Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.

Development and Testing of An Automatic Lung IMRT Planning Algorithm

Knowledge-based radiation treatment is an emerging concept in radiotherapy. It

mainly refers to the technique that can guide or automate treatment planning in

clinic by learning from prior knowledge. Dierent models are developed to realize

it, one of which is proposed by Yuan et al. at Duke for lung IMRT planning. This

model can automatically determine both beam conguration and optimization ob-

jectives with non-coplanar beams based on patient-specic anatomical information.

Although plans automatically generated by this model demonstrate equivalent or

better dosimetric quality compared to clinical approved plans, its validity and gener-

ality are limited due to the empirical assignment to a coecient called angle spread

constraint dened in the beam eciency index used for beam ranking. To eliminate

these limitations, a systematic study on this coecient is needed to acquire evidences

for its optimal value.

To achieve this purpose, eleven lung cancer patients with complex tumor shape

with non-coplanar beams adopted in clinical approved plans were retrospectively

studied in the frame of the automatic lung IMRT treatment algorithm. The primary

and boost plans used in three patients were treated as dierent cases due to the

dierent target size and shape. A total of 14 lung cases, thus, were re-planned using

the knowledge-based automatic lung IMRT planning algorithm by varying angle

spread constraint from 0 to 1 with increment of 0.2. A modied beam angle eciency

index used for navigate the beam selection was adopted. Great eorts were made to assure the quality of plans associated to every angle spread constraint as good

as possible. Important dosimetric parameters for PTV and OARs, quantitatively

re

ecting the plan quality, were extracted from the DVHs and analyzed as a function

of angle spread constraint for each case. Comparisons of these parameters between

clinical plans and model-based plans were evaluated by two-sampled Students t-tests,

and regression analysis on a composite index built on the percentage errors between

dosimetric parameters in the model-based plans and those in the clinical plans as a

function of angle spread constraint was performed.

Results show that model-based plans generally have equivalent or better quality

than clinical approved plans, qualitatively and quantitatively. All dosimetric param-

eters except those for lungs in the automatically generated plans are statistically

better or comparable to those in the clinical plans. On average, more than 15% re-

duction on conformity index and homogeneity index for PTV and V40, V60 for heart

while an 8% and 3% increase on V5, V20 for lungs, respectively, are observed. The

intra-plan comparison among model-based plans demonstrates that plan quality does

not change much with angle spread constraint larger than 0.4. Further examination

on the variation curve of the composite index as a function of angle spread constraint

shows that 0.6 is the optimal value that can result in statistically the best achievable

plans.