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Int J Epidemiol. 2018 Feb 1;47(1):236-245. doi: 10.1093/ije/dyx134.

Incidence rate estimation, periodic testing and the limitations of the mid-point imputation approach.

Author information

Africa Health Research Institute, KwaZulu-Natal, South Africa.
Nelson R Mandela School of Medicine, College of Health Sciences, University of KwaZulu-Natal, South Africa.
Department of Statistics, Department of Biobehavioral Nursing and Health Informatics, Center for Statistics and the Social Sciences, and Center for Studies in Demography and Ecology, University of Washington, Seattle, WA, USA.
Heidelberg Institute for Public Health, University of Heidelberg, Heidelberg, Germany.
Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, USA.
Research Department of Infection and Population Health, University College London, London, UK.
Centre for the AIDS Programme of Research in South Africa (CAPRISA), Durban, South Africa.
School of Nursing and Public Health, University of KwaZulu-Natal, South Africa.



It is common to use the mid-point between the latest-negative and earliest-positive test dates as the date of the infection event. However, the accuracy of the mid-point method has yet to be systematically quantified for incidence studies once participants start to miss their scheduled test dates.


We used a simulation-based approach to generate an infectious disease epidemic for an incidence cohort with a high (80-100%), moderate (60-79.9%), low (40-59.9%) and poor (30-39.9%) testing rate. Next, we imputed a mid-point and random-point value between the participant's latest-negative and earliest-positive test dates. We then compared the incidence rate derived from these imputed values with the true incidence rate generated from the simulation model.


The mid-point incidence rate estimates erroneously declined towards the end of the observation period once the testing rate dropped below 80%. This decline was in error of approximately 9%, 27% and 41% for a moderate, low and poor testing rate, respectively. The random-point method did not introduce any systematic bias in the incidence rate estimate, even for testing rates as low as 30%.


The mid-point assumption of the infection date is unjustified and should not be used to calculate the incidence rate once participants start to miss the scheduled test dates. Under these conditions, we show an artefactual decline in the incidence rate towards the end of the observation period. Alternatively, the single random-point method is straightforward to implement and produces estimates very close to the true incidence rate.

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