Mf?dic~~-Hypofkses (1990) 32,129-135 0 Longman Group UK Ltd 1990
The Age Incidence of Multiple .Decision Theory Model
Sclerosis: A
J. A. MORRIS Consultant Pathologist,
Department
of Pathology,
Lancaster Moor Hospital Lancaster LA1 3JR, UK
Abstract - It is proposed that multiple sclerosis (MS) arises as an auto-immune response to antigens shared by common commensal bacteria and brain tissues. In particular it is suggested that the causative bacteria are normally spread by the faecal-oral route but first exposure can occur in the nasopharynx, particularly following a viral respiratory infection, and this increases the risk of MS. The interaction between bacterial colonisation and the immune response is analysed in terms of an information model derived from statistical decision theory. The model predicts a finite chance of outoimmune disease on first exposure which rises with age at exposure. The predicted age incidence of MS, which is the resultant of the rising error function and the age incidence of first exposure to common bacteria, rises to a peak in the third decade and matches published age incidence data. Furthermore the model predicts that subsets of the population, such as women, in whom the risk of MS is increased will have an earlier mean age of onset. This accords with observation which is hitherto unexplained. The model also explains the decreased incidence of MS in equatorial regions, data on migration studies, and is consistent with the observation that the mean age of onset is not concsistently lower in low incidence regions. It also offers an explanation for conflicting data on the effect of social class, economic conditions and birth order. The hypothesis is amenable to laboratory investigation and should be pursued.
Introduction
The major epidemiological features of MS are well documented (1, 2). The disease is uncommon with a prevalence of less than 10 to 144 per 100 000 (1). It is more common in temperate climates and the incidence increases with distance Date received 19 June 1989 Date accepted 21 August 1989
from the equator (3, 4). The age incidence curve is similar in regions of differing prevalence.5,6 It rises to a peak in the late third or early fourth decades and then falls rapidly so that onset after 60 years is rare. The disease is more common and the peak incidence is a few years earlier in women than in men (5, 7). Those who migrate keep the risk of the country in which they were born and spent their childhood (2). The relationship of risk to social class and birth order (12)
129 c
130 is, however not clear. Some studies have shown an effect, whilst others have not. These features have never been adequately explained, but a number of hypotheses have been proposed, including a possible role for micro organisms (13-17). The latte! could either cause MS directly by invasion of the nervous system or trigger an autoimmune response to brain antigens. A problem with microbial hypotheses is that the age incidence of MS, which is one of its most characteristic features. does not fit with any known viral or bactetia infection (1). However a recently published model of autoimmune disease (18), based on the idea that common commensal bacteria can precipitate an immune response to antigens shared with host tissues predicts an age incidence curve for autoimmune diseases which is similar to that seen in MS. This model uses concepts from statistical decision theory to analyse the problem faced by an immune system in setting responses to bacterial antigens. In this sense the immune system is an information processing system and will demonstrate the general properties of such systems. These include 1) information is processed in noise so that decisions are made in uncertainty and there is a finite chance of error 2) the performance of the components of the system will decay at random with time according to the laws of entrophy so that the error rate will rise with age. In this paper the predictions 07 the decision theory model are compared with the published data on the age incidence of MS. The decision theory model
The body is colonised after birth by micro-organisms which form a varied and varying microbial flora. The potential pathogenicity of these organism also varies considerably and although many are regarded as harmless commensals it is clear that some, and in certain circumstances most Yf not all, can cause disease (18). A further problem is that there is evidence of extensive cross reaction between microbial antigens and host tissues (19-24). Thus the immune system faces a complex detection problem. It is necessary to set responses to non cross reacting microbial antigens so as to reduce the chance to infection whilst avoiding response to cross reacting antigens which could initiate autoimmune disease. This problem can be analysed in terms of decision theory (25). It can be shown that the optimum decision strategy in distinguishing between two states of the world, ho and h,, is to accept h1 rather than ho if
MEDICAL HYPOTHESES
LO
(4 > B
where Llo (e) = P[e/hl]
WI. 11
PM01
andB
= [z:;;]
[$$
[Eq.2]
Llo (e) is the likelihood ratio of event e for h1 relative to ho P[e/h] is the probability of event e given h1 P[e/ho] is the probability of event e given ho P[ho] is the a priori probability of ho P[hl] is the priori probability of hl VW is the value of choosing ho given ho [H,,/h,J Vol is the cost of choosing hl given ho [H& ] VI1 is the value of choosing hl given h1 {H J;1 I] VI0 is the cost of choosing b given h, [H&I~] H1 is the decision to accept hl I-I,, is the decision to accept b Let ho be the condition that the bacterial antigen resembles a self antigen, whilst h, is the condition that the bacterial antigen is foreign. Then according to the model the information processing system gathers evidence about the bacterial antigen and computes a likelihood ratio [L1o] which is the probability of obtaining the evidence (e) given h1 [P(e/hl)] divided by the probabilit of obtaining the same evidence given ho [P(e iKo)] The antigen is accepted as hl and response H1 is instituted if Llo exceeds a certain value B which is determined by the a priori probablities of hl and ho and the values and costs associated with correct and incorrect decisions. The error H& increases the chance of infection, whilst the converse error HJho gives a risk of autoimmune disease. The problem is illustrated in Figure 1. Assume that the information processing system gathers evidence from the antigen by multiple sampling along one or many dimensions. The various measurements are then transformed onto a single linear scale and a mean (e) is computed. Then the frequency distribution of e/h1 and e/ho is shown in Figure 1. It IS reasonable to assume chat these distributions are approximately normal because IZ is a sample mean. The variance of the two distributions, however, need not to be the same. A decision criterion placed at x (i.e. respond H1 if e > x and respond Ho if e < will maximise the correct number of responses if
THE AGE INCIDENCE OF MULTIPLE SCLEROSIS: A DECISION THEORY MODEL
131
recognise a self antigen at birth after one examination is l-R, and the system deteriorates with a decay constant kZ, then the chance of failing to detect the self antigen as self on every one of n independent examinations at time t is; [l - R exp(-kz t)]”
Eq. 41
This function is not exactly the same as a cumulative probability function of a normal curve but it has similar properties and for practical purFig. 1 The theoretical frequency distributions of the mean of poses it produces virtually indentical graphs. The sampled evidence (8) bf bacterial antigens which do (hn) and advantage is that it is easier to programme a comdo not (h,) resemble host antigens. puter with this function in order to generate theoretical curves than to construct the curves P[h,] = P[ha]. However if P[hs] < P[hi] the using tables of normal values. If exposure to the putative micro-organisms ocdecision criterion should be moved to the left to maintain the highest correct response rate. The curs at random then age incidence of first contact with any particular organism will be a falling exopitmum stategy, however, maximises expected value in which case values and costs as well as a ponential curve whose half life depends on the priori probabilities have to be considered in prevalence of the organism. The chance of deciding the position of x. Thus if the error H1/110 autoimmunity (and infection) occuring on first has a high penalty (high VO1) x needs to be contact will be given by; moved to the right. It should also be noted that strategies which seek to reduce the chance of one I, = (1 - R exp [-k2 t])]” [k3 exp [-k3 t]] type of error increase the frequency of the con- I, = incidence of disease at time t k3 = rate constant of exposure to the putative verse error. A second property of information systems is microbe [Eq. 51 that the performance of the components will The assumption that the chance of encounterdecay with time according to the laws of entropy. In other words P[HJho] and P[H&i] will both ing the causative organisms is constant is increase which in terms of Figure 1 implies an probably reasonable for the more common bacteria which colonise the body surfaces although increase in the variance of both distributions this assumption obviously does not apply to all leading to greater overlap. This can be modelled most simply by assuming that the number of micro-organisms. samples of information (N) obtained decreases at The age incidence of multiple sclerosis random with time. For those who find the above mathematical treati.e. N, = NO exp [-kItI ment daunting it is worth emphasising that the NO = number of samples at birth basic ideas are simple. Most people meet comN, = number of samples at time t mon micro-organisms early in life and only a k, = decay constant Wq. 31 small fraction of the population will encounter a common organism for the first time in the third The variance of the sample mean (E is inverseor fourth decade. However the chance of dealing ly proportional to N so that it increases as N inappropriately with the organism so that serious decreases. If x is constant then P[Hi/ho] will in- infection or autoimmune disease ensues increases crease as a cumulative probability function of a with age due to decay in the immune system. The normal random variable. This function has been resulting age incidence curve of disease is a used previously to generate theoretical age in- product of these two functions leading to a curve cidence curves (18). There are, however, some which rises to a peak in early or middle life. The purely technical problems in using it in this paper shape of the curve and the position of the peak an alternative mathematical approach is used. is determined by the constants in equation 5. In Consider an information processing system Figure 2 the model is used to generate a theoretiwith n fold redundancy i.e. the antigen is cal curve which matches the general form of the analysed n times. If the chance of failing to observed age distribution of MS. In this example
132
Fig. 2 A hiqtogram of the age incidence of MS (from Acheson E D, 1985 page 8, data from Rochester) together with a theoretical curve from equation 5. R = 0.9, k, = 0.03 yr-‘, K, = 0.145 yr-l, n = 7.
MEDICAL HYPOTHESES
Fig. 3 Theoretical age incidence curves from equation 5. curve curve curve curve
a b c d
R kz lyr-‘I 0.86 0.03 0.95 0.03 0.99 0.03 0.99 0.02
k-&C’] 0.145 0.145 0.2 0.16
n 7 7 7 7
mode[yr] 25 28 24 31
mean[yr 29.7 32.5 28 35
reducing R (equivalent to moving x to the left) the mode of the theoretical curve is 26 years, whilst the mean is a little later at 31 years due to for curve a and increasing R (equivalent to moving x to the right) for curve b. In other words the slight skew in the distribution. The constant ks has a value 0.145 per year indicating that 50% curve a is the predicted incidence for men. The of the population encounter the causative or- ratio between the lifetime prevalence for curve a and b is 1.56 : 1. Curve a peaks at 25 years with ganism. in just under 5 years. a mean of 29.7 years, whilst curve b peaks at 28 MS is more common in women than in men years with a mean of 32.5 years. The predicted (1, 5, 7). If the rate of exposure to the relevant earlier mean age of onset in women is in fact a micro-organisms is similar in men and women constant finding in MS (1). then according to this model it indicates that women operate a slightly different decision stratIf the rate of circulation of the putative microegy. In terms of Figure 1 the decision criterion organism varies in different countries then the ismoved to the left of x, or, in terms of function model predicts that the incidence will also vary. 4, R is less in women than in men. It is interestThis could explain the georgraphical distribution of MS. In countries around the equator poor soing to note that as a general rule autoimmune cial conditions and a warm climate will increase disease is more common in women whilst serious infection is more common in men, and this con- the rate of circulation leading to a low incidence. verse relationship is neatly explained by the Thus if k3 in Figure 2 is increaased from 0.145 to decision theory model. It is important to appre0.29 the lifetime prevalence would fall ninefold, ciate that there is no single optimum position for but the peak incidence would also fall to 15 x in Figure 1 because values and costs [Vil, VW, years. In most series, however, there is no clear relationship between incidence and age of onset Vol, Via] are subjective judgements and different and there is no evidence that the age of onset is subsets of the population will have slightly different perceptions of them. This leads to an less in low incidence countries (1). This is the interesting prediction from the model. If the de- single major problem with this model. It is possible, of course, that there is an increased delay cision criterion is moved to the left of x in Figure 1 then not only will the incidence of the disease between disease onset and diagnosis in low incirise in that subset, but also the mode and mean dence countries due to less developed medical of the distribution will decrease. This is illus- services or because low incidence leads to low ditrated in Figure 3. Curves a and b are generated agnostic expectation. There is, however, a by using the same constants as in Figure 2 but second possible explanation of this discrepancy
THE AGE INCIDENCE OF MULTIPLE SCLEROSIS: A DECISION THEORY MODEL
which is potentially more valuable. The first encounter with commensal bacteria can occur at a variety of sites on the body surface, although the gastro-intestinal tract and the respiratory tract are quatitatively the most important. Let us assume that MS arises as an autoimmune response to certain bacteria which are normally spread by the faecal oral route but in which first contact can occur in respiratory tract. It is known that following a viral infection of the respiratory tract there is bacterial overgrowth in the nasopharynx by a variety of organisms which can include faecal streptococci and gram negative bacilli (26, 27). If first exposure to the causative bacteria occurs in this way in the nasopharynx then the immune system must respond swiftly because bacterial overgrowth on well vascularised mucous membranes with direct access to the systemic circulation is potentially dangerous. A swift response antigen means reduced sampling (decreased N) thereby increasing the variance of the distributions in Figure 1 and increasing the error rate. Viral respiratory tract infection are more prevalent in temperate climes so that the chance of MS occuring on first exposure, regardless of age, is raised. In terms of the model R is less in temperate climes. Thus the incidence in equatorial climates will be less than in temperate regions because of a more rapid circulation of bacteria and a rise in the value of R. The former will decrease the mean age of onset whilst the latter will raise it. In Figure 3 curve c is generated by increasing the values of k and R. The incidence is low, the mode is 24 years and the mean is 28 years. Furthermore the amount of information processing capacity committed to the gut might be greater than the respiratory tract because of the increased antigenic load. If the increase is accompanied by increased repair capacity delaying the rate of decay then k2 could be less in the equatorial zone. Curve d &Figure 3 is generated by reducing k2 and this leads to an even lower incidence with a mode of 31 years and a mean of 35 years. Thus if the full complexity of the interaction between bacteria and the immune system is considered it is possible to explain a falling incidence without a major change in mean age of onset. The model also fits with data on migration (1, 2). The place that people are born and spend their childhood determines their risk of MS. Thus people born in Northern Europe, a high risk area, who migrate as adults to South Africa, a low risk area, keep their high risk (28, 29). How-
133
ever their children born in South Africa have a low risk. Equally people born in low risk areas who migrate as adults to the United Kingdom have a low risk (30), but their children born in the United Kingdom will have a high risk (31). Those who migrate as children from a high risk to a low risk area have an intermediate risk (29). These observations are consistent with the model which predicts that the earlier in life that migration occurs the closer will be the incidence to the country of destination. If migration occurs late in life the incidence experienced will be closer to the place of origin. It is also worth pointing out that those who pay a brief or a holiday visit to a tropical country will not significantly alter their risk of developing MS as a result of the visit. The risk of first exposure to the bacteria might rise in this period, but if that exposure is more liable to occur in the gut the risk of MS might actually fall. Discussion The concept of analysing the interaction between micro-organisms and the immune system in terms of information theory has been discussed previously (18). Bacteria of the normal body flora are potentially pathogenic and an immune response to contain them is required. Secondly there is extensive cross-reaction between bacterial antigens and host tissues (19-24) which leads to the possibility of autoimmune disease. If the problem of establishing an immune response to bacteria is analysed in terms of decision theory it is clear that even with an optimum decision strategy there is a finite chance of error which will increase with age. If the decision strategy deviates from the ideal this will only serve to amplify the errors which have been identified with the above model. It is not suggested that there is structural entity performing the calculations in equation 1 and 2, but that the combined actions of the diverse arms of the immune response approximates to an optimum strategy. The idea that micro-organisms might have a pathogenic role in MS first gained credence when an outbreak of MS was reported in 4 of 8 research workers studying swayback in lambs (32, 33). The chance of a cases of MS in a random sample of 8 adult males is one in a thousand million (33). This idea has received further support from a reported epidemic of MS in the Faroe Islands (34), and more importantly from migration studies (28-31) which are most easily
134
MEDICAL HYPOTHESES
explained if it is assumed that infection in child- in which economic advance has occurred (1). hood determines the subsequent risk of MS in This can be understood if improved socio-economic conditions are associated with opposing adult life. Micro-organisms could have pathoeffects, a decreased rate of bacterial circulation genic role in MS either by invading the nervous tending to increase the incidence of MS, but a system or by precipitating an autoimmune decreased rate and severity of respiratory infecresponse. Although the model could be applied to both possibilities the latter hypothesis is con- tion tending to decrease the incidence. One of the cardinal features of autoimmune sidered in this paper as it fits more easily with what is known about MS. In fact the failure to disease, and this applies particularly to MS, is demonstrate viruses or other microbes in MS that the course is one of exacerbation followed plaques despite many years of search argues by remission. This also fits with the hypothesis. against direct infection. Whilst ecidence of cross The disease is precipitated by first exposure when reaction between microbial antigens and host tis- the allergic response is established. The subsequent course will depend on bacterial carriage sues, including brain antigens (23, 24), supports the autoimmune hypothesis. In this paper it is which will wax and wane under a variety of influences including viral infections of the host. If suggested that the causative organisms are bactebacterial carriage is eliminated then the host will ria of the body flora which are normally spread be disease free until second exposure. The other by the faecal-oral route. On occasion, however, first exposure can occur in the respiratory tract extreme will be sustained high carriage giving and if this follows a viral infection, bacterial over- rapidly progressive disease without remission, growth will ensue increasing the risk of MS. This which is seen in a small percentage of cases. The hypothesis is amenable to laboratory infits with the observation that viral infections can vestigation. It will be necessary to determine the precipitate exacerbations of MS (35) and the microbial flora, particularly the upper respiratory recent evidence of an increased incidence of tract flora, during disease exacerbations to see if sinusitis (36) in those who subsequently develop there is any constant pattern. If so the isolates MS. can be examined using monoclonal antibodies to The major value of the ideas presented is that search for antigens in common with brain tissues. they offer an explanation for the age incidence of MS. It is true that the match in Figure 2 The iong term aim being to ensure early exdepends upon a judicious choice of constants for posure by the appropriate route so as to avoid the disease. which there is no direct experimental support. The additional prediction, however, that an incidence ratio of 1.56 : 1 for women : men leads to an earlier mean age of onset of approximately 3 years in women provides independent support for References the model. This in fact a consistent finding and 1. Acheson E D. The epidemiology of multiple sclerosis. In: is hitherto without adequate explanation (1). Matthews W B, Acheson E D, Batchelor J R, Weller _. R 0, eds. McAlpine’s multiple sclerosis. Edinburgh: The model predicts a low incidence in tropical Churchill Livingstone. 1985: 3-46. countries and other countries with poor hygiene, 2. Dean G. l?pide&ology of multiple sclerosis. poor social condition and low levels of Neuroepidemiology 1984; 3: 58-73. respiratory tract infection. This fall in incidence 3. Kurtzke J F. The georgraphic distribution of multiple sclerosis: an update with special reference to Europe and need not necessarily be associated with a marked the Mediaterranean region. Acta Neurologica Scandecrease in mean age of onset if the fully comdinavica 1980; 62: 65-80. plexity of the interaction between bacteria and 4. Norman J E, Kurtzke J F, Beebe G W. Epidemiology of host defences at different sites is considered. The multiple sclerosis in US veterans 2. Latitude, climate and data on changing incidence with migration is also risk of multiple sclerosis. Journal of Chronic Diseases 1983; 36: 551-560. neatly explained by the model. 5. Acheson E D. Epidemiology of multiple sclerosis. British There are other features of MS which are conMedical Bulletin 1977; 33: 9-14 sistent with this model. In some studies MS was 6. Kurtzke J F. Epidemiology of multiple sclerosis. In: found to be more common in first born childcen Hallpike J F, Adams C W M, Tourtellotte W W, edq .I. Mul&ple sclerosis, pathology, diagnosis and management. (12) and those from more priviledged SOCIOChapman and Hall, London, 1983: 47-95. economic backgrounds (8,9), whilst other studies 7. Kuizke J F, Beebe G W, Norman J E. Epidemiology of failed to confirm this relationship (10-12). Furmultiple sclerosis in US veterans 1. Race, sex and thermore there is no evidence of an increased georgraphic distribution. Neurology 1979; 29: 1228-1235. 8. Miller H, Ridley A, Schapira K. Multiple sclerosis a note incidence of MS in Western Countries in a period
THE AGE INCIDENCE OF MULTIPLE SCLEROSIS: A DECISION THEORY MODEL
on social incidence. British Medical Journal 1960; 2: 343345 9. Beebe G, Kurtzke J F, Kurland L T, Auth T L, Nazler 6. Studies on the natural history of multiple sclerosis. Neurology 1967; 17: 2-17. 10. Stazio A, Paddeson R M, Kurland L T. Multiple sclerosis in New Orleans, La, and Winnipeg, Man: follow-up of a previous survey. Journal of Chronic Disease 1967; 20: 311-332. 11. Antonovosky A, Leibowitz V, Medalie J M, Halpern L, Smith H A, Alter M. Reappraisal of possible aetiological factors in multiple sclerosis. American Journal of Public Health 1968; 58: 836-848. 12. James W H. Multiple sclerosis and birth order. Journal of Eoidemiologv and Community Health 1984; 38: 21-22. 13. Adams J M. Imagawa D T. Measles antibodies in multiple sclerosis. Proceedings of the Society for Experimental Biology and Medicine 1962; 3: 562-566. 14. Poskanzer D C. Schaoira K, Miller H. Multiple sclerosis and poliomyelius. La&t 1963; 2: 917-921. . 15. Chan W W C. Possible role of dogs in multiple sclerosis infection. Lancet 1977; 1: 487-488. 16. Morris J A. Clinical viral infections and multiple sclerosis. Lancet 1985; ii: 273. 17. Gay D, Dick G. Is multiple sclerosis caused by an oral spirochaete. Lancet 1986; 11: 75-77. 19. Anonymous. Thyroid disease and antibodies to Yersinia (editorial). Lancet 1977; ii: 734-735. 20. Marcio T, Cohen H, Segal S J, Koide S S. Production of choriogonadotrophin like factor by micro-organisms. Proc Nat1 Acad Sci USA 1979; 76: 6622-6626. 21 Le Roith D, Shiloach J. Roth J, Lesniak M A. Insulin or a closely related molecule is native to Escherichia coli. J. Biol Chem 1981; 256: 6533-6536. 22 Weiss M, Ingbar S H, Winblad S, Kasper D L. Demonstration of a saturable binding site for thyrotrophin in Yersinia enterocolitica. Science 1983; 219: 1331-1333. 23 Finne J. Leionun M, Makela P H. Antigenic similarities between brain components and bacteria causing meningitis: implication for vaccine development and pathogenesis. Lancet 1983; ii: 355-357.
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24. Stefansson K, Dieperink M E, Richman D P, Gomez C M, Marton L S. Sharing of antigenic determinants between the nicotinic acetycholine receptor and proteins in Escherichia Cole, Proteus vulgaris, and Klebsiella pneumoniae. Possible role in the pathogenesis of myasthenia gravis. New England Journal of Medicine 1985; 312: 221-225. 25. Green D M, Swets J A. Signal detection theory and psychophysics. London: John Wiley and Sons, 1966. 26. Mackowiak P A. The normal microbial flora. New England Journal of Medicine 1982; 307: 83-93. 27. Ramfrez-Ronda C H. Fuxench-Looez Z. Nevarex M. Increased pharyngeal ‘bacterial colbnisation during viral illness. Arch, Intern. Med. 1981; 141: 1599-1603. 28. Dean G. Annual incidence, prevalence and mortalitv of multiple sclerosis in white South African born and white immigrants to South Africa. BMJ 1967: 2: 724-730. 29. Dean-G, Kurtzke J F. On the risk of multiple sclerosis according to age at immigration to South Africa. BMJ 1971; 3: 725-729. 30. Dean G, McLaughlin H, Brady R. Adelstein A M, Tallett-Williams J. Multiple sclerosis among immigrants in Greater London. BMJ 1976; 1: 861-864. 31. Elian M, Dean G. Multiple sclerosis among the United Kingdom-born children of immigrants from the West Indies. J. Neural. Neurosurg and Psych. 1987; 50:327-332. 32. Campbell A M G, Daniel P, Porter R J, Russel W R, Smith H V, Innes J R M. Disease of the nervous system occuring among research workers on swayback in lambs. Brain 1947; 70: 50-58. 33. Dean G, McDougall E I, Elian M. Multiple sclerosis in research workers studying swayback in lambs: an updated report. J. Neural, Neurosurg. and Psych. 1985; 48: 859865. 34. Dean G. Was there an epidemic of multiple sclerosis in the Faroe Islands? Neuroepidemiology 19881; 7: 165-167. 35. Sibley W A, Bamford C R, Clark K. Clinical viral infections and multiple seclerosis. Lancet 1985; i: 1313-1315. 36. Gay D, Dick G, Upton G. Multiple sclerosis associated with sinusitis: case-controlled study in general practice. Lancet 1986; i:815-819.
The Age Incidence of Multiple .Decision Theory Model
Sclerosis: A
J. A. MORRIS Consultant Pathologist,
Department
of Pathology,
Lancaster Moor Hospital Lancaster LA1 3JR, UK
Abstract - It is proposed that multiple sclerosis (MS) arises as an auto-immune response to antigens shared by common commensal bacteria and brain tissues. In particular it is suggested that the causative bacteria are normally spread by the faecal-oral route but first exposure can occur in the nasopharynx, particularly following a viral respiratory infection, and this increases the risk of MS. The interaction between bacterial colonisation and the immune response is analysed in terms of an information model derived from statistical decision theory. The model predicts a finite chance of outoimmune disease on first exposure which rises with age at exposure. The predicted age incidence of MS, which is the resultant of the rising error function and the age incidence of first exposure to common bacteria, rises to a peak in the third decade and matches published age incidence data. Furthermore the model predicts that subsets of the population, such as women, in whom the risk of MS is increased will have an earlier mean age of onset. This accords with observation which is hitherto unexplained. The model also explains the decreased incidence of MS in equatorial regions, data on migration studies, and is consistent with the observation that the mean age of onset is not concsistently lower in low incidence regions. It also offers an explanation for conflicting data on the effect of social class, economic conditions and birth order. The hypothesis is amenable to laboratory investigation and should be pursued.
Introduction
The major epidemiological features of MS are well documented (1, 2). The disease is uncommon with a prevalence of less than 10 to 144 per 100 000 (1). It is more common in temperate climates and the incidence increases with distance Date received 19 June 1989 Date accepted 21 August 1989
from the equator (3, 4). The age incidence curve is similar in regions of differing prevalence.5,6 It rises to a peak in the late third or early fourth decades and then falls rapidly so that onset after 60 years is rare. The disease is more common and the peak incidence is a few years earlier in women than in men (5, 7). Those who migrate keep the risk of the country in which they were born and spent their childhood (2). The relationship of risk to social class and birth order (12)
129 c
130 is, however not clear. Some studies have shown an effect, whilst others have not. These features have never been adequately explained, but a number of hypotheses have been proposed, including a possible role for micro organisms (13-17). The latte! could either cause MS directly by invasion of the nervous system or trigger an autoimmune response to brain antigens. A problem with microbial hypotheses is that the age incidence of MS, which is one of its most characteristic features. does not fit with any known viral or bactetia infection (1). However a recently published model of autoimmune disease (18), based on the idea that common commensal bacteria can precipitate an immune response to antigens shared with host tissues predicts an age incidence curve for autoimmune diseases which is similar to that seen in MS. This model uses concepts from statistical decision theory to analyse the problem faced by an immune system in setting responses to bacterial antigens. In this sense the immune system is an information processing system and will demonstrate the general properties of such systems. These include 1) information is processed in noise so that decisions are made in uncertainty and there is a finite chance of error 2) the performance of the components of the system will decay at random with time according to the laws of entrophy so that the error rate will rise with age. In this paper the predictions 07 the decision theory model are compared with the published data on the age incidence of MS. The decision theory model
The body is colonised after birth by micro-organisms which form a varied and varying microbial flora. The potential pathogenicity of these organism also varies considerably and although many are regarded as harmless commensals it is clear that some, and in certain circumstances most Yf not all, can cause disease (18). A further problem is that there is evidence of extensive cross reaction between microbial antigens and host tissues (19-24). Thus the immune system faces a complex detection problem. It is necessary to set responses to non cross reacting microbial antigens so as to reduce the chance to infection whilst avoiding response to cross reacting antigens which could initiate autoimmune disease. This problem can be analysed in terms of decision theory (25). It can be shown that the optimum decision strategy in distinguishing between two states of the world, ho and h,, is to accept h1 rather than ho if
MEDICAL HYPOTHESES
LO
(4 > B
where Llo (e) = P[e/hl]
WI. 11
PM01
andB
= [z:;;]
[$$
[Eq.2]
Llo (e) is the likelihood ratio of event e for h1 relative to ho P[e/h] is the probability of event e given h1 P[e/ho] is the probability of event e given ho P[ho] is the a priori probability of ho P[hl] is the priori probability of hl VW is the value of choosing ho given ho [H,,/h,J Vol is the cost of choosing hl given ho [H& ] VI1 is the value of choosing hl given h1 {H J;1 I] VI0 is the cost of choosing b given h, [H&I~] H1 is the decision to accept hl I-I,, is the decision to accept b Let ho be the condition that the bacterial antigen resembles a self antigen, whilst h, is the condition that the bacterial antigen is foreign. Then according to the model the information processing system gathers evidence about the bacterial antigen and computes a likelihood ratio [L1o] which is the probability of obtaining the evidence (e) given h1 [P(e/hl)] divided by the probabilit of obtaining the same evidence given ho [P(e iKo)] The antigen is accepted as hl and response H1 is instituted if Llo exceeds a certain value B which is determined by the a priori probablities of hl and ho and the values and costs associated with correct and incorrect decisions. The error H& increases the chance of infection, whilst the converse error HJho gives a risk of autoimmune disease. The problem is illustrated in Figure 1. Assume that the information processing system gathers evidence from the antigen by multiple sampling along one or many dimensions. The various measurements are then transformed onto a single linear scale and a mean (e) is computed. Then the frequency distribution of e/h1 and e/ho is shown in Figure 1. It IS reasonable to assume chat these distributions are approximately normal because IZ is a sample mean. The variance of the two distributions, however, need not to be the same. A decision criterion placed at x (i.e. respond H1 if e > x and respond Ho if e < will maximise the correct number of responses if
THE AGE INCIDENCE OF MULTIPLE SCLEROSIS: A DECISION THEORY MODEL
131
recognise a self antigen at birth after one examination is l-R, and the system deteriorates with a decay constant kZ, then the chance of failing to detect the self antigen as self on every one of n independent examinations at time t is; [l - R exp(-kz t)]”
Eq. 41
This function is not exactly the same as a cumulative probability function of a normal curve but it has similar properties and for practical purFig. 1 The theoretical frequency distributions of the mean of poses it produces virtually indentical graphs. The sampled evidence (8) bf bacterial antigens which do (hn) and advantage is that it is easier to programme a comdo not (h,) resemble host antigens. puter with this function in order to generate theoretical curves than to construct the curves P[h,] = P[ha]. However if P[hs] < P[hi] the using tables of normal values. If exposure to the putative micro-organisms ocdecision criterion should be moved to the left to maintain the highest correct response rate. The curs at random then age incidence of first contact with any particular organism will be a falling exopitmum stategy, however, maximises expected value in which case values and costs as well as a ponential curve whose half life depends on the priori probabilities have to be considered in prevalence of the organism. The chance of deciding the position of x. Thus if the error H1/110 autoimmunity (and infection) occuring on first has a high penalty (high VO1) x needs to be contact will be given by; moved to the right. It should also be noted that strategies which seek to reduce the chance of one I, = (1 - R exp [-k2 t])]” [k3 exp [-k3 t]] type of error increase the frequency of the con- I, = incidence of disease at time t k3 = rate constant of exposure to the putative verse error. A second property of information systems is microbe [Eq. 51 that the performance of the components will The assumption that the chance of encounterdecay with time according to the laws of entropy. In other words P[HJho] and P[H&i] will both ing the causative organisms is constant is increase which in terms of Figure 1 implies an probably reasonable for the more common bacteria which colonise the body surfaces although increase in the variance of both distributions this assumption obviously does not apply to all leading to greater overlap. This can be modelled most simply by assuming that the number of micro-organisms. samples of information (N) obtained decreases at The age incidence of multiple sclerosis random with time. For those who find the above mathematical treati.e. N, = NO exp [-kItI ment daunting it is worth emphasising that the NO = number of samples at birth basic ideas are simple. Most people meet comN, = number of samples at time t mon micro-organisms early in life and only a k, = decay constant Wq. 31 small fraction of the population will encounter a common organism for the first time in the third The variance of the sample mean (E is inverseor fourth decade. However the chance of dealing ly proportional to N so that it increases as N inappropriately with the organism so that serious decreases. If x is constant then P[Hi/ho] will in- infection or autoimmune disease ensues increases crease as a cumulative probability function of a with age due to decay in the immune system. The normal random variable. This function has been resulting age incidence curve of disease is a used previously to generate theoretical age in- product of these two functions leading to a curve cidence curves (18). There are, however, some which rises to a peak in early or middle life. The purely technical problems in using it in this paper shape of the curve and the position of the peak an alternative mathematical approach is used. is determined by the constants in equation 5. In Consider an information processing system Figure 2 the model is used to generate a theoretiwith n fold redundancy i.e. the antigen is cal curve which matches the general form of the analysed n times. If the chance of failing to observed age distribution of MS. In this example
132
Fig. 2 A hiqtogram of the age incidence of MS (from Acheson E D, 1985 page 8, data from Rochester) together with a theoretical curve from equation 5. R = 0.9, k, = 0.03 yr-‘, K, = 0.145 yr-l, n = 7.
MEDICAL HYPOTHESES
Fig. 3 Theoretical age incidence curves from equation 5. curve curve curve curve
a b c d
R kz lyr-‘I 0.86 0.03 0.95 0.03 0.99 0.03 0.99 0.02
k-&C’] 0.145 0.145 0.2 0.16
n 7 7 7 7
mode[yr] 25 28 24 31
mean[yr 29.7 32.5 28 35
reducing R (equivalent to moving x to the left) the mode of the theoretical curve is 26 years, whilst the mean is a little later at 31 years due to for curve a and increasing R (equivalent to moving x to the right) for curve b. In other words the slight skew in the distribution. The constant ks has a value 0.145 per year indicating that 50% curve a is the predicted incidence for men. The of the population encounter the causative or- ratio between the lifetime prevalence for curve a and b is 1.56 : 1. Curve a peaks at 25 years with ganism. in just under 5 years. a mean of 29.7 years, whilst curve b peaks at 28 MS is more common in women than in men years with a mean of 32.5 years. The predicted (1, 5, 7). If the rate of exposure to the relevant earlier mean age of onset in women is in fact a micro-organisms is similar in men and women constant finding in MS (1). then according to this model it indicates that women operate a slightly different decision stratIf the rate of circulation of the putative microegy. In terms of Figure 1 the decision criterion organism varies in different countries then the ismoved to the left of x, or, in terms of function model predicts that the incidence will also vary. 4, R is less in women than in men. It is interestThis could explain the georgraphical distribution of MS. In countries around the equator poor soing to note that as a general rule autoimmune cial conditions and a warm climate will increase disease is more common in women whilst serious infection is more common in men, and this con- the rate of circulation leading to a low incidence. verse relationship is neatly explained by the Thus if k3 in Figure 2 is increaased from 0.145 to decision theory model. It is important to appre0.29 the lifetime prevalence would fall ninefold, ciate that there is no single optimum position for but the peak incidence would also fall to 15 x in Figure 1 because values and costs [Vil, VW, years. In most series, however, there is no clear relationship between incidence and age of onset Vol, Via] are subjective judgements and different and there is no evidence that the age of onset is subsets of the population will have slightly different perceptions of them. This leads to an less in low incidence countries (1). This is the interesting prediction from the model. If the de- single major problem with this model. It is possible, of course, that there is an increased delay cision criterion is moved to the left of x in Figure 1 then not only will the incidence of the disease between disease onset and diagnosis in low incirise in that subset, but also the mode and mean dence countries due to less developed medical of the distribution will decrease. This is illus- services or because low incidence leads to low ditrated in Figure 3. Curves a and b are generated agnostic expectation. There is, however, a by using the same constants as in Figure 2 but second possible explanation of this discrepancy
THE AGE INCIDENCE OF MULTIPLE SCLEROSIS: A DECISION THEORY MODEL
which is potentially more valuable. The first encounter with commensal bacteria can occur at a variety of sites on the body surface, although the gastro-intestinal tract and the respiratory tract are quatitatively the most important. Let us assume that MS arises as an autoimmune response to certain bacteria which are normally spread by the faecal oral route but in which first contact can occur in respiratory tract. It is known that following a viral infection of the respiratory tract there is bacterial overgrowth in the nasopharynx by a variety of organisms which can include faecal streptococci and gram negative bacilli (26, 27). If first exposure to the causative bacteria occurs in this way in the nasopharynx then the immune system must respond swiftly because bacterial overgrowth on well vascularised mucous membranes with direct access to the systemic circulation is potentially dangerous. A swift response antigen means reduced sampling (decreased N) thereby increasing the variance of the distributions in Figure 1 and increasing the error rate. Viral respiratory tract infection are more prevalent in temperate climes so that the chance of MS occuring on first exposure, regardless of age, is raised. In terms of the model R is less in temperate climes. Thus the incidence in equatorial climates will be less than in temperate regions because of a more rapid circulation of bacteria and a rise in the value of R. The former will decrease the mean age of onset whilst the latter will raise it. In Figure 3 curve c is generated by increasing the values of k and R. The incidence is low, the mode is 24 years and the mean is 28 years. Furthermore the amount of information processing capacity committed to the gut might be greater than the respiratory tract because of the increased antigenic load. If the increase is accompanied by increased repair capacity delaying the rate of decay then k2 could be less in the equatorial zone. Curve d &Figure 3 is generated by reducing k2 and this leads to an even lower incidence with a mode of 31 years and a mean of 35 years. Thus if the full complexity of the interaction between bacteria and the immune system is considered it is possible to explain a falling incidence without a major change in mean age of onset. The model also fits with data on migration (1, 2). The place that people are born and spend their childhood determines their risk of MS. Thus people born in Northern Europe, a high risk area, who migrate as adults to South Africa, a low risk area, keep their high risk (28, 29). How-
133
ever their children born in South Africa have a low risk. Equally people born in low risk areas who migrate as adults to the United Kingdom have a low risk (30), but their children born in the United Kingdom will have a high risk (31). Those who migrate as children from a high risk to a low risk area have an intermediate risk (29). These observations are consistent with the model which predicts that the earlier in life that migration occurs the closer will be the incidence to the country of destination. If migration occurs late in life the incidence experienced will be closer to the place of origin. It is also worth pointing out that those who pay a brief or a holiday visit to a tropical country will not significantly alter their risk of developing MS as a result of the visit. The risk of first exposure to the bacteria might rise in this period, but if that exposure is more liable to occur in the gut the risk of MS might actually fall. Discussion The concept of analysing the interaction between micro-organisms and the immune system in terms of information theory has been discussed previously (18). Bacteria of the normal body flora are potentially pathogenic and an immune response to contain them is required. Secondly there is extensive cross-reaction between bacterial antigens and host tissues (19-24) which leads to the possibility of autoimmune disease. If the problem of establishing an immune response to bacteria is analysed in terms of decision theory it is clear that even with an optimum decision strategy there is a finite chance of error which will increase with age. If the decision strategy deviates from the ideal this will only serve to amplify the errors which have been identified with the above model. It is not suggested that there is structural entity performing the calculations in equation 1 and 2, but that the combined actions of the diverse arms of the immune response approximates to an optimum strategy. The idea that micro-organisms might have a pathogenic role in MS first gained credence when an outbreak of MS was reported in 4 of 8 research workers studying swayback in lambs (32, 33). The chance of a cases of MS in a random sample of 8 adult males is one in a thousand million (33). This idea has received further support from a reported epidemic of MS in the Faroe Islands (34), and more importantly from migration studies (28-31) which are most easily
134
MEDICAL HYPOTHESES
explained if it is assumed that infection in child- in which economic advance has occurred (1). hood determines the subsequent risk of MS in This can be understood if improved socio-economic conditions are associated with opposing adult life. Micro-organisms could have pathoeffects, a decreased rate of bacterial circulation genic role in MS either by invading the nervous tending to increase the incidence of MS, but a system or by precipitating an autoimmune decreased rate and severity of respiratory infecresponse. Although the model could be applied to both possibilities the latter hypothesis is con- tion tending to decrease the incidence. One of the cardinal features of autoimmune sidered in this paper as it fits more easily with what is known about MS. In fact the failure to disease, and this applies particularly to MS, is demonstrate viruses or other microbes in MS that the course is one of exacerbation followed plaques despite many years of search argues by remission. This also fits with the hypothesis. against direct infection. Whilst ecidence of cross The disease is precipitated by first exposure when reaction between microbial antigens and host tis- the allergic response is established. The subsequent course will depend on bacterial carriage sues, including brain antigens (23, 24), supports the autoimmune hypothesis. In this paper it is which will wax and wane under a variety of influences including viral infections of the host. If suggested that the causative organisms are bactebacterial carriage is eliminated then the host will ria of the body flora which are normally spread be disease free until second exposure. The other by the faecal-oral route. On occasion, however, first exposure can occur in the respiratory tract extreme will be sustained high carriage giving and if this follows a viral infection, bacterial over- rapidly progressive disease without remission, growth will ensue increasing the risk of MS. This which is seen in a small percentage of cases. The hypothesis is amenable to laboratory infits with the observation that viral infections can vestigation. It will be necessary to determine the precipitate exacerbations of MS (35) and the microbial flora, particularly the upper respiratory recent evidence of an increased incidence of tract flora, during disease exacerbations to see if sinusitis (36) in those who subsequently develop there is any constant pattern. If so the isolates MS. can be examined using monoclonal antibodies to The major value of the ideas presented is that search for antigens in common with brain tissues. they offer an explanation for the age incidence of MS. It is true that the match in Figure 2 The iong term aim being to ensure early exdepends upon a judicious choice of constants for posure by the appropriate route so as to avoid the disease. which there is no direct experimental support. The additional prediction, however, that an incidence ratio of 1.56 : 1 for women : men leads to an earlier mean age of onset of approximately 3 years in women provides independent support for References the model. This in fact a consistent finding and 1. Acheson E D. The epidemiology of multiple sclerosis. In: is hitherto without adequate explanation (1). Matthews W B, Acheson E D, Batchelor J R, Weller _. R 0, eds. McAlpine’s multiple sclerosis. Edinburgh: The model predicts a low incidence in tropical Churchill Livingstone. 1985: 3-46. countries and other countries with poor hygiene, 2. Dean G. l?pide&ology of multiple sclerosis. poor social condition and low levels of Neuroepidemiology 1984; 3: 58-73. respiratory tract infection. This fall in incidence 3. Kurtzke J F. The georgraphic distribution of multiple sclerosis: an update with special reference to Europe and need not necessarily be associated with a marked the Mediaterranean region. 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THE AGE INCIDENCE OF MULTIPLE SCLEROSIS: A DECISION THEORY MODEL
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