Marketed nanopharmaceuticals for brain disorders.
\r\n\tGeothermal energy is recognized as a potential renewable energy source, immense and practically inexhaustible, with a solid technological maturity, clean, versatile, and useful to generate electricity, among other multiple applications. However, as in any transformation process, environmental and social impacts cannot be excluded.
\r\n\r\n\tThis book will compile scientific research from geothermal areas where environmental and social issues have been successfully addressed as an example of social, environmental, and economic equilibrium. Based on participatory monitoring as a strategy for social acceptance or corporate responsibility from a deep-rooted environmental ethic that has become a social commitment. This natural resource is very complex therefore, environmental and social knowledge and experience are of great importance for its further sustainable development.
",isbn:"978-1-80356-999-4",printIsbn:"978-1-80356-998-7",pdfIsbn:"978-1-83880-282-0",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,isSalesforceBook:!1,hash:"339e74c3bcb3c7725a830d8b41278ca1",bookSignature:"D.Sc. Zayre Ivonne González Acevedo and Dr. Marco Antonio García Zarate",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/11933.jpg",keywords:"Engineering Developments, Gas Filters, Reinjection, Cascade Uses, Environmental Monitoring, Greenfield, Brownfield, Environmental Indicators, Environmental Impact Assessment, Environment and Social Acceptance, Social Engagement, Corporate Social Responsibility",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"April 12th 2022",dateEndSecondStepPublish:"May 10th 2022",dateEndThirdStepPublish:"July 9th 2022",dateEndFourthStepPublish:"September 27th 2022",dateEndFifthStepPublish:"November 26th 2022",remainingDaysToSecondStep:"12 days",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Pioneer researcher in the analysis of the environmental, social, and economic impact of Mexican geothermal zones, with more than 15 years of experience, and awarded her Ph.D. degree from the University of Heidelberg.",coeditorOneBiosketch:"A researcher in the analysis of the total environment and its impact on society, with more than 40 years of experience in the field and awarded his Ph.D. degree from the Autonomous University of Baja, California.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"260177",title:"D.Sc.",name:"Zayre Ivonne",middleName:null,surname:"González Acevedo",slug:"zayre-ivonne-gonzalez-acevedo",fullName:"Zayre Ivonne González Acevedo",profilePictureURL:"https://mts.intechopen.com/storage/users/260177/images/system/260177.jpg",biography:"Chemical Engineer on Environment (Dec 98), Technological Institute of Toluca, Mex. Chemical Engineer Master of Process Integration (Sep 02), University of Guanajuato. Gto. Mex. Dr.rer.nat. magna cum laude Environmental Geochemistry (July 06), University of Heidelberg, BW, Germany. Sabbatical Stay (Sept 19 - 20), Department of Renewable Resources, University of Alberta, Canada. \r\nResearcher in the Department of Environmental Studies. National Institute of Nuclear Research, Mex. (Oct 07-Dec 11). Researcher Geology Department, Center of Scientific Research and High Education of Ensenada, Baja California (Jan 12 up today). \r\nResponsible Work Package 9, “Environmental, Social and Economic Impacts of Enhanced and Super-Hot Geothermal Systems” in the GEMex project, “International Cooperation in Research and Development between Mexico and the European Union in Geothermal Energy”. Responsible specific project 25, “Sustainable Development and Environmental Impact Assessment of three Geothermal Exploration Zones with Exploitation Potential in Mexico”.",institutionString:"Center for Scientific Research and Higher Education at Ensenada",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Center for Scientific Research and Higher Education at Ensenada",institutionURL:null,country:{name:"Mexico"}}}],coeditorOne:{id:"260179",title:"Dr.",name:"Marco Antonio",middleName:null,surname:"García Zarate",slug:"marco-antonio-garcia-zarate",fullName:"Marco Antonio García Zarate",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRXp9QAG/Profile_Picture_2022-04-01T07:16:47.jpg",biography:'Course of "Technical Specialization in Optical Laboratorian" at the Applied Physics Department of CICESE, with a scholarship from CONACYT from July 1980 to July 1981. Industrial Engineer, Technologic Institute of Ensenada 2010. Master of Science in Arid Zone Ecosystem Management at the Faculty of Sciences of the UABC, scholarship from CONACYT (August 2013), obtaining Honorable Mention and Ph.D. in Environment and Development at the Institute of Oceanographic Research of the UABC, scholarship from CONACYT achieving Honorable Mention (October 2016), Scholar Merit awarded by the UABC Ensenada Baja California Unit; February 2017. Teaching classes and workshops at undergraduate, master\'s, and industry levels, participation in disciplinary and multidisciplinary projects.',institutionString:"Center for Scientific Research and Higher Education at Ensenada",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Center for Scientific Research and Higher Education at Ensenada",institutionURL:null,country:{name:"Mexico"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"11",title:"Engineering",slug:"engineering"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"444315",firstName:"Karla",lastName:"Skuliber",middleName:null,title:"Mrs.",imageUrl:"https://mts.intechopen.com/storage/users/444315/images/20013_n.jpg",email:"karla@intechopen.com",biography:"As an Author Service Manager, my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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From outside, this delicate organ is protected by a bony structure called skull while internally it is sheltered from noxious substances via some complex barrier systems. These protective barriers impede the treatment strategies adopted for therapeutic purposes [1]. The management of CNS disorders such as dementia, epilepsy, panic disorders, meningitis, and brain tumors greatly depends on the means of attaining higher drug levels at the targeted sites. Physico-chemical properties of the drug molecule mainly dictate its ability to penetrate these barriers and achieve a therapeutic outcome. Thus the ultimate pharmacological response obtained by the potential drug depends on multiple factors like its effectiveness, its uptake or penetration through protective barriers or its ability to bind with specific carrier proteins for efficient transport across the membrane [2]. Among these barriers, blood-brain barrier (BBB) presents one of the types that hinder the transport of the medicinal compounds for treating brain ailments. BBB serves as both physical and transport barrier and is present at the interface of blood and brain. It is a tight junction made of microvascular endothelial cells, astrocytes, and pericytes [3]. Therefore, the development of newer therapeutic strategies is the need of the hour to overcome these transport hurdles.
It is a tight physical junction present at the interface of CNS and blood circulation. It consists of endothelial cells that do not have fenestrations and thus restrict the influx of ions and other solutes into the brain from surrounding blood capillaries. Astrocytes and pericytes surround endothelial cells and thus make it almost an impermeable barrier. BBB allows paracellular transport of small lipophilic compounds (<400 Da) via passive diffusion. This barrier also offers active transport of some hydrophilic compounds by the means of transport proteins (e.g., P-glycoprotein) present at the junction. The transcellular pathway that is used by some compounds to enter the brain includes different mechanisms such as passive diffusion, specific transporters, and transcytosis [4].
Among the primary brain tumors, gliomas are considered the most common. These tumors make a barrier at their early stage termed as blood-brain tumor barrier (BBTB). Although BBTB is permeable at the core of glioblastomas, however, it closely resembles BBB at the peripheral regions. This combination of BBB and BBTB leads to an additional hindrance for drug delivery to reach the glioblastoma cells and thus requires newer drug development strategies to aid drug delivery to the tumor site [5].
Efflux pumps also serve as additional barriers in drug delivery to the brain that are present in endothelial cells lining. These efflux pumps are made up of protein complexes called adherens junctions primarily regulate the permeability of the endothelial barrier [6].
Blood-cerebrospinal fluid also acts as a barrier that limits the free movement of molecules and drug compounds across the brain by strictly regulating the transfer of solutes between the blood and CSF [7].
Mainly lipophilic drugs are used to treat CNS ailments and possess a molecular weight below 400 Da and log P between −0.5 and 6.0 [8, 9]. For drugs that are ionized at physiologic pH, it is their unionized fraction that determines the concentration gradient across the BBB for passive diffusion [2]. By considering these facts, a drug should be designed in such a manner that it has optimal lipid solubility so that it penetrates BBB and maintains a therapeutic concentration in the brain. But this is not that simple because only increasing the lipophilicity of the drug molecule via certain chemical modifications may not attain the desired pharmacokinetic effects as it may lead to decreased systemic solubility and bioavailability. It may also have increased protein binding and higher uptake by liver and reticuloendothelial system which ultimately leads to increased metabolism thus leading to diminished active drug concentration at the target site [2]. There are certain drug molecules that penetrate the BBB besides what their lipid solubility suggest. This penetration is attributed to the carrier-mediated transport of these polar compounds present at the tight junctions [10].
Brain targeting is potentially difficult because of multiple barriers. Recent advances in nanotechnology present opportunities to overcome such limitations and to deliver the drug to the brain targets. Nanopharmaceuticals are the relatively newer field that employed “therapeutic containing nanomaterial” with unique physicochemical properties due to their small size (one to several 100 nm), high surface to volume ratio and flexibility to alter their properties [11]. An alternate definition can be pharmaceuticals engineered on the nanoscale for the therapeutic purpose [12]. Nanopharmaceuticals comprised of different nanomaterial like polymers, lipids, amphiphilic material, metals, inorganic elements, carbon nanotubes, dendrimers, etc., to constitute nanocarriers which can be fabricated in different sizes, shapes, morphology, surface charges and surface groups for the brain-specific targeted delivery of the drug across barriers. Nanopharmaceuticals mediated drug delivery system has the power to penetrate drug moieties across CNS, either passively or actively, and improve bioavailability and therapeutic efficacy of the drug even at a lower concentration. Currently, available marketed nanopharmaceuticals for the brain are mentioned in Table 1.
Route | Brand | Nanocarrier | Indication | Manufacturer |
---|---|---|---|---|
SC | Copaxone | Glatiramer acetate | Multiple sclerosis | TEVA |
IV | DepoCyt® | Cytarabine encapsulated in multivesicular liposomes (20 μm) | Lymphomatous malignant meningitis | Leadiant Biosciences |
Epidural space injection | DepoDur® | Morphine sulfate encapsulated in multivesicular liposomes (17–23 μm) | Chronic pain | Pacira Pharmaceuticals |
IV | Opaxio® | Paclitaxel covalently linked to SLN | Glioblastoma | Cell Therapeutics |
Intratumoral Injection | NanoTherm® | Aminosilane-coated superparamagnetic iron oxide (15 nm) nanoparticles | Local ablation in glioblastoma, prostate, and pancreatic cancer | Magforce |
Oral | Avinza® | Morphine sulfate nanocrystals | Psychostimulant | Pfizer/King Pharma |
Oral | Focalin XR® | Dexmethylphenidate HCl nanocrystals | ADHD | Novartis |
Oral | Ritalin LA® | Methylphenidate HCl nanocrystals | ADHD | Novartis |
SC injection | Plegridy® | Polymer-protein conjugate (PEGylated IFN Beta-1a) | Multiple sclerosis | Biogen |
IM injection | Invega Sustenna® | Paliperidone | Schizophrenia | Janssen Pharms |
IV | AmBisome® | Amphotericin B liposome | Cryptococcal meningitis | Gilead Sciences, Inc. |
IV | Abelcet® | Amphotericin B liposome | Cryptococcal meningitis | Enzon Pharma |
IV | DaunoXome® | Daunorubicin liposome | Pediatric brain tumors | Under Phase I trial |
IV | Doxil®/Caelyx® | Doxorubicin HSPC, cholesterol, and DSPE-PEG2,000 | Glioblastoma and Pediatric brain tumors | Phase II Phase II |
IV | Myocet® | Doxorubicin EPC and cholesterol | Glioblastoma | Phase II |
IV | SGT-53 (SynerGene Therapeutics) | Cationic liposome with anti-transferrin antibody | Glioblastoma | Phase II |
— | Cornell Dots | Silica nanoparticles with a fluorophore, PEG-coated | Malignant brain tumors imaging | Phase I |
Marketed nanopharmaceuticals for brain disorders.
SC, subcutaneous; IM, intramuscular; IV, intravenous; AHDH, attention deficit hyperactivity disorder; IFN, interferon; DSPE, distearoylphosphatidylethanolamine; EPC, egg phosphatidylcholine; PEG, polyethylene glycol.
Nanopharmaceuticals could able to breach blood-brain barriers through various mechanisms. On the simple edge, their smaller size leads to passive delivery of the drugs through transcellular route across brain’s epithelial cells or choroid plexus. Criteria for the simple passive diffusion across the barriers are molecular size less than 400 Da, low hydrogen bonding capacity and lipophilicity [13, 14]. Therefore, lipophilic and tailored nanocarriers could deliver the drug through this mechanism.
While extremely hydrophobic molecules like nutrients (glucose and amino acids) pass through active diffusion mechanism with the aid of special transporter proteins. On the other hand, hydrophilic and larger molecules like transferrin and insulin pass through receptor-mediated transport across the membrane [15]. BBB majorly comprised of the endothelial layer which possessed tight junctions; the presence of proteins, namely occludins, claudins and adhesion molecules in the tight junction, make it a tougher barrier [16].
Nanopharmaceuticals are custom-made to surpass the brain barriers through these mechanisms:
Lipophilic nanocarriers (liposomes, solid lipid nanoparticles SLN) fuse with the endothelial cells and transport the drug through the transcellular pathway or endocytosis. Moreover, nanoparticles provide a sustained drug release pattern in the bloodstream, enabling higher drug concentration to cross BBB [17].
Furthermore, nanoparticles are functionalized with ligands or specific surfaces to trigger receptor-mediated transcytosis or carrier-mediated transport across BBB. Attachment of ligands like lactoferrin, transferrin, insulin facilitated receptor-mediated transport. Cationized ligands and peptides like albumin cross through receptor-mediated absorptive transport. Nanoparticles surface can be modified to utilize active transport system comprising P-glycoproteins, L-transporters, nucleoside transporter, ionic transporter, multidrug-resistant proteins that transfer the molecules into the brain by consuming adenosine triphosphate (ATP) [17]
Liposomes have been extensively studied and even FDA approved nanocarrier for brain disorders. Surface modulation of liposomes with functional proteins, peptides and polyethers aided targeted drug delivery for brain diseases [18]. PEGylated liposomes and glutathione-PEGylated liposomes evade body’s reticuloendothelial system and facilitate enhanced drug uptake across BBB [19]. Moreover, transferrin-modified liposomes [20], TAT peptide-conjugated liposomes [21], glucose-modified liposomes [22], and transferrin-folate bound liposome effectively deliver the drug across the barrier to treat multiple sclerosis [23]. Similarly, transferrin bound SLN and thiamine coated SLN were found to be efficacious in the treatment of cerebral malaria and increased drug uptake in the brain [24]. Mechanisms of transport across BBB are shown in Figure 1.
Different pathways for nanopharmaceuticals mediated transport across the blood-brain barrier (Under Creative Commons Attribution License 4.0,
Polymeric nanoparticles accumulate in the brain tissue by both passive and active mechanisms. Chitosan-poly lactic-co-glycolic acid (PLGA) nanoparticles showed enhanced delivery of coenzyme Q to the brain of transgenic mice through absorption mediated endocytosis [25]. In another study, PLGA was coupled with Tet-1 peptide to achieve neuronal targeting of curcumin in the treatment of Alzheimer’s disease. Retrograde transportation of curcumin across the barriers destroyed amyloid aggregates and scavenges oxidative radicals in the brain [26]. Similarly, ligand attached polymeric-lipidic nanoparticles like nerve growth factor (NGF) loaded poly butyl cyanoacrylate (PBCA) liposomes considerably deliver the drug across the BBB cholinergic system in the amnesic rodent model [27]. Likewise, inorganic nanocarriers show promising outcomes in terms of brain targeting. Amine functionalized multi-walled carbon nanotubes adopted transcytosis mechanism to pass BBB [28]. A natural substance wheat germ agglutinin-horseradish peroxide (WGA-hrp) was conjugated to gold nanoparticles (AuNPs) and administered in the IM injection into the mice. Results were remarkable in terms of drug penetration across BBB [29].
Dendrimers are the excellent drug carriers; their surface functionalization with folic acid, peptides, aptamers, amino acids, biotin, antibodies facilitated more site-specific targeting. To penetrate CNS barriers, dendrimers were conjugated with transferrin, lactoferrin, D-glucosamine, and leptin for more effective brain drug delivery [30].
Some other nanoparticulate systems like nanoemulsion and nanogel can be functionalized with targeting moieties (transferrin, insulin, peptides) for CNS drug delivery. Nanogels made up of PEG-polyethylenimine (PEI) and N-vinylpyrrolidone/isopropyl acrylamide have been tested to ensure CNS drug delivery potential [30].
BBB mediated drug uptake restrictions prompt scientists to investigate drug delivery potential of the nanopharmaceuticals to the brain through various routes. The ultimate objective was to enhance drug penetration across BBB and to reduce disease index. Up till now, the most commonly employed route was systemic administration through Intravenous (IV) injection. Other natural routes like oral, intranasal (IN), intrathecal (IT), intraperitoneal (IP) have been used as well. Some novel strategies like cerebral devices, implants, Ultrasound-guided nanoparticle delivery, osmotic delivery gain much attention in the recent era. Different nanopharmaceuticals are illustrated in Figure 2. List of all nanopharmaceuticals delivered through different routes have been mentioned in Table 2.
Nanopharmaceuticals classification on the basis of route and nanocarriers.
Route | Drug | Particle size | Nano component | Active ligand | Indication | References |
---|---|---|---|---|---|---|
Oral | Dalargin | ~100 nm | poly (butylcyanoacrylate) nanoparticle | Tween 80-PEG 20000 | Analgesic effect | [33] |
Oral | Indomethacin | ~320 nm | Lipidic core | poly (ε-caprolactone) coat | Glioblastoma treatment | [31] |
Oral | Saquinavir | 100–200 nm | polyunsaturated fatty acids (PUFA), Lipoid-80 and deoxycholic acid | Increase oral bioavailability and brain distribution | [32] | |
Oral | Estradiol | 138.8 ± 4.3 nm | polylactide-co-glycolide (PLGA) nanoparticles | Tween 80 coated | Alzheimer’s disease treatment | [34] |
Intraperitoneal (IP) | None | 220 ± 35 nm | Iron oxide (Fe3O4) nanoparticles | coated with a carbon shell derived from glucose | Brain cells localization | [36] |
Intranasal (IN) | Bromocriptine | 161.3 ± 4.7 nm | Chitosan nanoparticle | — | Parkinson’s disesase | [48] |
IN | Clonazepam | 15 ± 10 nm | Microemulsion | — | Increase brain/blood uptake ratio | [52] |
IN | Nimodipine | 30.3 ± 5.3 nm | Microemulsion | — | High brain uptake | [53] |
IN | Risperidone | 15.5 nm-nanoemulsion; 16.7 nm-mucoadhesive nanoemulsion | Nanoemulsion; mucoadhesive nanoemulsion | — | Schizophrenia treatment | [54] |
IN | Diadanosine-dideoxyinosine (dd) | 269–382 nm | Chitosan nanoparticles | — | Increase brain/plasm, CSF/plasma ratio | [12] |
IN | Rivastigmine | 143.1 to 3300 nm | Chitosan nanoparticle | — | Alzheimer’s disease | [50] |
IN | Venlafaxine | 167 ± 6.5 nm | Chitosan nanoparticles | — | Major depressive disorders and anxiety disorder | [51] |
IN | Duloxetine | 137.2 ± 2.88 nm | Nanostructured lipid carriers | — | Behaviorial improvement in major depressive disorder | [55] |
IN | Coumarin | 100 to 600 nm | methoxy-PEG-polycaprlactone | — | Enhanced brain penetration | [58] |
IN | Vasoactive intestinal peptide (VIP) | 90–100 nm | PEG-PLA nanoparticles (NP) | — | Protein translocation across BBB | [79] |
IN | Sumatriptan | 23.1 ± 0.4 nm | Miceller nanocarrier | — | Migraine therapy | [56] |
IN | Zolmitriptan | 23 nm | Miceller nanocarrier | Migraine therapy | [57] | |
IN | FITC labeled | 5 nm | AuNP | FITC | Brain specific delivery | [80] |
Intravenous (IV) | Azidothymidine | Transferrin anchored PEG nanoparticles | Viral infection | [81] | ||
IV | Valproic acid | Nanoparticles | Epilepsy | [82] | ||
IV | Tacrine | 35.58 ± 4.64 nm | PBCA NPs | Alzheimer’s disease | [83] | |
IV | Cabazitaxel | 24–68 nm | PEG modified Cellulose (Cellax) NPs | Glioblastoma | [84] | |
IV and intratumoral | Docetaxel/SiRNA | 110–150 nm | Peptide modified Cationic liposomes | Glioma | [85] | |
IV/Intranasal | Catalase | 9.5 nm | Exosomes | Parkinsonism | [86] | |
IV | HCFU | 50 nm | Nanogels | Glioma | [87] | |
IV (MRI) | Curcumin | <100 nm | Magnetic NPs | Detection of amyloid plexus in Alzheimer’s | [88] | |
IV | Sunitinib/anti-miR-21 oligonucleotide | <190 nm | NPs | Glioblastoma | [89] | |
IV | Monocolonal antibody (OX26) | 300–600 nm | PEG-chitosan NPs | Cerebral ischemia | [90] | |
Focused ultrasound+IV | FE3O4/SPAnH | — | Nanoparticles | Malignant glioma | [91] | |
Convection-enhanced delivery | CPT-11 | 96–101 nm | Liposomes | Intracranial tumor | [92] | |
Intrathecal | Fasudil | 100 nm | Liposomes | Subarachnoid hemorrhage | [93] | |
Intracranial | Paclitaxel | 3 mm | Nanoscale PLGA implants | Intracranial glioblastoma | [94] | |
Neural probes | Dexamethasone | 400–600 nm | PLGA nanoparticles in alginate hydrogel | Glial inflammation | [95] |
Nanopharmaceuticals administration through various routes.
PEG, polyethylene glycol; PLA, polylactic acid; FITC, fluorescein isothiocyanate; SPAnH, poly[aniline-c-sodium N-(1-one-butyric acid)] aniline; PBCA, poly(n-butyl cyanoacrylate); HCFU,
The oral route is the most convenient, non-invasive and compliant mode of administration. However, brain targeting through the oral route was not investigated largely mainly due to indirect systemic entry through absorption from the gastrointestinal tract (GIT). Harsh GIT environment, slow onset of action, shorter half-life, first pass elimination and reduced systemic absorption hampered drug therapeutic efficacy and bioavailability. Thus, oral drug delivery failed to deliver the therapeutic moiety to the brain efficiently. In this regard, nanopharmaceuticals must possess the properties to bear harsh enzymatic environment, overcome first pass metabolism and efficiently permeate through the intestinal epithelial barrier to reach the systemic circulation.
Scientists developed lipid nanocore surrounded by poly (e-caprolactone) and orally administered to the mice. The concentration of the loaded drug, indomethacin, was successively increased in the brain and efficiently treat glioblastoma in the mice model without causing BBB vessel alteration. This could serve as a basis for safe and effective brain targeting via oral route [31].
Similarly, orally administered saquinavir-loaded nanoemulsion significantly delivers the drug across BBB. Nanoemulsion was stabilized by deoxycholic acid which overpasses first-pass elimination of the drug. The oily phase, polyunsaturated fatty acids (PUFA) facilitates rapid transport to the brain. It laid the foundation for effective brain targeting through oral route [32].
Researchers formulated poly (butyl cyanoacrylate) nanoparticles, double coated with Tween 80 and polyethylene glycol (PEG)-2000 for the oral delivery of the dalargin to the brain. Dalargin is a hexapeptide, anti-nociceptive agent which could not cross BBB. However, its nanoformulation showed promising analgesic effects in the mice model, which demonstrated the potential of the nanoformulation for brain targeting via oral route [33].
Orally administered Tween 80 coated PLGA deliver estradiol successfully to the brain. The therapeutic efficacy in elevating Alzheimer’s disease was parallel to the nanoformulation administered intramuscularly [34]. In short, oral delivery of drug-loaded nanopharmaceuticals achieved preliminary success but still need to be further explored in the near future.
Intraperitoneal administration involved peritoneal cavity of the abdomen. The route is still under investigation. It has an advantage of delivering a larger amount of the drug and it is employed when a vein for the IV injection is not easily located. In addition, it can be employed when animals are not ready for oral administration. However, the route is currently limited to pre-clinical research in small animals and need to be scaled up [35].
Iron oxide nanoparticles were fabricated with the aim to target subcellular compartment of the brain cells. For this purpose, iron oxide nanoparticles with different shapes (round, biconcave, spindle, nanotube) were synthesized and coated with glucose derived fluorescent carbon layer. In-vivo administration through IP route indicated biconcave nanoparticles localized in the nuclei and nanotube-shaped nanoparticles located in the cytoplasm of the brain cells. While the carbon coated surface on iron oxide nanoparticles facilitated attachment of several therapeutic moieties on the nanoparticles for their delivery inside the brain cells [36]. Therefore, the IP route could serve as a major route to deliver the drug across the brain barriers.
Systemic route including IV drug delivery to the brain involves the receptor-mediated and adsorptive mediated transcytosis. It is the most exploited route of administration for the nanoparticles because of the immediate action systemically and locally by targeted delivery. Polybutyl cyanoacrylate (PBCA) was first used for the synthesis of the NPs intended for the brain. Analgesic dalargin was incorporated in the PBCA NPs with Polysorbate 80 coating and a marked level of analgesia was seen in the animal studies after IV administration of the NPs [37]. PBCA NPs with doxorubicin coated with Polysorbate 80 were studied for their brain delivery in the rats and showed the promising result in 2–4 hours as compared to the uncoated NPs after IV drug delivery [38]. In a similar study, Polysorbate 80 coated PBCA NPs with a size of 280 nm were evaluated for the delivery of Loperamide across BBB following IV injection. Results were quite promising in the
Recently, intranasal (IN) route for the drug delivery to the brain proved to be a reliable and non-invasive mode to cross BBB while possessing the ability to deliver a wide range of drug moieties like smaller molecules, larger macromolecules, growth factors, viral vectors and even stem cells to the brain. The transport involves either olfactory or trigeminal nerve which has a direct link from the brain and terminated in the nasal cavity at respiratory epithelium or olfactory neuroepithelium [47]. The nasal mucosa is the target tissue for the drug administration and possessed features like a larger surface area, porous endothelial membrane, huge blood flow, the absence of first-pass elimination and readily accessible. Olfactory region of nasal mucosa provide nose to brain targeting feature and could able to treat various CNS disorders like depression, pain, Alzheimer’s disease, glioblastoma, multiple sclerosis etc. Several dosage forms, sprays, suspensions, nebulizers, aerosols, gel, solutions can be utilized for IN drug delivery [47]. On the other hand, barriers like mucociliary clearance from nasal mucosa, enzymatic degradation and low degree of permeability across nasal epithelium hinder the drug targeting efficiency to the brain. As a solution, nanopharmaceuticals were used which overcome the clearance and other nasal problems due to their unique nature.
One of the studies demonstrated IN administration of chitosan nanoparticle to deliver bromocriptine, a dopaminergic agonist, to minimize motor function disorder associated with prolonged levodopa usage in the Parkinson’s disease. Results were promising in terms of motor function [48]. Didanosine-dideoxyinosine (ddI) is an antiretroviral therapy (HAART) and available in oral dosage forms, however, faced extensive degradation and elimination in GIT which decreases its bioavailability. To overcome the issues, dd loaded chitosan nanoparticles were administered through IN route. Results indicated higher brain to plasma, CSF to plasma and olfactory blood to plasma ratios in the case of IN delivered dd nanoparticles. It shows that nanoformulation can be directly delivered to the brain compartment through IN route [49].
Another research group fabricated rivastigmine loaded chitosan nanoparticle for inhibiting acetylcholinesterase in the brain through IN administration. The free drug had severe bioavailability issues and distributed to the non-targeted site with severe side effects when administered through oral or IV route. Here, chitosan nanocarrier and administration through nasal route enhanced brain uptake with higher brain/blood ratio. It further highlighted the role of nanocarrier and route in brain targeting [50]. Similarly, Venlafaxine (VLF) chitosan nanoparticles were administered to the brain through the nasal route for the treatment of major depressive disorders and anxiety disorder with improved brain uptake and enhanced bioavailability [51].
Another study showed microemulsion and mucoadhesive delivering clonazepam, an anxiolytic, sedative, hypnotic, anticonvulsant drug to the brain. The brain/blood uptake ratio of the intranasal microemulsion and mucoadhesive microemulsion were significantly higher than the IV administered microemulsion, indicating the effectiveness of IN route for brain-specific drug delivery [52]. Similarly, the microemulsion was used for the IN delivery of nimodipine to the brain cells. The microemulsion leads to 3-fold more drug uptake by the olfactory bulb than the IV route. AUC ratio of brain to plasma and cerebrospinal fluid (CSF) to plasma were higher after IN administration in comparison to IV injection. Thus, it could be a promising approach to treat neurodegenerative disorders [53]. Risperidone nanoemulsion and mucoadhesive nanoemulsion were administered through IN route for the treatment of schizophrenia. The composition of nanoemulsion included glyceryl monocaprylate as an oily phase, tween 80 as a surfactant and mixture of propylene glycol and transcutol as a co-surfactant. While mucoadhesive microemulsion had chitosan polymer which induces mucoadhesive properties. The nanoemulsion and mucoadhesive nanoemulsion improved risperidone bioavailability, prevent first pass metabolism and bypass BBB to achieve desired drug concentration at the targeted site. The brain/blood uptake ratio and drug transport efficiency were found to be significantly higher through nasal administration in comparison to the IV injection [54].
Furthermore, nanostructured lipid carriers comprising duloxetine was prepared and delivered to the brain via IN route for the treatment of the major depressive disorder. The results revealed prolonged drug release and therapeutic effect as demonstrated from improved behavior analysis after 24 hours [55].
Furthermore, micellar nanocarrier (amphiphilic nanocarriers) of sumatriptan was developed to treat an acute migraine to improve cerebral blood flow. Limitations of the drug associated with oral dosage forms and subcutaneous administration like poor bioavailability, shorter plasma half-life, and hepatic elimination have been resolved to much extent through incorporation in micellar nanocarrier. And increased brain concentration of the drug and site-retention can be achieved via nose to brain drug delivery [56]. Similarly, zolmitriptan-loaded micellar nanocarriers were prepared to target brain serotonin receptors and inhibit cranial vessel inflammation. Micellar nanocarriers were administered through nasal route with enhanced characteristics like lower particle size, higher permeation across nasal mucosa, appropriate flow rate, ability to load hydrophilic as well as hydrophobic drugs, enhanced site-retention and ultimately enhanced drug therapeutic activity [57].
Another polymer methoxy-PEG-polycaprolactone was used to encapsulate coumarin with promising brain penetration and myelin binding properties, while administered through nasal route [58]. Bioadhesive nanocarriers reported in the above studies overcome many hurdles associated with a nasal route like protection of drug against enzymatic degradation, enhanced permeability, and avoidance of mucociliary clearance. However, IN delivery of nanopharmaceuticals should be further improved with targeting moieties and incorporation of cost-effective approach.
Potential brain barriers can be by-passed by injecting the drug directly into the tissues using catheter. Such a direct delivery of therapeutic agent to the target site is termed as conventional enhanced delivery (CED). Many pre-clinical studies adapted CED to infuse nano-formulations directly into the brain [59]. C57BL/6 J mice were used to infuse a 10 μL solution of lipid nanocapsules (LNCs) having an average size of 70 nm into their skull at an infusion rate of 0.5 μL/min [60]. An alternate method for direct infusion was also reported in which drug-loaded micelles were injected by making small incisions on the skull. A foremost shortcoming CED technique is its invasiveness which requires high anesthetic doses prior to incisions, which resulted in the death of the experimental rats [61]. This technique also requires the optimization of certain factors like pH and osmolarity to surpass any brain damage [62].
Administering the drug into the carotid artery provides an alternative solution to direct delivery. This direct systemic delivery requires a catheter to directly inject drugs into the bloodstream. In a study, the efficacy of direct systemic delivery was reported almost twice to that of CED in terms of brain damage [63]. IV route is also used to deliver the drug directly into systemic circulation. Ferrociphenol-loaded lipid nanoparticles were infused to manage glioma via the IV route. The outcomes showed that mean survival of the rats was 28 days while mean survival rate recorded foe CED was of 24 days [62, 64].
Polylactic acid (PLA) and poly-dimethylaminoethyl methacrylate (PDMAEMA) were used to synthesize amphiphilic star-branched co-polymeric nanoparticles for intratumor delivery of the drugs for treating brain tumors. In a study, this system was used to deliver combined DOX and miR-21 inhibitor (miR-21i) into LN229 glioma cells directly. These micelles protected miR-21i from lysosome degradation and the release of DOX to the nucleus, which ultimately decreased the miR-21 expression. This combined DOX and miR-21i delivery surprisingly displayed an anti-proliferative efficiency compared with separate treatment of DOX or the miR-21. The outcomes revealed that this co-polymeric system was a better option for delivering genes and hydrophobic therapeutic agents [65].
Delivering the drug directly into the brain is another way of treating brain disorders. This local drug delivery has been approved by the US FDA [66]. Intrathecal administration of nanopharmaceuticals delivers the nano-drugs in the CSF. However, this route of administration is most commonly used for anesthetics and neurotic pain [67]. This route is under experimental phases in humans. It includes two different ways of delivering the therapeutic moiety, either by infusion in the intralumbar region or intraventricularly using an Ommaya reservoir placed subcutaneously and connected to the brain with a catheter [68]. Thioflavin-T was delivered by intrahippocampal injection for targeting the β amyloid in the brain using the nanoparticles. The data reported localization of thioflavin-T in the intracellular and extracellular spaces of the brain, which prevented the formation of β-amyloid aggregates in the Alzheimer’s disease. This same method can be adapted to deliver the anticancerous drugs as well as other analgesic peptides [69]. In an
Ultrasound facilitated drug penetration through brain barriers is yet another option for safe and reversible targeted drug delivery [72]. In this technique, ultrasound radiations are employed to generate shear stress on the vascular endothelium for a transient and reversible perforation in the BBB which facilitates the nanoscaled drug delivery to the targeted site. It appeared in a research outcome that docosahexaenoic acid binding with low-density lipoprotein NPs can penetrate the BBB by the application of ultrasound sonication. A near IR fluorescent dye examination revealed about 60 times greater accumulation of sonication facilitated drug delivery to the targeted site. The main advantage reported was lack of cytotoxicity or neuronal damage due to pointed ultrasound irradiation [73]. PEGylated PLA nanoparticles delivery to the brain was facilitated via ultrasound-induced perforation. β-specific antibody 6E10 was conjugated on PEG-PLA along with the coumarin 6 and DiR as fluorescent probes to assess the target site accumulation. Ultrasonication facilitated NPs penetration was about 2.5-fold more than the complementary non-sonicating therapy [74]. Ultrasound techniques can be used to aid the enhanced delivery of PEG-b-poly(l-Lysine) coupled with siRNA into glioma cells by 10-fold in conjunction with a newer gas-cored nanobubble [75].
Another targeted approach to the brain for delivering drugs is through the ocular route. The ocular route has so many advantages like reduced peripheral toxicity and direct delivery of therapeutic moiety in the target site [76]. Ocular and intranasal drug delivery for the brain was compared by a group, in which nerve growth factor (NGF) was used for treating Alzheimer’s disease. However, it was found out that intranasal drug administration was more effective and potent for brain disorders and ocular route did not perform well. However, many scientists are working for making the ocular route a success because of it being the compliant and non-invasive route [77]. There has been a huge room for the administration of nanocarrier through ocular route to the brain. Nanocarrier can facilitate drug delivery to the brain because of their size, site-retention properties and enhanced adhesion to the lacrimal fluid. The route can be exploited for the delivery of drugs and genes to CNS by avoiding systemic exposure via nanopharmaceuticals [78].
Brain-targeted drug delivery is a difficult matter due to anatomic and pathophysiological brain barriers. The current advances in nanotechnology provide a solution in the form of nanopharmaceuticals, drug containing nanocarriers, to cross the CNS barriers and to target the brain tissue in various disorders. Nanopharmaceuticals’ mode of administration into the body is an important aspect, which ultimately effects drug concentration in the brain and drug therapeutic effect. Current chapter highlighted the routes of administration through which nanopharmaceuticals can be delivered to reach the brain. Every route has pros and cons, nanopharmaceuticals overcome the route associated limitations in the delivery of drug to the brain due to their peculiar physicochemical properties and surface modulation. Translation this research area into the clinic still require investigations, as safety is the foremost concern and distribution to other body organs must be eradicated. Moreover, there is a need to control the drug delivery rate when nanopharmaceuticals reach the brain for safer action.
The authors declared no conflict of interest.
Binary classification when compared to multiple classification has wide range of real-world applications in many areas of human endeavors, such as criminal justice, education, medicine, email analysis, human resources management, pattern recognition, energy and environmental management, financial data analysis and economics, production systems management and technical diagnosis, marketing among others. Where the classification criterion comprises one or several predictor variables along with a categorical criterion, such a prediction will require the use of a predictive discriminant analysis (PDA). PDA is still the optimal method when the cost of misclassifying groups is clearly different and when there is greater interest in the accuracy of classifying separate groups. In most cases, evaluating the proportion of correct classification of a predictive discriminant function (PDF) in all sub-populations is equivalent to the estimation of the actual hit rate,
In general, the task of enhancing or improving classification accuracy was examined in two ways. Several researchers use feature or variable selection techniques to select the best subset of predictors to construct a classification model. In addition to conventional feature selection techniques, including the stepwise and all possible subset methods [4, 8, 9]. Some widely known and used methods include the principal component analysis (PCA) used to obtain a set of low-dimensional features from a large set of features [10, 11]. The branch and bound technique which uses a greedy procedure to obtain the best subset [12], the genetic search algorithm [13, 14], the shrinkage methods [10, 15], the particle swarm optimization (PSO) approach which is a meta-heuristic technique used to enhance classification accuracy [16], representative methods based on dictionary learning (DL) for classification [17, 18, 19], support vector machines (SVMS) [20], and the hyper parameter tuning approach [21, 22]. We have the sequential analysis approach as well [23]. The heteroscedastic discriminant analysis merged with feature selection [24] and the modified leave-one-out (LOOCV) cross-validation method used as an alternative to the all-possible subset method [25]. A PDF’s classification accuracy is only statistically optimal if each group sample is normally distributed with different group means, and each predictor variance is similar between the groups [7]. None of these basic assumptions regarding the validity/reliability of the PDF are considered by any of the above methods. To address these gaps in feature selection techniques, other investigators are seeking alternatives to robust PDA by replacing conventional estimators with robust estimators. Some variants of these alternative methods include the dimensionality reduction/feature extraction for outlier detection (DROUT) [26], the minimum covariance determinant (MCD) [27],
This paper provides a more comprehensive analysis of the idea and concept of the MW-GD method, as well as proposed an alternative statistical interpretation of the informative graphical diagnostic associated with the method when confronted with the challenge of differentiating between a variable shape in the groups of the 2-D area plot. The remaining sections of this paper are organized as follows. Sections 2 and 3 discuss the problems posed by the presence of outliers and legitimate contaminants in the training sample that yields the PDF, the concept of statistical optimality of the PDF classification accuracy, and the robustness of PDF, respectively. Section 4 describes in details the idea and concept of the modified winsorization with a graphical diagnostic for obtaining a statistically optimal training sample, as well as presents the proposed alternative statistical or numerical interpretation of the informative graphical diagnostic. Section 5 presents the results and discussions based on the application of two real life samples, while Section 6 presents the conclusions.
In PDA, an outlier is an observation which is not a member of a group, and is often indicative of an incorrect measurement or an incorrect allocation of the unit or observation. Such an outlying observation can cause severe problems that even the robustness of PDA may not overcome. Over the last two decades, many articles have been published about detecting outliers in discriminant analysis (DA) [31, 32, 33, 34, 35, 36, 37, 38]. In PDA, a popular means of treating outliers is to construct multiple PDFs with assumed outliers added and with assumed outliers removed [1]. The primary issue with this method is whether potential outliers should be remove one at a time, two at a time, or all at a time. With the SPSS DISCRIMINANT procedure, the chi-squared distribution is used to establish the typicality probability. These typicality probabilities are used to identify potential outliers in the context of PDA. However, Huberty and Olejnik [1] pointed out that when the group covariance matrices are not equal, the unit typicality probabilities are difficult to interpret because different distance metrics are used in the calculation. A common distance index used for detecting outliers or influential observations in the context of PDA is the Mahalanobis distance [39] which is also calculated as a byproduct in SPSS DISCRIMINANT procedure.
However, there are also hidden influential observations (or legitimate contaminants) resulting either from an incorrect distributional assumption (i.e., when the data turns out with a different structure than originally assumed) or an inherent variability of the dataset, see Osborne [30], and Iglewicz and Hoaglin [40] for more details. While hidden influential observations may actually belong to a training sample, but if not distributed randomly may reduce normality which often leads to violation of sphericity and multivariate normality assumptions in PDA. Hidden influential observation can also adversely affect the quality of the PDA solution and its generality. But how to identify and remove hidden influential observations before building a classification model (particularly in the PDA) has not receive any significant attention in the literature by statisticians or by methodologist and therefore not by any substantive researchers. Besides, the SPSS typicality or Mahalanobis index may not be able to identify hidden influential observations because their unit often belongs to a different group compared to outliers.
Therefore, much emphasis should be placed on cleaning the training sample to ensure that it meets its near-optimum condition by removing all legitimate contaminants from the training sample. This method is similar to optimizing decision trees (in particular classification trees) which consists in reducing the amount of impurity—see Myatt [41] for details. In the context of PDA, it will improve the similarity of each predictor variable variance between groups, thus improving the approximation of the true shape. This will in no doubt guarantee the statistical optimality of the PDF solution or classification accuracy.
A PDF’s classification accuracy is only statistically optimal if each group sample is normally distributed with different group means, and each predictor variance is similar between the groups [5, 7]. In addition to the above requirements, it is recommended that there be at least four to five times as many cases as predictors in order to produce more accurate estimates. Note that in PDA, the failure of the training sample to meet the assumption of normality can result in a decrease in efficiency and accuracy—see Lachenbruch [42] as cited in Klecka [43]. However, a minor violation of this assumption will not decrease the accuracy of the classification. As long as the distributions of predictors are reasonably comparable, the estimation of most multivariate parameters does not require multivariate normality [44]. Moreover, under the central limit theorem, there is no need to worry about the assumption of normality as long as each group sample contains a very large number of observations. As a general rule, a PDF will still perform strongly against non-normality as long as the smallest group has over 20 cases, and the number of predictors is less than six [45]. Due to these robustness properties of PDA, researchers are barely concerned about the assumption of normality.
But where non-normality is due to outliers and/or hidden influencing observations other than skewness, violating this assumption has serious consequences, because PDA is very sensitive to outliers [45]. Likewise, more cases could be classified into the group with greater dispersion when the assumption of equality of variance-covariance matrices is not tenable [45]. In addition, the likelihood of belonging to a group may be distorted, and the PDF may also not be able to separate the groups as much as possible [43]. The accuracy of the discriminant weights estimates may be reduced if the variances of the predictors are not all similar between groups. They may be precise but not unbiased [46]. When the homogeneity of variance test is significant, it indicates that the training sample is contaminated with outliers and/or hidden influence observations, and the significance tests are unreliable [3, 45]. It is apparent from the foregoing that, if the assumption of homogeneity of variances is not satisfied, it is probable that the assumption of multivariate normality is not equally satisfied. This suggests that multivariate normality and homogeneity of variance assumptions can be taken into account if outliers and hidden influential observations are completely removed from a training sample. The practice of researchers relying on the robustness properties of PDA without checking for outliers and hidden influential observations, which may hinder maximal separation between the groups seems to be a norm. This practice is further encouraged by the general acceptance of a hit rate of 25% above that of chance. Assuming that you get a 95% hit rate, it is certain that you will not care about the two basic assumptions of PDA.
Whereas the reason for such good performance might be that the data support simple linear or quadratic separation boundaries. The general belief that linear classifiers are robust to minor violations of its basic assumptions (in particular is the assumption of multivariate normality) is often not tenable. Studies have shown that the reliability of a PDF solution is dependent upon adherence to the underlying assumptions [5]. The primary objective of PDA is classification, and if the percentage of correct classifications is not satisfactory, it is likely that variances in predictors are not similar across groups. That is to say the training sample is not statistically optimal. Therefore, it is necessary to adopt a screening method that will effectively identify and remove legitimate contaminants from training samples before using them to build a PDF. Iduseri and Osemwenkhae [6] proposed the modified winsorization with graphical diagnostic (MW-GD) method to identify and remove legitimate contaminants from training samples. The MW-GD method produced a statistically optimal training sample when applied to a real dataset, and the resulting PDF yielded a hit rate that was statistically optimal. As a result, the uncertainty about the PDF’s actual hit rate was greatly reduced. However, the informative graphical diagnostic associated the proposed method may be difficult to interpret if there are no significant differences between a variable shape in the groups of the 2-D area plot.
This paper proposes an alternative statistical interpretation of the informative graphical diagnostic when confronted with the challenge of differentiating between a variable shape in the groups of the 2-D area plot.
In general, extreme scores or outliers bias estimates of any parameter. One notable way to correct for bias is to change the data by changing the scores so as to reduce the impact of the extreme scores or adjust the shape of the distribution. Notable variants of changing the scores method include transforming the data, trimming the data and winsorizing the data. However, in PDA, where one is interested in differences between set of variables or groups, transformation may not be a good choice to correct for bias of discriminant weights. This is because, transformation can change the units of measurements, which may in turn affects the interpretation of the data because the data now relate to a different construct compared to the original data [47]. Similarly, trimming of data seemed odd since one could just discard lots of data. To overcome these inherent drawbacks associated with both methods, the winsorization method was adopted. These approach involves replacing a percentage of the highest score with the next highest score in the data and the same percentage of the lowest score are replaced with the next lowest score in the data. One major challenge with this method is that even the next higher or lowest score might still be an extreme score. Another variant of the winsorization involves replacing extreme score with a score three standard deviations from the mean. This variant of winsorization also suffers a major drawback. As noted by Field [47], the standard deviation will be biased by extreme scores, so this means that you are replacing scores with a value that has been biased by extreme scores. To address the observed shortcomings of both variants of the winsorization method, Iduseri and Osemwenkhae [6] proposed the modified winsorization with graphical diagnostic (MW-GD) method. The method proved very effective in identifying and removing legitimate contaminants.
In this section, the modified winsorization with graphical diagnostic (MW-GD) method originally proposed by Iduseri and Osemwenkhae [6] is presented. In addition, a proposed alternative statistical interpretation of the informative graphical diagnostic associated with MW-GD method when confronted with the challenge of differentiating between bar shapes of the 2-D area plot is also presented. The MW-GD method, which involves a three-step procedure, will effectively identify and eliminate legitimate contaminants from predictor variables so that their variances between the groups are similar. The aim is to ensure that the training sample,
Let
For the training sample,
To determine what percentage of winsorization is required to eliminate the legitimate contaminants, the modified winsorization process is repeated only for the predictive variable(s) identified with the legitimate contaminants until the highest hit rate is attained, thus obtaining a near optimal training sample given as:
The optimal training sample of Eq. (1), was then used to build the optimized PDF,
where
To get a statistically optimal hit rate, let:
where
where
where
where
As described in Step 1 of Section 4.2.1, the graphical representation of the modified winsorized means makes it possible to easily identify the predictor variable(s) whose variance is not significantly similar between the groups. If the variance of a predictor variable is not similar between groups, the bars representing the modified winsorized mean values for the variable in the 2-D area plot will not have similar shape. Such a variable is interpreted to be the identified variable that contains legitimate contaminants. This means that the more the shape of the bars differ between the groups, the easier it is to interpret the 2 D area plot. It is therefore necessary to provide an alternative interpretation when it is difficult to differentiate between a variable shape in the groups of the 2-D area plot. Therefore, a simple statistical or numerical interpretation is proposed for the informative graphical diagnosis when it is difficult to differentiate between a variable shape in the groups of the 2-D area plot. This alternative numerical interpretation consists of the following two simple steps:
For each group, the modified winsorized means and their corresponding winsorized percentage values for each predictor variable are fitted to a linear regression model given as:
and
where,
The absolute difference between the obtained regression coefficients (i.e., the slope) in group 1 and 2 is computed as:
where the subscripts 1 and 2 represents groups 1 and 2. The predictor variable that has an absolute difference of 0.75 or greater will be the variable identified with legitimate contaminants. In PDA, if two samples are equal in size, there is always a 50/50 chance. Most researchers would accept a classification accuracy of 25% greater than that caused by chance. Hence, the choice of 0.75 as the decision boundary.
To evaluate the effectiveness of the modified winsorization with graphical diagnostic (MW-GD) method, two real samples (see [6] for the two data sets) were considered with the second used as a validation sample. The first training sample is from a renowned financial journal, among Japanese business leaders, which can be compared to the Economist, Financial Times, and Business Week in Europe and the United States of America. This dataset contains 50 observations from each of the two groups of Japanese financial institutions, each bank being evaluated using the following seven performance indexes: (1) return on total assets (= total profits/average total assets), (2) labor profitability (= total profits/total employees), (3) equity to total assets (= total equity/average total assets), (4) total net working capital, (5) return on equity (= earnings available for common/average equity), (6) cost-profit ratio (= total operating expenditures/total profits), and (7) bad loan ratio (= total bad loans/total loans). However, taking into account the beneficial effect of feature selection and outlier detection as a preprocessing step, a best subset and critical value of Mahalanobis distance were first obtained using the SPSS stepwise method, and its compute command for critical value of Mahalanobis distance. The stepwise approach produced a best subset which comprises return on total assets (
Thus, the classification accuracy of the PDF,
While the two critical values from the SPSS outputs for 0.95 and 0.99 used as the probabilities in the IDF.CHISQ function with four predictor variables were given as:
The Mahalanobis distance values for all cases, as reported in the case wise statistics table, were all lower than the two critical values. This means that there are neither outliers nor hidden influential observations in the dataset or training sample. Next, the MW-GD algorithm was applied to the training sample,
At
Groups | No. of replaced sample points | Modified winsorized mean values | Winsorized % | |||
---|---|---|---|---|---|---|
1 | 0 | 428.70 | 329.48 | 536.34 | 821.32 | 0 |
2 | 421.08 | 317.32 | 533.90 | 824.50 | 4 | |
4 | 415.50 | 307.60 | 533.70 | 827.40 | 8 | |
6 | 412.28 | 298.32 | 533.56 | 830.36 | 12 | |
8 | 408.90 | 290.30 | 534.46 | 833.62 | 16 | |
10 | 406.20 | 282.70 | 535.42 | 835.56 | 20 | |
2 | 0 | 341.50 | 177.20 | 368.46 | 778.70 | 0 |
2 | 335.24 | 173.20 | 366.92 | 785.80 | 4 | |
4 | 329.66 | 169.16 | 365.20 | 790.74 | 8 | |
6 | 324.76 | 166.68 | 362.94 | 794.22 | 12 | |
8 | 319.86 | 166.22 | 360.68 | 797.30 | 16 | |
10 | 315.44 | 165.94 | 358.66 | 800.12 | 20 |
Modified winsorized means for up to five pairs of winsorized values.
To provide a meaningful interpretation of Table 1, the modified winsorized means or averages for both groups, as shown in Table 1, were plotted with a 2D area plot in Excel Package. The process involves entering the first variable
Graphical representation of the modified winsorized mean values in
A cursory look at Figure 1 shows that the winsorized average values for the four predictor variables in both groups represented by the 2-D area plot have similar shape (or have similar variances within the groups) except for predictor variable
At
% of winsorization | No. of replaced sample points | % of training sample correctly classified |
---|---|---|
4 | 2 | 85.00 |
8 | 4 | 88.00 |
12 | 6 | 91.00 |
16 | 8 | 94.00 |
20 | 10 | 97.00a |
24 | 12 | 96.00 |
Summary of hit rate results for each percent of modified winsorization for predictor variable,
Optimal winsorization occurs at 20% with hit rate = 97.00%.
The optimized training sample,
Thus, the PDF,
In addition to the dataset from Japanese banks, a second real dataset was used to validate the first sets of results (11), (12), (14), and (15). This validation sample was obtained from the academic records of junior secondary school (JSS) 2, University Demonstration Secondary School (UDSS), University of Benin, Nigeria. The dataset contains 30 observations for both classes: Science and Art. The dataset consists of average scores for the three consecutive terms obtained for eleven (11) subjects, including English Language (
Thus, the PDF,
Also, the two critical values from the SPSS outputs for 0.95 and 0.99 used as the probabilities in the IDF.CHISQ function with three predictor variables were given as:
The Mahalanobis distance values for all cases, as reported in the case wise statistics table, were all lower than the two critical values. This means that there are neither outliers nor hidden influential observations in the dataset or training sample. Once again, the proposed algorithm is applied to this second training sample,
At
Groups | No. of replaced sample points | Modified winsorized mean values | Winsorized % | ||
---|---|---|---|---|---|
1 | 0 | 67.27 | 69.77 | 73.30 | 0.00 |
2 | 67.40 | 70.07 | 73.43 | 6.67 | |
4 | 67.43 | 70.17 | 73.60 | 13.33 | |
6 | 67.47 | 70.13 | 73.67 | 20.00 | |
8 | 67.53 | 70.13 | 73.70 | 26.67 | |
10 | 67.60 | 70.17 | 73.73 | 33.33 | |
2 | 0 | 51.47 | 62.40 | 63.93 | 0.00 |
2 | 51.27 | 62.53 | 63.97 | 6.67 | |
4 | 51.07 | 62.70 | 63.73 | 13.33 | |
6 | 50.97 | 62.83 | 63.60 | 20.00 | |
8 | 50.77 | 63.00 | 63.50 | 26.67 | |
10 | 50.73 | 63.23 | 63.30 | 33.33 |
Winsorized means for up to five pairs of winsorized values.
Again, to interpret Table 3, the modified winsorized means or averages for both groups, as shown in column three of Table 3, were plotted with a 2D area plot in Excel Package. The graphical representation is presented in Figure 2.
Graphical representation of winsorized mean values in
A cursory look at Figure 2 shows that the winsorized average values for the four predictor variables in both groups represented by the 2-D area plot have similar shape (or have similar variances within the groups). The similar shape shown by the three variables in each group indicates that there are no legitimate contaminants in the training sample,
If the modified winsorized means for each variable in Table 1 are denoted as the independent variable
At
Group | Regression coefficients, | |||
---|---|---|---|---|
1 | −1.088 | −2.316 | −0.022 | 0.725 |
2 | −1.295 | −0.569 | −0.500 | 1.036 |
0.2 | 1.8 | 0.5 | 0.3 |
Regression coefficients,
At
The two step approach of the proposed alternative method was repeated using the data of Table 3. The summary of the obtained values of the regression coefficient,
Group | Regression coefficients, | ||
---|---|---|---|
1 | 0.009 | 0.009 | 0.013 |
2 | −0.023 | 0.024 | −0.020 |
0.0 | 0.0 | 0.0 |
Regression coefficients,
A cursory look at Table 4 shows that the regression coefficient (−2.316) of
This paper addresses the issue of achieving a statistically optimal classification accuracy in PDA by first achieving an optimal training sample. For the first real dataset, a training sample of four variables was obtained using the SPSS stepwise method. The training sample gave a hit rate of 86.0%. When all legitimate contaminants in one of the four variables have been identified and eliminated using the MW-GD method, an optimal training sample was achieved. The optimized training sample was used to construct the PDF,
The uniqueness of the MW-GD method lies in its ability to effectively identify and eliminate legitimate contaminants in one or several predictor variables, thus resolving any significant differences in the variances of the predictor variables between the groups. In other words, the MW-GD method is unique in its ability to sufficiently account for the basic assumptions required to achieve statistically optimal classification accuracy in PDA. As a result, an optimal training sample obtained from the first real dataset gave a statistically optimal hit rate of 97.0% compared to an initial maximum hit rate of 86.0%. For the second real dataset, the method was successful in confirming the optimality of the initial training sample obtained using the SPSS stepwise method. Similarly, the graphical diagnostic was able to identify the predictor variable(s) whose variance was not similar within the groups. Consequently, the graphical diagnostic associated with the proposed method could be used as an alternative graphical test of homogeneity of variances in PDA.
Another important contribution to the MW-GD method in this paper was the proposed alternative statistical interpretation for the graphical diagnostic associated with the MW-GD method demonstrated in Subsection 5.2. This proposed alternative statistical interpretation proved very effective in terms of identifying the variable with legitimate contaminants, and could serve as a useful alternative tool for identifying variables with legitimate contaminants in the event of any difficulties in differentiating between a variable shape in the groups of the 2-D area plot.
Finally, two real training samples have been used. Consequently, the validity of the experimental results is limited to the scope of the datasets used. Therefore, this paper believes that more experimental results are needed in order to reach a final conclusion on the efficiency of the MW-GD method compared to classical alternatives known to improve classification accuracy in PDA.
this is the complete list of objects used in building the predictive discriminant function (PDF)
this is the complete list of objects without outliers and hidden influential observation used in building the predictive discriminant function (PDF)
the number of groups or categorical criterion
total number of cases over all groups in a dataset
total number of cases over all groups in the optimized training sample
the number of validation samples
the number of predictor variables
this is the percentage of cases on the diagonal of the confusion matrix, or simply the percent of correct classification
this is the hit-rate obtained by applying a rule based on a particular training sample to future samples taken from the same population
this is the leave-one-out cross-validation (LOOCV) estimate of the optimized hit rate
predictor variables
discriminant weights
a predictive discriminant function (PDF) created by a linear combination of observable variables
an optimized predictive discriminant function (PDF) created by a linear combination of observable variables without outliers and hidden influential observations
value for the jth observation in the optimized training sample
predicted response for the jth observation in the optimized training sample
predicted response for the jth observation calculated with the jth observation removed from the training sample
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