series of differential equations, and including the graphs that show the percentage
of unaware cases using the Monte Carlo simulation approach and the sensitivity analysis on the
length of life for people living with diagnosed HIV infection.
Figure A1 is the model stock-and-flow diagram that is identical to Figure 1 in the
manuscript, except that the verbal variable descriptions in the manuscript are replaced with
variable letters. Table A1 lists each variable, labels them as stocks or flows, and lists the
differential equations for each stock variable.
Figure A2 shows the Monte Carlo simulation results for the proportion of New Yorkers
living with HIV who are unaware of their infection. Rather than the three distinct scenarios for
new infections used in the manuscript, the simulation varied the number of new infections at the
start by 20%. All simulations are within the bands, with 95% of the simulations within the blue
bands, 75% of the simulations within the green bands, and 50% of the simulations within the
yellow bands. During all years, the percentage of unaware cases is between 10% and 15%, and
there is a declining trend.
Figures A3-A5 show the simulated values of the number of New Yorkers living with
diagnosed HIV, proportion living with HIV who are unaware of their infection, and estimated
percentage of HIV tests with positive results, in the base case scenario using the point estimate
-A2from the time series for new infections. In each scenario, the length of life was varied from 50%
lower to 50% higher than in the models presented in the text. The band colors should be
interpreted in the same way as Figure A2. The assumed length of life does affect the number of
people living with diagnosed HIV (Figure A3). This is not surprising, as it means that individuals
stay in box C (Figure A1) longer. However, when this assumption is varied, the estimated
proportion of unaware cases (Figure A4) yields the same two conclusions from the manuscript:
that this value declines over time, and that the estimated proportion is lower than the value
estimated using the CDC methodology. When the length of life is adjusted, there is no visible
impact on the percentage of HIV tests with a positive result (Figure 5). This is because the
denominator (all New Yorkers eligible for testing) is so large compared to the numerator
(positive tests).
-A3Figure A1. Stock and Flow Diagram of Mathematical Model with Shorthand Variable
Notation
-A4Table A1. List of Stock-and-Flow Model Variables and Differential Equations
Variable
Acutely Infected Unaware of
HIV Infection
Early Stage HIV Unaware of
HIV Infection
Mid State HIV Unaware of
HIV Infection
Late Stage HIV Unaware of
HIV Infection
People Living with Diagnosed
HIV Infection
New Infections per Month
Notation
Z
Type
Stock
Change
Zt = Zt-1 + dt * (c – j – f )
Y
Stock
Yt = Yt-1 + dt * (f – g – k)
A
Stock
At = At-1 + dt * (g – h – l)
B
Stock
Bt = Bt-1 + dt * (h – i – m)
C
Stock
Ct = Ct-1 + dt * (j + k + l+ m – u)
c
Flow
Acutely Unaware Moving to
Early Stage
Early Stage Unaware Moving
to Mid Stage
Mid Stage Unaware Moving to
Late Stage
Late Stage Unaware Deaths
f
Flow
g
Flow
h
Flow
i
Flow
Acutely Infected Tested
j
Flow
Early Stage Tested
k
Flow
Mid Stage Tested
l
Flow
Late Stage Tested
m
Flow
Diagnosed Deaths
u
Flow
-A5Figure A2: Estimated Percentage of New Yorkers Living with HIV Who Are Unaware of
Percentage Unaware
Their Infection from 2006 to 2010, using Monte Carlo Simulation
The graph illustrates simulated results, with Monte Carlo simulation on variation in the number
of new infections. All simulations are within the gray bands, with 95% of the simulations within
the blue bands, 75% of the simulations within the green bands, and 50% of the simulations
within the yellow bands.
-A6Figure A3: Estimated Number of New Yorkers Living with Diagnosed HIV from 2005 to
People Living With HIV Diagnoses
2010, with Sensitivity Analysis on Length of Life
The graph illustrates simulated results, with Monte Carlo simulation on variation on the average
length of life. All simulations are within the gray bands, with 95% of the simulations within the
blue bands, 75% of the simulations within the green bands, and 50% of the simulations within
the yellow bands.
-A7-
Figure A4: Estimated Proportion of New Yorkers Living with HIV Who Are Unaware of
Proportion Unaware
their Infection from 2005 to 2010 for Base Case, with Sensitivity Analysis on Length of Life
The graph illustrates simulated results, with Monte Carlo simulation on variation on the average
length of life. All simulations are within the gray bands, with 95% of the simulations within the
blue bands, 75% of the simulations within the green bands, and 50% of the simulations within
the yellow bands.
-A8-
Figure A5: Estimated Percentage of HIV Tests with Positive Results in New York from
Percent Positive
2005 to 2010 for Base Case, with Sensitivity Analysis on Length of Life
The graph illustrates simulated results, with Monte Carlo simulation on variation on the average
length of life. The variance in the variable is not visible because the denominator (total New
Yorkers eligible for testing) is so large. Changes in the numerator are insignificant.