484

DECISION THEORY TO ESTIMATE DELTA

Decision theory puts V(1-P)+PO=O(P+)+1(1-[P+4]) so thatA=1 -P-V(1-P). Thus for P=06, A=004 for V=0 9. 002 for V--0 95, and0008 for V--098.

(4) Most clinicians are concerned, not with the null hypothesis(since few treatments are likely to give identical results) but with themagnitude of any treatment effect. Therefore, the concern in a trialis not only to avoid missing a positive result but also to provideacceptably 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. Therelative disadvantages of different treatments can be taken intoaccount, not by manipulating a and 0, but by ensuring that A (thesize of difference that a trial is designed to detect) is sufficient toinfluence clinical practice. The best method to determine A so that itis neither too small to warrant the side-effects of the more costlytreatment nor too large to demonstrate worthwhile differences, isdecision theory. In the following example, based on a proposed trialof mastectomy vs lumpectomy in breast cancer, P is the probabilityof dying from cancer after mastectomy and (P-A) is this probabilityafter lumpectomy, and the value of intact life is 1, the value of cancerdeath is 0, and the value of life following the mutilation ofmastectomy is V (table): if V is 0-9 (implying that the patient wouldrun 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% to56%, would make the mutilation of surgery worthwhile. If,however, V was 0-95, the "level of indifference" moves to 2%. Thebest way to measure V is by certainty equivalence multiplegambles.’ which can be done amongst doctors, patients, or randomsections of the population. Clinicians cannot be expected to

recommend randomised trials to their patients where the study isincapable of demonstrating clinically important differences orwhere it will continue to accept patients long after worthwhiletreatment 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 shouldbe equal. N Engl J Med (in press).

4. Torrance GW. Measurement of the health state utilities for economic appraisal: areview. J Health Econ 1986; 5: 1-30.

Risk estimates for screening adenomatouspolyposis coli

SIR,-Adenomatous polyposis coli (APC) is a dominantly inheritedcondition characterised by multiple adenomatous polyps in thecolon and rectum and a high risk of malignant change. Other seriousextracolonic manifestations may appear. Screening by yearlysigmoidoscopy is usually offered to those at risk. Genetic

counselling should be available to all family members at risk andpresymptomatic diagnosis may be helpful. For first-degree relativesat risk there is a 50% chance of inheriting the mutant gene atconception. The likelihood of being affected diminishes with age asnegative results are obtained by sigmoidoscopy.lWith localisation of the mutant gene for APC to the long arm of

chromosome 5 linked gene markers can be used to identify affectedfamily members with 95-99-9% certainty.,3 However, our clinicalexperience is that only 38% of pedigrees are informative. Now it isrecognised that 75-80% of APC gene carriers have congenital

hypertrophy of retinal pigment epithelium (CHRPE).’ Furtherinformation about the probability of being affected can be obtainedby 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 anaccurate estimation of the probability of a first-degree relative beingaffected:

% probability of APC with negative sigmoidoscopyAge Negative Negative Negative CHRPE

Age only CHRPE* genemarkerst and gene markers*t0 50 - 5-0 5-010 49 17-0 50 1-015 30 8-0 18 0-520 20 4-8 12 0-230 8 2-2 0-5 0-1

*80% manifestmg; tat 5% recombination

With this information, it is possible to provide appropriatecounselling and screening to individuals at risk and it may be

possible to obviate years of needless endoscopic screening. By age 30the 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

1. Murday V, Slack J. Inherited disorders associated with colorectal cancer. CancerSurveys 1989; 8: 139-57.

2. Bodmer WF, Bailey CJ, Bodmer J, et al. Localisation of the gene for familialadenomatous polyposis on chromosome 5. Nature 1987; 328: 614-16.

3. Tops CMJ, Wijnem, J Th, Griffioen G, et al. Presymptomatic diagnosis of familialadenomatous polyposis by bridging DNA markers. Lancet 1989; ii: 1361-63.

4. Chapman PD, Church W, Bum J, Gunn A. The detection of congenital hypertrophyof retinal pigment epithelium (CHRPE) by indirect ophthalmoscopy: a reliableclinical feature of familial adenomatous polyposis. Br Med J 1989; 298: 353-54

Shadow method for sun protectionSiR,—To protect the public from skin damage by the sun’sultraviolet (UV) rays, doctors warn their patients to avoid themidday sun between 1100 h and 1500 h or during similar periodswhen the radiation from the sun is assumed to be at maximum

intensity. Unfortunately, these rules based on clock time are flawedand do not tell people when midday truly occurs or for how long itlasts. The strength of the sun’s UV-B radiation depends mainly onthe height of the sun in the sky, but clock time is often a poorindicator of solar height because of seasonal changes, wide timezones, daylight saving time, and the large differences in latitude andlongtitude in various locations. When clock rules are working asintended, the limits of the unsafe period correspond roughly totimes when the sun is halfway between the horizon and theoverhead 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 toobserve the lengths of shadows outdoors. When shadow lengths onlevel surfaces are equal to the height of objects casting them, the sunis at 45°. Shorter shadows imply stronger radiation. The shadowmethod is therefore a better approximation of the information thatclock rules are trying to provide. Physical measurements of thediurnal variation of UV-B radiation weighted by the erythemalaction spectrum of human skin confirm this method. Thesecalculations show that the effective sun protection factor (SPF) ofthe 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 shadowis shorter than you are tall, the sun is much more likely to bum youthan 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