Benefits of a new Metropolis–Hasting based algorithm, in non-linear regression for estimation of ex vivo antimalarial sensitivity in patients infected with two strains

• We model the antimalarial sensitivity in a blood sample with two strains of parasite.
• We develop a Metropolis–Hasting algorithm to estimate parameters of the model.
• We compare our estimation results with three other algorithms.
• We evaluate our algorithm on a simulation study, on in vitro and ex vivo data.
• For poor concentration design, our algorithm gives accurate results.

Malaria is one of the world׳s most widespread parasitic diseases. The parasitic protozoans of the genus Plasmodium   have developed resistance to several antimalarial drugs. Some patients are therefore infected by two or more strains with different levels of antimalarial drug sensitivity. We previously developed a model to estimate the drug concentration (IC50)(IC50) that inhibits 50% of the growth of the parasite isolated from a patient infected with one strain. We propose here a new Two-Slopes model for patients infected by two strains. This model involves four parameters: the proportion of each strain and their IC50, and the sigmoidicity parameter. To estimate the parameters of this model, we have developed a new algorithm called PGBO (Population Genetics-Based Optimizer). It is based on the Metropolis–Hasting algorithm and is implemented in the statistical software R. We performed a simulation study and defined three evaluation criteria to evaluate its properties and compare it with three other algorithms (Gauss–Newton, Levenberg–Marquardt, and a simulated annealing). We also evaluated it using in vitro data and three ex vivo datasets from the French Malaria Reference Center.Our evaluation criteria in the simulation show that PGBO gives good estimates of the parameters even if the concentration design is poor. Moreover, our algorithm is less sensitive than Gauss–Newton algorithms to initial values. Although parameter estimation is good, interpretation of the results can be difficult if the proportion of the second strain is close to 0 or 1. For these reasons, this approach cannot yet be implemented routinely.