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Cancer as a systemic disease
Medical Hypotheses, 4:
193-207, 1978
CANCER AS A SYSTEMIC DISEASE G. Zajicek. Department of Experimental Medicine and Cancer Research and Computer Unit, The Hebrew University-Hadassah Medical School, P.O.Rox 1177, Jerusalem, Israel.
ABSTRACT Theories on the nature of cancer may be classified into two categories. One regards cancer strictly as a local phenomenon while the second looks at cancer as a local manifestation of a systemic process or disease. Although the first dominates current medical thought, the theories of immunological surveillance and of protovirus-oncogene implicitly assume cancer to represent a local manifestation of a systemic process or disease. This is supported also by epidemiological data forwarded in the present paper. Jn order to clarify the exact meaning of a systemic disease, cancer and its manifestation are compared with arteriosclerosis and its seouelae. Arteriosclerosis could be regarded as a prototype of a systemic disease. It presents itself clinically solely by its local manifestations, like myocardial infarction or stroke. These local manifestations may be followed by secondary systemic sequelae like congestive heart failure. In the same context, it is proposed to regard cancer as one systemic disease which presents itself clinically by local phenomena like carcinoma, lymphoma and sarcoma. These local manifestations may lead further to secondary systemic sequelae like metastasis. Neoplasms, Diagnosis, Mortality.
193
INTRODUCTIOI’J Theories on the nature of cancer may be classified into two categories. One regards cancer strictly as a local phenomenon while the second looks at cancer as a local manifestation of a systemic process or disease. Since the dawn of medicine both categories have competed for heqemony, a continuous struggle which has been extensively reviewed by Wolff (1). The present version of the local theory was formulated durinq the previous century by J. Muller, Rokitansky and others who initiated the search for the anatomo-pahtological characteristics of the cancer cell, formulating the "Blastema theory". This was followed by attempts to elucidate the nature of the malignant transformation. Such a transformation was believed by Vfrchow to be caused by chronic irritation, and by Rovery to result from somatic mutation which is assumed to play the main role in cell transformation durinq chemical carcinogenesis and processes leading to differentiation abberations. This theory was rivaled by the infective theory of cancer introduced by Pasteur, which has been qradually replaced by its modern version the "virus infective theory" initiated by Ellerman and Bang's discovery of the leukosis virus and ROUS' discovery of the sarcoma virus which bears his name. Roth theories, the mutation as well as the infective theory, dominate current cancer research. The second category, which regards cancer as a local manifestation of a systemic process or disease, ruled medical thought in ancient times and through the medieval period, until its decline with the advent of modern pathology. Hfppocrates thought cancer to result from a dyscrasia or disharmony of certain body constitutents. Galen believed cancer to be a constitutional disease resulting from an overflow of "atra bilis", the black bile. Both theories ruled medicine for a millenium. Paracelsus regarded cancerous growth to be the port of exit for certain salts trying to escape the organism, a concept which was succeeded by the lymph theory which dominated medicine until the dawn of the nineteenth century. To the modern physician these theories seem bizarre and have therefore been opposed by medical schools which regard cancer strictly as a local phenomenon. However, recent developments in cancer research have reintroduced, although implicitly, the systemic cancer theories. The theory of immunological surveillance and that of protovirus-oncogene implicitly assume cancer to represent a local manifestation of a systemic process or disease, According to Thomas (2) and Burnet (3) ordinarily the immune response destroys cancer cells while they are still in the incipient stage of tumor formation. A failure of the "systemic" surveillance mechanism leads to the nloaal" appearance of a tumor. The deterioration of this surveillance mechanism proceeds continuously in a random fashion, and could result from somatic mutations affecting cell clones responsible for its proper function.
194
Huebner and Todaro's oncogene theory, (4) claims aenetic information for cancer to exist in every cell. Neoplasia arises when ore-existant qenetic information is derepressed. Temin's protovirus theory (5) maintains that genetic information for cancer is synthesized de novo. k?alianancy arises through a process of genetic chanqe in which pieces of aenetic information which exist in all the cells, happen to be so assembled that cell transformation occurs through "misevolution". Both theories imoly therefore that random chanqes in an ubiquitous or systemic phenomenon may result in the local appearance of malionancy. CANCER EPIDFMIOLOGY Cancer epidemiology too is dominated by the dooma of local cancer, hiohlighted by Awnitage and Doll's model for carcinoaenesis, known as the "power" model (6). It has been developed to explain the peculiar shaoe of adult cancer age specific mortality rates, which differ markedly from aqe soecific mortality rates due to all chronic diseases (73). Adult aoe specific mortality curves are best described by the qompertz model q(a) = c(n) exp(ka) in which 'a' stands for age and 'k' known as the Gompertz coefficient, describes the rate of increase of G(a) with aqe. G(q) marks the hypothetical mortality at birth. G(a) implies the existence of a random systemic deterioration which leads to the clinical appearance of the chronic disease or even to death, as highlighted in Strehler and mildvan's aaino theory (g). According to this theory the organism consists of a set of sub-systems each with a certain maximum ability to restore its initial condition after a challenge. Tha magnitudes of challenges are distributed energetically like a Maxwell-Boltzmann distribution. Death occurs when the rate et which an organism recruits work to restore the oriqinal state is less than that demanded to overcome the effects of a given challenge. A further qeneralization proposed by Atlan (lo), describes the orqanism deterioration in entropy units in order to utilize information theory jn the prediction of aaina. Both models are isomorphic with the Gompertz function G(a) and could therefore be applied to chronic systemic diseases. Arteriosclerosis for instance affects all the systems in the body and reduces their efficiency to withstand external noxae. Since its aqe specific mortality rates are compertzian, Strehler and Mildvan's theory seem an adequate model to describe arteriosclerotic age specific mortality rates, or even its local manifestations, like myocardial infarction,which also exhibits Gompertzian aae specific mortality rates. Up to the age of 50 years cancer age specific mortality rates fo?low those of chronic diseases, whereupon they qradually depart from the Gompertzian model and in some cancers like bronchus carcinoma they even decline. This discrepancy lead to the formulation of a "power" model for adult cancer age specific rates (6). In the power model: P(a) = P(D)ak. k stands for the mutation number a clone has to undergo to achieve a complete malignant transformation. P(0) marks the initial condition and 'a' represents aqe. P(a)is assumed to describe the evolution of a local process proceedinn in random steps while G(a) implies a random deterioration of a qeneralizkd
195
system which leads to a local phenomenon. Since in most cases cancer presents itself clinically as a systemic disease it seem plausible to extend Strehler and Mildvan's theory to describe cancer as well. G(a) could be regarded as an universal function describing mortality rates of all chronic systemic diseases including cancer (8). The deviation of observed cancer age specific mortality rates from G(a) could be ascribed to an error in cancer diagnosis which increases with age. Since age specific death rates of all chronic diseases increase with age more and more ailments besides cancer compete for the conquest of the human body. The probability of their coexistence with cancer increases and thus the risk of its under diagnosis. Since in young adults the probability of coexistence of several diseases in one individual is minimal, cancer age specific death rates in the 30-55 years interval ought to be the most reliable, and indeed, in this age interval, all carcinoma age specific mortality rates follow the Gompertzian model (8). Moreover the slopes of age specific mortality rate curves of all carcinomata at the age of 30 years are the same (to.158 t 0.009 standard error). They differ only slightly from+the mean slope of age specific incidence rate curves which equals 0.142- 0.01. This observation depicts a phenomenon comnon to all carcinomata and since the slope 'k' in the Gompertz function stands for a random systemic deterioration rate, the above findinq could be interpreted as follows: at the age of 30 years the systemic deterioration of all carcinomata patients proceeds at the same rate. GENERALIZATION
In order to extend this theory to describe age specific mortality rates beyond the age of 55 years the notion of cancer diagnostic error which increases with age had to be introduced. In its present form G(a) does not account for this error. However a more generalized Gompertzian function N(a) to be presented further meets this objective adequately. In order to utilize N(a) the integral of age specific mortality rates M(a) has to be formed. Given the observed aoe specific mortality function m(a), its cumulative counterpart M(a)sm(a). M(a) may now be fitted by the generalized Gompertz function N(a) (11,12, 13). N(a) represents the simultaneous solution of two differential equations (14). dN(a)/da = klN(a). D(a) dD(a)/da =-k2D(a) stands for the observed adult cumulative age specific mortality rate
D(a) describes the decline of cancer diagnosability with age 'a'. kl represents the true rate of increase in the cumulative age specific mortality rate curve and k2 describes the rate of decline of cancer diagnosability with age.
The solution of these equations leads to:
N(a) =
N(0)exp((kl/k2). D(O)(l-exp(-k2a))).
196
In order to study the adequacy of this model N(a) has been fitted to observed M(a) functions of various carcinomata as well as chronic systemic diseases. DATA SOURCES The following computations are based on ase specific distributions found in three sources: 'Pattern in Cancer Mortality in the US', 1950-67, comprisina 4.6 million Alaths from cancer (15). 2. 'The Third National Cancer Survey', 1969-71 incidence, which comprises about 10% of the U.S. population (16). 3. 'U.S. Metropolitan Mortality, 1959-61 (17), which describes the fate of several million people. The four parameter Gompertz function N(a) has been fitted to cumulative age specific rates M(a) observed in the 25-85 year age interval utilizina the non linear least square method (18). Since cancer epidemiology groups cancers accordina to organ of origin we shall define in this study as carcinomata, all orqans in which carcinomata predominate. RESULTS Fig. 1 depicts the observed male cancer age specific mortality curve m(a) (empty circles) and its cumulative counterpart V(a) (black circles). All m(a) points up to the age of 25 years have been excluded from the fitting process. Up to this age m(a) is strongly affected by childhood cancer mortality, which is assumed to be a different disease entity. N(a) has been fitted to the observed cumulative age specific rates M(a). Its derivative dN(a)/da has been computed from the estimated V(a) function x+5 and its five year integrals dN(a)da were drawn alonq the observed male $ cancer age specific mortality rites m(a). The hatched part represents the extrapolated adult mortality rates to childhood. Roth curves depict the excellent fit achieved in all age specific rates. The multiple correlation coefficient R2 (19) for all curves in this study exceeded the value of 0.99 indicating all fits to be highly significant ( p < 0.001). Whereas cumulative cancer age specific mortality curves deviate markedly from log linearity, chronic systemic diseases age specific mortality curves proceed nearly exponentially (Fig. 2). It is strikinq that during yound adulthood, the cancer cumulative rate is steeper than that of other systemic diseases. The initial slope k, of cancer N(a) and non-cancer N(a) being respectively 0.147 and 0.097 (Table 1). The gradual decline of both
197
80 AGE
(years >
Fiq. 1 Male cancer age specific mortality rates m(a) (empty circles) and cumulative male cancer age specific mortality rates, M(a) (black circles). Hatched lines mark the extrapolated rates to childhood, based on Burbank's data (15). Expressed for a population at risk of 100,000.
198
4 Fig. 2 Cumulative age specific mortality M(a) due to chronic diseases other than cancer (empty circles) and cancer (black circles). The curve at the bottom represents the ratio, cancer/non cancer. Its ordinate is depicted on the right side of the picture. Based on metropolitan data (17). The dotted line depicts true exponentTa1 increase. Expressed for a population at risk of 100,000.
199
curves is accounted for by the increasing weight with age of D(a) which stands for the hypothetical underdiagnosis in N(a). The estimated error rate k2 for cancer and non-cancer M(a) are respectively 0.023 and 0.06 (Table 1). The ratio between neoplastic and non-neoplastic diseases, which
CunulatfveMortalfty Rate kl
k2
In R(O)
CUulattve Incidmce Rate
O(O)
t1
K2
In N(O)
O(0) 2.667
LIP
0.132
0.014
-9.751
1.853
0.1%
0.032
-9.758
TOIQW
0.196
0.028
-13.119
2.737
0.175
0.028
-9.119 2,442
ltasopharynx
0.201
0.035
-12.53B
2.808
0.150
0.03o
5sop)ugus
0.233
0.033
-16.695
3.267
0.185
0.024
Stmach
0.173
0.023
-9.462
2.423
0.158
0.020
-7.682 2.214
Small tntcstlne
0.154
0.023
-9.335
2.150
0.146
0.023
-7.256 2.O47
Large fntcstlne
0.150
0.018
-6.820
2.098
0.144
0.018
-5.267 2.609
Rectu
0.163
0.021
-8.852
2.281
0.195
0.027
-10.901 2.732
-6.568 2.093 -11.650 2.5%
Blllary 6 Liver
0.143
0.017
-7.810
2.003
0.138
0.016
-6.529 1.927
Pancreas
0.191
0.027
-10.753
2.671
0.1%
0.028
-11.326 2.746
Larynx
0.308
O.o43
-25.697
4.316
0.288
0.044
-20.110 4.036
Bronchus. trachea
0.286
0.043
-19.505
4.032
0.284
0.043
-17.971 3.976
Breast
0.182
0.027
-12.834
2.547
0.187
0.031
-11.494 2.622
Prostate
0.184
0.016
-15.601
2.578
0.174
0.015
-11.743 2.435
Kidney
0.207
0.032
-12.303
2.900
0.2%
0.034
-10.931 2.883
Bladder
0.205
0.025
-14.951
2.875
0.152
0.020
-6.415 2.133
Thymld
0.145
0.020
-8.999
2.030
0.136
0.033
-3.667 1.927
0.191
0.026
2.673
0.185
0.027
2.586
0.013
o.oo2
0.175
0.011
0.002
0.159
0.017
-1.464 1.855
Mean mlc nmata
carcl-
Standard error
Hean male cancer
0.158
0.142
Standard error
0.009
0.010
All sites mslc
0.141
0.018
-2.952
1.974
0.133
~.*............*.*.1......*.........*......"..~..........~.................~.......-.. All causes
0.105
o.oo9
1.164
1.465
Cancer all sites
0.147
0.023
-2.959
2.051
Chronic diseases
0.097
o.oo6
1.347
1.363
ArterloscleruSfs Heart
0.166
0.022
-5.494
2.330
Arteriosclerosis pcmral
0.131
0.005
-8.806
1.827
Table 1 - Estimated parameters of N(a) in male cumulative carcinomata and other chronic diseases, : true rate of increase in mortality. kl : rate of decline in diagnosability with age. k2 In N(0) : logarfthm of the extrapolated age specific mortality at birth. D(0) : the error in diagnosability at birth.
200
reaches 0.38 at the age of 50 years, declines thereafter. This chanaing ratio reflects an increasing tendency to underdiagnose cancer in favour of a more common systemic disease like myocardial infarction or a cerebral vascular event. Although the epidemiological meaning of m(a) is quite straight forward, its cumulative counterpart M(a) merits further elaboration. The main reason for its formulation is technical. It is much easier to fit F(a) to "(a) than dN(a)/da to m(a). In spite of this,M(a) has also an epidemioloaical interpretation. Age specific death rate m(a) represents the number of observed deaths in age x to x+5 per lOD,ODO at risk of this aoe. m(a) is closely related to the probability of dying at the age of x. M(a) stands for the cumulative probability of dying up to the age of x. D(a) describes the rate of underdiagnosis in a disease represented by N(a). If in cancer, for instance, D(a) would equal zero, all dyl’na cancer patients would be recognized to die from that disease. Since D(a) > 0, some cancer patients are assumed to die from other causes. k2 (Table 1) which describes the rate of underdiagnosis with age equals 0.023 for cancers of all sites pooled together and only 0.006 for other chronic systemic disease. This relationship reflects the tendency to underdiagnose cancer in death certificates in favour of other chronic systemic diseases. It has to be remembered that most death certificates are not based on autopsy reports. Such a discrepancy has been noted in an autopsy study of 3535 patients over 65 years of aqe, 4DF of whom had cancer (20). much higher than that reported in age specific mortality reports. Out of 10,977 autopsy records which had been performed at the Mallory Institute of Pathology between 1955-1965, 26% had clinically undiagnosed cancer (21). In spite of this alarmino findinq the systemic study into the under-reporting of cancer in medical surveys has been attempted only by few aroups (22). These arguments justify the inclusion of an error function in the analysis of observed age specific mortality rates. It seems striking that while k2 exhibits marked variation, D(0) which reflects hypothetical diagnostic error at birth clusters in carcinomata around the value of 2.6 Since k, describes the true mortality rate of N(a) it seemed natural to study its variability among carcinomata and compare it with that observed previously (8). k, for mortality and incidence rate exhibit a narrow variability 0.191 + 0.026 and D.185 + 0.027 respectively. It differs slightly from that estimated previously, which amounts to 0.158 z O.Dqo and 0.142 + D.01 respectively (Table 1). This discrepancy may reflect the low resolution power of the method which in carcinomata leans upon 13 data points. This could be the explanation for the marked deviation in bronchus and larynx carcinoma estimated parameters (Table 1). The close agreement between the estimated parameters for cancer of all sites pooled together which are based in this report on two independent sources, with those estimated in a previous study, supports the above reasoning. k, which represents the true rate of increase in cancer mortality equals in male cancers 0,141, in
201
cancers reported in metropolitan mortality, 0.147 and in our orevious report = 0.158. It may be therefore concluded that the four parameter Gompertzkl ian N(a) preserves two important features which had been previously demonstrated. 1. a narrow variability in kl and 2. kl (mortality) > kl(incidence).
HOWSYSTEVICIS SYSTEMIC? The study of relative cancer survival rates (23) indicates that cancer cure still remains an exception in oncology. Vast curves instead or reaching a zero slope, which would indicate cure, decline asymptotically toward the abscissa. Obviously cancer is detected too late. According to the present dogma, by the time of its clinical appearance, the local disease had spread far beyond its point of incipience to become systemic, and systemic means metastatic spread. An early detection should therefore prevent this spread and assure complete cure. Epidemiological data presented above support a different hypothesis. Cancer could start as a systemic disease which manifests itself by local phenomena. An early detection should therefore assure a comolete cure of the local manifestation only, leaving the generalized process unaffected. At first sight such a hypothesis seems superfluous. What does one qain by postulating a systemic process if the main cause of death is believed to be due to metastases? In order to refute this statement it seems worthwhile to examine it in the light of another systemic disease which also manifests itself clinically by local phenomena, namely, arteriosclerosis. ARTERIOSCLEROSIS AS AN ANALOGUE The first manifestations of this disease which affects all the systems in the organism are already detectable in necropsfes performed on youna adults who had passed away due to another cause. Its age specific mortality curves are stricly Gomperttian (Fig. 3; Table l),indicating that its systemic deterioration proceeds randomly. Arteriosclerosis manifests itself clinically solely by its local sequelae: myocardial infarction, stroke or gangrene, all exhibitina Gomperttian age-specific mortality rates, indicatins that the local manifestations too present themselves clinically in a random fashion. The comparison between arteriosclerosis and cancer highlights some semantic difficulties which haunt oncology. First let us differentiate between true systemic manifestation of the disease and systemic sequelae of a local manifestation (Table 2). Congestive heart failure for instance represents a systemic manifestation of a local phenomenon, myocardial infarction. Similar is hemiparesis which results from a local cerebral vascular event. Metastasis should be regarded in the same context: though systemic, it represents a systemic manifestation of a local phenomenon. Thus early cancer detection assures solely a proper treatment of local phenomena and never a cure of the systemic disease. It seems therefore striking that while hardly any clinician would dare to proclaim a patient with a healed
202
myocardial infarction as cured, and hopes instead for prolonged remission, cure remains the main oncological goal.
Hme
of SystanicDisease
Arterlosclemsls
Local mnlfestations
hyocardial infarction Hypertension Cerebm-vascular event
Carcinoma Sarcoed Lwphom
Systcnicrranifestations
Senility Aging General deterioration
Cachexia Iawunologicaldeterioration Sepsis
Systemicsquelae of local msnifestations
Cardiogenicshock Congestiveheart failure Hemiparesis
Metastasis
Trtatmentof local aunifestations
Surgical: Coronary bypass Sympathectony
Surqical: Ablation
Medical: Antihypertensive Coronary dilators
Table
2
Cancer
SYStmic indicatorsfor an increasedrisk of local wnifestations
Hypercholestemlemia
Envimmenta? Systemic risk
Smoking
Medical:
Chemotherapy
7
Smoking Carcinogens
The comparison between cancer and arteriosclerosis.
203
102
0
10:
IO:3
IO:2
IO
0 AGE
(yeurs
>
Fia. 3 Cumulative age specific mortality M(a) due to arteriosclerosis (black circles), arteriosclerotic heart disease (empty circles) and hypertensive heart disease (crosses). Based on metropolitan mortality data. The systemic disease as well as its local sequela proceed in Gompertzfan fashion. Expressed for a population at risk of 100,000.
204
"Senility", general deterioration in old age, could be reqarded as a systemic manifestation of arteriosclerosis. Cachexia represents the main systemic manifestation in cancer (24). Although it is believed to result from massive metastasis it could be viewed as an independent phenomenon. True, metastasis and cachexia proceed side by side but this does not assure a cause and effect relationship. Patients in which metastasis hits a vital function generally succumb without cachexia, only in those who survive lonq enough does cachexia dominate. Similarly the sepsis and bleedinq tendency which accompany most dying cancer patients could be reoarded as signs of sysetmic deterioration which develop in line with the metastatic process. Out of 157 patients studied by Klastersky et al (25), 32X died of gram negative infection. In 14% infection accompanied another fatal process. 117 died from haemorrhage. Only in 20% could the death be attributed to neoplastic extension into vital organs. This led the authors to conclude that: "although 90% of the patients had very extensive tumoral spread .... it is believed that supportive care aimed at the prevention and treatment of infection in such patients might improve their chance for lonqer survival". The distinction between a true systemic disease and systemic sequelae of a local disease has far reaching implications. First it ought to initiate the search for risk factors which could indicate a rapid systemic deterioration. Like hypercholesterolemia in arteriosclerosis, which is believed to indicate a higher risk for myocardial infarction. The immunoloqical surveillance theory, for instance, predicts a deterioration of immunological processes other than those eliminating incipient tumor foci, which could indicate the oncoming of neoplasia. The susceptibility to infection could represent such a risk factor. According to the oncogene theory, a derepression of genetic information which results in neoplasia ought to release also "marker proteins" unrelated to cancer which could indicate a systemic deterioration. Even Temin's theory implicitly predicts a possible aeneration of such risk factors, in form de novo synthesized viruses lacking any neoplastic potency. The renewed interest in the systemic aspect of cancer ouqht to channel clinical science into a search for systemic therapies, other than anti infective, which might improve the patient's chance for longer survival.
205
REFERENCES I .
Wolff J. Die Lehre von der Krebskrankheit Vol. 1 Jena Verlag G. Fischer 1911.
2.
Thomas L. Cellular and humoral aspects of the hypersensitive states. (HS Lawerence, ed). N.Y. Hoeber-Hoeber 1959.
3.
Burnet FM. The concept of immunological surveillance. Prog. Fxp. Tumor Res. 13:1, 1970.
4.
Huebner RJ, Todaro GJ. Oncogenes of RNA tumor viruses as determinants of cancer. Proc. Natl. Acad. Sci. USA. 64:1087, 1961.
5.
Temin HM. On the origin of the genes for neoplasia. Cancer Res. 34:2835, 1974.
6.
Armitage P, Doll R. The age distribution of cancer and a multistage theory of carcinogenesis. Brit. 3. Cant. 8:1, 1954.
7.
Jones HB. A special consideration of the aging process and life expectancy. Adv. Biol. Med. Phys. 4:281, 1956.
8.
Zajicek G. On the age specific incidence and death rates of carcinomata. 3. Chron. Dis. 29:549, 1976.
9.
Strehler BL, Mildvan AS. General theory of mortality and aging. Science 132:14, 1960.
10. Atlan H. Strehler's theory of mortality and the second priniciple of thermodynamics. J. Gerontol. 23:196, 1968. 11.
Burton AC. Rate of growth of solid tumors as a problem of diffusion. Growth 30:157, 1966.
12.
Laird AK. Dynamics of tumor growth. Brit. J. Cant. 18:490, 1964.
13.
Deakin MAB. Gompertt curves, allometry and embryogenesis. Bull. Math. Biophys. 32:445, 1976.
14.
Norton L, Simon L, Brereton HD, Bodgen AE, Predicting the course of Gompertzian growth. Nature 264:542, 1976.
15.
Burbank F. Patterns in cancer mortality in the US : 1950-67. Natl. Cant. Inst. Monogr. 33, 1971.
16.
Cutler SJ, Young JL. Third National Cancer Survey: Incfdence Data. Natl. Cant. Inst. Monogr. 41, 1975.
17.
Duffy EA, Carroll RE. U.S. Metropolitan Mortality 1959-61. Cincinati Ohio PHSP No. 999-AP-39, 1967.
206
18. Marquardt DW. Least square estimation of non linear parameters. J. Sot. Indust. and Appl. Math. 11:431, 1963. 19.
Brownlee KA. Statistical theory and methodology in science and engineering. Wiley New York, 447, 1965.
20.
Suen KC, Lau LL, Yermakow V. Cancer and old age. An autopsy study of 3535 patients over 65 years old.
21.
Cancer 33:1164, 1974.
Bauer FW, Robbins SL. An autopsy study of cancer patients. I. Accuracy of the clinical diagnoses (1955-65). Boston City Hospital. JAMA. 221, 147, 1972.
22.
Chamber LW, Spitter WO, Hill GE, Helliwell BE. Under-reportina of cancer in medical surveys: A source of systematic error in cancer research. Am.J.Epidemiol. 104:141, 1976.
23.
Axtell LM, Cutler SJ, Meyer MH. End results of cancer. Cancer Report NO. 4. DHEW Publ. NO (NTH) 73-272, 1972.
24.
Theologides A. Pathogenesis of cachexia in cancer. Cancer 29:484, 1972.
25.
Klastersky J, Daneau D, Verhest A. Causes of death in patients with cancer. Emp.
J.Cancer 8:149, 1972.
2n7
193-207, 1978
CANCER AS A SYSTEMIC DISEASE G. Zajicek. Department of Experimental Medicine and Cancer Research and Computer Unit, The Hebrew University-Hadassah Medical School, P.O.Rox 1177, Jerusalem, Israel.
ABSTRACT Theories on the nature of cancer may be classified into two categories. One regards cancer strictly as a local phenomenon while the second looks at cancer as a local manifestation of a systemic process or disease. Although the first dominates current medical thought, the theories of immunological surveillance and of protovirus-oncogene implicitly assume cancer to represent a local manifestation of a systemic process or disease. This is supported also by epidemiological data forwarded in the present paper. Jn order to clarify the exact meaning of a systemic disease, cancer and its manifestation are compared with arteriosclerosis and its seouelae. Arteriosclerosis could be regarded as a prototype of a systemic disease. It presents itself clinically solely by its local manifestations, like myocardial infarction or stroke. These local manifestations may be followed by secondary systemic sequelae like congestive heart failure. In the same context, it is proposed to regard cancer as one systemic disease which presents itself clinically by local phenomena like carcinoma, lymphoma and sarcoma. These local manifestations may lead further to secondary systemic sequelae like metastasis. Neoplasms, Diagnosis, Mortality.
193
INTRODUCTIOI’J Theories on the nature of cancer may be classified into two categories. One regards cancer strictly as a local phenomenon while the second looks at cancer as a local manifestation of a systemic process or disease. Since the dawn of medicine both categories have competed for heqemony, a continuous struggle which has been extensively reviewed by Wolff (1). The present version of the local theory was formulated durinq the previous century by J. Muller, Rokitansky and others who initiated the search for the anatomo-pahtological characteristics of the cancer cell, formulating the "Blastema theory". This was followed by attempts to elucidate the nature of the malignant transformation. Such a transformation was believed by Vfrchow to be caused by chronic irritation, and by Rovery to result from somatic mutation which is assumed to play the main role in cell transformation durinq chemical carcinogenesis and processes leading to differentiation abberations. This theory was rivaled by the infective theory of cancer introduced by Pasteur, which has been qradually replaced by its modern version the "virus infective theory" initiated by Ellerman and Bang's discovery of the leukosis virus and ROUS' discovery of the sarcoma virus which bears his name. Roth theories, the mutation as well as the infective theory, dominate current cancer research. The second category, which regards cancer as a local manifestation of a systemic process or disease, ruled medical thought in ancient times and through the medieval period, until its decline with the advent of modern pathology. Hfppocrates thought cancer to result from a dyscrasia or disharmony of certain body constitutents. Galen believed cancer to be a constitutional disease resulting from an overflow of "atra bilis", the black bile. Both theories ruled medicine for a millenium. Paracelsus regarded cancerous growth to be the port of exit for certain salts trying to escape the organism, a concept which was succeeded by the lymph theory which dominated medicine until the dawn of the nineteenth century. To the modern physician these theories seem bizarre and have therefore been opposed by medical schools which regard cancer strictly as a local phenomenon. However, recent developments in cancer research have reintroduced, although implicitly, the systemic cancer theories. The theory of immunological surveillance and that of protovirus-oncogene implicitly assume cancer to represent a local manifestation of a systemic process or disease, According to Thomas (2) and Burnet (3) ordinarily the immune response destroys cancer cells while they are still in the incipient stage of tumor formation. A failure of the "systemic" surveillance mechanism leads to the nloaal" appearance of a tumor. The deterioration of this surveillance mechanism proceeds continuously in a random fashion, and could result from somatic mutations affecting cell clones responsible for its proper function.
194
Huebner and Todaro's oncogene theory, (4) claims aenetic information for cancer to exist in every cell. Neoplasia arises when ore-existant qenetic information is derepressed. Temin's protovirus theory (5) maintains that genetic information for cancer is synthesized de novo. k?alianancy arises through a process of genetic chanqe in which pieces of aenetic information which exist in all the cells, happen to be so assembled that cell transformation occurs through "misevolution". Both theories imoly therefore that random chanqes in an ubiquitous or systemic phenomenon may result in the local appearance of malionancy. CANCER EPIDFMIOLOGY Cancer epidemiology too is dominated by the dooma of local cancer, hiohlighted by Awnitage and Doll's model for carcinoaenesis, known as the "power" model (6). It has been developed to explain the peculiar shaoe of adult cancer age specific mortality rates, which differ markedly from aqe soecific mortality rates due to all chronic diseases (73). Adult aoe specific mortality curves are best described by the qompertz model q(a) = c(n) exp(ka) in which 'a' stands for age and 'k' known as the Gompertz coefficient, describes the rate of increase of G(a) with aqe. G(q) marks the hypothetical mortality at birth. G(a) implies the existence of a random systemic deterioration which leads to the clinical appearance of the chronic disease or even to death, as highlighted in Strehler and mildvan's aaino theory (g). According to this theory the organism consists of a set of sub-systems each with a certain maximum ability to restore its initial condition after a challenge. Tha magnitudes of challenges are distributed energetically like a Maxwell-Boltzmann distribution. Death occurs when the rate et which an organism recruits work to restore the oriqinal state is less than that demanded to overcome the effects of a given challenge. A further qeneralization proposed by Atlan (lo), describes the orqanism deterioration in entropy units in order to utilize information theory jn the prediction of aaina. Both models are isomorphic with the Gompertz function G(a) and could therefore be applied to chronic systemic diseases. Arteriosclerosis for instance affects all the systems in the body and reduces their efficiency to withstand external noxae. Since its aqe specific mortality rates are compertzian, Strehler and Mildvan's theory seem an adequate model to describe arteriosclerotic age specific mortality rates, or even its local manifestations, like myocardial infarction,which also exhibits Gompertzian aae specific mortality rates. Up to the age of 50 years cancer age specific mortality rates fo?low those of chronic diseases, whereupon they qradually depart from the Gompertzian model and in some cancers like bronchus carcinoma they even decline. This discrepancy lead to the formulation of a "power" model for adult cancer age specific rates (6). In the power model: P(a) = P(D)ak. k stands for the mutation number a clone has to undergo to achieve a complete malignant transformation. P(0) marks the initial condition and 'a' represents aqe. P(a)is assumed to describe the evolution of a local process proceedinn in random steps while G(a) implies a random deterioration of a qeneralizkd
195
system which leads to a local phenomenon. Since in most cases cancer presents itself clinically as a systemic disease it seem plausible to extend Strehler and Mildvan's theory to describe cancer as well. G(a) could be regarded as an universal function describing mortality rates of all chronic systemic diseases including cancer (8). The deviation of observed cancer age specific mortality rates from G(a) could be ascribed to an error in cancer diagnosis which increases with age. Since age specific death rates of all chronic diseases increase with age more and more ailments besides cancer compete for the conquest of the human body. The probability of their coexistence with cancer increases and thus the risk of its under diagnosis. Since in young adults the probability of coexistence of several diseases in one individual is minimal, cancer age specific death rates in the 30-55 years interval ought to be the most reliable, and indeed, in this age interval, all carcinoma age specific mortality rates follow the Gompertzian model (8). Moreover the slopes of age specific mortality rate curves of all carcinomata at the age of 30 years are the same (to.158 t 0.009 standard error). They differ only slightly from+the mean slope of age specific incidence rate curves which equals 0.142- 0.01. This observation depicts a phenomenon comnon to all carcinomata and since the slope 'k' in the Gompertz function stands for a random systemic deterioration rate, the above findinq could be interpreted as follows: at the age of 30 years the systemic deterioration of all carcinomata patients proceeds at the same rate. GENERALIZATION
In order to extend this theory to describe age specific mortality rates beyond the age of 55 years the notion of cancer diagnostic error which increases with age had to be introduced. In its present form G(a) does not account for this error. However a more generalized Gompertzian function N(a) to be presented further meets this objective adequately. In order to utilize N(a) the integral of age specific mortality rates M(a) has to be formed. Given the observed aoe specific mortality function m(a), its cumulative counterpart M(a)sm(a). M(a) may now be fitted by the generalized Gompertz function N(a) (11,12, 13). N(a) represents the simultaneous solution of two differential equations (14). dN(a)/da = klN(a). D(a) dD(a)/da =-k2D(a) stands for the observed adult cumulative age specific mortality rate
D(a) describes the decline of cancer diagnosability with age 'a'. kl represents the true rate of increase in the cumulative age specific mortality rate curve and k2 describes the rate of decline of cancer diagnosability with age.
The solution of these equations leads to:
N(a) =
N(0)exp((kl/k2). D(O)(l-exp(-k2a))).
196
In order to study the adequacy of this model N(a) has been fitted to observed M(a) functions of various carcinomata as well as chronic systemic diseases. DATA SOURCES The following computations are based on ase specific distributions found in three sources: 'Pattern in Cancer Mortality in the US', 1950-67, comprisina 4.6 million Alaths from cancer (15). 2. 'The Third National Cancer Survey', 1969-71 incidence, which comprises about 10% of the U.S. population (16). 3. 'U.S. Metropolitan Mortality, 1959-61 (17), which describes the fate of several million people. The four parameter Gompertz function N(a) has been fitted to cumulative age specific rates M(a) observed in the 25-85 year age interval utilizina the non linear least square method (18). Since cancer epidemiology groups cancers accordina to organ of origin we shall define in this study as carcinomata, all orqans in which carcinomata predominate. RESULTS Fig. 1 depicts the observed male cancer age specific mortality curve m(a) (empty circles) and its cumulative counterpart V(a) (black circles). All m(a) points up to the age of 25 years have been excluded from the fitting process. Up to this age m(a) is strongly affected by childhood cancer mortality, which is assumed to be a different disease entity. N(a) has been fitted to the observed cumulative age specific rates M(a). Its derivative dN(a)/da has been computed from the estimated V(a) function x+5 and its five year integrals dN(a)da were drawn alonq the observed male $ cancer age specific mortality rites m(a). The hatched part represents the extrapolated adult mortality rates to childhood. Roth curves depict the excellent fit achieved in all age specific rates. The multiple correlation coefficient R2 (19) for all curves in this study exceeded the value of 0.99 indicating all fits to be highly significant ( p < 0.001). Whereas cumulative cancer age specific mortality curves deviate markedly from log linearity, chronic systemic diseases age specific mortality curves proceed nearly exponentially (Fig. 2). It is strikinq that during yound adulthood, the cancer cumulative rate is steeper than that of other systemic diseases. The initial slope k, of cancer N(a) and non-cancer N(a) being respectively 0.147 and 0.097 (Table 1). The gradual decline of both
197
80 AGE
(years >
Fiq. 1 Male cancer age specific mortality rates m(a) (empty circles) and cumulative male cancer age specific mortality rates, M(a) (black circles). Hatched lines mark the extrapolated rates to childhood, based on Burbank's data (15). Expressed for a population at risk of 100,000.
198
4 Fig. 2 Cumulative age specific mortality M(a) due to chronic diseases other than cancer (empty circles) and cancer (black circles). The curve at the bottom represents the ratio, cancer/non cancer. Its ordinate is depicted on the right side of the picture. Based on metropolitan data (17). The dotted line depicts true exponentTa1 increase. Expressed for a population at risk of 100,000.
199
curves is accounted for by the increasing weight with age of D(a) which stands for the hypothetical underdiagnosis in N(a). The estimated error rate k2 for cancer and non-cancer M(a) are respectively 0.023 and 0.06 (Table 1). The ratio between neoplastic and non-neoplastic diseases, which
CunulatfveMortalfty Rate kl
k2
In R(O)
CUulattve Incidmce Rate
O(O)
t1
K2
In N(O)
O(0) 2.667
LIP
0.132
0.014
-9.751
1.853
0.1%
0.032
-9.758
TOIQW
0.196
0.028
-13.119
2.737
0.175
0.028
-9.119 2,442
ltasopharynx
0.201
0.035
-12.53B
2.808
0.150
0.03o
5sop)ugus
0.233
0.033
-16.695
3.267
0.185
0.024
Stmach
0.173
0.023
-9.462
2.423
0.158
0.020
-7.682 2.214
Small tntcstlne
0.154
0.023
-9.335
2.150
0.146
0.023
-7.256 2.O47
Large fntcstlne
0.150
0.018
-6.820
2.098
0.144
0.018
-5.267 2.609
Rectu
0.163
0.021
-8.852
2.281
0.195
0.027
-10.901 2.732
-6.568 2.093 -11.650 2.5%
Blllary 6 Liver
0.143
0.017
-7.810
2.003
0.138
0.016
-6.529 1.927
Pancreas
0.191
0.027
-10.753
2.671
0.1%
0.028
-11.326 2.746
Larynx
0.308
O.o43
-25.697
4.316
0.288
0.044
-20.110 4.036
Bronchus. trachea
0.286
0.043
-19.505
4.032
0.284
0.043
-17.971 3.976
Breast
0.182
0.027
-12.834
2.547
0.187
0.031
-11.494 2.622
Prostate
0.184
0.016
-15.601
2.578
0.174
0.015
-11.743 2.435
Kidney
0.207
0.032
-12.303
2.900
0.2%
0.034
-10.931 2.883
Bladder
0.205
0.025
-14.951
2.875
0.152
0.020
-6.415 2.133
Thymld
0.145
0.020
-8.999
2.030
0.136
0.033
-3.667 1.927
0.191
0.026
2.673
0.185
0.027
2.586
0.013
o.oo2
0.175
0.011
0.002
0.159
0.017
-1.464 1.855
Mean mlc nmata
carcl-
Standard error
Hean male cancer
0.158
0.142
Standard error
0.009
0.010
All sites mslc
0.141
0.018
-2.952
1.974
0.133
~.*............*.*.1......*.........*......"..~..........~.................~.......-.. All causes
0.105
o.oo9
1.164
1.465
Cancer all sites
0.147
0.023
-2.959
2.051
Chronic diseases
0.097
o.oo6
1.347
1.363
ArterloscleruSfs Heart
0.166
0.022
-5.494
2.330
Arteriosclerosis pcmral
0.131
0.005
-8.806
1.827
Table 1 - Estimated parameters of N(a) in male cumulative carcinomata and other chronic diseases, : true rate of increase in mortality. kl : rate of decline in diagnosability with age. k2 In N(0) : logarfthm of the extrapolated age specific mortality at birth. D(0) : the error in diagnosability at birth.
200
reaches 0.38 at the age of 50 years, declines thereafter. This chanaing ratio reflects an increasing tendency to underdiagnose cancer in favour of a more common systemic disease like myocardial infarction or a cerebral vascular event. Although the epidemiological meaning of m(a) is quite straight forward, its cumulative counterpart M(a) merits further elaboration. The main reason for its formulation is technical. It is much easier to fit F(a) to "(a) than dN(a)/da to m(a). In spite of this,M(a) has also an epidemioloaical interpretation. Age specific death rate m(a) represents the number of observed deaths in age x to x+5 per lOD,ODO at risk of this aoe. m(a) is closely related to the probability of dying at the age of x. M(a) stands for the cumulative probability of dying up to the age of x. D(a) describes the rate of underdiagnosis in a disease represented by N(a). If in cancer, for instance, D(a) would equal zero, all dyl’na cancer patients would be recognized to die from that disease. Since D(a) > 0, some cancer patients are assumed to die from other causes. k2 (Table 1) which describes the rate of underdiagnosis with age equals 0.023 for cancers of all sites pooled together and only 0.006 for other chronic systemic disease. This relationship reflects the tendency to underdiagnose cancer in death certificates in favour of other chronic systemic diseases. It has to be remembered that most death certificates are not based on autopsy reports. Such a discrepancy has been noted in an autopsy study of 3535 patients over 65 years of aqe, 4DF of whom had cancer (20). much higher than that reported in age specific mortality reports. Out of 10,977 autopsy records which had been performed at the Mallory Institute of Pathology between 1955-1965, 26% had clinically undiagnosed cancer (21). In spite of this alarmino findinq the systemic study into the under-reporting of cancer in medical surveys has been attempted only by few aroups (22). These arguments justify the inclusion of an error function in the analysis of observed age specific mortality rates. It seems striking that while k2 exhibits marked variation, D(0) which reflects hypothetical diagnostic error at birth clusters in carcinomata around the value of 2.6 Since k, describes the true mortality rate of N(a) it seemed natural to study its variability among carcinomata and compare it with that observed previously (8). k, for mortality and incidence rate exhibit a narrow variability 0.191 + 0.026 and D.185 + 0.027 respectively. It differs slightly from that estimated previously, which amounts to 0.158 z O.Dqo and 0.142 + D.01 respectively (Table 1). This discrepancy may reflect the low resolution power of the method which in carcinomata leans upon 13 data points. This could be the explanation for the marked deviation in bronchus and larynx carcinoma estimated parameters (Table 1). The close agreement between the estimated parameters for cancer of all sites pooled together which are based in this report on two independent sources, with those estimated in a previous study, supports the above reasoning. k, which represents the true rate of increase in cancer mortality equals in male cancers 0,141, in
201
cancers reported in metropolitan mortality, 0.147 and in our orevious report = 0.158. It may be therefore concluded that the four parameter Gompertzkl ian N(a) preserves two important features which had been previously demonstrated. 1. a narrow variability in kl and 2. kl (mortality) > kl(incidence).
HOWSYSTEVICIS SYSTEMIC? The study of relative cancer survival rates (23) indicates that cancer cure still remains an exception in oncology. Vast curves instead or reaching a zero slope, which would indicate cure, decline asymptotically toward the abscissa. Obviously cancer is detected too late. According to the present dogma, by the time of its clinical appearance, the local disease had spread far beyond its point of incipience to become systemic, and systemic means metastatic spread. An early detection should therefore prevent this spread and assure complete cure. Epidemiological data presented above support a different hypothesis. Cancer could start as a systemic disease which manifests itself by local phenomena. An early detection should therefore assure a comolete cure of the local manifestation only, leaving the generalized process unaffected. At first sight such a hypothesis seems superfluous. What does one qain by postulating a systemic process if the main cause of death is believed to be due to metastases? In order to refute this statement it seems worthwhile to examine it in the light of another systemic disease which also manifests itself clinically by local phenomena, namely, arteriosclerosis. ARTERIOSCLEROSIS AS AN ANALOGUE The first manifestations of this disease which affects all the systems in the organism are already detectable in necropsfes performed on youna adults who had passed away due to another cause. Its age specific mortality curves are stricly Gomperttian (Fig. 3; Table l),indicating that its systemic deterioration proceeds randomly. Arteriosclerosis manifests itself clinically solely by its local sequelae: myocardial infarction, stroke or gangrene, all exhibitina Gomperttian age-specific mortality rates, indicatins that the local manifestations too present themselves clinically in a random fashion. The comparison between arteriosclerosis and cancer highlights some semantic difficulties which haunt oncology. First let us differentiate between true systemic manifestation of the disease and systemic sequelae of a local manifestation (Table 2). Congestive heart failure for instance represents a systemic manifestation of a local phenomenon, myocardial infarction. Similar is hemiparesis which results from a local cerebral vascular event. Metastasis should be regarded in the same context: though systemic, it represents a systemic manifestation of a local phenomenon. Thus early cancer detection assures solely a proper treatment of local phenomena and never a cure of the systemic disease. It seems therefore striking that while hardly any clinician would dare to proclaim a patient with a healed
202
myocardial infarction as cured, and hopes instead for prolonged remission, cure remains the main oncological goal.
Hme
of SystanicDisease
Arterlosclemsls
Local mnlfestations
hyocardial infarction Hypertension Cerebm-vascular event
Carcinoma Sarcoed Lwphom
Systcnicrranifestations
Senility Aging General deterioration
Cachexia Iawunologicaldeterioration Sepsis
Systemicsquelae of local msnifestations
Cardiogenicshock Congestiveheart failure Hemiparesis
Metastasis
Trtatmentof local aunifestations
Surgical: Coronary bypass Sympathectony
Surqical: Ablation
Medical: Antihypertensive Coronary dilators
Table
2
Cancer
SYStmic indicatorsfor an increasedrisk of local wnifestations
Hypercholestemlemia
Envimmenta? Systemic risk
Smoking
Medical:
Chemotherapy
7
Smoking Carcinogens
The comparison between cancer and arteriosclerosis.
203
102
0
10:
IO:3
IO:2
IO
0 AGE
(yeurs
>
Fia. 3 Cumulative age specific mortality M(a) due to arteriosclerosis (black circles), arteriosclerotic heart disease (empty circles) and hypertensive heart disease (crosses). Based on metropolitan mortality data. The systemic disease as well as its local sequela proceed in Gompertzfan fashion. Expressed for a population at risk of 100,000.
204
"Senility", general deterioration in old age, could be reqarded as a systemic manifestation of arteriosclerosis. Cachexia represents the main systemic manifestation in cancer (24). Although it is believed to result from massive metastasis it could be viewed as an independent phenomenon. True, metastasis and cachexia proceed side by side but this does not assure a cause and effect relationship. Patients in which metastasis hits a vital function generally succumb without cachexia, only in those who survive lonq enough does cachexia dominate. Similarly the sepsis and bleedinq tendency which accompany most dying cancer patients could be reoarded as signs of sysetmic deterioration which develop in line with the metastatic process. Out of 157 patients studied by Klastersky et al (25), 32X died of gram negative infection. In 14% infection accompanied another fatal process. 117 died from haemorrhage. Only in 20% could the death be attributed to neoplastic extension into vital organs. This led the authors to conclude that: "although 90% of the patients had very extensive tumoral spread .... it is believed that supportive care aimed at the prevention and treatment of infection in such patients might improve their chance for lonqer survival". The distinction between a true systemic disease and systemic sequelae of a local disease has far reaching implications. First it ought to initiate the search for risk factors which could indicate a rapid systemic deterioration. Like hypercholesterolemia in arteriosclerosis, which is believed to indicate a higher risk for myocardial infarction. The immunoloqical surveillance theory, for instance, predicts a deterioration of immunological processes other than those eliminating incipient tumor foci, which could indicate the oncoming of neoplasia. The susceptibility to infection could represent such a risk factor. According to the oncogene theory, a derepression of genetic information which results in neoplasia ought to release also "marker proteins" unrelated to cancer which could indicate a systemic deterioration. Even Temin's theory implicitly predicts a possible aeneration of such risk factors, in form de novo synthesized viruses lacking any neoplastic potency. The renewed interest in the systemic aspect of cancer ouqht to channel clinical science into a search for systemic therapies, other than anti infective, which might improve the patient's chance for longer survival.
205
REFERENCES I .
Wolff J. Die Lehre von der Krebskrankheit Vol. 1 Jena Verlag G. Fischer 1911.
2.
Thomas L. Cellular and humoral aspects of the hypersensitive states. (HS Lawerence, ed). N.Y. Hoeber-Hoeber 1959.
3.
Burnet FM. The concept of immunological surveillance. Prog. Fxp. Tumor Res. 13:1, 1970.
4.
Huebner RJ, Todaro GJ. Oncogenes of RNA tumor viruses as determinants of cancer. Proc. Natl. Acad. Sci. USA. 64:1087, 1961.
5.
Temin HM. On the origin of the genes for neoplasia. Cancer Res. 34:2835, 1974.
6.
Armitage P, Doll R. The age distribution of cancer and a multistage theory of carcinogenesis. Brit. 3. Cant. 8:1, 1954.
7.
Jones HB. A special consideration of the aging process and life expectancy. Adv. Biol. Med. Phys. 4:281, 1956.
8.
Zajicek G. On the age specific incidence and death rates of carcinomata. 3. Chron. Dis. 29:549, 1976.
9.
Strehler BL, Mildvan AS. General theory of mortality and aging. Science 132:14, 1960.
10. Atlan H. Strehler's theory of mortality and the second priniciple of thermodynamics. J. Gerontol. 23:196, 1968. 11.
Burton AC. Rate of growth of solid tumors as a problem of diffusion. Growth 30:157, 1966.
12.
Laird AK. Dynamics of tumor growth. Brit. J. Cant. 18:490, 1964.
13.
Deakin MAB. Gompertt curves, allometry and embryogenesis. Bull. Math. Biophys. 32:445, 1976.
14.
Norton L, Simon L, Brereton HD, Bodgen AE, Predicting the course of Gompertzian growth. Nature 264:542, 1976.
15.
Burbank F. Patterns in cancer mortality in the US : 1950-67. Natl. Cant. Inst. Monogr. 33, 1971.
16.
Cutler SJ, Young JL. Third National Cancer Survey: Incfdence Data. Natl. Cant. Inst. Monogr. 41, 1975.
17.
Duffy EA, Carroll RE. U.S. Metropolitan Mortality 1959-61. Cincinati Ohio PHSP No. 999-AP-39, 1967.
206
18. Marquardt DW. Least square estimation of non linear parameters. J. Sot. Indust. and Appl. Math. 11:431, 1963. 19.
Brownlee KA. Statistical theory and methodology in science and engineering. Wiley New York, 447, 1965.
20.
Suen KC, Lau LL, Yermakow V. Cancer and old age. An autopsy study of 3535 patients over 65 years old.
21.
Cancer 33:1164, 1974.
Bauer FW, Robbins SL. An autopsy study of cancer patients. I. Accuracy of the clinical diagnoses (1955-65). Boston City Hospital. JAMA. 221, 147, 1972.
22.
Chamber LW, Spitter WO, Hill GE, Helliwell BE. Under-reportina of cancer in medical surveys: A source of systematic error in cancer research. Am.J.Epidemiol. 104:141, 1976.
23.
Axtell LM, Cutler SJ, Meyer MH. End results of cancer. Cancer Report NO. 4. DHEW Publ. NO (NTH) 73-272, 1972.
24.
Theologides A. Pathogenesis of cachexia in cancer. Cancer 29:484, 1972.
25.
Klastersky J, Daneau D, Verhest A. Causes of death in patients with cancer. Emp.
J.Cancer 8:149, 1972.
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