Myopia or nearsightedness is a condition in which the axial length of the eye is too long relative to its optical focal length. This condition is reaching epidemic levels worldwide, and has become a tremendous public health burden. Myopia is one of the leading causes of vision loss and high myopia significantly increases the risk of permanent blindness. Consequently, myopia cannot be considered as a benign condition and early interventions aimed at slowing down or even stopping the progression of myopia rather than merely correcting the associated optical focusing error is of great importance.

The consistent evidence from animal model studies showing that imposed hyperopic defocus, if sustained, comprises an effective myopogenic stimulus, accelerating eye growth, while imposed myopic defocus slows ocular elongation, has motivated clinical studies using bifocal and progressive addition spectacles for myopia control. While these studies, reviewed in Chapter 2 of this dissertation, failed to provide convincing evidence for a clinically significant treatment effect, i.e., slowed myopia progression; smaller scale, non-randomized studies using multifocal soft contact lenses and orthokeratology lenses have shown much more promising effects in terms of slowing myopia progression. However, the mechanism(s) underlying the latter anti-myopia treatment effects are poorly understood, thereby limiting their further refinement. In addition to the aforementioned systematic review of relevant clinical evidence for optical interventions for myopia control, this dissertation described 3 other studies using chick model, representing efforts to further understand how multifocal optical environments affect normal ocular development, specifically the process of emmetropization. These manipulations have also been used as a tool to investigate the mechanism underlying the myopia controlling effect of the novel contact lens applications referred above.

Chapter 2 describes a systematic review and meta-analysis performed on randomized controlled trials investigating the effects of three traditional optical interventions, bifocal and progressive addition spectacles, and rigid contact lenses, all believed to control myopia progression, based on anecdotal evidence. The overall treatment effect was estimated to be only small and clinically insignificant. A number of reasons were proposed to explain the discrepancy between the results of related animal studies and these clinical trials - strong support for optical control of myopia from the former studies and inconclusive results from the latter studies. Poor compliance to the spectacle corrections in clinical studies, inaccurate measurement of adherence to the treatments, inadequate and potentially, ambiguous classification systems for clinical myopia, and potential flaws in the optical designs are likely to have contributed to the discouraging results from the clinical trials.

Chapter 3 describes the first of three studies in which the chick model was used to test the effects on ocular growth of a series of custom-designed 2-zone multifocal "spectacle" lenses. This and the two follow-up studies using this model have the following merits; they made use of standardized experimental paradigms and objective methods of measurement to track ocular changes. The first study applied the lenses in a simple experimental paradigm, in which monocular lenses were attached to the normal eyes of young chickens. The 2-zone lenses included a plano zone, either in the center or peripheral surround, with either positive or negative power (+5 or -5 D) incorporated into the other zone. The size of the central zone was also allowed to vary, to control the size of the unifocal central and peripheral retinal areas, and intermediate multifocal zone, as was the placement of the powered zone, i.e. in the center or periphery of the lenses. Single vision lenses were included as a control treatment. Two important observations from this study were that 1) peripheral optical defocus can influence both peripheral (off-axis) and central (on-axis) refractive error development and 2) the inhibitory effect on axial ocular growth of myopic defocus imposed using 2-zone lenses (positive zones) could exceed that induced by single vision lenses of the same power. These results suggested complex interactions between adjacent retinal regions, with the peripheral retina apparently able to decode optical defocus, as well as complex interactions between the eyes own optical aberrations and those of the 2-zone lenses, which introduced large amounts of spherical aberration.

Chapter 4 described a closely related study in which subsets of the same 2-zone lenses were tested on eyes that had undergone surgical manipulations (sectioning of the ciliary nerve, CNX or iridectomy, ID) to investigate the influence of the pupil size of the eye as well as accommodation on the effects of the 2-zone lenses. Both were uncontrolled in the first study; yet create a dynamic optical system on which the multifocal optical environment was imposed. The ID surgery produced a fixed dilated pupil without any effect on accommodation (confirmed in another study, reported in Appendix I), while the CNX surgery produced a similarly enlarged pupil while also eliminating accommodation. This study revealed pupil size to be a critical factor in the treatment effects of 2-zone lenses, likely to reflect at least in part, its influence on the optical experience of various retinal zones (center to periphery), and also suggested a significant role of accommodation in the decoding of imposed optical defocus stimuli, in this case, complex multifocal optical stimuli.

Chapter 5 described a third study which attempted to develop a clinically more relevant scenario; specifically, 2-zone lenses that incorporated two different negative powers (-5 & -10 D) in two optical zones (center & periphery or vice versa), were tested on both normal eyes and eyes made myopic before being fitted with one of the 2-zone lenses. The latter combination was intended to simulate the ocular conditions created when concentric multifocal contact lenses, i.e. with a near addition, are prescribed to human myopes, one of the novel, myopia control treatments currently being explored. When the 2-zone lenses were fitted to normal eyes, they induced myopia, of a magnitude falling between the values expected, had single vision lenses of the same powers been used. However, on myopic eyes, the lenses had a strong myopia inhibiting effect with the already induced myopia undergoing substantial regression. This result supports the further investigation of appropriately designed concentric multifocal contact lenses for the control of myopia progression.

In summary, the studies reported in this dissertation indicate complex interactions between central and peripheral retinal regions in decoding and responding to complex defocus signals as well as critical influences of pupil size and accommodation on these processes. The strong and consistent inhibitory effects on ocular growth of concentric 2-zone lenses incorporating a zone of either positive power or a near addition, 2-zone designs lend plausibility to the notion of using custom-designed novel optical treatments for the control of myopia progression.

In the first chapter of this thesis, we propose a penalized splines (P-splines) estimator for random effects panel data model. While being a nonparametric technique, one of the most attractive properties of splines methods is their analogous setup to parametric regression model. Compared to kernel-based methods, however, splines methods are far less developed at least for econometric models. The asymptotic results of our P-splines estimator are established in this chapter. Monte Carlo simulation is conducted to compare the performance of our P-splines estimator with different kernel-based estimators proposed in recent literature. It turns out that the P-splines estimator consistently performs well and is computationally efficient.

In the second chapter, we develop a general procedure to derive the asymptotic variance-covariance matrices of two-stage estimators that can be used to estimate simultaneous equation systems with a mixture of any number of binary and continuous dependent variables. To demonstrate the usefulness of our procedure, we apply our formulas to empirical data with one continuous and two binary dependent variables in the simultaneous equations system. Our results are expected to be of tremendous help to numerous practitioners of econometrics using two-stage procedures to estimate their simultaneous equations models.

Myopia, or nearsightedness, is a common vision disorder characterized by an abnormal increase in eye elongation, leading to a mismatch in the refractive power of the eye and the location of the retina. Myopia has dramatically increased in prevalence over the last 50 years, currently affecting half of college-aged individuals in the United States and almost all young adults in certain Asian populations. This trend is not a temporary aberration; myopia is projected to afflict nearly half of the global population by the year 2050.

Traditionally, myopia is "corrected" using glasses, contact lenses, or refractive surgery. Although these solutions allow for clear vision, they do not rectify the underlying structural changes associated with myopia, including the lengthening of the eye and the thinning of its layers. As a result, there remains an increased risk of vision-threatening complications, such as glaucoma, retinal detachment, myopic maculopathy, and choroidal neovascularization. In the past, these complications were regarded as characteristic of "pathological" myopia. However, it is now known that no amount of myopia is considered safe; the more severe the myopia, the greater the risk, starting from even the smallest measurable amounts.

In addition, not all myopes have access to refractive correction. Uncorrected refractive error accounts for over half of global vision impairment. It has also been estimated that uncorrected myopia is associated with an annual global potential productivity loss of $244 billion.

With these startling figures, there have been renewed efforts to develop and prescribe treatments for myopia. Inspired by the influence of animal models on myopia research thus far, we sought to further one of the most popular mammalian models of myopia, the guinea pig, to allow for mechanistic exploration that is not possible in human clinical trials.

Chapter 1 reviews the process of emmetropization and refractive error development as understood from observations in humans and experiments in animal models. Current clinical recommendations are also summarized.

Chapter 2 presents a qualitative synthesis of the known relevant ocular characteristics of the guinea pig myopia model. Guinea pigs have emerged as a popular mammalian model because of the relative ease of housing and husbandry, larger eyes, and better visual acuity compared to other laboratory rodents. However, guinea pigs aren't perfect subjects for the human condition we are attempting to model. Knowledge of the optical quality of the guinea pig eye isn't firmly established, and experimental models of myopia depend on manipulating the visual experience.

In Chapter 3, we detail the optical aberrations of the guinea pig eye. Using a custom-built Shack-Hartmann wavefront sensor, we fit a Zernike polynomial function to the images collected from adolescent guinea pigs. The optical quality of the eyes was assessed in terms of individual Zernike coefficients, and data were further analyzed to derive root-mean-square wavefront errors, modulation transfer functions, point spread functions, and depth of focus. These data are compared with visually normal young adult human eyes. While visual acuity is much poorer in the guinea pig eye compared to the human eye, high order aberrations do not appear to be major sources of image quality degradation. It is still unknown what optical information the eye is using to generate growth modulatory signals. However, the measurement of the optical aberrations of the guinea pig eye is an important step forward, allowing the nature of the defocus stimuli and their effects on retinal image quality to be better understood in this mammalian model.

Chapter 4 presents the results of a novel method of inducing myopia in the guinea pig model. Historically, spectacle-mounted lenses and diffusers are used to induce myopia in guinea pigs. These lenses are typically mounted on Velcro ring supports, which are then glued to the fur surrounding the guinea pigs' eyes. While shown to be safe and effective, there are significant limitations with this process. The lenses (or diffusers) can be removed by the guinea pigs if they scratch at the velcro site, requiring very frequent monitoring and reapplication. As a result, experiments using spectacle-mounted lenses cannot be conducted over a long period of time. We designed and tested rigid gas permeable contact lenses as an alternative method for inducing myopia in guinea pigs, which will also allow for testing contact lens treatments in this animal model.

Finally, the ability of atropine to prevent the development of myopia is a fairly consistent finding in animal studies. However, important exceptions have been noted. In Chapter 5, we establish that topically applied 1\% atropine is effective in reducing myopia progression in guinea pigs. After two weeks of treatment with either daily or weekly applied atropine, guinea pigs treated with our contact lens-induced myopia model developed significantly less myopia compared to those treated with a placebo drop.

The overarching goal of this research is to further our basic understanding of the guinea pig eye so that we can continue to use this model to test translational clinical treatments.