Prostate Cancer Screening: The Lens Model Clarifies a Comparison Between the Health Beliefs Model and a Descriptive Expected Utility Model.

Robert M. Hamm Department of Family and Preventive Medicine University of Oklahoma Health Sciences Center robert-hamm@ouhsc.edu

I applied a lens model analysis to cross person data, concerning beliefs about the benefits of prostate cancer screening. The judgment was the man's stated intention to get PSA screening in the next six months. The criterion was his self report, after 6 months, of whether he had gotten PSA screening. For predictors, there were 19 questions, on a 1 to 5 scale. I had also combined the 19 items into theoretically inspired indices: a) 4 Health Beliefs Model measures: benefits, barriers, severity and susceptibility; or b) 10 Descriptive Expected Utility Model component measures; and also c) the EU components were organized through a decision tree into a single measure, the difference between the EU of getting screened and the EU of not getting screened.

The correlation between PSA intention and PSA behavior (each 1 or 0) was .315. The lens model parameters using the 19 items, the 4 HBM measures, the 10 EU components, and the 1 EU difference score, were as shown in this table:

Linear

Nonlinear

All 19 items

0.117

0.198

4 HBM factors

0.059

0.235

10 EU components

0.072

0.213

EU difference

0.052

0.234

While it appears the models are inadequate, since even the full linear model explains less than half of the correlation, this may be due to the binary nature of the predicted variables. I would like to talk with those of you who have explored logistic regression versions of the lens model at the November Brunswik meeting, or hear from you by email.

More detailed inspection of the Lens Model components shows that Rs (the predictability of the PSA screening intention) was higher than Re (the predictability of the actual behavior), which is plausible since the intention was stated on the same day, while the behavior happened during the subsequent six months. Curious, also, is the perfect correlation between the predictions of the two models, for the one-predictor (EU difference) Lens Model.

Re

Rs

G

C

All 19 items

0.368

0.475

0.668

0.242

4 HBM

0.197

0.296

0.96

0.277

factors 10 EU components 1 EU difference

0.312

0.364

0.72

0.263

0.206

0.275

1

0.274

The exercise of applying the Lens Model gave a different perspective than the initial analyses I did of these data, comparing alternative logistic regression models.

# Progress?

K.R.Hammond krhammond@earthlink.net

I continue to work on the development of a book ms tentatively titled "The Structure of Human Judgment and the Softening of Rationality" but I am having trouble developing the appropriate theme for this book. However, a new event has occurred that all Brunwsikians should appreciate, to which I now turn.

# Last year Elise Weaver alerted me to the

appearance of a book titled "The Number Sense" by a French neuropsychologist (and mathematician), Stanislas Dehaene. It is indeed a splendid book but most important is the fact that it provides neuropsychological support for cognitive continuum theory, and the concept of quasirationality, although Dehaene knew (knows) nothing of either. As a result I wrote a draft chapter in my ms on his work and asked OUP to send it to him for his approval, which he gave. In addition, however, he sent an attachment containing an article he and his colleagues published in Science in 1999, that can only be described as striking. It is a great step forward for Brunswikian theory. The article can be found at http://www.sciencemag.org/cgi/content/full/284/541 6/970 and is reprinted as an addendum to the paper version of the newsletter with permission from the American Association for the Advancement of Science. The full reference for this article is Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., and Tsivkin, S. (1999) Sources of Mathematical Thinking: Behavioral and Brain- Imaging Evidence. Science, 284, pp. 970-974 (7 May 1999). Dehaene also has an article on the Edge website at: http://www.edge.org/3rd culture/dehaene/dehaene th

_p2.html.

Newsletter 2002 page 12 of 28