Appendix A: Description of distributions fitted to parameters in the probabilistic sensitivity analysis.
Model
Distribution.
parameter.
Distribution
Mean (SE).
parameters.
Moments of
relevant
distribution.
Costs.
None: costs are
-
-
-
1.01D (0.308)
Alpha = 10.7342,
regarded as a
fixed
parameter
because they
arise from NHS
national tariff
and therefore
reflect
accurately the
costs that
would be
incurred in
practice.
Utility.
Normal;
Mean, standard
multivariate
error.
normal.
Rate of
Gamma.
Alpha, beta.
progression
(control
group).1
Beta = 0.094
0.20D (0.093)
Alpha = 4.574,
Beta = 0.044
Probability of
Uniform.
grafting per
Lower and
0.001
Upper bounds.
Lower = 0.0003
Upper = 0.003
cycle once in
AK Stage 4.
Efficacy of
Beta.
Alpha, beta.
0.076
initial collagen
Alpha =7.6
Beta = 92.4
crosslinking
treatment.
Efficacy of
Uniform.
Lower and
No fixed
Lower=
upper bounds.
value as this
proportion
crosslinking at
is a
successful at
5 year
conditional
first treatment
retreatment
distribution
Upper = 1
interval
based on the
(Expressed as
value
the proportion
selected for
of treatments
the first five
which fail).
years3.
collagen
Proportion of
Standard
Lower and
patients
Uniform.
upper bounds.
Standard
Lower and
0.5
0,1
0.5
0,1
retreated with
collagen
crosslinking at
5 year interval.
Probability of
starting model
Uniform.
upper bounds.
in AK state 1 or
State 2 is
2.
conditional on
state 1.
Probability of
Beta.
Alpha, beta.
3/93
cataract after
Alpha = 3
Beta = 90
grafting.
Probability of
Beta.
repeat
Alpha, beta.
1/93
Alpha = 1
Beta = 92
grafting.
Notes
1. Rates of progression for the treatment group were calculated by multiplying control rates by a
constant, with standard errors adjusted accordingly. The rate of progression in the second eye never
exceeds that of the first.
2. All gamma and beta parameters were calculated by the method of moments.
3. That is to say, if the initial efficacy for the first five years is expressed as some value k (0<k<1), and
u ~ U(0,1), then the values ud this distribution are given by ud = 1-((1-k)u).
Utilities for the bilateral states were correlated using the Cholesky decomposition method, in order
to prevent simulations arising in which utility increased with worsening disease. To do this we used
a correlation coefficient between visual acuity and utility of -0.477, derived by taking Brown’s
measured correlation of 0.477, and adding the minus sign to account for the change in unit from
Snellen (Brown) to logMAR. Although correlation coefficient does not normally change with the
change of units, in this case a change was required because the measurement concept behind each
method is different. Specifically, Snellen values (when expressed as a decimal) decrease as vision
worsens, whereas logMAR values will increase. The adequacy of this substitution was established
using a simulation, in which a set of visual acuities, measured in both units, was correlated to a set of
utility values.