484

DECISION THEORY TO ESTIMATE DELTA

of retinal pigment epithelium (CHRPE).’ Further information about the probability of being affected can be obtained

hypertrophy

by ophthalmological examination. Combining the probabilities of identifying the gene carriers by negative sigmoidoscopy with increasing age, the absence of CHRPE, and a favourable result with gene markers allows an accurate estimation of the probability of a first-degree relative being affected: % probability of APC with negative

Decision theory puts V(1-P)+PO=O(P+)+1(1-[P+4]) so that A=1 -P-V(1-P). Thus for P=06, A=004 for V=0 9. 002 for V--0 95, and 0008 for V--098.

(4) Most clinicians are concerned, not with the null hypothesis (since few treatments are likely to give identical results) but with the magnitude of any treatment effect. Therefore, the concern in a trial is not only to avoid missing a positive result but also to provide

acceptably precise estimates of treatment effects. A lot of confusion could be avoided if a and P errors were always set equal/,3 whether or not treatments have similar costs. The relative disadvantages of different treatments can be taken into account, not by manipulating a and 0, but by ensuring that A (the size of difference that a trial is designed to detect) is sufficient to influence clinical practice. The best method to determine A so that it is neither too small to warrant the side-effects of the more costly treatment nor too large to demonstrate worthwhile differences, is decision theory. In the following example, based on a proposed trial of mastectomy vs lumpectomy in breast cancer, P is the probability of dying from cancer after mastectomy and (P-A) is this probability after lumpectomy, and the value of intact life is 1, the value of cancer death is 0, and the value of life following the mutilation of mastectomy is V (table): if V is 0-9 (implying that the patient would run a 10% risk of cancer death to avoid mutilation) then a A of 4% improvement in the risk of dying from breast cancer, from 60% to 56%, would make the mutilation of surgery worthwhile. If, however, V was 0-95, the "level of indifference" moves to 2%. The best way to measure V is by certainty equivalence multiple gambles.’ which can be done amongst doctors, patients, or random sections of the population. Clinicians cannot be expected to recommend randomised trials to their patients where the study is incapable of demonstrating clinically important differences or where it will continue to accept patients long after worthwhile treatment effects may have been established. Department of Obstetrics and Gynaecology, St James’ University Hospital, Leeds LS9 7TF, UK

R.

J.

LILFORD

1. Schwartz

D, Flamant R, Lellouch J. Methods of comparison. In: Clinical trials. (Translated by M. J. R. Healy). London: Academic Press, 1980: 77-86. 2. Lilford RJ. Evaluating new treatments and diagnostic technologies in obstetrics: practical problems, ethics and solutions. Int J Technol Asssess Health Care 1989; 5: 459-72. 3. Lilford RJ,

Johnson N. The alpha and beta errors in randomised clinical trials should be equal. N Engl J Med (in press). 4. Torrance GW. Measurement of the health state utilities for economic appraisal: a review. J Health Econ 1986; 5: 1-30.

Risk estimates for

screening polyposis coli

adenomatous

SIR,-Adenomatous polyposis coli (APC) is a dominantly inherited condition characterised by multiple adenomatous polyps in the colon and rectum and a high risk of malignant change. Other serious extracolonic manifestations may appear. Screening by yearly sigmoidoscopy is usually offered to those at risk. Genetic counselling should be available to all family members at risk and presymptomatic diagnosis may be helpful. For first-degree relatives at risk there is a 50% chance of inheriting the mutant gene at conception. The likelihood of being affected diminishes with age as negative results are obtained by sigmoidoscopy.l With localisation of the mutant gene for APC to the long arm of chromosome 5linked gene markers can be used to identify affected family members with 95-99-9% certainty.,3 However, our clinical experience is that only 38% of pedigrees are informative. Now it is recognised that 75-80% of APC gene carriers have congenital

Age

Age only

0 10 15 20 30

50 49 30 20 8

Negative CHRPE*

sigmoidoscopy Negative CHRPE Negative genemarkerst and gene markers*t

5-0 17-0 50 8-0 18 4-8 12 2-2 0-5 *80% manifestmg; tat 5% recombination -

5-0 1-0 0-5 0-2 0-1

With this information, it is possible to provide appropriate counselling and screening to individuals at risk and it may be possible to obviate years of needless endoscopic screening. By age 30 the risk

can

be

as

low

as

1 in 1000.

Department of Clinical Genetics, Royal Free Hospital, London NW3 2QG, UK

RICHARD HOULSTON JOAN SLACK

Department of Clinical Genetics, Leeds General Infirmary

VICTORIA MURDAY

Murday V, Slack J. Inherited disorders associated with colorectal cancer. Cancer Surveys 1989; 8: 139-57. 2. Bodmer WF, Bailey CJ, Bodmer J, et al. Localisation of the gene for familial adenomatous polyposis on chromosome 5. Nature 1987; 328: 614-16. 3. Tops CMJ, Wijnem, J Th, Griffioen G, et al. Presymptomatic diagnosis of familial adenomatous polyposis by bridging DNA markers. Lancet 1989; ii: 1361-63. 4. Chapman PD, Church W, Bum J, Gunn A. The detection of congenital hypertrophy of retinal pigment epithelium (CHRPE) by indirect ophthalmoscopy: a reliable clinical feature of familial adenomatous polyposis. Br MedJ 1989; 298: 353-54 1.

Shadow method for sun protection SiR,—To protect the public from skin damage by the sun’s

(UV) rays, doctors warn their patients to avoid the midday sun between 1100 h and 1500 h or during similar periods ultraviolet

when the radiation from the sun is assumed to be at maximum intensity. Unfortunately, these rules based on clock time are flawed and do not tell people when midday truly occurs or for how long it lasts. The strength of the sun’s UV-B radiation depends mainly on the height of the sun in the sky, but clock time is often a poor indicator of solar height because of seasonal changes, wide time zones, daylight saving time, and the large differences in latitude and longtitude in various locations. When clock rules are working as intended, the limits of the unsafe period correspond roughly to times when the sun is halfway between the horizon and the overhead point (ie, at 45°). A simple, more accurate, and direct method for estimating the height of the sun and thereby the strength of its UV-B rays is to observe the lengths of shadows outdoors. When shadow lengths on level surfaces are equal to the height of objects casting them, the sun is at 45°. Shorter shadows imply stronger radiation. The shadow method is therefore a better approximation of the information that clock rules are trying to provide. Physical measurements of the diurnal variation of UV-B radiation weighted by the erythemal action spectrum of human skin confirm this method. These calculations show that the effective sun protection factor (SPF) of the atmosphere is about 2-4 at a 45° solar altitude and increases rapidly below this point. I therefore suggest that doctors recommend to their patients the following rule of thumb for UV-B protection: "When your shadow is shorter than you are tall, the sun is much more likely to bum you than at other times, so seek protection then with proper clothing, shade, sunscreens, or other means." 10500 Rockville Pike, Apt M-10, Rockville, MD 20852, USA

LEITH HOLLOWAY