05/01/93
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STANFORD - Widely used to improve efficiency in industry, mathematical models are now being applied to AIDS policy decisions by two researchers at Stanford University and the Veterans Administration Medical Center in Palo Alto.
Margaret Brandeau and Douglas Owens have found, for example, that offering HIV screening tests to all women of child-bearing age would be cost effective if the women found to be infected decreased their risky behavior by at least 13 percent.
"The largest benefit of screening women accrues not from preventing the infection in newborns, since relatively few births of HIV- infected children are prevented, but from reducing the spread of infection to other adults," they wrote in a journal article with two former colleagues, Carol Sox and Robert Wachter.
A clinic serving a higher risk subset of the population would find screening tests even more cost effective from society's point of view, said Owens, a researcher with the V.A. and the Stanford School of Medicine.
It was not cost effective, however, for the state of Illinois to require HIV tests of couples applying for marriage licenses, because the group screened was disproportionately made up of low-risk people, said Brandeau of Stanford's School of Engineering.
"After the first 12,000 people planning to marry in that state were screened, only four people were found to be infected. A study showed that with the same amount of money, the state could have purchased 160 million condoms, paid for AZT treatment for one year for everybody with AIDS in Illinois or quadrupled their annual expenditure on AIDS education," said Brandeau, who is co-editing a book due out later this year on modeling the AIDS epidemic.
In a separate study, Owens found that the risk to doctors and nurses from treating HIV-infected patients "is comparable in magnitude to other risks that health-care workers have faced knowingly and have accepted, such as the risk from Hepatitis B infection."
"HIV infection has a much higher mortality than Hepatitis B, but your chance of being infected with HIV from a needle-stick is about 1 in 300, compared with 1 in 5 for Hepatitis B," Owens said.
The occupational risks from both HIV and Hepatitis B are large enough that the medical profession should continue to look for cost- effective methods to increase the safety of medical personnel without reducing patients' access to health care, he said.
The researchers have yet to formally model the effectiveness of programs to make condoms available in high schools, but Brandeau said that simple "back-of-the-envelope calculations" tell her that high school students would have to increase their unprotected exposures to HIV by more than tenfold before providing condoms, which have a 10 percent failure rate, would lead to more cases of HIV infections than would occur if condoms were not made available to the students.
"We don't think this simple argument is sufficient to overcome some people's political or moral objections to condom availability programs, but it may nonetheless change one's opinion about whether a controlled experiment is necessary to investigate a program's effectiveness," she said.
The point of all their research on AIDS, Brandeau and Owens say, is not to tell health officials and elected officials what decisions to make, but to provide them with a way to compare the effectiveness of various proposals. "We don't have unlimited resources to fight this disease, so we need to choose to spend our money where it will do the most good," Brandeau said. To their economic analysis, she said, policy- makers must add consideration of the legal, social and ethical implications of proposed policies.
As a professor of industrial engineering and engineering management, Brandeau spends much of her time working on planning problems for manufacturing systems, such as how to set up printed circuit board assembly processes and how to design efficient automated material-handling systems. She became interested in how her mathematical skills could be applied to health policy when she was a Stanford student research assistant. She worked with former Stanford Professor David Eddy on calculating the social benefits and costs of different strategies of screening for colorectal cancer.
Owens, a medical doctor and professor, focuses his research on problems of health policy, such as using mathematical modeling to develop better screening and treatment guidelines for various medical conditions.
Owens and Brandeau began their work on AIDS by refining a turn-of-the-century model of how malaria spreads through a population.
"A good analogy to how an epidemic develops is the spread of a rumor or knowledge," Brandeau said. "Let's say one person in 100 at a cocktail party knows something, and people are walking around talking with each other. The process can be modeled with a differential equation that will tell you how many people will know the information at any point in time. With AIDS, our model can tell us how many will be infected with the disease."
To model AIDS well, Brandeau needed to work with Owens who better understood what characteristics of the disease and treatment were important to capture in the model.
"In the case of HIV infection, you may have 8 to 10 years without significant symptoms, so people can go a long period without knowing they are infected," he said. "That's one of the important features we have to capture in our model, because an infected person has more opportunities to unknowingly transmit infection if the disease progresses slowly."
The researchers divided the infected group into subcategories - those who don't know they have the disease, those who know it but are not sick, and those who are sick. Using other research on people's risky sexual and needle-sharing behavior, they then divided the population into people with high, low and medium risk for spreading and getting the disease.
In this basic framework, the model can mathematically incorporate the effects of a particular screening, education or partner- tracing program and the behavior changes expected to go along with them.
"Our purpose, unlike some other research, is not really to determine how many people will be in the high-risk group five years from now," Owens said. "We are asking what happens when you perform an intervention, such as screening for AIDS, that changes the course of the epidemic. We want to know how many cases of HIV infection will be prevented, along with the associated monetary costs and benefits."
In general, the researchers say they've found screening programs are cost effective, because it costs society little to screen compared to the value of the forgone labor that results from each new infection.
"Assuming that the cost of screening and counseling is $40 per woman screened, then the cost of identifying 10 HIV positive women is approximately $40,000," Brandeau said, since approximately 1,000 women screened would turn up 10 positives.
"Our analysis takes a societal perspective. If the identification of these 10 women leads to just one fewer HIV infection in total among their adult contacts, and the discounted future earnings of such an adult equal $500,000, then the $40,000 spent on testing and counseling yields $500,000 in indirect economic savings to society," Owens said.
Said Brandeau: "Even if an individual earns only $5,500 a year, getting sick with AIDS at age 30 leads to $100,000 in lost earnings."
Brandeau and Owens plan to continue their AIDS modeling work by assessing interventions targeted to adolescents, such as high-school- based condom availability programs, and by developing screening guidelines that are tailored to specific clinical settings.
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