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Biostatistics

22/10/2020 Client: mmm78901 Deadline: 3 days

A study was conducted to assess the sensitivity and specicity of four dif-


ferent human immunodeciency virus (HIV) serology tests (Koblavi-Deme


et al. 2001). The Determine test was among the four, it was developed by


Abbott Laboratories (an American provider of health care, medical devices


and pharmaceuticals) and was found to have a true negative rate (the true


negative rate is also called specicity) of 99.4% and a true positive rate (the


true positive rate is also called sensitivity) of 100%. The true negative rate


of a test for a disease is the probability that someone without the disease


tests negative. The true positive rate of a test for a disease is the probabil-


ity that someone with the disease tests positive. HIV may be transmitted


from an expecting parent to their child by transmission during childbirth


or by transmission to the fetus during pregnancy (throughout, assume that


there's no other way for a newborn to be infected). Treatment by the drugs


zidovudine or nevirapine has been shown to reduce the rate of these sorts


of transmission of HIV by 38% to 50% in the absence of other intervention


(Koblavi-Deme et al. 2001).




a) Suppose that an expecting parent is infected with HIV and they are


treated with zidovudine or nevirapine during pregnancy. Suppose that


after they give birth, a Determine serology test reports a positive test


for HIV. What is the probability that the child does not have HIV?


Round your answer to the nearest 10-th of a percent.




b) UNAIDS (an organization established by the United Nations Economic


and Social Council) estimates the prevalence of HIV in C^ote d'Ivoire


among people aged 15-49 to be 2.6%. If a Determine serology test re-


ported a positive test for HIV in someone selected uniformly at random


among all people in C^ote d'Ivoire aged 15-49, what is the probability


that the person does not have HIV? Round your answer to the nearest


10-th of a percent.




c) In the USA, according to the Centers for Disease Control (a public


health institute within the United States Department of Health and


Human Services), if someone has a positive serology test for HIV they


are not diagnosed as HIV-positive until a second follow-up test also


yields a positive test result. What is the probability that someone is


incorrectly diagnosed as HIV-positive (i.e., if someone is not infected


with HIV, what is the probability that their rst test and also their


second follow-up test are both positive)? Suppose that both tests are


Determine serology tests, and also assume that the test results are


statistically independent. Express your answer in expected number of


events in a million (i.e. something like `a 36 in a million chance' or


`a one in a million chance'). Also: In one sentence, what is a possible


argument as to why the assumption of independence of the two test


results might be wrong? (Your argument does not have to be sound,


but it must be valid without being tautological).




d) What is the probability that an HIV infected expecting parent trans-


mits HIV to their child either during childbirth or through transmit-


ting HIV to the fetus during pregnancy, given that the parent has not


received treatment with the drugs zidovudine or nevirapine, and in


the absence of other intervention, according to the preamble of this


problem (in concordance with Koblavi-Deme et al. 2001)?

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