![](bg9.png)
increasing the Ki amount for the data without noise.
A one-way repeated measurements ANOVA test
indicated that there is significant evidence to reject
the null hypothesis and confirm that those statistical
models reveal different results for the final Ki value.
Each statistical regression model dealt with the
simulation data in a different way, and based on the
goodness of fit evaluations, the best fitted regression
model can be chosen. Follow-up comparisons
indicated that each pairwise difference was
significant except between OLS and TLS. The p-
value between OLS and TLS shows that null-
hypothesis about equality can not be rejected at
confidence level 0.05 that is used with this test. The
significant difference between the statistical models
used, suggesting that using a different linear
regression model reveals a different Ki value, which
is the main parameter of Parkinson’s disease
diagnosis. The min SE and SSE were found with
FGLS, and this suggests that FGLS is the best of these
models to fit the noisy data. FGLS also had the second
lowest fold change rate, which measures the change
difference from the Ki value without noise. OLS and
TLS showed the lowest fold change rate, and that
indicates more resistance to the noise effect than the
other methods. RFR had the highest fold change rate
compared to the data without noise, which indicates
sensitivity to noise.
In the first simulation, the OLS Ki data had similar
values at all levels of noise, unlike the other data for
the rest of the simulations. For the first two
simulations, all statistical regression models behaved
similarly at all noise levels; thus, the Ki data points
were close in value. This could happen in link to the
original Ki values without noise where considered the
lowest among the other simulations. Other
simulations with low Ki values below 0.012, which
represents the diseased levels, could reveal more
details about how statistical models will behave. In
addition, Ki values lower than 0.012 could clarify
whether the noise could lead to moving the Ki values
to be considered normal. The big difference within
the SE from one noise level to another indicates the
high sensitivity to noise in linear regression analysis,
which confirms the previous results in the published
literature review. The experiment has contributed to
the knowledge in the field by suggesting using FGLS
as a linear regression method for Patlak graphical
analysis. From the above results, using FGLS could
provide better data fitting with low SE and SEE,
indicating more accurate results than other
approaches. Including lower Ki values without noise
could give more details and better confirms the best
fitting model from regression methods. Repeating the
experiment with different equivalent time (t*) points
could reveal more details and alter the accuracy of
those methods. It would be useful to apply those
models on clinical data obtained from patient
dynamic images and compare the results to the
outcome of this experiment.
6 CONCLUSION
Graphical techniques in PET data analysis from
reference tissue are considered simple means of
analysis to obtain physiological parameters. One
issue usually generated with this type of analysis is
the bias introduced, which is caused by the sensitivity
to statistical noise. The study shows there is a
significant difference between the statistical models
used, suggesting that using a different linear
regression model reveals a different Ki value, which
is the main parameter of Parkinson’s disease
diagnosis. Analysing the PET data with different
statistical regression approaches and evaluating each
approach graphically and numerically could improve
the final result for more accurate diagnosis. FGLS
regression model could provide better data fitting in
Patlak analysis with low SE and SEE, indicating more
accurate results than other approaches. In the next
work, these methods will be applied to clinical PET
data obtained from a clinical trial to see how the final
result will be affected.
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