### Abstract

We propose a method to estimate the usually unknown time since infection for individuals infected with human immunodeficiency virus type 1 (HIV‐1). If we assume the time since infection has an exponential prior distribution, then under the model the conditional distribution of time since infection, given the CD4 level at the time of the first positive HIV‐1 antibody test, is a truncated normal density. We applied the method to prevalent cohort data both from intravenous drug users and from homosexual/bisexual men. For the intravenous drug users the estimated mean time since infection was 15.0 months from infection at a presumed mean CD4 level of 1060 cells/ml to first positive antibody test at a CD4 level of 597 cells/ml, which was the average CD4 at enrolment for infected subjects. For the homosexual/bisexual men the estimated mean time since infection was 16.7 months from infection at a presumed mean CD4 level of 699 cells/ml to first positive antibody test at an average CD4 level of 577 cells/ml. We performed a validation study using initially seronegative subjects in these cohorts who seroconverted to HIV‐1‐positive antibody status during the follow‐up period. For the intravenous drug users, data were too few to provide definitive verification of the method. In the cohort of homosexual/bisexual men, however, there was a total of 70 seroconverters with relevant data. Among them, the median absolute difference between the midpoint of the known seroconversion interval and the estimated mean infection date was 4.6 months, conditional on CD4‐lymphocyte measurements taken approximately 18 months subsequent to infection. Conditional on CD4 approximately 30 months after infection, this median difference increased modestly to 8.2 months. Our analysis suggested that the underlying mathematical model tends to overestimate short times since infection and underestimate long times since infection. We consider potential corrective modifications to the model.

Original language | English (US) |
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Pages (from-to) | 231-244 |

Number of pages | 14 |

Journal | Statistics in Medicine |

Volume | 13 |

Issue number | 3 |

DOIs | |

State | Published - Feb 15 1994 |

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### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability

### Cite this

*Statistics in Medicine*,

*13*(3), 231-244. https://doi.org/10.1002/sim.4780130306