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Logistic regression is a common classification method in supervised learning. Surprisingly, there are very few solutions for performing it and selecting variables in the presence of missing values. We develop a complete approach, including the estimation of parameters and variance of estimators, derivation of confidence intervals and a model selection procedure, for cases where the missing values can be anywhere in covariates. By well organizing different patterns of missingness in each observation, we propose a stochastic approximation version of the EM algorithm based on Metropolis-Hasting sampling, to perform statistical inference for logistic regression with incomplete data. We also tackle the problem of prediction for a new individual with missing values, which is never addressed. The methodology is computationally efficient, and its good coverage and variable selection properties are demonstrated in a simulation study where we contrast its performances to other methods. For instance, the popular multiple imputation by chained equation can lead to biased estimates while our method is unbiased. We then illustrate the method on a dataset of severely traumatized patients from Paris hospitals to predict the occurrence of hemorrhagic shock, a leading cause of early preventable death in severe trauma cases. The aim is to consolidate the current red flag procedure, a binary alert identifying patients with a high risk of severe hemorrhage. The methodology is implemented in the R package misaem.

To decrease d-lactic acid production cost, sugarcane molasses and soybean meal, low-cost agro-industrial wastes, were selected as feedstock. First, sugarcane molasses was used directly by Lactobacillus delbrueckii S–NL31, and the nutrients were released from soybean meal by protease hydrolysis. Subsequently, to ensure intensive substrate utilization and enhanced d-lactic acid production from sugarcane molasses and soybean meal, adaptation of L. delbrueckii S–NL31 to substrates was performed through adaptive laboratory evolution. After two-phase adaptive laboratory evolution, the evolved strain L. delbrueckii S–NL31-CM3-SBM with improved cell growth and d-lactic acid production on sugarcane molasses and soybean meal was obtained. To decipher the potential reasons for improved fermentation performance, a metabolomics-based approach was developed to profile the differences of intracellular metabolism between initial and evolved strain. The in-depth analysis elucidated how the key factors exerted influence on d-lactic acid biosynthesis. The results revealed that the enhancement of glycolysis pathway and cofactor supply was directly associated with increased lactic acid production, and the reinforcement of pentose phosphate pathway, amino acid metabolism, and oleic acid uptake improved cell survival and growth. These might be the main reasons for significantly improved d-lactic acid production by adaptive laboratory evolution. Finally, fed-batch simultaneous enzymatic hydrolysis of soybean meal and fermentation process by evolved strain resulted in d-lactic acid levels of 112.3 g/L, with an average production efficiency of 2.4 g/(L × h), a yield of 0.98 g/g sugar, and optical purity of 99.6%. The results show the applicability of d-lactic acid production in L. delbrueckii fed on agro-industrial wastes through adaptive laboratory evolution.