Biostatistics Case Studies

CASE 4: Study "Power" and Error

Clinical History:

A 62-year-old woman has noted decreasing visual acuity, mainly in her peripheral vision, over the past year. She states that "everything just seems to be darker." She goes to her optometrist. The optometrist, using an "air puff" tonometer discovers that she has increased intraocular pressure bilaterally. The cornea and sclera of each eye appear normal. There is no opacification of the crystalline lens. However, on fundoscopy there is cupping of the optic discs.


Visual fields show reduced peripheral vision. There is cupping of the optic disk as a consequence of the increased intraocular pressure, leading to atrophy of the optic nerve head.


  1. What condition is present? Who is at risk?

  2. This is glaucoma. Older persons, black race, history of diabetes mellitus, and history of corticosteroid use increase the risk for glaucoma.

  3. How is this condition detected?

  4. Methods include tonometry (measuring intraocular pressure), funduscopy (viewing the retina; also called ophthalmoscopy), and perimetry (measuring visual fields). Tonometry is often performed with a device that is "non-contact" with the eye, using a puff of air to determine intraocular pressure.

    A more sensitive and exact measurement can be taken with a Goldmann applanation tonometer mounted on a slit lamp. Gonioscopy, utilizing a goniolens, can be used to view the angle of the anterior chamber to determine if "open angle" or "closed angle" glaucoma is present.

    However, not all persons with increased intraocular pressure will develop glaucoma, and not all persons with glaucoma have a measurable increase in intraocular pressure. Thus, it is recommended to screen patients by funduscopy and ophthalmoscopy (slit-lamp exam) as well as for pressure. Testing of visual fields (perimetry) may be indicated.

  5. How does this condition occur?

  6. There are several ways that intraocular pressure can be increased. In most cases the process is generally slow and painless, so the affected person is not often aware of the condition until substantial visual problems have occurred. Some cases present more acutely.

    The drainage of the aqueous humor in the anterior and posterior chambers of the eye occurs at the angle of the ciliary body with the cornea, where a trabecular meshwork of veins leads to the canal of Schlemm.

    Eyes that are small and hyperopic (farsighted) have a narrower angle that reduces resorbtion of fluid, leading to the so-called "primary angle-closure glaucoma." There is a propensity for an acute exacerbation marked by intense pain and redness of the eye, and the perception of halos around lights, as if looking through a steamy shower door. This is an emergency that must be immediately treated. For closed angle glaucoma, iridotomy introduces a small hole through the iris to allow drainage of aqueous.

    However, most cases of glaucoma (about 1 in 100 persons under age 65 and up to 1 in 25 persons over age 75) are of the "primary open-angle glaucoma" type in which there is no perceptible anatomic abnormality, but decreased resorbtion of aqueous occursfor an unknown reason. Persons with open angle glaucoma tend to lose peripheral vision first and have a sensation that everything appears darker. In the U.S. persons of African-American ancestry develop this disorder more often than caucasians.

    Much rarer are congenital glaucoma and glaucoma due to increased produced of aqueous. Signs of congenital glaucoma in an infant may include increased rubbing of eyes and a hazy corneal appearance.

  7. If a study were performed comparing drug treatments for this condition, how could one avoid type II error and what would determine the "power" of the study?

  8. In comparing two sets of values from population groups, one can make the assumption that they will be the same. This is called the "null hypothesis". For most statistical studies the goal is to show that the null hypothesis is unlikely, so a difference which is greater than the limits set, and which we therefore regard as "significant", will make the null hypothesis unlikely.

    To reject the null hypothesis when it is true is to make what is known as a type I error, or "alpha" error (a false positive). The level at which a result is declared significant is known as the type I error rate, often denoted by alpha. This is defined in relation to a threshold "P" value. The typical P value for alpha is usually <0.05, or less than 5% of the time when performing the experiment one would expect results for the measured groups to be similar.

    If the null hypothesis is not rejected when there is a real difference between the groups, then this is known as a type II error, or "beta" error (a false negative).

    The "power" of a study is its ability to find a significant difference in the populations studied. All studies have low power to find small differences and high power to find large differences among persons in a study. Thus, if the differences in intraocular pressure measured with and without therapy are not great, then the study will not have as much power as when the measured differences are great. This can be offset by increasing the number of subjects in the study: the more subjects, the smaller the measured differences need to be to detect a statistical significance.

  9. For a patient with significant visual impairment who continues to operate a motor vehicle, what should you do?

  10. The best thing to do is tell the patient to be tested by the department of motor vehicles (DMV) and that this is important for their safety as well as others. State that their safety is part of your responsibility so if they don't contact the DMV, you will.

    Typical visual requirements for operating a motor vehicle are: 20/70 vision in either eye, or both eyes together, with or without corrective lenses. If one eye is 20/200 or worse, the other eye must be 20/40 or better, with or without a corrective lens. 130 degrees is the minimum acceptable field of vision (normal is 180 degrees).

    The types of problems that can impair ability to operate a motor vehicle include: seizure disorders or blackouts, dizzy spells, severe cardiovascular problems, memory or judgment impairment, drug or alcohol problems, progressive neurological disorders, severe psychiatric disorders, visual impairments, sleep disorders, poorly controlled diabetes mellitus, and severe head injuries.