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Regression Toward the Mean01:52

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Glaucoma: Overview01:25

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Glaucoma is an eye condition characterized by increased intraocular pressure that damages the retina and optic nerve, leading to irreversible blindness if left untreated. The human eye has various components, including the cornea, iris, pupil, lens, and optic nerve. Aqueous humor is secreted by the epithelium of the ciliary body in the posterior chamber and flows through the trabecular meshwork and canal of Schlemm, maintaining normal intraocular pressure. The trabecular meshwork and the canal...
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Open Angle Glaucoma: Treatment01:27

Open Angle Glaucoma: Treatment

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In open-angle glaucoma, the iridocorneal angle remains open, but the trabecular meshwork becomes stiff, slowing down the outflow of aqueous humor. This causes a buildup of aqueous humor in the anterior chamber, leading to a sudden increase in intraocular pressure. The treatment for open-angle glaucoma focuses on reducing the elevated intraocular pressure by either decreasing the secretion of aqueous humor or increasing its outflow.
Drugs such as carbonic anhydrase inhibitors, α2- and...
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Estimating Population Mean with Unknown Standard Deviation01:22

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Angle-closure glaucoma, or closed-angle glaucoma, is an eye condition where the iris bulges out and blocks the iridocorneal angle, resulting in a buildup of aqueous humor and increased intraocular pressure. Immediate medical attention is necessary due to the sudden onset of symptoms. The treatment for angle-closure glaucoma includes short-term and long-term approaches. Short-term treatment involves using eye drops like pilocarpine to lower intraocular pressure by increasing aqueous humor...
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Estimating Population Mean with Known Standard Deviation01:16

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
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Assessing Early Stage Open-Angle Glaucoma in Patients by Isolated-Check Visual Evoked Potential
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Pronóstico de la desviación media en pacientes con glaucoma mediante un método de series temporales autorregresivas

Carlyn Childress1, Stuart K Gardiner2, Manoj Pathak3

  • 1Murray State University, Murray, KY, 42071, USA.

Scientific reports
|December 19, 2025
PubMed
Resumen

El pronóstico de la progresión del glaucoma utilizando la autorregresiva irregular de orden 1 (IAR (1)) es más preciso que la regresión ordinaria por mínimos cuadrados (OLSR). El método IAR (1) proporciona un enfoque estadísticamente válido para analizar datos de perimetría y predecir la progresión de la enfermedad.

Palabras clave:
autorregresivo irregulardesviación mediaregresión ordinaria por mínimos cuadradoscampo visual

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Área de la Ciencia:

  • Oftalmología
  • Bioestadística
  • Análisis de Datos Médicos

Sus antecedentes:

  • La predicción precisa de la progresión del glaucoma es crucial para el manejo eficaz del paciente.
  • La regresión ordinaria por mínimos cuadrados (OLSR) a menudo es inapropiada para analizar datos de perimetría longitudinal debido a la violación de las suposiciones.
  • Las series de desviación media (MD) de la perimetría son indicadores clave de la progresión del glaucoma.

Objetivo del estudio:

  • Examinar la aplicabilidad del método de autorregresivo irregular de orden 1 (IAR (1)) para modelar series de desviación media (MD) de glaucoma.
  • Comparar la validez y la precisión del pronóstico de IAR (1) frente a OLSR para datos de perimetría longitudinal.
  • Determinar si IAR (1) ofrece un método estadísticamente superior para el análisis de la progresión del glaucoma.

Principales métodos:

  • Se analizaron datos de perimetría longitudinal de 42 ojos con glaucoma progresivo.
  • Las series de desviación media (MD) se ajustaron utilizando los métodos de regresión ordinaria por mínimos cuadrados (OLSR) y autorregresivo irregular de orden 1 (IAR (1)).
  • La validez del modelo se evaluó utilizando correlogramas para verificar los errores correlacionados y las suposiciones de normalidad. La precisión del pronóstico se comparó utilizando el error cuadrático medio (MSE).

Principales resultados:

  • Los residuos de OLSR estaban correlacionados y no cumplían las suposiciones de normalidad, lo que indica una inadecuación del modelo.
  • El modelo IAR (1) demostró una validez mejorada con autocorrelación insignificante (p > 0,05) y un mejor ajuste para distribuciones de colas pesadas.
  • Significativamente más ojos ajustados con IAR (1) mostraron un menor Error Cuadrático Medio (MSE) de pronóstico en comparación con OLSR (62 % frente a 38 %, P = 0,02).

Conclusiones:

  • El método IAR (1) aborda eficazmente las limitaciones de OLSR al analizar mediciones repetidas de perimetría en glaucoma.
  • IAR (1) proporciona un enfoque estadísticamente más válido para ajustar series de MD en glaucoma.
  • El método IAR (1) ofrece una predicción más precisa de la progresión de la desviación media del glaucoma en comparación con OLSR.