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2/1/99 Chapter 2 Study Design page 2-16
rates. In Specific Aims B, C, and D, we propose to evaluate risk factors that contribute to
worsening visual acuity, increasing corneal curvature, and increasing central corneal
scarring respectively. Projecting rates of progression from the above data or projecting
incidence of corneal scarring requires great caution, because it is clear that a high degree
of migration into and out of this patient sample occurs. The low number of patients
older than 50 years suggests a marked out migration, for example. A sample size of
1000 will provide reasonable power for detecting risk factors with odds ratios of 2.00 or
greater for events of relatively low occurrence, such as central cornea scarring, that have
high clinical relevance and functional significance.
Table 2-6. Power for detecting an odds ratio of ≥2.00 for various sample sizes.
Total sample
size
% with risk
factor
P1= 0.10
P2= 0.18
P1= 0.15
P2= 0.26
P1= 0.20
P2= 0.33
P1= 0.25
P2= 0.40
600 15% .530 .671 .737 .805
20% .626 .768 .828 .884
25% .695 .830 .882 .928
800 15% .652 .792 .850 .902
20% .750 .875 .919 .954
25% .814 .920 .953 .977
1000 15% .748 .873 .918 .953
20% .838 .935 .963 .983
25% .890 .964 .982 .993
P1 is the probability of the event in the group without the risk factor.
P2 is the probability of the event in the group with the risk factor.
w=odds ratio
P2=wP1/(wP1+Q1) (Fleiss, 1981)
2.9 Analysis of Data
2.9.1 General Considerations
As embodied in Specific Aim A, the primary goal of the CLEK Study is to
provide a comprehensive description of both baseline and longitudinal data from
patients with keratoconus. Two fundamental features of our analytic plans for the
remaining Aims are: (1) the implementation of procedures that account for the inherent
pairing of the data and (2) for longitudinal data, utilizing models that permit missing
data. We will employ longitudinal models that do not require that measurement times
be the same across patients. For both dichotomous and continuous outcomes,
traditional repeated measures designs cannot be appropriately applied when data are
missing or when patients have different evaluation schedules. Moreover, a fundamental
assumption of both linear and logistic regression, whether applied cross-sectionally or
longitudinally, is the independence of the error terms. In the CLEK Study, the unit of
observation will be the eye. However, the association between the characteristics of two
eyes in the same individual is likely to be stronger than the association between the
characteristics of two eyes of different individuals (Ederer, 1971). That is, the
independence assumptions of ordinary linear and logistic regression are almost certain
to be violated when applied to these data.