J Clin Pathol 1987;40:210-215

Autoimmunity: a decision theory modelJ A MORRIS

From the Department of Pathology, Lancaster Moor Hospital, Lancaster

SUMMARY Concepts from statistical decision theory were used to analyse the detection problemfaced by the body's immune system in mounting immune responses to bacteria of the normal bodyflora. Given that these bacteria are potentially harmful, that there can be extensive cross reactionbetween bacterial antigens and host tissues, and that the decisions are made in uncertainty, thereis a finite chance of error in immune response leading to autoimmune disease. A model of ageingin the immune system is proposed that is based on random decay in components of the decisionprocess, leading to a steep age dependent increase in the probability of error. The age incidence ofthose autoimmune diseases which peak in early and middle life can be explained as the resultant oftwo processes: an exponentially falling curve ofincidence of first contact with common bacteria, anda rapidly rising error function. Epidemiological data on the variation of incidence with social class,sibship order, climate and culture can be used to predict the likely site ofcarriage and mode of spreadof the causative bacteria. Furthermore, those autoimmune diseases precipitated by common viralrespiratory tract infections might represent reactions to nasopharyngeal bacterial overgrowth, andthis theory can be tested using monoclonal antibodies to search the bacterial isolates for crossreacting antigens. If this model is correct then prevention of autoimmune disease by early exposureto low doses of bacteria might be possible.

There are many autoimmune diseases and there areprobably many causes of them. Drugs are known toprecipitate autoimmune disease by several mech-anisms.' It is thought that viruses might precipitateautoimmune disease2 3 by changing the host immuneresponse, releasing sequestered antigens, changinghost antigens, cross reacting with host antigens, or bythe development of antibodies to host antiviralidiotypes. Bacteria can also promote autoimmunedisease. Streptococcus pyogenes infection can leadto the development of immune complex mediatedglomerulonephritis and rheumatic fever.4 The formeris thought to arise because the bacteria secrete prod-ucts which form the antigenic component of immunecomplexes, while the latter is probably a result ofcrossreaction between bacterial surface antigens and hosttissues, particularly heart muscle. The associationbetween streptococcal infection and autoimmune dis-ease was recognised because S pyogenes produceslocal tissue damage as well as the more remoteimmune mediated damage. In this paper I will arguethat immune responses to normal commensal bacte-ria, which do not normally produce clinical disease,might be responsible for some examples of auto-immune disease. The approach depends critically onstatistical decision theory, the general principles of

Accepted for publication 9 July 1986

which apply to all decisions made in uncertainty.5

Elements of decision theory

Consider an ideal detection system attempting todifferentiate a signal (hl) of constant intensity Y, andassume that in the absence of the signal (ho) there isbackground noise, which is normally distributed withmean intensity p and variance S (fig 1). If, in a definedobservation interval, h, and ho are equally likely thenthe maximum number of correct responses will beobtained by regarding all intensities above x (fig 1) ashl, and those below as ho. If, however, the a prioriprobability of h, exceeds that of ho the decision crite-rion should be reduced below x. Equally, if therewards associated with correct responses and thecosts associated with incorrect responses are not equalthen the decision criterion needs to be modified.

According to decision theory,5 the optimumresponse (the response that maximises expected value)is to accept h, rather than ho whenL,o (e) > B

where LI0 (e) = P[elhl]P [eIh0I

andB= [V11+v1Vo [

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Autoimmunity: a decision theory model

p ocIntensity

Fig 1 Frequency distributions of intensity givenbackground noise (ho), which is normally distributed withmean p and signal (h1) of constant intensity Y, which issuperimposed on background noise. If ho and h1 are equallylikely then a decision criterion placed at x will minimise,but not eliminate, errors.Llo (e) is the likelihood ratio of event e for h, relativeto ho.P [elhj] is the probability of event e given h1P [elho] is the probability of event e given hoP [ho] is the a priori probability of hoP [h1] is the a priori probability of h1VOO is the value of choosing ho given hoVol is the cost of choosing h, given hoV11 is the value of choosing h1 given hIV1o is the cost of choosing ho given h,H1 is the decision to accept hiHo is the decision to accept ho

There is no single correct answer but only an opti-mum strategy to maximise expected value. It is clearfrom fig 1 that any strategy that leads to an increasein the probability of accepting h, given h, [P(H1Ihl)]will lead to an inevitable increase in the probability ofaccepting h , given ho[P(H Iho)]. The relation betweenP (Hllh1) and P (H1lho) is plotted in fig 2 for twovalues of Y where Y1 > Y2. For a constant Y, thecurve is generated by varying the value ofB (changingthe decision criterion).The analysis so far applies to a simple idealised

detection problem. If a decision is to be made, how-ever, between two states h1 and ho then no matter howcomplex the task and no matter how much informa-tion is to be sifted and integrated, the optimal decisionrule will depend on likelihood ratio-that is, a simpleratio of the probability of all the evidence given h1divided by the probability of obtaining that evidencegiven ho. Thus the general principles outlined aboveapply to all decisions made in uncertainty.

The microbial flora

The body surfaces, particularly the gastrointestinaland upper respiratory tracts, have a complex micro-bial flora.6 Although it is often thought that thesebacteria are harmless commensals, there is, in fact,clear evidence that many if not most are potentially

0-2

0.1

Y1

0 0.1 0:2 03 0-4 0-5 06 07 0:8 09 10:P (HI/ho)

Fig 2 Probability of true positive P[H,/h,] plotted againstprobability offalse positive P[HI/ho] for two values of Ywhere Y1 > Y2.

pathogenic. For example, most cases of bron-chopneumonia in the elderly are caused by bacteriaaspirated from the upper respiratory tract. Per-foration of gastrointestinal viscera can lead to peri-tonitis and septicaemia. Bacterial endocarditis can becaused by organisms such as Streptococcus viridansand Staphylococcus albus, which are often regarded asharmless commensals. Furthermore, sites ofcommen-sal microbial flora can provide temporary or longterm residence for a variety of clearly pathogenic bac-teria such as Staph pyogenes, Spyogenes, Haemophilusinfluenza type B, encapsulated pneumococci, Clostri-dium sp, Neisseria meningitidis etc. This potential forharm can be further extended; bacteria can produceharmful and perhaps lethal toxins (Stephen J, Pie-trowski RA, Van Noostrand Reinhold UK, 1981)which might diffuse into the bloodstream. This hasbeen dramatically illustrated with the recent recog-nition of the toxic shock syndrome caused by toxinsproduced by certain strains of Staph pyogenes.7 8 Thiscondition can produce severe multisystem disease andsudden death in otherwise healthy adults.9 It has beenknown for many years, however, that many staphy-lococci produce a range of haemolysins which disruptlipoprotein membranes and are lethal to experimentalanimals after intravenous injection (Stephen J, Pie-trowski RA, Van Noostrand Reinhold UK, 1981).Streptococci,'0 including the ubiquitous viridansgroup, and clostridia are known toxin producers. Fur-thermore, bacteria can acquire the capacity to codefor toxins on their DNA by plasmid transfer or bacte-riophage infection, and this might underlie the toxi-genic capacity of Escherichia coli (Glass RE. gene

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function; Croom Holm Ltd, 1982) corynebacteria,and staphylococci.1A host immunological response to contain bacterial

growth on body surfaces and prevent tissue invasionand toxaemia is therefore required. There is a furtherproblem: cross reaction between bacterial surfaceantigens and host tissues is widespread. Thus E colireacts with antibodies to insulin and braingangliosides' 2; Yersinia enterocolitica have thyr-otropin receptors13 14; streptococci have surface com-ponents cross reacting with HLA antigens13;antibodies to chorionic gonadotrophin react withSepidermidis, E coli, and Pseudomonas maltophilia. "Glycopeptides from human and rat brains share anti-genic determinants with meningococcus group B andE coli. 6 Monoclonal antibodies to nicotinic acety-lcholine receptors react with proteins in E coli, Proteusvulgaris, and Klebsiella pneumonia. 17

Consequently, the immune system is faced with acomplex detection problem, as it needs to classify bac-terial antigens into foreign or non-cross reacting(equivalent to group h1) and self or cross reacting(group ho) and respond appropriately. No matter howsophisticated the detection system, and no matter howmuch information is sampled, there must be someresidual uncertainty in this distinction. Indeed, as thecompatibility of an antigen with an antibody dependson complementary electron cloud shapes and the pos-ition of an electron is a random variable, therefore theelectron cloud shape is also a random variable, albeitwith smaller variance. The response H1 or Ho willdepend on information (e) gained about the antigen,on the perceived a priori probability of the antigenbeing self or not self, and on the perceived values VOO,V1,9 V1,0 Vol. Perceived a priori probability will beinfluenced by previous experience of how frequentlycross reacting antigens are found on bacteria, andwhether certain types of bacteria or bacteria acting incertain ways are more or less likely to express crossreacting antigens. Perceived values will be influencedby assessment of the likely pathogenicity of theorganisms. These calculations represent further deci-sions made in uncertainty. Vol will be a measure of theharm arising by committing a clone of B or T lympho-cytes to attack a self antigen, while Vlo is the penaltyof not responding and increasing the chance of bacte-rial infection. It is possible that once a clone of cellsis committed to an antigen (Hl) then the response ispermanent, while a failed response (Ho) could be sub-sequently rectified. It is also possible that there arelevels of lymphocyte control which could delete auto-aggressive clones, but these control systems will alsobe subject to uncertainty so there is always a finitechange of a permanent autoimmune response follow-ing contact with surface bacteria that have antigens incommon with the host.

Morris

The age incidence of autoimmune disease

Consider the problem of an ideal detection systemattempting to distinguish self (ho) from non-self anti-gens (h,) on bacteria. The detection system must insome way obtain samples of information (e) byanalysing the antigen along one or many dimensions.It will then be necessary to compute the probability ofthe totality of information obtained given h1 [P(elhl)]and ho [P(elho)] to determine the likelihood ratio.Finally, the decision made will depend on the value ofB, which will be influenced by perceived utilities VOO,VOI, VI1, V10 and perceived a priori probabilities. Tosimplify the model let us assume that a large number[N] of samples of information (e) are obtained fromeach antigen and transformed on to some linear scaleand that the mean of the observations (e) is deter-mined. Then the probability distribution eIh, and flhowill tend to have a normal distribution if N is large(central limit theorem). The variance of the distribu-tion will be inversely proportional to N (samplingtheorem). The problem is therefore analagous to thatin fig 1, with overlapping distributions lh, and lhoand a decision criterion (x) whose position is deter-mined by the value of B.The performance of any complex system must

decay with time. This law also applies to biologicalsystems, even though repair systems might limit therate of decay. A first approximation would be to allowN to decrease at random with time so that the functionNexp (-kt) determines the variance of elho and lh,(fig 1). Then the probability of Hllho [P(Hj1ho)],which is the area under the frequency distribution ofalho to the right of the decision criterion, will increasewith age as the variance of alho increases. The timewhen immune responses to bacteria are set, however,is when the organisms are first encountered. For mostcommon bacteria, this will be early in life, and the agedistribution of first contact with any particularorganisms will show a roughly exponential curve fall-ing from birth with a half life determined by the prev-alence of the bacterium. Thus the age incidence ofonset of autoimmune disease arising as a consequenceof this contact will be the resultant of a rising curveP(Hjjho) interacting with a falling exponential curve.Fig 3 shows a representative result from the model.The exponential curve has a half life of four years,while P (Hllho) is determined by a decision criterionmoving from 5 5 standard deviations from the meanat birth at a rate determined by constant k in thefunction Nexp (- kt). The incidence of the disease inthis example rises to a peak at 32 to 36 years, andabout 65 cases will arise in a birth cohort of 500 000.If the rate of circulation of the bacteria decreases sothat the half life lengthens then the incidence of thedisease would rise substantially. Equally, a relatively

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Autoimmunity: a decision theory model

[00 ] No of cases in birth cohort of 500000

sol RJ1 1

Age (years)

Fig 3 Theoretical age distribution histogram ofautoimmune disease produced by rising error functionP[HjfhoJ interacting with falling curve of susceptibility.

small increase in the rate of bacterial circulationwould cause a substantial reduction in disease inci-dence, and if this model is correct efforts to ensure thatchildren meet the putative bacteria early could in the-ory virtually eliminate the condition.

This type ofage incidence curve with a peak in earlyor middle life is seen in many putative examples ofautoimmune disease,"8 including multiple sclerosis,19thyrotoxicosis, insulin dependent diabetes mellitus,20ulcerative colitis and Crohn's disease.

Discussion

There is clear evidence to show that many bacteria ofthe normal microbial flora are capable of causing dis-ease either by tissue invasion or by elaborating toxins.There is also evidence of extensive cross reactionbetween bacterial antigens and host tissues. Theimmune system is faced with an exceedingly complextask in determining responses to bacterial antigens soas to avoid both infection and autoimmune disease.The fact that it is successful in most cases indicatesthat the decision strategy adopted is close to the ideal,so that modelling the decision process using the prop-erties of an ideal detector is a reasonable approxi-mation. If the immune system deviates from anoptimal strategy then this will only amplify errors thatare inherent in the decision process and which havebeen identified using the ideal detector model. It is notassumed that there is a structural entity correspondingto the ideal detector, but that the integrated action ofthe many and diverse arms of the immune system

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approximates to an optimum strategy. As the immuneresponse to bacteria is decided in uncertainty therewill be a finite change of the error H1I ho, and it can bepredicted that at least some examples of autoimmunedisease will arise as a response to microbial flora anti-gens. Obviously this in no way implies that this is theonly way in which autoimmune disease arises. It iscertainly possible that autoimmune disease could ariseas a result of cross reacting antigens present onviruses. Interestingly, while viruses have a codingcapacity of between 3 and 50 kilobases of DNA orRNA, bacteria have up to 5000 kilobases of DNA.21Given the large number of bacteria resident on thebody surface, the antigenic challenge posed bybacterially coded polypeptides is many 100-fold morecomplex than even a lifetime's accumulation of viralinfections.The age incidence of many examples of auto-

immune disease, which show a peak in early or middlelife, can be explained using this model. The assump-tions are that the immune response is set at first con-tact and that the performance of the ideal detectordecays at random with time. The latter assumptionmeans that a simple exponential decrease in the num-ber of samples of information (N) leads to a steep agedependent increase in P[H Ilhol. Burch has shown thatthere is an approximate linear relation between logincidence and log age for many diseases of aging22 - 24including malignant disease, degenerative diseases,and cardiovascular disease. It is therefore of interestthat there is also an approximate linear relationbetween log P[H 1 ho1 and log age over a wide range ofvalues. The concept of random decay in the com-ponents of a decision process leading to increasingprobability of errors of function might have a widerapplication.

If the age at first contact with a bacterium deter-mines the probability of autoimmune disease thencommunities in which the bacteria circulate more rap-idly will have a lower incidence of the disease. Thespread of enteric bacteria might be influenced bysocial class, sibship order, and climate. In this respectthe observation that multiple sclerosis is more com-mon in higher social classes,25 first born children,26and colder climates27 is of considerable interest. Onthe other hand, the spread of respiratory tract bacteriamight be influenced by sibship order, but is less likelyto be affected by social class, and might actuallyincrease in colder climates. Consequently, the epi-demiological features of autoimmune disease couldgive a clue to the normal mode of spread of the ini-tiating organisms.There is some evidence to suggest that common

viral respiratory tract infections can precipitate auto-immune disease.28 30 When this is observed it is usu-ally assumed that the virus acts directly, either by

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214 Morrispresenting new antigens, changing host antigens, orinterfering with lymphocyte function. There areseveral problems associated with this explanation.Different viruses seem to be capable of initiating thesame disease, and waves of viral infection in a commu-nity only precipitate disease in a fraction of the popu-lation at risk. Furthermore, although the incidence ofany one virus fluctuates considerably from year toyear, the incidence of autoimmune disease shows onlysmall yearly fluctuation.30 Viral infections of therespiratory tract also disturb the normal microbialflora and lead to overgrowth of staphylococci, strep-tococci, or Gram negative bacilli.3` As the antigenicchallenge posed by this bacterial overgrowth is manyfold greater than that of the initiating virus, it is notunreasonable to suggest that at least some examples ofautoimmune disease might arise as a response to thebacterial antigens.32 If by chance the first encounterwith a particular bacterium follows a viral infectionand the bacteria overgrow in the nasopharynx thenthe host is faced with a potentially threatening infec-tion necessitating a swift response. According to deci-sion theory, swift responses mean that lessinformation is sampled (decreased N), potentiallythreatening infections increase Vlo, and both thesechanges increase P[H1Ihoj. This idea would explainwhy autoimmune disease only arises as a very rarecomplication of a common viral infection and whydifferent viruses could precipitate the same disease.Furthermore, as the spread of bacteria that grow onthe body surface is less affected by host immunity thanis the spread of viruses this would explain why auto-immune disease shows less yearly fluctuation thandoes epidemic viral disease.Autoimmune disease may be acute, subacute, or

chronic but often shows a characteristic remitting andrelapsing course. This is understandable in terms ofthis hypothesis, as the microbial flora undergoes con-stant change under a variety of influences, not least ofwhich are viral infections of the host and bacte-riophage infections of the bacteria. If the activity ofautoimmune disease is related to antigenic challengethen it will wax and wane as the bacterial florachanges.One aspect of autoimmune disease that has received

a great deal of attention is the role of genetic consti-tution, in particular HLA phenotypes.33 Ninety fiveper cent of whites with insulin dependent diabetesmellitus express the class II HLA alleles DR3 or DR4,or both.34 These alleles are only expressed in 40% ofthe general white population. Similar associationsbetween HLA phenotype and other examples of auto-immune disease have been reported.33Although gen-etic factors are important, however, concordance inidentical twins for diseases such as insulin dependentdiabetes mellitus29 30 is less than 100%, indicating the

importance of environmental factors. The HLA com-plex is a multigene family on the short arm ofchromo-some 6 concerned with self- and non-selfdiscrimination. Class I HLA molecules participate intarget cell recognition by suppressor and cytotoxic Tcells, while class II HLA molecules, which areexpressed on the surface of antigen presenting cells,participate in antigen recognition by T helper cells.The relation between HLA antigens, autoimmunity,and infection is undoubtedly complex. If some exam-ples of autoimmune disease arise in response to bacte-rial antigens as suggested in this paper then as HLAmolecules have a central role in T cell recognition offoreign antigens, it is not surprising that HLA pheno-types influence the risk of autoimmune disease. Otherways in which this association might arise includeincreased susceptibility to certain viral infections anddefective T cell suppressor activity, allowing the pro-liferation of autoreactive clones. Genetic factors couldinfluence the decision theory model in several ways.As genetic factors influence the structure of cell sur-face antigens they will determine the bacterial anti-gens to which the individual is susceptible. In fact, thecomposition of the bacterial flora is influenced bygenetic factors as the colonisation of epithelial sur-faces by bacteria depends on specific bacterial adhe-sions combining with cell surface molecules.6Furthermore, the incidence of autoimmune diseasewill vary between subjects who operate different riskstrategies. Different perceptions of values [Voo, V10,Vol, V1 1] and a priori probability will influence B, andthereby vary the probability of error [HlIhol. Indeed,the higher incidence ofautoimmune disease in womenmight be explained in this way as men seem to be moreprone to infection and malignant disease, which canbe regarded as the consequence of the converse error(HoIhl).The hypothesis presented is amenable to laboratory

investigation, although testing it will be a formidabletask. Epidemiological data can be used to determinethe likely mode of spread of the causative bacteria.For those diseases that are precipitated by commonviral respiratory tract infections the bacterial flora inthe upper respiratory tract should be determined tosee of there is any constant pattern preceding onset orexacerbations of the disease. If there is, monoclonalantibodies can then be used to search the bacterialisolates for antigens that cross react with host tissues.

References

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2 Mims CA. Immunopathology in virus disease. Philosophical- Transactions of the Royal Society of London, series B

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17 Stefansson K, Dieperink ME, Richman DP, Gomez CM, MartonLS. Sharing of antigenic determinants between the nicotinicacetylcholine receptor and proteins in Escherichia coli, Proteusvulgaris, and klebsiella pneumoniae. Possible role in the patho-genesis of myasthenia gravis. New EnglJ Med 1985;312:221-5.

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29 Barrett-Connor E. Is insulin dependent diabetes mellitus causedby Coxsackievirus B infection? A review of the epidemiologicevidence. Rev Infect Dis 1985;7(2):207-15.

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Requests for reprints to: Dr JA Morris, Consultant Patholo-gist, Department of Pathology, Lancaster Moor Hospital,Lancaster LAI 3JR, England.

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