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Logistic regressions are subject to high uncertainty when the data are not past the inflection point. For example, for logistic regressions estimated with data up to or before inflection point, uncertainties in the upper asymptotic value $K$ can be of the same order of magnitude of the population under analysis. This paper presents a method for uncertainty reduction in logistic regression using data from a surrogate logistic process. We illustrate the procedure using the Richards\' growth function (Generalized Logistic Function) to make predictions for COVID-19 evolution in Brazilian cities at stages before and during their epidemic inflection points. We constrain the logistic function regression with $K$ calculated from selected surrogate international cities where the epidemic is clearly past its inflection point. Information gained with this constraint stabilizes the logistic regression, reducing the uncertainty in the curves\' parameters, including the rate of growth at the inflection point. The uncertainty is reduced even when the actual surrogate $K$ is used just as an anchor to simulate different epidemic scenarios. Results predicted for COVID-19 trajectories within Brazil agree with actual data. These results suggest that in the absence of big data, a simple logistic regression may provide low uncertainty if surrogate cities have been identified for estimates of $K$, even if the specifics of the evolution in the surrogate cities are different. The method may be used for other logistic models and for other logistic processes in other areas such as economics and biology, if surrogate processes can be identified.
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?:doi
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10.1101/2020.12.14.20248184
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document_parses/pdf_json/39d9c79d4e1e50747f0850cc54e1482e83b71eaf.json
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Uncertainty reduction in logistic regressions: a COVID-19 case-study using surrogate locations\' asymptotic values
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