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3 Uncertainty and estimation 179

3 Uncertainty and estimation

3.1 Uncertainty
In ophthalmology we face many uncertainties and they can be of many types. For
example, we may not know if a treatment will work for a specific patient i.e. an un-
certainty for one particular patient. Another example can be that we do not know the
true corneal thickness due the precision of the measurement i.e. we face uncertainty
in the measurement caused by a measurement error, which can be either due to the
device, the slight change in the light conditions, the training of the technician taking
the measurement, or patient’s fatigue. A third example can be that we are not certain
how a treatment affects visual acuity in diabetic patients i.e. we are uncertain how
patients with treatment compare to patients with standard care and we may not be
certain if there are other factors to take into account like age or life style.
What do we humans do when we face uncertainty? We rationalize by listing all
possible outcomes and assign probabilities of how likely each outcome is. Some of
us may be better at this, some of us may panic, but usually our estimation of uncer-
tainty and our decisions get better as we get older. For example, in rolling a fair six-
sided dice with numbers 1–6, we may be interested in the outcome of having an odd
number. Such an outcome is uncertain and we can estimate the uncertainty easily re-
alizing that there is a probability of exactly ½ of observing the odd number in any of
the dice rolls. Throwing a fair dice and estimating the probability is simple. A more
challenging can be estimating the chance of a rain. Some of us may not like taking
a walk in the rain so we estimate the probability of the rain and if the probability is
sufficiently small we go for a walk. An even more challenging scenario is to estimate
the uncertainty of a person dying in a car accident. We may decide to estimate the
probability ourselves or we can let someone else to estimate it. If we let someone else
to estimate the probability of dying in a car crash, then we need to decide if we trust
such an estimate, as there is an also an uncertainty on how good is his/her estimation.
In other words we need to judge the credibility of the estimation, and to do so we may
want to consider factors of how credible is this statistician judging by the quality of
his/her publications in the area of car crashes and the risk estimation.
In ophthalmology, we typically have complex scenarios of uncertainty and they
follow three main types (as in most of the medical fields). Firstly, we face uncer-
tainty in the values of patients’ outcomes. For example, we may be clear about the
plausible range of visual acuity in patients with diabetes, but we maybe uncertain
about which visual acuity value will be measured and recorded for the right eye of
a randomly chosen patient. Visual acuity can take on many values (on e.g. Early
Treatment Diabetic Retinopathy Study (ETDRS) scale) and each value has a differ-
ent probability of occurring. In statistical terms this means that we quantify the un-
certainty in VA via a probability distribution. We usually do not know this probability
distribution so we can estimate this uncertainty via e.g. a histogram. Secondly, we
may be clear that age affects the visual acuity but we may be uncertain about other
factors affecting the visual acuity, such as treatment, diet of the patient and life style.