Comparison of machine learning algorithms for clinical event prediction (risk of coronary heart disease).

AIM: The aim of this study is to compare the utility of several supervised machine learning (ML) algorithms for predicting clinical events in terms of their internal validity and accuracy. The results, which were obtained using two statistical software platforms, were also compared. MATERIALS AND METHODS: The data used in this research come from the open database of the Framingham Heart Study, which originated in 1948 in Framingham, Massachusetts as a prospective study of risk factors for cardiovascular disease. Through data mining processes, three data models were elaborated and a comparative methodological study between the different ML algorithms - decision tree, random forest, support vector machines, neural networks, and logistic regression - was carried out. The global selection criterium for choosing the right set of hyperparameters and the type of data manipulation was the area under a curve (AUC). The software tools used to analyze the data were R-Studio® and RapidMiner®. RESULTS: The Framingham study open database contains 4240 observations. The algorithm that yielded the greatest AUC when analyzing the data in R-Studio was neural network applied to a model that excluded all observations in which there was at least one missing value (AUC = 0.71); when analyzing the data in RapidMiner and applying the same model, the best algorithm was support vector machines (AUC = 0.75). CONCLUSIONS: ML algorithms can reinforce the diagnostic and prognostic capacity of traditional regression techniques. Differences between the applicability of those algorithms and the results obtained with them were a function of the software platforms used in the data analysis.

π-Hydrogen Bonding Probes the Reactivity of Aromatic Compounds: Nitration of Substituted Benzenes.

The shifts of phenol O-H stretching vibration frequencies [Δν(OH)exp] upon π-hydrogen bonding with aromatic compounds is proposed as a spectroscopic probe of the reactivity of aromatic substrates toward electrophiles. A single infrared spectrum reflecting the Δν(OH)exp shift for an aromatic species in a reference solvent (CCl4 in this study) provides a good estimate of reactivity. The methodology is applied in rationalizing reactivity trends for the BF3 catalyzed nitration by methylnitrate in nitromethane of 20 aromatic reactants, including benzene, 11 methylbenzenes, several monoalkyl benzenes, the four halobenzenes, and anisole. Literature kinetic data are employed in the analysis. Very good correlations between relative rates of nitration and Δν(OH)exp are obtained. The approach is best applied to reactions, where the initial interactions between the reactants controls the rates. A new theoretical quantity, the shifts (with respect to benzene) of the molecular electrostatic potential at 1.5 Å over the centroid of the aromatic ring [Δ V(1.5)] is defined and shown to provide a good description of substituent effects on properties of the aromatic species. B3LYP density functional and MP2 ab initio methods combined with the 6-311++G(3df,2pd) basis set are employed in evaluating the Δ V(1.5) values.

Nucleophilic Influences and Origin of the SN 2 Allylic Effect.

The potential energy surfaces for the SN 2 reactions of allyl and propyl chlorides with 21 anionic and neutral nucleophiles was studied by using ωB97X-D/6-311++G(3df,2pd) computations. The "allylic effect" on SN 2 barriers was observed for all reactions, and compared with propyl substrates, the energy barriers differed by -0.2 to -4.5 kcal mol-1 in the gas phase. Strong correlations of the SN 2 net activation barriers with cation affinities, proton affinities, and electrostatic potentials at nuclei demonstrated the powerful influence of electrostatic interactions on these reactions. For the reactions of anionic (but not neutral) nucleophiles with allyl chloride, some of the incoming negative charge (0.2-18 %) migrated into the carbon chains, which would provide secondary stabilization of the SN 2 transition states. Activation strain analysis provided additional insight into the allylic effect by showing that the energy of geometric distortion for the reactants to reach the SN 2 transition state was smaller for each allylic reaction than for its propyl analogue. In many cases, the interaction energies between the substrate and nucleophile in this analysis were more favorable for propyl chloride reactions, but this compensation did not overcome the predominant strain energy effect.

An Experimentally Established Key Intermediate in Benzene Nitration with Mixed Acid.

Experimental evidence is reported for the first intermediate in the classic SEAr reaction of benzene nitration with mixed acid. The UV/Vis spectroscopic investigation of the reaction showed an intense absorption at 320 nm (appearing as a band shoulder) arising from a reaction intermediate. Our theoretical modeling shows that the interaction between the two principal reactants with solvent (H2SO4) molecules significantly affects the structure of the initial complex. In this complex, a larger distance between the aromatic ring and nitronium ion precludes the possibility for electronic charge transfer from the benzene π-system to the electrophile. The computational modeling of the potential energy surface reveals that the reaction favors a stepwise mechanism with intermediate formation of π- and σ-(arenium ion) complexes.

Arenium ions are not obligatory intermediates in electrophilic aromatic substitution.

Our computational and experimental investigation of the reaction of anisole with Cl2 in nonpolar CCl4 solution challenges two fundamental tenets of the traditional SEAr (arenium ion) mechanism of aromatic electrophilic substitution. Instead of this direct substitution process, the alternative addition-elimination (AE) pathway is favored energetically. This AE mechanism rationalizes the preferred ortho and para substitution orientation of anisole easily. Moreover, neither the SEAr nor the AE mechanisms involve the formation of a σ-complex (Wheland-type) intermediate in the rate-controlling stage. Contrary to the conventional interpretations, the substitution (SEAr) mechanism proceeds concertedly via a single transition state. Experimental NMR investigations of the anisole chlorination reaction course at various temperatures reveal the formation of tetrachloro addition by-products and thus support the computed addition-elimination mechanism of anisole chlorination in nonpolar media. The important autocatalytic effect of the HCl reaction product was confirmed by spectroscopic (UV-visible) investigations and by HCl-augmented computational modeling.

Electrophilic aromatic sulfonation with SO3: concerted or classic S(E)Ar mechanism?

The electrophilic sulfonation of several arenes with SO(3) was examined by electronic structure computations at the M06-2X/6-311+G(2d,2p) and SCS-MP2/6-311+G(2d,2p) levels of theory. In contrast to the usual interpretations, the results provide clear evidence that in nonpolar media and in the absence of catalysts the mechanism of aromatic sulfonation with a single SO(3) is concerted and does not involve the conventionally depicted 1:1 σ complex (Wheland) intermediate. Moreover, the computed activation energy for the 1:1 process is unrealistically high; barriers for alternative 2:1 mechanisms involving attack by two SO(3) molecules are 12-20 kcal/mol lower! A direct 2:1 sulfonation mechanism, involving a single essential transition state, but no Wheland type intermediate, is preferred generally at MP2 as well as at M06-2X in isolation (gas phase) or in noncomplexing solvents (such as CCl(4) or CFCl(3)). However, in polar, higher dielectric SO(3)-complexing media, M06-2X favors an S(E)Ar mechanism for the 2:1 reaction involving a Wheland-type arene-(SO(3))(2) dimer intermediate. The reaction is slower in complexing solvents, since the association energy, e.g., with nitromethane, must be overcome. But, in accord with the experimental kinetics (second-order in SO(3)), attack by two sulfur trioxide molecules is still favored energetically over reaction with a single SO(3) in CH(3)NO(2). The theoretical results also reproduce the experimental reactivity and regioselectivity trends for benzene, toluene, and naphthalene sulfonation accurately.

Electrophile affinity: quantifying reactivity for the bromination of arenes.

Electrophile affinity (Ealpha), a recently proposed theoretical construct based on computed energies of arenium ion formation, rationalizes the substrate reactivity and regioselectivity of S(E)Ar bromination of three sets of available experimental arene data where closely related conditions had been employed uniformly. The Ealpha parameters (computed at B3LYP/6-311+G(2d,2p)) correlated very well (r = 0.987) with the partial rate factors (log f) for 18 regiospecific brominations of benzene and various methyl benzenes. Analysis of the bromination reactivities of 32 mono- and polysubstituted benzenes including various polar groups gave similar results (r = 0.982). The electrophile affinity treatment also accounted satisfactorily (r = 0.957) for bromination reactivities of polybenzenoid hydrocarbons. Conversely, comparisons with NBO-based charges and the electrostatic potential at nuclei (EPN) were not generally successful. The uniform effectiveness of Ealpha treatments for the cases analyzed with regard both to relative substrate reactivity (e.g., benzene vs toluene) and to regiospecificity (e.g., the positional reactivity of toluene) supports the "limiting case" conventional interpretation of the electrophilic aromatic substitution mechanism as being governed by the energy of sigma-complex formation. Although other mechanisms are possible under different conditions, the computed energies of arene-dibromine pi-complex formation for the polysubstituted benzene set examined correlated poorly with experimental reactivity data (r = 0.714) and only varied from 1.8 (for benzene) to 3.5 kcal/mol, in contrast to the 10(12) range in reactivity measured experimentally.

Electrophile affinity: a reactivity measure for aromatic substitution.

The reactivity and regioselectivity of the electrophilic chlorination, nitration, and alkylation of benzene derivatives were rationalized by comparing literature data for the partial rate factors (ln f) for these S(E)Ar processes with theoretical reactivity parameters. The Electrophile Affinity (Ealpha), a new quantity, is introduced to characterize reactivity and positional selectivity. Ealpha is evaluated theoretically by the energy change associated with formation of an arenium ion by attachment of a model electrophile to the aromatic ring. The dependence between Ealpha and ln f values for chlorination for 11 substitutions of benzene and methyl benzenes had a high correlation coefficient (r = 0.992). Quite satisfactory correlations between Ealpha values and partial rate factors also were obtained for the nitration of substituted benzenes (r = 0.971 for 12 processes) and benzylation of benzene and halobenzenes (r = 0.973 for 13 processes). These results provide clear evidence for the usefulness of the electrophile affinity in quantifying reactivity and regiochemistry. Satisfactory relationships (r >0.97) also were found between EPN (electrostatic potential at nuclei) values, which reflect the variations of electron density at the different arene ring positions, and the experimental partial rate factors (ln f) for the chlorination and nitration reactions, but not for the benzylation. This disaccord is attributed to strong steric influences on the reaction rates for substitutions involving the bulky benzyl moiety.