Working Paper Series 

Congressional Budget Office 

Washington, D.C. 

Does Experience Make Better Doctors?

Evidence from LASIK Eye Surgeries 

Juan M. Contreras 

Congressional Budget Office 

juan.contreras@cbo.gov 

Beomsoo Kim 

University of North Carolina at Greensboro 

b_kim@uncg.edu 

Ignez M. Tristao 

Congressional Budget Office 

ignez.tristao@cbo.gov 

August 2007 

2007-12 

__________________________ 

We are very grateful to the Maryland Population Research Center at the University of Maryland for providing 

financial support to fund this research. We are also thankful to the administration and doctors of the Clínica 

Oftalmológica de Antioquia (CLOFAN) for their help and collaboration, especially to Dr. Luis Fernando Pelaez, Dr. 

Mauricio Jaramillo, and Dr. Leonardo Orjuela for their support during our data collection in Colombia. We also 

would like to thank William Evans, Seth Sanders, John Rust, and Mark Duggan for helpful discussions and advice 

during the elaboration of this work. Chris Ruhm, David Ribar, Stephen Holland, Chris Swann, Doug Hamilton and 

Bob Dennis also provided many helpful comments. All errors are our own. Working papers in this series are 

preliminary and are circulated to stimulate discussion and critical comment. These papers are not subject to CBO’s 

formal review and editing processes. The analysis and conclusions expressed in them are those of the authors and 

should not be interpreted as those of the Congressional Budget Office. References in publications should be cleared 

with the authors. Papers in this series can be obtained at http://www.cbo.gov/publications/. 
1

ABSTRACT 

We examine the “learning by doing” hypothesis in medicine using a longitudinal census of laser 

in situ keratomileusis (LASIK) eye surgeries collected directly from patient charts. LASIK 

surgery has precise measures of presurgical condition and postsurgical outcomes. Unlike any 

other surgery, the impact of unobservable conditions on outcomes is minimal. Learning by 

doing is identified through observations on surgical outcomes over time for each doctor. Our 

unique data set overcomes some of the major measurement problems in health outcomes, and 

enhances the possibility of identifying the impact of learning by doing separate from other 

effects. Our results do not support the hypothesis that doctors’ individual learning improves 

outcomes, but we find strong evidence that experience accumulated by doctors as a group in a 

clinic significantly improves outcomes. 
2

1. INTRODUCTION 

How much does experience enhance a physician’s skills and improve outcomes for patients? 

Although economists have tried hard to empirically determine the existence of “learning by 

doing” in medicine, isolating its effects from other types of effects has proved elusive. 

In this paper, we address this question using a new and unique data set of LASIK 

refractive eye surgeries, an operation with well-defined eligibility criteria, precise measures of 

previous conditions and postsurgery outcomes, and minimal postsurgical care. The data we use 

were taken directly from individual patients’ charts and are part of a two-year longitudinal 

census of LASIK surgery patients from one of the largest ophthalmologic clinics in Colombia. 

Although our results do not support the hypothesis of doctors’ individual learning, we find strong 

evidence that experience accumulated by doctors as a group improves outcomes. 

In the last thirty years, many studies have analyzed the relationship between physician (or 

hospital) volumes of surgical procedures and patient outcomes. Halm et al. (2002) reviewed 135 

papers studying this correlation in the health care industry between 1980 and 2000 and found 

that around 70 percent of the studies reported a statistically significant association between 

higher volume and better outcomes. Based on these studies, the Washington Post wrote that it is 

now a virtually sacrosanct belief in the medical world that patients fare better if operated on by a 

doctor who frequently performs the same operation (October 28, 2003). Researchers often have 

interpreted this correlation as evidence of a causal relationship that “practice makes perfect.” 

Moreover, the view that “practice makes perfect” provides support for the expansion of regional 

or specialized medical centers to facilitate learning by doing.1

 But it is often debated whether 

 

1

 In this context, regionalization of medical care entails the financing of larger medical centers instead of many small 

ones. See Luft et al. (1976) and Rathore et al. (2006).
3

society can get more benefit by receiving expensive care such as critical care or cardiovascular 

surgical services in specialized centers or by distributing those services among small clinics 

(Thompson et al. 1994; Menke and Wray 2001). 

However, there are other possible explanations for the observed correlation between 

volume and outcome. One of them is selective referral. Primary care physicians may refer their 

surgery patients to more skilled surgeons, causing more skilled surgeons to show a higher 

volume and better outcomes, not because of their experience but because of their innate ability. 

If selective referral is indeed the cause of this high-volume/better-outcome relationship, then 

regionalization could increase the price of medical care by reducing competition without 

improving outcomes. Determining the existence and magnitude of a physician learning curve is 

at the heart of this issue. 

The challenge of empirically measuring a learning curve in medical procedures is twofold: 

data limitations and hard to measure outcomes. Data limitations prevented previous studies from 

being able to observe the evolution of an individual doctor’s experience over time. Instead, the 

studies could identify only the annual (or quarterly) volume for each surgeon or hospital. By 

contrast, we can observe the exact time of each surgery (with a precision of seconds), which 

enables us to measure a physician’s experience directly and precisely from the cumulative 

number of procedures performed by the doctor at specific points in time. 

The difficulty of defining and measuring health outcomes constitutes another challenge. 

Postoperative mortality is commonly used as an indicator of an adverse outcome because it is 

accurately recorded. But mortality is an extreme outcome, and relying on it alone is an 

inadequate means to capture both qualitative information and the full range of outcomes.2

 In 

addition, the effect of a surgeon’s skill is hard to isolate from a patient’s underlying conditions 

 

2

 For example, morbidity or quality of life might also be important outcomes of a health procedure. 
4

that may be closely related to outcomes.3 Even in the most detailed data some patients’ 

conditions are not available. And last, patients’ outcomes also depend on many other factors 

such as the quality of the surgical team or of the postsurgical care provided by the hospital staff. 

Thus it is difficult for researchers to measure the impact of an individual physician’s learning 

curve. 

Focusing on LASIK surgery enables us to overcome these limitations. The outcome of 

this surgery is measured precisely on a detailed scale and is relatively unaffected by patients’ 

unobserved underlying conditions (if patients are eligible for the surgery).4 In addition, the 

procedure is performed by only one doctor, so we can measure the effect of each doctor’s 

experience on outcomes. And patients require almost no postsurgical care, which can complicate 

the measurement of the effect of a physician’s experience on outcomes. 

This paper is divided into five sections. Section 2 provides a short review of the literature. 

Section 3 describes the data, the measures of outcome, and our empirical methodology. Section 4 

presents and discusses our findings, and section 5 concludes. 

2. LITERATURE REVIEW

There has been a great deal of research on the relationship between volume and outcomes in 

medical care, and most studies have found a positive correlation between the two. The first 

analysis of the correlation between volume and outcome in health care was done by Luft et al. 

 

3

 For example, in coronary surgery some conditions like smoking behavior or history of previous heart disease can 

affect the outcome of the surgery. 

4

 LASIK surgery is not recommended for everyone with poor visual acuity. The presence of subclinical keratoconus, 

corneal warpage syndrome, irregular astigmatism, or a thin cornea are generally contraindications for refractive 

surgery. LASIK also is not recommended for patients with an autoimmune disease (e.g., lupus, rheumatoid arthritis) 

or immunodeficiency (e.g., HIV). Some doctors also do not operate on patients younger than 18 years old or with 

diabetes. For details see Pallikaris and Siganos (1997) and FDA guidelines on laser surgeries 

http://www.fda.gov/cdrh/LASIK/when.htm). 
5

(1979).5 They compared outcomes between low- and high-volume hospitals for twelve surgical 

procedures and found that for certain operations mortality decreased with increases in hospital 

volume. 

More recently, Halm et al. (2002) reviewed 135 papers studying this correlation in the 

health care industry between 1980 and 2000 and found that around 70 percent of the studies 

reported a statistically significant and positive association between higher volume and better 

outcomes. However, 90 of the studies reviewed by Halm et al. examined patient outcomes using 

the variation in cross-sectional hospital volume as Luft et al.6 One shortcoming of this approach 

is that unobserved hospital characteristics can drive the results. For example, if high-volume 

hospitals have better technology than low-volume hospitals, then the difference in outcomes may 

be due to the difference in technology, which are often not well observed in the data. In addition, 

the volume-outcome relationship analyzed in those studies measured only correlation, not 

causality, because volume may be endogenous to outcomes—better outcomes may also lead to 

higher volume. 

To overcome the problem of unobserved heterogeneity in cross-hospital comparisons, 

some researchers have tried different identification strategies. Ho (2002) examined variation 

across hospitals over time using the cumulative annual volume of percutaneous transluminal 

coronary angioplasty surgeries as a measure of experience. She found some evidence of learning 

by doing by observing outcome improvement over time using 13 years of annual volume of 

coronary surgery for hospitals in California. However, she could not control for the evolution of 

technology, which could have changed significantly over the 13-year span of the data. As a 

result, it is unclear from her results whether more experience or better technology improves 

 

5

 Learning curves have been studied earlier in other areas. One example is Asher (1956), who studied the costquantity relationships in the airframe industry. 

6

 This class of studies includes Hughes et al. (1988), Phillips et al. (1995), Jollis et al. (1994), and Kimmel et al. 

(1995). 
6

outcomes over time. In addition, a hospital is a complex organization and postsurgical outcome 

depends on multiple factors such as the surgical team, operating surgeon’s skill, technology, and 

postsurgical care. Because Ho could not measure the impact of each of these learning factors 

separately, the exact source of the improvement in outcomes is uncertain. 

Several researchers have used comparisons among surgeons, based on the assumption 

that learning by doing occurs at the individual level. Birkmeyer et al. (2003) compared 

outcomes across high- and low-volume surgeons and found that outcomes had a stronger 

correlation with the volumes of individual surgeons than with volumes based on hospitalwide 

measures. However, the direction of causation with this correlation is unclear. Did experience 

improve outcomes (as implied by the learning by doing hypothesis)? Or did better outcomes 

lead to higher volumes (as implied by the competing hypothesis of selective referral)? The 

evidence presented in the study cannot distinguish between these two hypotheses. 

Recently, a few papers have tried to determine the causal relationship between outcomes 

and volume using instrumental variables (IV) estimation. Gowrisankaran et al. (2006) focused 

on the outcome of three surgical procedures using quarterly hospital volume as an explanatory 

variable. They used the predicted quarterly hospital volume for each procedure as an 

instrumental variable and assumed that people would go to the closest hospital without selective 

referral. Their results indicate that for at least two of the three procedures they studied learning 

by doing plays an important role in explaining differences across hospitals in their risk-adjusted 

outcomes. 

Ramanarayana (2006) tested learning by doing in a surgeon-level study using the annual 

volume of coronary artery bypass graft (CABG) surgeries in Florida. He used an exogenous 

increase in CABG volume caused by the exit of surgeons who practiced in the same area a year 
7

earlier.7 His results support the existence of learning by doing in CABG surgery. By following 

doctors who perform surgeries in multiple hospitals in the same year, he also found that a 

surgeon’s skill transfers across hospitals. 

In comparison with previous studies, this paper has several advantages for the study of 

learning by doing in surgery. While other studies have used data that identify time of surgery 

only by year, forcing researchers to use annual volume as a proxy for experience,8 our data 

identify the exact time of surgery as well as the day, month, and year. Therefore, we can 

measure experience directly from the first to the nth surgery for each surgeon. Moreover, we do 

not need to be concerned about changing technology, as all the surgeries were performed with 

the same machine. Using LASIK to analyze surgeons’ learning by doing has other important 

advantages, which we discuss after giving some background on this surgery in the following 

section. 

3. BACKGROUND ON LASIK SURGERY

LASIK is an elective refractive surgery that corrects visual acuity by reshaping the cornea using 

a special laser.9

 Figure 1 shows how the surgery is performed. First, a surgeon creates a thin flap 

on the cornea with a special tool called a microkeratome. The flap is folded back, and a laser is 

 

7

 Volume increased for the remaining surgeons who took over the surgeries for their colleagues that left the area. 

8

 In the most disaggregated unit of data that researchers have used, volume was given by quarters in each year. 

9

 LASIK became very popular due to the fast vision recovery and minimal pain that accompany the procedure. 

Although there are other techniques for refractive surgery, LASIK is the most popular nowadays in most countries 

including the United States and Colombia, where we obtained our data set. Moreover, Colombia has been at the 

leading edge of developments in refractive surgeries (LASIK being one of multiple options) since Dr. José 

Barraquer laid down its theoretical and empirical bases in Bogotá in 1948. He provided doctors with knowledge 

about how much of the cornea had to be left unaltered to provide a stable long-term result, and created the procedure 

(called keratomileusis) and instrumentation (including the first microkeratoma) to cut and reshape the cornea. Later 

technical and procedural developments included the RK (radial keratomileusis) in the 1970s in Russia by Svyatoslav 

Fyodorov, the development of PRK (photorefractive keratomileusis) in the 1980s in Germany by Theo Seiler, and 

finally the introduction in the early 1990s by Italian doctor Luccio Burroto and Greek ophthalmologist Ioannis 

Pallikaris of laser techniques to reshape the cornea. It was only in 1999 that LASIK was approved by the US FDA. 
8

used to remove a certain amount of corneal tissue. Before using the laser, some surgeons clean 

the cornea under the flap with sterilized drops, while others prefer to leave it as is to avoid 

injecting moisture into the corneal tissue. These surgeon-specific preferences and habits affect 

the final ablation10 since dryness alters the absorption rate of the laser on the cornea. Therefore, 

each surgeon might use a different duration of the laser pulse for the same patient to get an 

identical ablation based on his or her own surgical habits. The surgeon pulses the laser on the 

targeted part of the cornea and then folds the flap down on the cornea. 

Outcomes of LASIK surgery depend mostly on two inputs: the machine used (i.e., the 

technology) and the skill of the ophthalmologist. There are two kinds of technology: hardware 

and software. In our paper, the hardware technology is fixed because we collected the data from 

a single machine.11 However, the software, provided by the manufacturer, was upgraded once 

and this upgrade, which controls the delivery and fluence of the laser beams, could change the 

performance of the machine.12

There are several ophthalmologic skills involved in LASIK surgery. First, 

ophthalmologists use intraocular lens (IOL) formulas to calculate how much adjustment the eye 

needs before they start any surgical procedure. Second, they use a special tool called a 

microkeratome to make a flap that provides access to the corneal stroma;13 the ability to make a 

smooth and clean flap is crucial for the outcome of the surgery as an irregular surface causes 

unclear vision. Third, doctors need to develop a surgical plan based on the patient’s age, degree 

 

10 Laser ablation is defined as the process of removing material from a surface using a laser beam. 

11 LASIK surgical techniques have been evolving rapidly. However, applications of new techniques depend on the 

use of new machines. For example, eye tracking can improve the precision of the ablation but requires a new 

machine with eye tracking technology. 

12 Laser beam fluency is defined as the amount of energy per pulse that is distributed over a defined area 

(mJoules/cm2; Machat et al. 1999). 

13 The stroma is the thickest layer of the cornea and it is the part that is re-shaped in laser eye surgery. 
9

of ametropia,14 sex, and other factors (Machat et al. 1999). Although, in theory, IOL formulas 

tell a doctor how to reshape the cornea, in practice getting the exact ablation using a laser is 

complicated. 

In particular, when doctors evaluate patients and make a plan for the surgery, they have 

to take into account the patient-specific factors listed above as well as their own surgical habits. 

To incorporate these elements into the surgical plan, doctors have developed an “adjustment 

rule” called a nomogram.15 As described by Machat et al. (1999, p. 67), “The process of 

developing a LASIK nomogram requires four steps: obtaining patient data, formulating an initial 

nomogram, entering data into the laser’s computer and evaluating data and outcomes, and 

making adjustments based on this information.” The manufacturer of the laser machine 

recommends an initial nomogram based on their test data. However, it is recommended that 

doctors develop a personalized nomogram based on their own surgical habits. The disadvantage 

of this approach is that it takes time to accumulate the data needed to formulate the nomogram. 

In the clinic where we collected data all the doctors use a single nomogram. They review 

their surgical data and outcomes regularly and, based on their conclusions, the nomogram is 

updated accordingly. Updates were done twice during our data period: in December 2003 and 

May 2004. Because all the doctors use and update the nomogram, it reflects learning as an 

accumulated experience for the whole clinic.16

 

14 In other words, the degree of an eye abnormality, such as nearsightedness, farsightedness, or astigmatism, 

resulting from faulty refractive ability of the eye. 

15 Nomograms are not unique to LASIK. The National Cancer Institute defines a nomogram as a mathematical

device or model that shows relationships between things. For example, a nomogram of height and weight 

measurements can be used to find the surface area of a person, without doing the math, in order to determine the 

right dose of chemotherapy (http://www.cancer.gov/Templates/db_alpha.aspx?CdrID=439410). 

16 Their update is mainly based on their experience as surgeons and not on econometric analysis of the data. Because 

we know only the month but not the day of the nomogram update, we assume it to be on the 15th. We checked the 

sensitivity of our results to this assumption by redoing our analysis using the first and the last date of the month. Our 

results are qualitatively robust. 
10

3.1 Why LASIK? 

LASIK surgery offers several advantages for measuring learning by doing. First, as mentioned 

above, the patient charts contain all the information relevant to the outcome of the surgery as 

impacts on outcome due to a patient’s unobserved underlying conditions are minimal in LASIK 

surgery compared to other types of surgeries. For example, outcomes of coronary surgeries, the 

most extensively studied surgical procedure, can be affected by weight, previous myocardial 

infarction, previous cardiac surgery, peripheral vascular disease, diabetes, renal function, 

hypertension, angina, dyspnoea (breathlessness), and smoking (National Adult Cardiac Surgical 

Database Report 1999-2000 (UK); Roques et. al 1999). In most studies, researchers have not 

been able to observe underlying conditions such as smoking behavior or a history of heart 

disease. 

Second, LASIK is performed in most cases by one operating doctor, unlike many other 

surgeries. In our data, the operating surgeon is assisted by a nurse and an optometrist, who is 

responsible for the maintenance of the LASIK machine. Because there is only one optometrist in 

the clinic and the role of the assisting nurse is minimal, LASIK is an ideal surgery for capturing 

the surgeon’s learning curve. In addition, LASIK does not require hospitalization, meaning that 

postsurgical care has a relatively limited impact on the final outcome compared to other surgeries 

that require a patient to stay in the hospital for several days.17

Third, LASIK offers a unique possibility of measuring the outcome of a surgery precisely 

because we can accurately measure pre- and postsurgery eyesight. We explain this in more detail 

in section 4.2. 

 

17 The mean length of hospital stay after CABG was 8.2 days (Lazar et al. 1995). 
11

4. EMPIRICAL METHODOLOGY 

4.1 Data 

The data set used in this study is the population of patients who underwent LASIK surgery in a 

surgical center by the ophthalmologists of the Clínica Oftalmológica de Antioquia (CLOFAN) in 

Medellín, Colombia. This surgical center opened in July 2003 with a brand new Schwind 

ESIRIS laser machine and now has the biggest market share in Medellín.18 Before July 2003, 

most CLOFAN doctors performed refractive surgery in two other surgical centers in Medellín 

with older laser technologies. However, because all CLOFAN doctors are shareholders of this 

new surgical center they have great incentive to use their own laser machine.19 In addition, at the 

time of the collection of the data, CLOFAN’s Schwind ESIRIS LASIK machine was the best 

available technology in the city.20

 

CLOFAN provides not only LASIK surgery but also other eye-related treatments. Due to 

the large number of patients’ charts that CLOFAN maintains, we could not collect them all. 

Patient charts are sorted by patient name and do not have any flag for LASIK surgery. 

Fortunately, CLOFAN’s new surgical center has a log file for each surgery performed using the 

Schwind ESIRIS laser machine. Using this log, we identified all the patients that underwent 

LASIK surgery and collected the data from their individual patient charts at the clinic. We did 

not have access to the files for the other two surgical centers that CLOFAN doctors used before 

opening the new surgical center.21

 

18 The clinic’s market share is estimated at about 57 percent of all refractive surgery procedures done in Medellín. 

19 In fact, CLOFAN doctors as a group need to perform a certain number of surgeries per month to make their 

equipment pay off its cost and generate a profit. 

20 Surgeons from other clinics can rent the laser machine for their surgeries. 

21 The exceptions are patients that had LASIK surgery with an older machine before having it redone with the new 

Schwind ESIRIS machine. In those cases, we observe the whole history since it is recorded in the same patient chart. 
12

We have 2 years of data, from July 2003 to August 2005, with a total of 2,042 patients 

and 3,892 surgery cases (unit of observation is an eye). From the patients’ charts, we collected 

presurgery eyesight measures, the name of the operating surgeon, and all postsurgery follow-up 

evaluations (“follow-ups”). We also recorded patients’ basic demographic characteristics such 

as gender, age, marital status, place of birth, occupation, neighborhood and city of residence. 

The patient charts also include detailed information about the surgery: the date, start time (to the 

precision of seconds), operating surgeon, laser control software version, and whether or not there 

was any complication during the procedure. 

We dropped the 5.98 percent of patients living abroad22 from our analysis since they can 

be different from the rest of patients. In particular, most of them did not stay in Medellín long 

enough for the follow-up evaluations.23 In addition, we dropped two other categories of patient 

observations: those that did not have a presurgery refraction measure,24 and those who failed to 

return after the surgery for any follow-ups (around 10 percent of LASIK surgery patients). We 

posit two possible reasons for patients not coming back for follow-ups: either complete 

satisfaction or strong dissatisfaction. The second case is unlikely as there are no charges for 

follow-ups or for resurgeries if they are needed; thus, we believe there is only a very small 

chance of losing observations with adverse outcomes. In addition, we checked whether followup observations are correlated with time or with the cumulative number of surgeries for each 

surgeon. We found that they are not. 

The ideal approach would be to observe each surgeon’s entire history of LASIK surgeries. 

However, our observations include only the census of LASIK surgeries performed by doctors 

 

22 The majority of patients living abroad are from the United States. Our conversations with the clinic staff 

confirmed that some people get their surgery while visiting family in Colombia. 

23 Based on conversations with the doctors, we learned that most of those patients had already booked their airline 

ticket and could not stay for the clinic follow-ups. 

24 The refraction measure gauges visual acuity using sphere, cylinder, and axis expression. More details are given in 

section 4.3. 
13

using the new Schwind ESIRIS laser machine. As a result, each surgeon had a different level of 

experience at the time they performed their first surgery with the new laser machine. To control 

for these time-invariant surgeon-specific differences we used a surgeon-specific fixed-effect 

model. A surgeon-specific fixed-effect model can accommodate time-invariant differences such 

as ability, education, and so forth. 

Our data is censored at the time of collection. A patient operated in July 2003 had two 

years for possible follow ups. However, a patient operated on a day before the data collection 

had only one day for possible follow ups. We use 200 days as a window to follow the patient 

throughout the data. We dropped the surgeries that happened less than 200 days from the end of 

our data period. We choose 200 days (just over 6 months) because 70 percent of repeat surgeries 

occurred within 200 days of the first surgery. Figure 2 presents the cumulative density function 

of the duration between the original surgery and resurgery dates. By choosing a shorter window, 

we would have had more observations but suffered from incomplete outcome measures. On the 

other hand, a longer window would probably have yielded better value for the final outcome but 

would have resulted in fewer observations. 

The key feature of these data is that we can observe each physician’s LASIK surgeries 

over time and thus test for the existence of learning by doing in this medical procedure. If 

indeed practice makes perfect, then we should observe a learning curve—that is, we should 

observe an improvement in the physicians’ outcomes as they accumulate more experience. 

4.2 Measures of Eyesight 

The availability of precise measures of eyesight to define previous patient conditions and 

surgical outcomes is one of the main advantages of using LASIK surgeries to examine learning 
14

by doing in surgery. In this section we describe how ophthalmologists measure eyesight and 

explain how we use these measures in our analysis. 

Two different methods are commonly used to examine visual acuity: the Snellen and the 

refraction measures. For the first, the patient reads letters of different sizes from a distance of 20 

feet. Snellen measures visual acuity on a scale from 20/10 to 20/800, depending on the letter 

sizes that the patient can read.25 Although the Snellen measure is informative, ophthalmologists 

need to perform a refraction assessment in order to determine the refractive error and prescribe a 

corrective lens.26 The results are expressed as sphere, cylinder, and axis.

27 The sphere and the 

cylinder are measured in units called “diopters” and determine the lens prescription; the axis is 

measured in degrees and signifies the direction of an astigmatism.28 A negative sphere indicates 

myopia (near-sightedness) and a positive sphere, hyperopia (far-sightedness). The higher the 

absolute value of the sphere, the worse the visual acuity. The cylinder reflects the degree of 

astigmatism.29 A value of zero indicates a perfect sphere or cylinder, meaning that the patient 

does not have myopia/hyperopia or astigmatism.30 

Ophthalmologists use a standard metric called the defocus equivalent to obtain a 

composite measure based on the refraction measure of the eye.31 The defocus equivalent is 

obtained by the following formula: 

 

25 The Snellen chart cannot measure visual acuity that is worse than 20/800. 

26 Refraction refers to how light waves are bent as they pass through the cornea and lens. 

27 The usual expression is sphere = cylinder * axis. The “=” and “*” do not mean the mathematical “equals” or 

multiplication but are a convention used in the field to express the refraction measure. 

28 The value of the axis is not necessary in order to calculate visual acuity. 

29 Ophthalmologists and optometrists use negative and positive signs as a custom. All the measures in our data set 

use the negative sign norm. 

30 In order to measure the cornea and obtain values for the sphere, the cylinder, and the axis, the doctor has several 

options; one is to measure the cornea directly with an automated refractometry; another is to try several 

combinations of lenses to correct the vision. These exams can be conducted with the eye muscles relaxed using eye 

drops (“dilated” measures) or without the use of drops. 

31 Spherical equivalence (SE) is used more widely and is calculated as |cylinder/2| + |sphere|. However, SE can be 

misleading as it does not fully consider the amount of astigmatism. In addition, it can have a negative sign not 
15

Defocus equivalent = |Cylinder/2 + Sphere| + |Cylinder/2|. 

If the refraction evaluation is –2.5 of sphere, –3.5 of cylinder, and 180° of axis (which 

means a myopia of 2.5 diopters and an astigmatism of 3.5 diopters, measured in the 180° axis), 

the defocus equivalent will be |(–3.5/2) + (–2.5)| + |(–3.5)/2| = |–4.25| + |–1.75| = 6. The defocus 

equivalent for a perfect eye is zero, but any measure between 0 and 0.5 diopters is considered 

close to perfect eyesight. In our data set we use the defocus equivalent to measure visual acuity 

because the Snellen test cannot measure high-degree visual acuity problems. 

Visual acuity is recorded several times for each patient. Before the surgery, 86 percent of 

our LASIK surgery patients had a refraction measure of their visual acuity.32 Because 

observations with no presurgery refraction measure are not correlated (i.e., associated) with any 

specific doctor, number of cumulative surgeries, or month, it seemed safe to drop these 

observations. 

After the surgery, doctors typically evaluate a patient’s eyesight with the Snellen measure; 

for patients that demonstrate good eyesight, doctors often do not perform a refraction evaluation. 

Based on this criterion, 24 percent of cases were evaluated using only the Snellen measure. We 

used observations for which both Snellen and refraction measures were reported to predict a 

measure of the defocus equivalent for the observations that have only Snellen measure.33

 

 

associated with any specific meaning. Holladay et al. (1991) proposed the defocus equivalent to overcome these 

shortcomings of SE. 

32 There are dilated and nondilated measures. For a dilated measure doctors use eye drops to stimulate or prevent the 

action of the iris muscle. Because only 32 percent of LASIK cases have dilated measures and postsurgery eyesight 

measures are not dilated, in our data set we use only nondilated measures both for calculations of the defocus 

equivalent and for pre- and postsurgery evaluations. 

33 A linear regression was used in order to fill out the missing data.The Snellen and refraction measures use different 

standards for evaluation. Snellen measures how well the patient can see, and refraction measures near- or farsightedness as well as astigmatism. In addition, Snellen can only measure up to 20/800. In our data set, 60 percent of 

the observations with a postsurgery Snellen measure but no refraction measure have 20/20 or better eyesight. We ran 

a regression with age, sex, and Snellen measure as independent variables. 
16

4.3 Measures of Outcomes 

We use four outcome measures. The first outcome is the postsurgical defocus equivalent, 

measured in the last follow-up observed, at least 1 day after the surgery.34 The second measure 

is a dummy for the success or failure of the procedure. A defocus equivalent of less than or 

equal to 0.5 diopters is considered a success, while values higher than 0.5 diopters are considered 

a failure in the ophthalmology literature.35 The third outcome measure is an indicator of whether 

the patient needed at least one repeat surgery.36 The fourth outcome measure is the number of 

follow-up visits after the surgery, used as a proxy of how often a patient had to return to the 

office in order to ensure a satisfactory outcome. Higher numbers of follow-ups are regarded as 

adverse outcomes as they may indicate complications after the surgery. 

Table 1 presents descriptive statistics of the data. The average number of surgeries per 

doctor through January 19, 2005, with the CLOFAN laser machine is 109. We present patient 

characteristics in the lower block. The mean age of patients in the sample is 38 years, and 64 

percent are female. At the bottom of Table 1, we present the mean and standard deviation of our 

four measures of outcomes. Mean postsurgery defocus equivalent is 1.07 diopters; 74 percent of 

surgeries had a defocus equivalent higher than 0.5; 8 percent of patients required resurgery; and 

on average, patients had three follow-ups. 

 

34 It is worth noting that the attempted outcome is not always a defocus equivalent of zero. For instance, based on 

the patient’s lifestyle (occupation, recreational activities, etc.), age, eyeglass prescription, and accommodation of the 

eye muscles, the physician may consider that a full correction is not attainable or advisable. Moreover, the physician 

may decide to specialize one eye for near-sightedness and the other for far-sightedness. 

35 See Waring (2000) for standard measures for reporting refractive surgery outcomes. 

36 It is worth noting that not all surgeries outside ±0.5 diopters required a repeat surgery. 
17

4.4 Econometric Model 

The main question of this paper is whether there is learning by doing in LASIK eye surgery. We 

define learning by doing as an improvement in surgery outcomes due to the ophthalmologist’s 

accumulated experience in performing LASIK procedures. Our empirical strategy aims to 

identify this effect. 

To test for learning by doing effects, we estimate the following equation: 

Outcomeijk = Xj

 ß + L δ + υk + ωi + μijk (1) 

Where Outcomeijk is the outcome for the surgery on the eye (i=[left,right]) of patient j operated 

on by doctor k. For the defocus equivalent outcome, the best possible outcome has a value of 

zero; a higher number indicates postoperative myopia/hyperopia and/or astigmatism. For this 

outcome we consider only the first surgeries in our sample, as a repeat surgery may differ in 

many ways,37 although we accumulate all surgeries (first and repeat surgeries) when calculating 

doctors’ experience. Xj is a vector of patient characteristics such as age, sex, and presurgery 

defocus equivalent. To control for the nonlinearity of presurgery eyesight we include the square 

of the presurgery defocus equivalent.38 

L = [ log(cumulative surgeriesk), dummies for nomogram updates ] is a vector of learning 

effects containing individual learning (represented by the cumulative number of LASIK 

surgeries for each surgeon k) and group learning (represented by the nomogram updates). We 

use the logarithm of the cumulative number of LASIK surgeries for each surgeon as the 

functional form that captures the learning curve and a dummy variable for each nomogram 

 

37 For example, the goal of repeat surgery may differ from that of the initial surgery as it corrects the remaining 

uncorrected visual acuity. Doctors might therefore choose a different approach for the follow-up surgery. In addition, 

postsurgery outcome from the initial surgery, used as a presurgery visual acuity for the follow-up surgery, is no 

longer exogenous. 

38 The results are robust even if we include higher-order terms. 
18

update to identify the clinicwide learning.39 δ = [ δINDIV , δGROUP ] is a vector that measures the 

slope of the learning curve. If there is individual learning by doing, doctors should get better 

outcomes (i.e., defocus equivalent measures closer to zero) in the n

th surgery than in the nth–1

surgery. If the experience accumulated by doctors as a group in the surgical center matters, 

doctors should get better outcomes after the nomogram is updated. We should expect a negative 

sign in δ when there is individual or group learning since our measures of outcome are defined as 

adverse. 

We include a surgeon-specific fixed effect (υk) to eliminate permanent differences across 

surgeons. Standard errors are clustered by surgeon to take into account any nonlinear surgeonspecific residuals not captured by this fixed effect. 

We also include type of surgery fixed effects (ω). The surgical methods are different 

depending on the refractive error. For example, myopia requires laser ablation to flatten the 

central cornea, whereas hyperopia requires laser ablation to make the cornea steeper (Machat et 

al. 1999, p. 17). Our data set comprises seven different surgical methods to treat myopia, 

myopic astigmatism, hyperopia, hyperopic astigmatism, and astigmatism as well as custom 

LASIK and a “multizone” technique.40 For higher-order aberrations, surgeons measure the 

complete shape of the surface of the cornea to prepare an individually tailored surgery plan.41 

 

39 We also tried square root and a quadratic in the vector of learning as a functional form. Results are robust to all 

these functional forms. 

40 “Multizone” is a technique in which the surgeon divides the cornea into small zones and makes a separate ablation 

for each zone. It has the advantage of a more accurate ablation. The choice of multizone might not be exogenous. 

However, we do not observe a time trend for the patients that chose multizone. 

41 This more personalized procedure is called custom LASIK. Higher-order aberrations cannot be corrected by 

optical devices such as glasses or by conventional LASIK surgery (http://www.seewithlasik.com/docs/customlasik.html). 
19

Last, we include a microkeratome fixed effect.42 To determine whether the type of 

microkeratome makes any difference in the outcome, we included four different versions of this 

tool (hansatome, hansatome excelsius, carriazo-barraquer, and pendular) in our data. 

Additionally, we controlled for the software version in our regressions. The software for 

the Schwind ESIRIS LASIK machine and its upgrade were provided by the manufacturer. We 

include a dummy variable to capture the upgrade installed in the clinic’s machine on June 24, 

2004.43

For the outcome that is measured as a dummy variable (= 1, if the postsurgery defocus 

equivalent is higher than 0.5 diopters—i.e., a failure), we apply a linear probability model using 

only the first surgery case for the same reason described above for the defocus equivalent 

outcome. In the case of the last two outcome measures, repeat surgery and number of follow-ups 

after surgery, we use the whole sample. 

4.5 Random Assignment 

Selection across doctors and over time is a possible source of bias.44 Selection across doctors 

can occur if some doctors treat more difficult cases compared to others. One possible scenario is 

that more experienced (or better performing) doctors would be assigned to more serious cases. 

In this case, outcomes for doctors treating severe cases would be underestimated. Selection over 

time may occur if a doctor treats more (or fewer) severe cases over time. 

 

42 As mentioned above, a microkeratome is a tool used to make a flap in the cornea that provides the surgeon access 

to the corneal stroma in order to reshape it. A smooth flap is crucial for the outcome of the surgery because an 

irregular surface causes unclear vision. 

43 Machat et al. (1999) list operating temperature and humidity as other factors that can affect surgery outcomes. 

Although we have those variables in our data, they are poorly recorded and therefore not regarded as an important 

part of the patient charts; for example, records show large variations within a day, which is impossible as the 

operating room is a temperature- and humidity-controlled space. Therefore, we decided not to use those variables in 

our analysis. 

44 In our case, two selections are possible: by the patient or by the doctor. We do not differentiate them here. 
20

Selection across doctors and over time depends on how many patients looked for a 

specific doctor, and how the clinic assigns patients among doctors. Our conversations with 

receptionists at CLOFAN revealed that most patients visit the clinic without a specific doctor in 

mind. When a patient arrives at the clinic for a LASIK surgery consultation without requesting a 

specific doctor, the receptionist assigns the patient randomly based on doctors’ availability. 

Because each doctor is an equal shareholder of the clinic, receptionists assign patients so that 

each doctor has the same workload. 

Nevertheless, LASIK surgeries were performed very disproportionately across doctors. 

The reason is that, although LASIK surgery is regarded as a general procedure that can be 

handled by any doctor in the clinic, some doctors specialize in performing specific procedures 

such as cataract surgery, and as a result have less available time to take LASIK cases. 

Unfortunately, we cannot observe this effect directly from our data because they include only 

LASIK patients. 

In order to check for selection in our data, we test whether patients’ observable 

characteristics vary over time or across doctors. As mentioned above, one of the big advantages 

of using LASIK surgery in our study is that unobservable conditions are minimal. To check 

selection across doctors, we ran a regression with the presurgery defocus equivalent as a 

dependent variable and the total number of LASIK surgeries for the operating surgeon as an 

independent variable. If there is no selection across doctors, we will not get a statistically 

significant coefficient. In fact, the coefficient is –0.0009 with a standard error of 0.0017, which 

is small and statistically insignificant. 

To check for selection over time, we analyzed the changes in presurgery defocus 

equivalent of all LASIK patients in the clinic (shown in Figure 3 by month of surgery) and did 

not observe any pattern. We also tested whether presurgery eyesight changes over time or over 
21

experience by using a separate regression. Monthly time trend was used as an independent 

variable and log cumulative number of surgeries was used for experience. We included a 

surgeon-specific fixed effect for both estimations. The result is statistically insignificant at the 5 

percent level, meaning that patients’ severity did not change over time or with the individual 

doctor’s level of experience. 

5. RESULTS 

If there is a learning curve in LASIK surgeries, outcomes will improve either with individual 

doctors’ experience (measured as the logarithm of the cumulative number of surgeries) or with 

their group experience (measured using the nomogram update). For all our measures of outcome, 

this translates into a negative slope for increases in the log of cumulative number of surgeries if 

individual experience matters, or for the nomogram updates if the group experience is relevant, 

given that better outcomes are associated with smaller numerical values. 

In order to illustrate graphically how outcomes evolve over time, Figure 4 presents the 

average postsurgery defocus equivalent by month. In reading this figure, it is useful to bear in 

mind that the nomogram was updated in December 2003 and May 2004, and that the bigger the 

average postsurgery defocus equivalent, the worse the outcome. During the LASIK machine’s 

first month of operation, we observed a high average postsurgery defocus equivalent—that is, 

more adverse outcomes; thereafter, outcomes remained stable until November 2003, except for a 

spike of bad outcomes in October 2003. From December 2003 to April 2004 outcomes varied 

little except for a relatively high number of adverse outcomes observed in March 2004, which 
22

occurred because of four surgeries with particularly bad outcomes.45 Although there is more 

variation in outcomes after May 2004, the overall levels are lower than those observed before 

then. 

In Table 2, we show the results under various specifications using the defocus equivalent 

as the outcome variable. In the first column, we include only observations with postsurgery 

visual acuity measured by refraction. The second column includes the estimated defocus 

equivalent imputed from the Snellen measure, which causes the number of observations to 

increase by 50 percent. This increase in turn causes the standard error for the log of the 

cumulative number of surgeries in the second column to decrease substantially with respect to 

the first column; at the same time, the point estimate decreases by 0.003 without changing the 

qualitative results. The sign is negative as we expected, meaning that adverse outcomes decrease 

with experience, but there is no statistically significant improvement as an individual doctor 

performs more surgeries using the same technique. 

In the third column we include other learning factors—specifically, the two nomogram 

updates. The coefficient for log cumulative surgeries in the third column is –0.0542 and is 

imprecisely measured. When a doctor performs 100 additional surgeries, outcomes improve 

0.05 percent, which constitutes a tiny improvement.

The coefficients corresponding to the two nomogram updates are presented in the second 

and third rows respectively. The first nomogram update does not have the expected negative 

sign and is estimated imprecisely. The coefficient that corresponds to the second nomogram 

update is negative and significant at the 5 percent level. The second update lowers the 

postsurgery defocus equivalent by 0.1 diopter, which is equivalent to 10 percent of the average 

postsurgery defocus equivalent and represents a substantial improvement. Age shows consistent 

 

45 We concluded that these adverse outcome are random after close examination of the data. 
23

significance, meaning that older patients have significantly worse outcomes. If a patient’s age 

increases by 1 year, the posturgery defocus equivalent is higher by 0.01 diopter. If the patient is 

a woman, the postsurgery defocus equivalent is again 0.1 diopter higher, and this variable shows 

consistent statistical significance except in the first column. 

To control for the nonlinearity of the presurgery eyesight measure, we included a 

quadratic term in our model. Both terms in this measure are jointly significant, meaning that 

when patients have particularly poor presurgery eyesight, the postsurgery outcome is likely to be 

worse. The software upgrade was imprecisely estimated in the third and fourth columns. The 

choice of microkeratome is not statistically significant in the regression.46 A microkeratome 

fixed effect, included in the last column, did not change any of the estimates qualitatively. 

Throughout the regression we included a surgeon-specific fixed effect, and a type of surgery 

fixed effect to control for time-invariant factors across surgeons and types of surgeries. Standard 

errors are clustered by surgeon to capture nonlinear common factors associated with a particular 

surgeon. 

In Table 3, we present the results for all four outcome variables. In the first column, the 

dependent variable is the postsurgery defocus equivalent, the same variable displayed in the last 

column of Table 2. In the second column, the outcome variable is whether the postsurgery 

defocus equivalent is greater than 0.5 diopter (i.e., a failure). When we use postsurgery defocus 

equivalent as an outcome, a single outlier could have a big effect on the estimates. Using a 

dummy for success or failure provides a different way of measuring learning that avoids this 

problem. Individual learning, measured by the logarithm of the cumulative number of surgeries, 

shows the expected sign but it is statistically insignificant and tiny in magnitude. Group learning, 

reflected in the nomogram updates, shows qualitatively the same results compared to the first 

 

46 We do not report those estimates in the table in order to save space. They are available upon request. 
24

column. The sign of the first nomogram update is positive but statistically insignificant. 

However, the second nomogram update lowers the adverse outcome rate by 0.07, which 

represents a 10 percent improvement and is statistically significant at the 5 percent level. 

In the third column we use repeat surgery as the adverse outcome. There are more 

observations here because we include all the resurgery cases that are excluded in the outcome 

measures shown in the first and second columns. The repeat surgery rate is 8.2 percent. In this 

case, the coefficient of individual experience is not precisely measured. Consistent with our 

previous results, the second nomogram update lowers the repeat surgery rate by 8 percentage 

points and is statistically significant. Repeat surgery outcome shows the most dramatic change 

in terms of magnitude after the second nomogram update. 

In the last column, we use the number of follow-ups as a measure of outcome. The log of 

the cumulative number of surgeries and the two nomogram updates shows a negative sign but we 

cannot reject the null hypothesis of no learning effects given the lack of statistical significance. 

The rest of the independent variables show stable estimates across different outcome variables. 

In Table 4 we sort the doctors based on their volume of surgeries. Because we observe 

from Tables 2 and 3 that group learning substantially improves the outcome, in Table 4 we want 

to examine possible heterogeneous effects by surgery volume on various outcomes and also 

determine whether specific doctors are driving the results. We divide our sample in two groups: 

doctors who performed more than 100 LASIK cases during our data period and those who 

performed fewer than 100. As mentioned above, the nomogram is updated in a meeting attended 

by all the ophthalmologists in the clinic. They review the surgeries performed using the existing 

nomogram and discuss possible changes to improve outcomes. In this process, it is possible that 

updates happened based on the opinion of doctors who performed more surgeries. 
25

The upper block of Table 4 repeats the results reported in Table 3 for all doctors, the 

middle block shows the results for doctors with more than 100 surgeries, and the bottom block 

shows the results for doctors with fewer than 100 surgeries. The number of observations in the 

middle and bottom blocks is similar. 

In the first column of Table 4, when individual learning is measured by the log of the 

cumulative number of surgeries, high-volume doctors show bigger point estimates in absolute 

terms than low-volume doctors, meaning that high-volume doctors learn faster (although none of 

the estimates are precise). Results in the case of the second nomogram are striking. The 

magnitude of the coefficient associated with the second nomogram update for high-volume 

doctors is almost twice as large as that for all doctors in absolute value, and 16 times larger than 

the coefficient for low-volume doctors. This coefficient is estimated precisely for high-volume 

doctors but not for low-volume doctors. This means that the second nomogram improves the 

surgery outcome for high-volume doctors much more than for low-volume doctors, who did not 

get nearly as much benefit from the nomogram update. This result is not surprising, as highvolume doctors probably play a larger role in defining the nomogram adjustments. 

In the second column, where we use failure (= 1 if the postsurgery defocus equivalent is 

greater than 0.5 diopter) as an outcome measure, we observe the same qualitative results as in the 

first column. High-volume doctors improve their outcomes after the second nomogram update, 

the magnitude of the improvement is bigger than that of all doctors, and the results are 

statistically significant. We cannot reject the null hypothesis of no improvement after the second 

nomogram update for low-volume doctors. The point estimate for low-volume doctors is onesixth the estimate for high-volume doctors in absolute value. 

When we consider repeat surgery as an outcome in the third column, none of the learning 

variables are estimated precisely, except for the second nomogram update in the case of low-
26

volume doctors. However, the magnitude of the estimates is almost the same for the high- and 

low-volume doctors. In the results presented in the last column, where the outcome measure is 

the number of follow-ups, none of the variables from the learning vector are precisely estimated. 

We also want to examine which patients achieve better outcomes due to learning and 

whether the severity of their presurgery condition affects outcomes. We analyze those cases in 

Table 5. Outcomes might improve with more experience on the margin, and easy cases are 

probably not the marginal cases. Therefore, we divide the patients based on the severity of their 

previous condition, measured by the presurgery defocus equivalent. 

The first column in Table 5 is analogous to the first column in Table 3, which contains 

the whole population. The second column includes patients with a presurgery defocus equivalent 

lower than the 50th percentile, and the third column shows those above the 50th percentile.47 In 

this table, we use postsurgery defocus equivalent as an outcome. If we look at the first row, 

where the coefficient associated with individual learning is presented, none of the columns show 

statistically significant estimates. The coefficient associated with the first nomogram update is 

also estimated imprecisely. In the third row, we observe that the second nomogram update was 

disproportionately more beneficial to patients with serious initial conditions. As reported in the 

third column, the coefficient of the second nomogram update is statistically significant for 

serious cases: The second nomogram update improved the postsurgery defocus equivalent for 

these cases by 19 percent, which is 7 percentage points higher than that of the whole sample. On 

the other hand, the easier cases, shown in the second column, did not obtain any statistically 

significant improvement on the postsurgery defocus equivalent after the second nomogram 

update. The improvement for the more severe cases, shown in the coefficient in column 3, is 

almost 4 times larger in absolute value than the improvement caused by the second nomogram 

 

47 We also tried 25th percentile and 75th percentile as cutoffs, but, we could not obtain precise estimates due to the 

decreased observation numbers. 
27

update to the easier cases shown in the second column. Severe cases constitute 58 percent of the 

sample. 

Table 6 reproduces the analysis presented in Table 5 for three other outcomes. In the 

case of the outcome measure that takes the value of 1 when the postsurgery defocus equivalent is 

higher than 0.5 diopter, we do not observe any significant results for individual or group learning. 

In the case of the repeat surgery outcome, shown in the middle block, individual learning does 

not reveal any consistent pattern; however, the second nomogram upgrade makes a big 

difference between the easy and serious cases. The latter improve more than the easy cases and 

the coefficient is statistically significant at the10 percent level as a result of group learning. In

contrast, easy cases did not show any statistically significant improvement after the second 

nomogram update. In the bottom block the number of follow-ups shows no significant changes 

in outcomes for either easy or serious cases. 

Finally, we explore the possibility that there is some learning from sources other than a 

doctor’s individual experience or from the clinic’s group experience. For example, learning 

could happen over time by reading professional journals. In order to capture general learning we 

add a monthly time trend to our model and present the results in Table 7. In the first column, the 

coefficient associated with the second nomogram update increases slightly and is significant at 

the 10 percent level. When we use failure as an outcome, the second nomogram update is no 

longer statistically significant after controlling for monthly time trend. However, the coefficient 

for repeat surgery is still statistically significant and has the same magnitude. For the number of 

follow-ups, monthly time trend is significant but lowers the number of follow-ups by only 0.04, a 

1.5 percent decrease. Using the outcome measure that defines a postsurgical defocus equivalent 

of 0.5 diopter or higher as a failure, we could not determine if doctors are learning from the 

second nomogram update or because there is general learning over time. However, results 
28

obtained using the other outcome measures were consistent with the previous results and 

qualitatively robust. 

6. CONCLUSIONS 

In this paper, we examine the existence of learning by doing in LASIK eye surgeries. We chose 

LASIK because this procedure has a well-defined outcome measure on which a patient’s 

unobservable conditions have little bearing. In addition, we use a remarkable data set that allows 

us to observe the evolution of these well-defined outcomes for a group of doctors since they 

began performing laser surgeries in June 2003. 

The distinguishing feature of this paper, in comparison with previous studies, is the use of 

a longitudinal data set with good measures of doctors’ experience and precisely defined medical 

outcomes. Past studies have used data that identify only annual surgical volumes and often 

confound measures of outcomes with many unobserved patient conditions; in those studies, it 

was difficult to isolate the effect of learning by doing from other effects such as selective referral. 

The main question addressed in this paper is whether patients’ outcomes improve with 

physicians’ experience. We use two different measures of learning in LASIK procedures. First, 

we measure individual learning by the cumulative number of surgeries for each doctor. Second, 

we measure group learning by using updates of a nomogram, an adjustment algorithm used in the 

LASIK surgeries. We did not find evidence that as doctors increase the number of surgeries 

performed they obtain better outcomes. However, we did find evidence of group learning, as 

outcomes significantly improved after the second nomogram update. 
29

We used four different measures of outcomes: postsurgery defocus equivalent, a dummy 

variable for success or failure, repeat surgery, and the number of follow-ups after the surgery. 

The first two measures of outcome show a consistent 10 percent improvement after the second 

nomogram update, with a statistical significance of 10 and 5 percent respectively. The other two 

measures of outcome show a similar improvement at the 5 percent level of statistical significance. 

Patients with serious cases benefited more as a result of the second nomogram update and 

doctors with higher volume showed a greater improvement. This may be because the highvolume doctors participate most actively in the updates of the nomogram. We found that group 

learning plays a substantial role in LASIK surgery performance whereas individual learning does 

not. 
30

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Figure 1. LASIK surgery procedure 

1-3: Cutting the flap in the cornea with the microkeratome. 

4. Folding the flap back. 

5. Correcting the corneal tissue through laser ablation. 

Source: Allaboutvision.com at: http://www.allaboutvision.com/visionsurgery/lasik.htm 

Figure 2. Cumulative probability of resurgeries 

CDF of re-surgery

when a surgery happened in 2003(by days)

0

20

40

60

80

100

0 30 60 90 120 150 180 210 240 270 300 330

(%) 

Days after surgery 
34

2.5

2.7

2.9

3.1

3.3

3.5

Jul-03

Aug-03

Sep-03

Oct-03

Nov-03Dec-03

Jan-04

Feb-04Mar-04

Apr-04

May-04

Jun-04

Jul-04

Aug-04

Sep-04

Oct-04

Nov-04Dec-04

Jan-05

Pre-Surgery Defocus Equ

Figure 4. Average postsurgery defocus equivalent (by month) 

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Jul-03

Aug-03

Sep-03

Oct-03

Nov-03Dec-03

Jan-04

Feb-04Mar-04

Apr-04

May-04

Jun-04

Jul-04

Aug-04

Sep-04

Oct-04

Nov-04Dec-04

Jan-05

Post-Surgery Defocus Equivalent
35

Table 1. Descriptive Statistics 

Data period July 1, 2003 ~ 

August 8, 2005 

Number of doctors 27 

Total number of observations 3,892 

Observations till Jan. 19, 20051 2,565 

Cumulative surgeries by each doctor 108.7 

(105.8) 

Patients’ Characteristics 

Age 38.3 

(12.3) 

Percent male 35.6 

(0.47) 

3.26 Presurgery defocus equivalent (2.29) 

 25th percentile 1.75 

 50th percentile 2.50 

 75th percentile 4.25 

 

Outcome Variables 

Postsurgery defocus equivalent2 1.07 

(0.83) 

 percent >0.51 73.7 

(0.44) 

 percent resurgery 8.2 

(0.27) 

Number of follow-ups 2.68 

(1.66) 

 ( ) standard deviations 

 1. Jan. 19, 2005 is 200 days before the data collection. We keep the window of 200 days 

throughout data. Therefore, we dropped the observations operated after Jan. 19, 2005. 

2. Including only the first surgery. We use the most up-to-date eyesight measure within 200 

days from the surgery date. 
36

Table 2. Impact of Learning Vector on Postsurgery Defocus Equivalent 

Without 

Imputation With Imputation 

(1) (2) (3) (4) 

-0.0188 -0.0219 -0.0542 -0.0404 

Log(cumulative surgeries) 

(0.0393) (0.0294) (0.0580) (0.0663) 

 0.1127 0.1194 

1

st nomogram update 

 (0.1076) (0.1029) 

 -0.1270 -0.1275 

2

nd nomogram update 

 (0.0475) (0.0465) 

0.0087 0.0085 0.0086 0.0084 

Age 

(0.0013) (0.0009) (0.0009) (0.0010) 

0.1088 0.1074 0.1068 0.1025 

Sex 

(0.0660) (0.0479) (0.0480) (0.0471) 

Presurgery defocus 0.0403 0.0235 0.0232 0.0230 

equivalent (0.0325) (0.0264) (0.0255) (0.0262) 

Presurgery defocus 0.0068 0.0072 0.0072 0.0070 

equivalent^2 (0.0031) (0.0027) (0.0027) (0.0027) 

-0.2390 -0.2092 0.0111 0.0225 

Software upgrade 

(0.1557) (0.0988) (0.1266) (0.1330) 

Microkeratome fixed 

effect N N N Y 

N 1,180 1,729 1,729 1,723 

The first column includes observations with postsurgery refraction measure to calculate defocus 

equivalent. The other columns include imputed defocus equivalent when postsurgery eyesight was 

measured by Snellen. We use the most up-to-date eyesight measure within 200 days after the surgery. A 

surgeon-specific fixed effect and type of surgery (myopia, myopic astigmatism, hyperopia, hyperopic 

astigmatism, astigmatism, custom LASIK, and multizone) fixed effects are included. A microkeratome 

(hansatome, hansatome excelsius, carriazo-barraquer, and pendular) specific fixed effect is also included 

in the last column. Robust standard errors are clustered by surgeon and included in parentheses. 
37

Table 3. Impact of Learning Vector on Various Outcomes 

Defocus 

Equivalent1

>0.5 D1

 Resurgery Number of 

Follow-ups 

Log(cumulative -0.0404 -0.0303 0.0046 -0.0851 

surgeries) (0.0663) (0.0293) (0.0166) (0.0866) 

0.1194 0.0809 -0.0230 -0.0247 

1

st nomogram update 

(0.1029) (0.0555) (0.0271) (0.1859) 

-0.1275 -0.0734 -0.0813 -0.1014 

2

nd nomogram update 

(0.0465) (0.0363) (0.0374) (0.1488) 

0.0084 0.0017 0.0018 0.0077 

Age 

(0.0010) (0.0012) (0.0005) (0.0043) 

0.1025 0.0571 0.0290 0.0843 

Sex 

(0.0471) (0.0178) (0.0164) (0.0907) 

Presurgery defocus 0.0230 0.0468 0.0268 0.0760 

equivalent (0.0262) (0.0148) (0.0098) (0.0374) 

Presurgery defocus 0.0070 -0.0015 -0.0011 -0.0037 

equivalent^2 (0.0027) (0.0011) (0.0008) (0.0034) 

N 1,723 1,723 2,007 2,007 

D = diopter 

Fixed effects are included for surgeon, type of surgery, and type of microkeratome . Robust standard 

errors are clustered by surgeon and are shown in parentheses. Linear Probability Model is used for the

regression of >0.5 D and resurgery. 

1 We used only the first surgery sample. 
38

Table 4. Impact of Learning Vector on Various Outcomes, 

by Surgeon Volume 

Defocus 

Equivalent1 >0.5 D1v Resurgery Number of Follow-ups 

(1) (2) (3) (4) 

All doctors 

Log(Cumulative -0.0404 -0.0303 0.0046 -0.0851 

surgeries) (0.0663) (0.0293) (0.0166) (0.0866) 

-0.1275 -0.0734 -0.0813 -0.1014 

2

nd nomogram update 

(0.0465) (0.0363) (0.0374) (0.1488) 

N 1,723 1,723 2,007 2,007 

Doctors with ≥ 100 volume 

Log(cumulative -0.0618 -0.0472 -0.0086 -0.0394 

surgeries) (0.1313) (0.0539) (0.0199) (0.1560) 

-0.2112 -0.1164 -0.0787 -0.0688 

2

nd nomogram update 

(0.0906) (0.0432) (0.0701) (0.1832) 

N 858 858 991 991 

Doctors with < 100 volume 

Log(cumulative -0.0206 -0.0169 0.0204 -0.0660 

surgeries) (0.0730) (0.0304) (0.0250) (0.0850) 

-0.0127 -0.0183 -0.0791 -0.1157 

2

nd nomogram update 

(0.0584) (0.0556) (0.0364) (0.2530) 

N 865 865 1,016 1,016 

D = diopter 

See notes for Table 3. 
39

Table 5. Impact of Learning Vector on Defocus Equivalent, 

by PreSurgery Defocus Equivalent 

 Whole Sample Easy cases 1 Severe cases 2

(1) (2) (3) 

Log(cumulative -0.0404 -0.0293 -0.0297 

surgeries) (0.0663) (0.0595) (0.1061) 

0.1194 0.2026 0.0583 

1

st nomogram update 

(0.1029) (0.1399) (0.1579) 

-0.1275 -0.0525 -0.2016 

2

nd nomogram update 

(0.0465) (0.0847) (0.0974) 

0.0084 0.0129 0.0062 

Age 

(0.0010) (0.0020) (0.0020) 

0.1025 -0.0283 0.1764 

Sex 

(0.0471) (0.0736) (0.0724) 

N 1,723 719 1,004 

Fixed effects are included for surgeon, type of surgery, and type of microkeratome. Robust 

standard errors are clustered by surgeon and are shown in parentheses. 

1. <50th Percentile of Presurgery Defocus Equivalent 

2. ≥50th Percentile of Presurgery Defocus Equivalent 
40

Table 6. Impact of Learning Vector on Various Outcomes, 

by Presurgery Defocus Equivalent 

 Whole Sample Easy cases 1 Severe cases 2

(1) (2) (3) 

Outcome: >0.5 D 

Log(cumulative -0.0303 -0.0178 -0.0373 

surgeries) (0.0293) (0.0492) (0.0299) 

-0.0734 -0.1276 -0.0289 

2

nd nomogram update 

(0.0363) (0.0954) (0.0639) 

Postsurgery defocus 

equivalent 1.07 0.95 1.07 

Outcome: Resurgery 

Log(cumulative 0.0046 -0.0090 0.0018 

surgeries) (0.0166) (0.0198) (0.0284) 

-0.0813 -0.0200 -0.0928 

2

nd nomogram update 

(0.0374) (0.0272) (0.0483) 

 Outcome: Number of follow-ups 

Log(cumulative -0.0851 -0.1406 -0.1677 

surgeries) (0.0866) (0.1707) (0.1605) 

-0.1014 0.1448 -0.0718 

2

nd nomogram update 

(0.1488) (0.1991) (0.2034) 

D = diopter 

See notes for Table 5. 

1. <50th Percentile of Presurgery Defocus Equivalent 

2. ≥50th Percentile of Presurgery Defocus Equivalent
41

Table 7. Impact of Learning Vector on Various Outcomes 

After Controlling Monthly Time Trend 

Defocus 

Equivalent1 >0.5 D1

 Resurgery Number of 

Follow-ups 

Log(cumulative -0.0210 -0.0276 0.0052 -0.0285 

surgeries) (0.1732) (0.0228) (0.0210) (0.0858) 

0.1547 0.0858 -0.0217 0.0856 

1

st nomogram update 

(0.1008) (0.0704) (0.0223) (0.1779) 

-0.0998 -0.0695 -0.0803 -0.0163 

2

nd nomogram update 

(0.0540) (0.0463) (0.0408) (0.1628) 

-0.0118 -0.0016 -0.0004 -0.0366 

Monthly time trend 

(0.0113) (0.0093) (0.0050) (0.0182) 

N 1,723 1,723 2,007 2,007 

D = diopter 

See note for Table 3.