Statistical Analysis (Specific Aim 3)

The two dose metrics, organ dose and effective dose, cannot be compared with each other. So, comparisons of the three organ dose estimate methods and comparisons of the three effective dose estimate methods were performed separately. All dose metrics were calculated from measurements taken on the same subject. Therefore, for the same subject, the three cannot be assumed to be independent. Accordingly, a Repeated Measures One-way Analysis of

Variance (RM-ANOVA) model was used to test for equality of the three organ dose methods and the three effective dose methods, see Table 3-1.

Table 3-1: RM-ANOVA tests hypotheses

Repeated Measures One-Way ANOVA (RM-ANOVA)

Dose Method Comparisons Null Alternative α

Organ Dose SSOD

(A)

SAOD (B)

NAOD

(C) Any violation of Null 0.05

Effective Dose SED (D)

AED (E)

k-factor

(F) Any violation of Null 0.05

RM-ANOVA is strongly dependent on two assumptions, namely, normality and sphericity. These assumptions must be validated before performing the RM-ANOVA test. The normality assumption for each data set was checked formally with a Chi-Square Goodness of Fit test, and graphically with a normal probability plot in Microsoft Excel. The sphericity

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Upon violations of the sphericity assumption, SAS prints a Greenhouse-Geisser (G-G) correction factor to adjust the degrees of freedom. This correction adjusts the final p-value estimate on the F statistic. Results and further descriptions of the assumption tests are in Appendix A.

Several pairwise comparisons of the population means were performed, using paired t- tests, if the RM-ANOVA null hypotheses were rejected. For the organ dose estimates, the SSOD and SAOD methods were compared (i.e. µA versus µB), as were the SSOD and NAOD and

methods (i.e. µA versus µC). SAOD was not compared to NAOD, since the difference between

the two is merely the average EDCF from AAPM 204. For the effective dose estimates, pair- wise comparisons of the SED, AED, and k-factor methods were made (i.e. µD versus µE, µD

versus µF, and µE versus µF).

For each comparison, two separate types of paired t-tests were performed, a conventional paired t-test using ordinary differences and a more unconventional paired t-test using relative differences. For example, the difference of organ dose methods SSOD (A) and SAOD (B), A – B, was used to test a hypothesis for µA - µB. The relative difference of organ dose methods

SSOD (A) and SAOD (B) is defined as A* - B*, where

[( ) ⁄ ⁄ ] [( ) ⁄ ⁄ ] Equation 3-4

This difference was used to test a hypothesis for µA* - µB*. Using both ordinary and relative

differences provide more information and allow more flexibility when determining whether or not to reject null hypotheses.

Two organ dose methods or two effective dose methods were declared clinically similar if the relative difference between the corresponding population means was less than 0.20 (20%) in magnitude. For example, in order for dose methods SSOD (A) and SAOD (B) to be clinically similar, -0.20 ≤ µA* - µB* ≤ 0.20. This is somewhat arbitrary but corresponds to Nuclear

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Regulatory Commission mis-administrations levels in Nuclear Medicine. Also, 20% is the maximum deviation allowed for CTDI dose report values from measured values in the Joint Commission recommendations (The Joint Commission, 2013). A 20% deviation in dose estimation may seem high, but it means very little if the total dose is very small.

In addition, two organ dose (effective dose) methods were declared clinically similar if the ordinary difference between the corresponding population means was less than 5 mGy (0.5 mSv) in magnitude. For example, in order for organ dose methods SSOD (A) and SAOD (B) to be clinically similar, -5 mGy ≤ µA - µB ≤ 5 mGy, while effective dose methods SED (D) and

AED (E) are clinically similar if -0.5 mSv ≤ µD - µE ≤ 0.5 mSv. As discussed in Section 1.2.6,

SB 1237 listed maximum organ and effective dose limits over the wrong region of body as, 500 mGy for organ dose and 50 mSv for effective dose. Also, the ACR-AAPM Resolution 47 suggests that the DRL for adult abdomen-pelvis scans is 25 mGy (ACR-AAPM, 2013). The values 5 mGy and 0.5 mSv correspond to to 1% respectively.

There is a direct relationship between confidence intervals and hypothesis tests. The (1- α)*100% confidence interval for, say, µA - µB consists of all λ values for which the null

hypothesis H0 : µA - µB = λ (versus Ha: µA - µB ≠ λ with P(I)= α) is accepted. Therefore, the

organ dose methods SSOD (A) and SAOD (B) would have been declared clinically similar (clinically dissimilar) with (1-α)*100% confidence if the entire interval of numbers [-5 mGy, 5 mGy] had been contained in (had been outside of) the (1-α)*100% confidence interval for µA -

µB . The effective dose methods SED (D) and AED (E) would have been declared clinically

similar (clinically dissimilar) with (1-α)*100% confidence if the entire interval of numbers [-0.2, 0.2 ] had been contained in (had been outside of) the (1-α)*100% confidence interval for µD* -

30 Table 3-2: Organ dose post-hoc paired t-tests

Post-hoc Organ Dose t-tests (Overall α = 0.12 – Bonferroni adjustment) Performed for each

Method Comparisons Difference Type CI Test α

SSOD (A) NAOD (C)

Absolute 0.03

Relative 0.03

SAOD (B) NAOD (C)

Absolute 0.03

Relative 0.03

Table 3-3: Effective dose post-hoc paired t-tests

Post-hoc Effective Dose t-tests (Overall α = 0.12 – Bonferroni adjustment)

Method Comparisons Difference Type CI Test α

SED (D) k-factor (F)

Absolute 0.02

Relative 0.02

SED (D) AED (E)

Absolute 0.02

Relative 0.02

AED (E) k-factor (F)

Absolute 0.02

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RESULTS AND DISCUSSION

CHAPTER 4.

4.1 Organ Dose Summary