PRE of the proposed estimator \n
\\n\\n
Dr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\\n\\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\\n\\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\\n\\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\\n\\nThank you all for being part of the journey. 5,000 times thank you!
\\n\\nNow with 5,000 titles available Open Access, which one will you read next?
\\n\\nRead, share and download for free: https://www.intechopen.com/books
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Preparation of Space Experiments edited by international leading expert Dr. Vladimir Pletser, Director of Space Training Operations at Blue Abyss is the 5,000th Open Access book published by IntechOpen and our milestone publication!
\n\n"This book presents some of the current trends in space microgravity research. The eleven chapters introduce various facets of space research in physical sciences, human physiology and technology developed using the microgravity environment not only to improve our fundamental understanding in these domains but also to adapt this new knowledge for application on earth." says the editor. Listen what else Dr. Pletser has to say...
\n\n\n\nDr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\n\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\n\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\n\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\n\nThank you all for being part of the journey. 5,000 times thank you!
\n\nNow with 5,000 titles available Open Access, which one will you read next?
\n\nRead, share and download for free: https://www.intechopen.com/books
\n\n\n\n
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Payan-Carreira",dateSubmitted:"April 21st 2020",dateReviewed:"September 10th 2020",datePrePublished:"October 8th 2020",datePublished:"January 20th 2021",book:{id:"8545",title:"Animal Reproduction in Veterinary Medicine",subtitle:null,fullTitle:"Animal Reproduction in Veterinary Medicine",slug:"animal-reproduction-in-veterinary-medicine",publishedDate:"January 20th 2021",bookSignature:"Faruk Aral, Rita Payan-Carreira and Miguel Quaresma",coverURL:"https://cdn.intechopen.com/books/images_new/8545.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"25600",title:"Prof.",name:"Faruk",middleName:null,surname:"Aral",slug:"faruk-aral",fullName:"Faruk Aral"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"38652",title:"Dr.",name:"Rita",middleName:null,surname:"Payan-Carreira",fullName:"Rita Payan-Carreira",slug:"rita-payan-carreira",email:"rtpayan@gmail.com",position:null,institution:{name:"University of Évora",institutionURL:null,country:{name:"Portugal"}}},{id:"309250",title:"Dr.",name:"Miguel",middleName:null,surname:"Quaresma",fullName:"Miguel Quaresma",slug:"miguel-quaresma",email:"miguelq@utad.pt",position:null,institution:{name:"University of Trás-os-Montes and Alto Douro",institutionURL:null,country:{name:"Portugal"}}}]}},chapter:{id:"73504",slug:"calf-sex-influence-in-bovine-milk-production",signatures:"Miguel Quaresma and R. 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\r\n\tIngredients of foods stimulate taste receptors and stimulated taste receptors send neural messages to the brain. Disorders of foods intake result in obesity, atherosclerosis, hormonal disturbances leading to type 2 diabetes mellitus and cardiovascular diseases. Brain cells need glucose for the activities. Increase in glucose intake results in obesity and metabolic syndromes. However, glucose intake is prerequisite for brain functions. Salt is also important for the electrolytes balances, but too much salt intakes result in hypertension and renal diseases. Hypertension causes atherosclerosis and thrombosis. In the brain, stroke takes place in narrowed arteries caused by constriction of vessels. Serotonin and kynurenine (tryptophan metabolites) are important factors in brain functions and periphery. IDO regulates functions of T-cells in tumors, especially in lung cancer.
\r\n\r\n\tIn this book, roles of tryptophan metabolites in activities of checkpoint inhibitors will be discussed. We welcome contribution of chapters from experts of nutrition and food related diseases to elucidate roles of eating in pathophysiology of body and brain functions.
",isbn:"978-1-83968-777-8",printIsbn:"978-1-83968-776-1",pdfIsbn:"978-1-83968-778-5",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"2464b5fb6a39df380e935096743410a0",bookSignature:"Dr. Akikazu Takada and Dr. Hubertus Himmerich",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10543.jpg",keywords:"Taste Receptors, Hypothalamus, Glucose, Sucrose, Type 2 Diabetes Mellitus, Obesity, Atherosclerosis, Lipid, Electrolytes, Hypertension, Tryptophan, Serum",numberOfDownloads:125,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 11th 2020",dateEndSecondStepPublish:"October 9th 2020",dateEndThirdStepPublish:"March 29th 2021",dateEndFourthStepPublish:"May 14th 2021",dateEndFifthStepPublish:"June 15th 2021",remainingDaysToSecondStep:"6 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Mr. Takada became Professor Emeritus of Hamamatsu University in 2001 and was named the honorary chairman of the Asia-Pacific Society of Thrombosis and Hemostasis in 2004.",coeditorOneBiosketch:"Professor Dr. med. Himmerich studied medicine at the University of Mainz, Germany. He received his scientific and clinical training at the Max-Planck-Institute of Psychiatry in Munich and at the University of Marburg. He gained further clinical experience at the University Hospitals in Aachen and Leipzig. In 2009 he was appointed Professor for Neurobiology of Affective Disorders at the University of Leipzig and in 2013 Clinical Senior Lecturer in Eating Disorders at King’s College London.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"248459",title:"Dr.",name:"Akikazu",middleName:null,surname:"Takada",slug:"akikazu-takada",fullName:"Akikazu Takada",profilePictureURL:"https://mts.intechopen.com/storage/users/248459/images/system/248459.png",biography:"Akikazu Takada was born in Japan, 1935. After graduation from Keio University School of Medicine and finishing his post-graduate studies, he worked at Roswell Park Memorial Institute NY, USA. He then took a professorship at Hamamatsu University School of Medicine. In thrombosis studies, he found the SK potentiator that enhances plasminogen activation by streptokinase. Using simultaneous analyses of plasma fatty acids, he indicated that plasma levels of trans-fatty acids of old men were far higher in the US than Japanese men. By using simultaneous LC/MS analyses of plasma levels of tryptophan metabolites, he recently found that plasma levels of serotonin, kynurenine, or 5-HIAA were higher in patients of mono- and bipolar depression, which is significantly different from observations reported before. In view of recent reports that plasma tryptophan metabolites are mainly produced by microbiota, he is now working on the relationships between microbiota and depression or autism.",institutionString:"Hamamatsu University School of Medicine",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"5",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Hamamatsu University School of Medicine",institutionURL:null,country:{name:"Japan"}}}],coeditorOne:{id:"231568",title:"Dr.",name:"Hubertus",middleName:null,surname:"Himmerich",slug:"hubertus-himmerich",fullName:"Hubertus Himmerich",profilePictureURL:"https://mts.intechopen.com/storage/users/231568/images/system/231568.jpg",biography:"Since 2015, Professor Dr. med. Hubertus Himmerich is a Clinical Senior Lecturer in Eating Disorders at King’s College London and a Consultant Psychiatrist on an inpatient ward for patients with eating disorders at the Bethlem Royal Hospital in London, UK. \nAfter studying medicine, he received his scientific and clinical training at the Max-Planck-Institute of Psychiatry in Munich and the Universities of Mainz and Marburg, Germany. In 2009 he was appointed Professor for Neurobiology of Affective Disorders at the University of Leipzig, Germany. \nHis scientific focuses include appetite regulation, psychoimmunology and military mental health. He has led and performed national and international scientific projects with researchers from Europe, Australia and North America, and has published more than 150 articles in peer-reviewed scientific journals, books and book chapters.",institutionString:"King’s College London",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"2",institution:{name:"King's College London",institutionURL:null,country:{name:"United Kingdom"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"21",title:"Psychology",slug:"psychology"}],chapters:[{id:"74591",title:"The Outcome of Eating Disorders: Relapse, Childbirth, Postnatal Depression, Family Support",slug:"the-outcome-of-eating-disorders-relapse-childbirth-postnatal-depression-family-support",totalDownloads:73,totalCrossrefCites:0,authors:[null]},{id:"75814",title:"Lactate and Ketone Bodies Act as Energy Substrates as Well as Signal Molecules in the Brain",slug:"lactate-and-ketone-bodies-act-as-energy-substrates-as-well-as-signal-molecules-in-the-brain",totalDownloads:42,totalCrossrefCites:0,authors:[null]},{id:"74852",title:"Attenuation of Food Intake by Fragrant Odors: Comparison between Osmanthus fragrans and Grapefruit Odors",slug:"attenuation-of-food-intake-by-fragrant-odors-comparison-between-osmanthus-fragrans-and-grapefruit-od",totalDownloads:17,totalCrossrefCites:0,authors:[null]}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"184402",firstName:"Romina",lastName:"Rovan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/184402/images/4747_n.jpg",email:"romina.r@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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Auxiliary information may be utilized at planning, design and estimation stages to develop improved estimation procedures in sample surveys. Sometimes, information on auxiliary variable may be readily available for all the units of population; for example, tonnage (or seat capacity) of each vehicle or ship is known in survey sampling of transportation and number of beds available in different hospitals may be known well in advance in health care surveys. If such information lacks, it is sometimes, relatively cheap to take a large preliminary sample where auxiliary variable alone is measured, such practice is applicable in two-phase (or double) sampling. Two-phase stratified sampling happens to be a powerful and cost effective (economical) technique for obtaining the reliable estimate in first-phase (preliminary) sample for the unknown parameters of the auxiliary variables. For example, Sukhatme [1] mentioned that in a survey to estimate the production of lime crop based on orchards as sampling units, a comparatively larger sample is drawn to determine the acreage under the crop while the yield rate is determined from a sub sample of the orchards selected for determining acreage.
\nIn order to construct an efficient estimator of the population mean of the auxiliary variable in first-phase (preliminary) sample, Chand [2] introduced a technique of chaining another auxiliary variable with the first auxiliary variable by using the ratio estimator in the first phase sample. The estimator is known as chain-type ratio estimator. This work was further extended by Kiregyera [3, 4], Tracy et al. [5], Singh and Espejo [6], Gupta and Shabbir [7], Shukla et al. [8], Choudhury and Singh [9], Parichha et al. [10] and among others, where they proposed various chain-type ratio and regression estimators.
\nIn practice, the population may often consist of heterogeneous units. For example, in socio-economic surveys, people may live in rural areas, urban localities, ordinary domestic houses, hostels, hospitals and jail, etc. In such a situation one should carefully study the population according to the characteristics of regions and then apply sampling scheme strata wise independently. This procedure is known as stratified random sampling. It may be noted that most of the developments in two-phase sampling scheme are based on simple random sampling only while limited number of attempts are taken to address the problems of two-phase sampling scheme in the platform of stratified random sampling. It may be also noticeable that the most of the research work on two-phase sampling are producing biased estimates. However, biased becomes a serious drawback in sample surveys. A sampling method is called biased if it systematically favors some outcomes over others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. For example, telephone sampling is common in marketing surveys. A simple random sample may be chosen from the sampling frame consisting of a list of telephone numbers of people in the area being surveyed. This method does involve taking a simple random sample, but it is not a simple random sample of the target population (consumers in the area being surveyed). It will miss people who do not have a phone. It may also miss people who only have a cell phone that has an area code not in the region being surveyed. It will also miss people who do not wish to be surveyed, including those who monitor calls on an answering machine and don’t answer those from telephone surveyors. Thus the method systematically excludes certain types of consumers in the area. It is obvious that the inferences from a biased sample are not as trustworthy as conclusions from a truly random sample.
\nEncouraged with the above work, we have proposed a class of product to regression chain type estimators in stratified sampling using two auxiliary variables under double sampling. The unbiased version of the proposed class of estimators has been obtained which make the estimation strategy more practicable. The dominance of the proposed estimation strategy over the conventional ones has been established through empirical investigations carried over the data set of natural as well as artificially generated population.
\nConsider a finite population U = {1, 2,…, N} of N identifiable units divided into
Let \n
Let \n
In the first phase, a preliminary large sample of size \n
In the second phase, a sub-sample of size \n
\n\n
The usual stratified mean estimator (\n
The mean square error (
Motivated with the technique adopted by Chand [2], one may frame the chain ratio-product type estimator in stratified sampling structure as
\nThe bias and
where
\nSimilarly, inspired with the technique adopted by Choudhary and Sing [9], one may frame the two-phase stratified random sampling estimator in stratified sampling as
\nwhere \n
Bias \n
Motivated with the earlier work, discussed above, we have constructed a class of product to regression chain type estimators as
\nwhere \n
It can be easily noted that the proposed class of estimators \n
and \n
Under above transformations the class of estimator tp may be represented as
\nWe have the following expectations of the sample statistics of two-phase stratified sampling as
\nwhere
\nExpanding binomially, using results from Eq. (1) and retaining the terms up to first order of sample size, we have derived the expressions of bias B(.) and mean square error M(.) of the class of estimators tp as
\nwhere \n
In recent time serious drawback is bias of an estimator. Therefore, unbiased versions of the proposed classes of estimators are more desirable. Motivated with this argument and influenced by the bias correction techniques of Tracy et al. [5] and Bandyopadhyay and Singh [11] we proceed to derive the unbiased version of our proposed class of estimator tp.
\nFrom Eq. (12), we observe that the expression of bias of the estimator tp contains the population parameters such as \n
where \n
Motivating with the bias reduction techniques of Tracy et al. [5] and Bandyopadhyay and Singh [11], we have derived the unbiased version of the proposed class of estimators tp to the first order of approximations two-phase stratified sampling.
\nwhich becomes
\nThus, the variance of \n
From Eqs. (10) and (15) it is to be noted that the class of estimators \n
It is obvious from the Eq. (16) that the variances of the proposed class of estimator \n
Substituting the optimum value of the constant kh in Eq. (19), we have the minimum variance of the class of estimators \n
It is important to investigate the performance of the proposed class of estimators with respect to the existing ones. We use the two natural population and one artificially generated population data set to justify the supremacy of the proposed strategy.
\nThe data set of two natural populations has been presented below.
The data consist of 80 observations which are divided into four strata according to the auxiliary variable
The percentage relative efficiencies (PRE) the proposed class of estimators \n
An important aspect of simulation is that one builds a simulation model to replicate the actual system. Simulation allows comparison of analytical techniques and helps in concluding whether a newly developed technique is better than the existing ones. Motivated by Singh and Deo [14], Singh et al. [15] and Maji et al. [16] who have been adopted the artificial population generation techniques, we have generated five sets of independent random numbers of size N (N = 100) namely \n
We have split total population of size N = 100 into 5 strata each of size 20 \n
The percentage relative efficiencies the proposed class of estimators \n
From the construction of estimation strategy and efficiency comparison of the proposed methodology, following matters are noted.
Form Table 1, it is clear that the proposed class of estimators is at least 1% better than the existing one in estimating the population mean.
Similarly from Table 2 it is found that the new estimator is at least 28% better than the existing one.
It may also be noted from Tables 1 and 2 that the artificially generated population is homogeneous (the mean and variance of the respective variables are almost same for different strata) where the natural populations are heterogeneous (the mean and variance of the respective variables are different for different strata) in nature. Our suggested estimators performs with equal efficiency for both the types.
The unbiased version of the proposed technique has been obtained which make the proposed class of estimators much more practicable.
Estimator | \nPRE | \n|
---|---|---|
Population I | \nPopulation II | \n|
\n\n | \n173.3608 | \n192.951 | \n
\n\n | \n101.1429 | \n131.5654 | \n
\n\n | \n118.3215 | \n172.226 | \n
PRE of the proposed estimator \n
We use following expression to obtain the percent relative efficiency (PRE) of the proposed estimator \n
Estimator | \nPRE | \n
---|---|
Artificially generated population | \n|
\n\n | \n179.623 | \n
\n\n | \n128.256 | \n
\n\n | \n154.879 | \n
PRE of the proposed estimator \n
We use following expression to obtain the percent relative efficiency (PRE) of the proposed estimator \n
Thus, it is found that the proposed estimation technique has addressed the problems of estimation through two-phase stratified sampling which may truthful for real life application where population is especially heterogeneous in nature and stratification is essential. Due to the benefits achieved by the new estimator, the survey statistician may be suggested to use it.
\nKeratoconus (KC) is the most common ectatic disease of the cornea. It is characterized by progressive thinning and protrusion of the cornea [1, 2]. Consequently, irregular astigmatism, myopia and a decrease in visual acuity occur. Therefore, the disease has a negative effect on vision-related quality of life. The disease has become an important public health problem due to the economic burden of treatment and vision rehabilitation related processes [3]. KC in children may have negative effects on social and educational development. In this respect, it is necessary to improve the vision in children at an acceptable level [4].
This disease, which mostly starts in young adults, can also be seen in children. It stabilizes in the fourth-fifth decades of life. KC, which usually shows bilateral asymmetric involvement, can be asymptomatic at the beginning, and visual acuity decreases as the disease progresses [1, 2]. Although some systemic involvement of KC is shown, it is generally known as a local corneal disease [5, 6]. Abnormalities in the corneal epithelium, Bowman’s layer and especially the collagen structure of the stroma play a role in the pathogenesis of the disease. Although it is suggested that various biochemical and genetic factors play a role in the etiology, its exact cause is not known exactly. The main diagnostic method of KC is placido disc-based corneal topography [2, 5, 7].
While surgical options in KC management aim to change the natural course of the disease and increase vision, the main goal of non-surgical options is to improve vision without damaging the ocular surface. Classical non-surgical treatment of vision rehabilitation in KC is glasses in a small number of patients and CLs in the majority of patients. In addition, modern surgical options such as intraocular lens implantation, corneal cross-linking (CXL), intra-stromal rings and anterior lamellar keratoplasty are also used in treatment. The common feature of these surgical methods is that they increase visual rehabilitation to a certain level due to residual refraction after surgery and ongoing irregular astigmatism, even if they are performed very successfully. Therefore, CLs are needed for vision rehabilitation after surgical methods [2, 7, 8].
Today, there is a global consensus that CLs play the most important role in the visual rehabilitation of KC patients [8]. Later developments in CL design and materials expanded the application options for KC patients. Considering that CLs cause ocular surface changes even in non-KC individuals, the main purpose of CL application in KC should be to increase visual acuity without compromising the health of the cornea and ocular surface [9]. While the patient should have good vision and comfort with the lens, the practitioner must find a suitable lens fitting that does not compromise the anterior ocular surface health. Therefore, the process is often time-consuming and difficult for both the patient and the ophthalmologist. Due to the nature of long-term CL use in KC, a careful CL selection should be made considering the physiological needs of the cornea according to the level of ectasia. Since CL movements can cause mechanical effects on the cornea with CL movements during millions of blinking, it is necessary to ensure that CL applies minimal contact and pressure on the cone in KC patients. In addition, since there are stem cells in the limbus region, which are hallmarks of corneal physiology and regeneration, contact with the limbal region should be minimized in order to prevent CLs from damaging the limbal region [2]. Scheimpflug imaging and anterior segment optical coherence tomography, which are frequently used in ophthalmology practice in recent years, can be used to evaluate CL fit. These imaging technologies can be used to reduce the time we spend evaluating CL fitting and to improve guides for CL fitting [10].
In addition to the severity of the KC, it is decided which type of CL will be selected according to the visual demand and comfort of the patient and the CL tolerance. With the latest advances in CL features and design, many CL options have been developed for patients with corneal irregularities, such as large diameter RGP lenses, scleral lenses, hybrid lenses and KC specific soft lenses. New data reveal that special design CLs, new design scleral lenses and hybrid lenses provide better visual acuity as well as better comfort than traditional RGPs [2, 8, 11].
Since astigmatism is mild in the early stages of KC, vision can be corrected with glasses. However, as irregular astigmatism increases in the middle and advanced stages, vision decreases dramatically and glasses play a limited role in correcting vision. In addition, since the disease is usually asymmetrical, correction with glasses can lead to anisometropia and anzioconia. Therefore, it is necessary to evaluate CL options for a better vision [8, 11, 12]. Glasses can only be given to selected patients who are intolerant to CL and who are not willing to undergo any surgery. Glasses can be prescribed on soft CL in some KC patients. Depending on the developments in CL technologies, the decrease in side effects due to CL and the effect of increased comfort may cause patients in the initial KC stage who can benefit from glasses nowadays to turn to CL. Because we can observe that CLs are frequently preferred instead of glasses due to esthetic concerns [11, 12, 13]. However it has been suggested that wearing rigid gas permeable CL (RGP) will increase the irregularities in the cornea and cloud the central cornea due to low corneal stiffness in KC patients under the age of 20. In order to prevent these problems, it has been stated that when visual impairment is detected in KC patients under the age of 20, it should be corrected with glasses as much as possible [14].
Conventional spherical or toric soft contact lenses (SCL) can provide benefit in improving vision by correcting myopia and regular astigmatism in early stage or form-frusted KC. Since they transfer the irregularities in the anterior surface of the cornea to their anterior surfaces, their ability to correct irregular astigmatism, high-order aberrations and vision level is very low in the KC, and therefore it limits the use of conventional SCLs in the KC. These conventional SCLs are generally ideal for those with a visual acuity of 1.0 with glasses [2]. They may be beneficial in some situations where high myopia is associated with KC disease [13]. After CXL treatment, they can assist in early vision rehabilitation. Hydrogel SCLs can be used in situations where comfort is more important [2]. The success of these lenses can be checked with a topography to be made over the lens. Depending on the needs of the patient, hydrogels with high water content and silicone hydrogel lenses with high oxygen permeability can be selected.
Developments in production technologies and specific basic curve designs have enabled the development of SCL specific to KC [15]. New design SCLs, customized hydrogel SCLs and pin-hole SCLs have expanded the usage spectrum of SCLs in KC [11]. It has also been found that they have similar quality of life between RGPs and SCLs [16]. Because of their good centralization, they can be used in decentralized cones and large diameter cones. In KC, it helps to increase visual acuity by making the anterior optic surface (front lens surface) more homogeneous topographically and by reducing high-order aberrations. In some sophisticated SCLs (customized SCL), asymmetric optical correction is performed, aberrations are further reduced and a better vision is achieved [17]. These special SCLs designed for KC have a greater central thickness than conventional SCLs (between 0.3 mm and 0.6 mm). This central thickness helps the CL to have a more stable structure and a regular anterior surface is tried to be created by preventing the direct adaptation of the lens on the irregular cornea. Increasing CL thickness contributes to the increase of visual performance, but also causes a decrease in oxygen permeability. This increases the risk of developing possible complications due to hypoxia. Therefore, they have a thinner peripheral thickness that can be adjusted independently of the silicone hydrogel central part and provides comfort with the movement of the lens. Since they are designed for use in KC, options with high spherical and toric values are available [12]. HydroCone® (Toris K) (SwissLens, Prilly, Switzerland) and KeraSoft® IC (Bausch & Lomb Inc., Rochester, NY) are silicone hydrogel SCLs specially designed for KC [18, 19]. It has been reported that with these lenses, visual acuity at a similar degree to RGPs is obtained in KC [15, 19]. It has been shown that SCLs increase vision in a significant portion of patients with corneal ring implantation. In cases where satisfactory vision cannot be achieved with SCLs, PBCL systems can be used in these patients [20].
It has been reported that visual performance decreases when the movement of the SCL exceeds 0.5 mm after blinking. Therefore, the movement of these lenses is requested not to exceed 0.5 mm, which may limit the tear change under the lens [12, 21]. These lenses, in which a sufficient visual level is obtained, have low infection rates due to a sufficient tear exchange. Although they provide more comfort, low oxygen permeability (excluding silicone hydrogels) compared to RGPs, failure to correct severe irregular astigmatism is the biggest disadvantage of SCLs [12]. As a result, with the developments in recent years, comfortable use and high visual performance have been achieved with SCLs specially produced for KC. However, it seems that the use of SCLs in KC will increase with future developments.
RGPs are the most frequently used CLs in the world to increase the vision level in KC. In a study, it was found that RGPs delay surgical interventions in 98.9% of KC patients [8, 22]. Today, there are various RGPs developed for KC, including multicurve, asferic and quadrant-specific designs [23]. The lens has a steeper central curvature, a flatter peripheral curve, and they have a non-fused surface appearance. It is indicated in KC patients in whom glasses or SCLs fail to improve vision [24]. RGPs provide a better vision in KC patients compared to glasses [25]. It has also been reported that it controls the progression of the disease with its mild shaping effect [22, 26]. Providing a smooth spherical anterior optic surface, RGP helps maintain the shape of the cornea by applying light pressure to the cone area (Figure 1). In addition, optically low order astigmatism and high order aberrations are corrected with the tear fluid under the lens. Thus, contrast sensitivity and visual acuity increases. When the limbal region is desired to be protected, corneal RGPs are placed in most cases because they do not have any interaction with the limbal region [12, 27, 28].
Rigid gas permeable contact lens on the cornea providing a smooth anterior optic surface.
The tear film under the lens is observed with fluorescent dye and the fitting can be evaluated and easily applied by an experienced practitioner. The disadvantage of these lenses is that the contrast sensitivity is low due to high-order aberrations, even if the visual acuity is good when the centralization is not good or when there is a tilt. To overcome this, RGPs with large optical zone (7.50–8.00) have been produced. Moreover, lenses with aspherical surfaces that correspond to the ectatic cornea have been produced with increased diameter up to 10.00–11.00 mm. Large diameter lenses are more complex to fit. Better fittings are obtained with small central or light cones [16, 29]. Dynamic and static fit should be evaluated 30 minutes after the CL is inserted. In dynamic fit, the centralization of the lens, its movement by blinking, and its stability in gaze positions are evaluated. The movement of the lens should not be more than 1 mm, it should not pass the limbus and its comfort should be maintained. In static fit, fluorescein is used to evaluate apical clearance, apical bearing, or three point touch [13]. Corneal astigmatism and higher order aberrations are reduced in all three methods. A larger diameter and flatter base curve is selected for apical bearing. The lens is directly supported by the corneal apex, and epithelial damage to the cornea secondary to the harsh between the lens and the corneal apex may develop an apical scar [30]. In this method, which provides a better visual quality, there is a risk of apical scarring. In apical clearance, a lens with a steeper base curve and smaller diameter is selected from the cornea, and the lens is supported by the cornea paracentral and there is a clear area between the central cornea and the lens. In this application where the risk of central corneal scar formation is reduced, tightening at periphery cornea may restrict tear exchange and may lead to hypoxic complications. In the three point touch method, which is the most popular method, the lens is supported mostly by the peripheral cornea and very little by the corneal apex [23, 31, 32]. In this method, attention should be paid to prevent contact of the lens with the corneal apex. Monocurve RGPs are used in mild to medium KC, and multicurve CLs are used in advanced KC. However, in some advanced KC, fitting of corneal RGPs may be more difficult and lens decentralization, dislocation, and disconfort may be encountered [33].
They can lead to a corneal warpage, especially in long-term use [34]. It can be a little difficult to get optimum comfort as it is made of rigid material only. There are studies showing that there is no relationship between KC severity and patient comfort, as well as studies showing that the opposite is valid [35, 36, 37]. Special cone-designed lenses such as Rose-K enabled RGPs to be very effective in visual acuity [38]. It has been reported that RGPs aggravate dry eye signs and symptoms in KC patients [39]. Since we may encounter a completely new eye after keratoplasty in liver patients, graft characteristics may make corneal RGPs contraindicated [40]. PBCL systems or scleral CLs can be used in these situations. RGPs allow for a good tear exchange. In advanced cases, a better vision can be obtained than SCLs, but discomfort, foreign body sensation and poor fitting in some advanced cases, especially in decentralized cones, are disadvantages of difficulty in centralization. Despite this, RGPs continue to be the first-line treatment in the visual rehabilitation of KC patients [8].
Piggyback contact lenses (PBCL) contain two CLs in one eye, one soft CL on the cornea and RGP above the soft CL. Thus, the optical performance of RGP and the comfort of SCL are utilized. It is thought that the placement of an SCL under the RGP protects the cornea from the excessive pressure of the RGP, thus minimizing this possible complication of RGP use and increasing comfort. If the patient has residual astigmatism, residual astigmatism can be placed in the SCL (toric) in the PBCL system and thus a spherical RGP can be used. It has also been suggested that the use of SCL with high positive power will help improve the centralization of RGP on the keratoconic cornea especially in KC patients with inferior cone [13, 23]. PBCLs can be used as an alternative option in patients with intolerance to RGPs due to ocular surface disorders, and eyes that cannot be stabilized with RGP and staining at 3–9 o’clock. It is also indicated in keratoplasty and KC patients in whom rehabilitation cannot be achieved with RGP [13]. It has been detected that 2% of KC patients using CL used PBCL [13, 41]. They may also help increase vision in KC patients with a corneal ring [42]. First, a soft CL (preferably a silicone hydrogel with minus power) is inserted, in which optimum fitting is achieved. This SCL covers the entire cornea, providing a bandage effect that helps protect the KC apex and a better centralization. Therefore, PBCL systems provide better comfort and longer duration of use, although their visual acuity is similar compared to RGP alone [12]. The base curve of the RGP is selected according to the values in the topography and keratometry applied over this soft CL, and it is inserted over this soft CL. After the RGP is inserted, the compatibility of the lenses with each other is evaluated using fluorescein dye. By changing the power of the soft CL, the compatibility of the RGP can be changed. For example, a positive powered soft CL can be used to flatten the RGP, and a negative powered RGP can be used to steep the base curve of RGP [13, 43]. Most practitioners use a low positive power SCL as it is considered to facilitate the centralization of RGP. However, it has also been suggested that the use of negative powered SCLs in the PBCL system results in better oxygen transmission. Refraction is measured over the two lenses and subjective refraction providing the best visual acuity is added to the RGP power [44, 45]. For an optimal fitting, it needs to move independently but harmoniously with blinking at the slit lamp and have minimal touch in the pattern of fluorescence. This independent movement allows tear exchange between the lenses, allowing the use of dissolved oxygen in the tear [46, 47]. In order to reduce the risk of hypoxia, care should be taken to ensure that both lenses have a high Dk value. In addition, there are custom PBCLs produced by opening a groove where RGP will sit on the soft CL to increase the centralization of RGP. Since the edges of the RGP fit into the groove in these lenses, they can provide better comfort [13]. PBCL improves vision and comfort, but potential hypoxia-related problems are among its disadvantages due to the application of maintenance procedures for both lenses and the double barrier that prevents oxygen transmission to the cornea. Today, a combination of high DK silicone hydrogel SLC and high Dk RGP is often preferred to prevent hypoxia complications [47, 48]. Although the corneal epithelium and endothelium are not affected in this system, giant papillary conjunctivitis and corneal neovascularization may develop in some patients due to the presence of two lenses on the corneal surface [2].
Hybrid contact lenses (HCL) consist of a combination of a rigid central zone and a soft peripheral skirt, manufactured using special technology. In these lenses, it tries to benefit from the best features of RGP (better vision) and soft materials (comfort). Therefore, HCLs can be an effective alternative to RGP and PBCLs. There are many special applications and designs that provide successful results in irregular corneas such as KC with these lenses [12, 49]. Modern HCLs are indicated when there is RGP intolerance or poor centralization, when an optimal RGP fit cannot be achieved, when there is reduced daily wearing time of RGP. They have also been shown to help improve vision after keratoplasty [33, 50]. Since these lenses with central RGP function and have soft peripheral skirt, they provide comfort as well as correcting vision. Therefore, they are preferred by many physicians and patients. Due to their design, HCLs distribute the contact equally between the cornea and conjunctiva or only touch the conjunctiva and peripheral cornea. Hybrid lenses generally consist of an 8.00 mm rigid part in the center and a soft hydrogel part with a total diameter of 14.50 mm. Correction principles are similar to those of RGPs. A good centralization is achieved in hybrid lenses owing to their soft skirt. However, they require special training and practice for successful application [2, 49, 50].
SynergEyes® Ultrahealth (SynergEyes Inc., Carlsbad, CA) HCLs are the next generation hybrid CLs that have been developed with a base curve design (KC), stronger RGP/silicone hydrogel coupling, and higher Dk of the central and peripheral region. Thus, hypoxia and fusion line tears are prevented. In the KC, the Vault of the rigid component and the skirt curvature of the soft component can be adjusted separately. In these lenses with a vault value ranging from 100 to 600 microns, optimum fitting is achieved with a full apical clearance with fluorescein dye and without air bubbles under the lens and a soft landing in the fusion area [12, 23]. There should be no air bubbles in the middle of the lens and a light touch on the rigid-soft junction. Unlike RGP lenses, the hybrid systems centralize the optics regardless of the cone position. Therefore it can be used in most central and decentralized cones. In this design, a steeper skirt enhances lens movement and prevents it from sticking. The data obtained from the corneal topography can be used to estimate the parameters when placing these lenses.
It has been shown in some studies that HCLs, which have the most superior features of comfort compared to RGPs, provide better visual acuity and contrast sensitivity than RGPs. For this reason, it has been stated that they have a higher vision-related quality of life score than RGPs. Disadvantages include giant papillary conjunctivitis and tearing of the soft skirt, corneal clouding [11, 51, 52]. In summary, HCLs serve the purpose of combining the superior features of rigid and soft CLs in a single lens. However, since studies in this area are limited, further research is needed.
The diameters of full scleral lenses range from 18.1–25.0 mm and have a scleral bed and maximum corneal clearance. Miniscleral lenses have scleral bed and minimal corneal clearance, with diameters between 15.0–18.0 mm. Semiscleral lenses have scleral and corneal beds and their diameters are between 13.6 and 14.9 mm. The corneoscleral lenses touch the corneal bed and sclera with a diameter between 12.9 and 13.5 mm [43]. Existing scleral lenses are produced from materials with high oxygen permeability such as fluorosilicon acrylate [53]. As the thickness of the lens increases, the oxygen permeability decreases, so nowadays it has become possible to make thin lens designs with new software. In addition, the lens surface is coated with plasma, increasing the surface wettability, thus increasing comfort and daily wearing time. Today, they can be produced with a very smoother surface and edge structure and less deficits during construction. Technological developments in lens materials, designs and lens production, lens placement techniques have led to an increase in interest in these lenses and increased acceptability of lenses in the treatment of KC [54, 55].
Scleral lenses rest on the sclera, do not touch the cornea and limbus, and leave a clear space between the cornea and the lens. Before the lens is placed in the eye, it is filled with a preservative-free saline. The lens consists of three parts: the optical part, the part extending over the sclera (haptic) and the Vault responsible for the corneal and limbal clearance of the lens. The optical part of the scleral contact lens (S-CL) is generally desired to be 0.2 mm larger than the horizontal visible iris diameter. However, it is also of great importance that the haptic part, which is more important in the fitting, and the corneal and limbal vault are appropriate for stabilization of vision [54, 55]. Today, the most commonly used S-CL fitting method is performed by the use of fitting trial sets. In addition, lens manufacturers can recommend a suitable guide. S-CLs mask irregular anterior corneal surface astigmatism with the fluid reservoir. The most important issue in applying these lenses is their alignment to the sclera. In some patients, edge lifts due to the toric structure of the sclera can be observed. Today, S-CLs with quadrant-specific peripheral designs can be produced for these KC patients with scleral asymmetry. This increases the comfort and lens wearing time of patients [56]. With the advances in CLs, S-CLs are also available today for elderly KC patients to rehabilitate near vision [8, 57]. However, studies on these are limited. Production of these specially designed lenses is still quite difficult, as they require special equipment and training and high cost [54].
Since the S-CL fits on the bulbar conjunctiva, minimal tear change occurs under the lens. The generally accepted minimum diameter for the cornea and limbal area to be unpressurized is 16 mm. Optical correction in these lenses is provided by the liquid under the well centralized lens. Therefore, anterior optical aberrations of the keratoconic cornea are neutralized. Front surface eccentricity in S-CLs aims to correct the optical quality and vision by compensating the back surface anomalies in the KC. Front surface eccentricity is zero in a spherical lens. Higher front surface eccentricity values indicate that the lens flattens rapidly from the center to the periphery [2, 27, 54, 58]. Providing continuous lubrication of the whole corneal surface ensures the stabilization of visual acuity [59]. S-CLs eliminate high grade aberrations and provide good centering and improve the visual quality. The complexity of the usage procedures and the poor comfort in long-term use limit their use [54]. S-CLs are generally not the first CLs to be applied in KC. They are preferred when tolerance problems are experienced with other CLs (SCL, RGP, PBCLs) or when acceptable vision cannot be obtained [49, 53, 54, 59]. S-CLs are indicated in RGP intolerance, very advanced and decentered cones, cornea staining at 3–9 o’clock, vascularization with PBCL, advanced KC. The fact that it is indicated in the presence of ocular surface disorder and in severe dry eye further expands the areas of use in the KC [60]. Corneal vaulting, centralization and perfect comfort have led to the preference of S-CLs in less severe cases, thus widening the indication for use of S-CLs in KC. S-CL designs are generally preferred after all corneal surgeries in the liver (CXL, intracorneal ring, keratoplasty). In such cases, higher Vault may be preferred if the ring or graft junction or sutures are to be protected [61, 62, 63]. If success is not achieved with these lenses, surgical methods are used. Contraindications are corneal edema due to decreased endothelial count, hydrops, and previous filtration surgery. Scleral lenses show success in extremely irregular and steep corneas because of their large diameters. Therefore, the role of treatment is increasing in advanced ectatic corneas where there is no option other than surgery. In addition, due to their large diameter and vaults, they are more comfortable than RGPs since they do not directly contact the cornea, which has much more innervation than the sclera. In recent years, new S-CL designs have expanded the scope of CL use in KC patients [11, 13].
Miniscleral lenses have less corneal opening than full scleral lenses. Small diameter lenses tend to adhere to the cornea due to the suction vacuum, which may cause difficulties for the practitioner [54, 64]. It has been shown that S-CLs reduce the need for keratoplasty and patients are successfully treated with S-CL instead of keratoplasty [65]. When the effect of CL on quality of life was evaluated in liver patients, it was seen that RGP, hybrid, soft CL had a similar effect. S-CLs are more comfortable than these lenses, but midday fogging continues to limit the quality of life in these lenses. In addition, unlike these lenses, S-CLs have been reported to reduce dry eye signs and symptoms [60, 66].
Haptic and vault are evaluated under biomicroscope in S-CLs. An acceptable fitting is defined by a corneal clearance, no air bubbles underneath, and no compression of the conjunctiva veins. After obtaining the appropriate fit, a trial use of 4–6 hours is required to evaluate the KC patient’s comfort and visual quality. A 400–600 micron Vault is acceptable for scleral lenses. However, a slightly higher vault may be prescribed due to the detection of a decrease in the vault after four hours of use and also considering that KC may progress over time. A convenient central and peripheral vault ensures patient comfort and tolerability. Feeling suction while removing the lens after four hours of CL application and the presence of staining in the conjunctiva are indicators of choosing a flatter haptic. It is recommended that patients be examined again 3–4 weeks after removing the lens to make a final decision [13].
Disadvantages are maintenance procedures, frequent replacement of saline bottles, insertion regimes using plungers, which can be more cumbersome than other methods, reduced tear exchange, and high costs. S-CLs in KC can cause infectious keratitis or other adverse events. It has been suggested that this may be due to inadequate cleaning of the plunger used for inserting and removing the lens and improper use of saline solution [8, 67, 68].
First of all, the data on the radii of curvature obtained in the corneal topography can be helpful in determining the initial base curve when placing the RGP. By evaluating the size and localization of the cone in the KC with the help of tangential maps in the topography, a more appropriate RGP diameter and base curve can be selected [69]. It has been reported that these data in the topography are also useful in hybrid lens fitting in KC [70]. These systems also include CL fitting simulation software to model the possible effects of lens designs and changes in parameters on the fitting. Rigid lens fluorescein simulations are based on corneal elevation data modeled on tangential maps. There are also studies showing that the video keratoscopic system gives successful results from standard methods in RGP fitting when compared to standard procedures. It was determined that the virtual sodium fluorescein staining pattern created based on the data from the CL simulator in the corneal topography and the actual staining pattern observed in the slit lamp were found to be highly matched. These findings show the importance of video keratoscopic virtual applications in CL management in KC patients and they have the potential to reduce the time we spend for CL [23, 71].
Previously, corneal clearance could roughly be estimated by comparing it with the thickness of the cornea. Today, with new technological devices such as anterior segment optical coherence tomography (AS-OCT), the amount of corneal clearance can be measured much more accurately (Figure 2). It is stated that the vault changed over time after the S-CL was inserted. It is important to follow this with AS-OCT in progressive diseases such as KC. Because, in patients with KC, with the advancement of the cone and the decrease of the Vault, it may cause the touch between the cornea and the lens, corneal scarring and decreased vision. Therefore, the idea (owing to AS-OCT) that lenses can be used for a long time by increasing the vault has emerged in KC patients [54, 72]. The fact that the anterior segment AS-OCT provides in vivo information that cannot be obtained with videokeratoscopy and standard methods in CL applications of KC patients has led to an increasing interest in AS-OCT in CL practitioners. AS-OCT helps to examine the corneal midperiphery, the limbus region, the border structure of CL [73, 74]. Although OCT can also help evaluate scleral curvature, which will be useful in peripheral designs of S-CLs, it is not yet possible to measure scleral shape. OCT also helps to accurately evaluate the interaction between the anterior corneal and conjuctival surface and CL (Figure 3). It can measure the central and peripheral tear film clearance under the CL and thus provides information about the fitting [75, 76]. Central and peripheral vaults of hybrid, scleral and miniscleral lenses can also be measured with OCT. This helps us to examine in detail the relationship between asymmetric cornea and CL in KC. With using AS-OCT in CL practice, the maximum central cone vault values required to prevent edema due to hypoxia in the cornea under the scleral lens have been suggested. OCT also plays a major role in defining the relationship between CL and tears [8, 77].
Anterior segment-optical coherence tomography image showing corneal clearance in a hybrid contact lens wearer.
Anterior segment-optical coherence tomography image showing the interaction between the contact lens corneal and the conjunctival surface in a hybrid contact lens wearer.
Despite current surgical advances in KC treatment, CLs continue to be important for visual rehabilitation (even after surgery) in KC. Advances in CL design and materials have significantly expanded the application area of CL in the KC and ensured that the majority of patients have a satisfactory visual acuity. Thus, the rate of patients undergoing keratoplasty has decreased or the need for keratoplasty has been delayed. Although it takes a lot of time to choose the appropriate lens in KC, most of the patients with KC can benefit from CL use with the new designs and materials developed. CLs offer non-surgical options generally preferred for vision rehabilitation in the KC. SCLs, RGPs, PBCLs, HCLs, S-CLs constitute the contemporary range of lens types available for the vision rehabilitation of KC patients. This wide CL range meets the optometric needs of most of the patients with KC disease today and eliminates the need for major surgical procedures such as keratoplasty for vision rehabilitation for most of the patients.
Today, while SCL and HCL are the most commonly used in mild KC, the most frequently used CL in advanced KC is still RGPs and S-CLs. Since KC is a progressive disease, CL compliance should be controlled dynamically in certain periods of the patient’s vision and comfort. If discomfort or intolerance develops in RGP, soft toric, PBCL or hybrid lenses may be considered. In the initial stages of the disease, SCLs are usually applied before other CLs are tried. Thus, the patient attains a good visual acuity and quality of life. When SCLs cannot provide this, secondly, RGPs are preferred because they provide a significant improvement in vision quality. When unsuccessful results are obtained with these CLs, PBCL or HCLs are used. If problems are encountered with these CLs, S-CLs are usually tried before surgery as a last option.
Imaging technologies such as corneal topography and OCT have enabled us to examine in vivo the relationship between asymmetric cornea and lens in the KC. Even with different modern CL treatments, it was found that both the quality of vision and life were lower in KC patients compared with the control group (healthy individuals without KC disease). This shows that CL treatment options and alternatives in KC treatment still need to be advanced.
The authors declare no conflict of interest.
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