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The natural history of lung cancer: A review based on rates of tumour growth
BY. J. Dis. Chest (1979) 73, 1
Hypothesis THE NATURAL HISTORY A REVIEW BASED ON RATES
OF LUNG CANCER: OF TUMOUR GROWTH
D. M. GEDDES Brompton Hospital, London Out of 100 patients with lung cancer discovered, fewer than 10 will live five years. Eighty will have inoperable disease at the time of diagnosis and most of these will die within three years; only one or two will be alive after five years. The 20 patients with localized disease will have an operation and about six of them will be alive after five years. These statistics have not changed over the past 30 years and this is in spite of many attempts at earlier diagnosis as well as a considerable improvement in operative mortality. In the face of these gloomy statistics there is a surprising lack of information about the natural history of the disease. There are no proper controlled studies of unselected patients in the literature. The few studies which have included an untreated control group have always been done on ‘inoperable’ patients, i.e. those with the most advanced disease. Trials of radiotherapy and chemotherapy show very little, if any, benefit in terms of survival and untreated control patients sometimes do better than those who are treated (Laing et al. 1975). The role of surgery appears at first sight to be better defined. Surgery is better than radiotherapy for squamous but not for oat-cell carcinomas (Morrison et al. 1963 ; Miller et al. 1969). However, since patients with early localized disease are considered to be curable, treatment cannot be withheld in the interests of a controlled trial. The result is that the natural history of limited operable disease is unknown. Radiotherapists and chemotherapists can justifiably complain that their treatment is never given to the patients with the best prospects of cure. Against this background of doubt about the best form of treatment, and certainty that most treatment is ineffective, is the obvious need for a better understanding of the natural history of the disease. Such understanding should help in three ways. First in assessing the true value of existing treatments. Second in judging an individual patient’s prognosis and so in choosing the most appropriate treatment. Third, and most important, in planning a rational search for new and more effective forms of treatment. We have used the considerable literature on tumour growth rates in lung cancer in an attempt to calculate the natural history of the disease. EXPONENTIAL
MODEL
OF TUMOUR
GROWTH
This hypothesis was first suggested by Collins et al. in 1956. The hypothesis assumes a tumour to start from a single cell. This cell then divides to become two cells, each of which divide to become four, eight, sixteen and so on. If this process goes on at a constant rate, then the tumour growth will be exponential and its volume at any time can be easily calculated. The simplest way to describe the growth rate is the volume doubling 1
2
D. M. Geddes
time-the time taken for the tumour volume to double. Exponential tumour growth is analagous to the exponential decay of a radioactive isotope. Growth is described by doubling time where decay is described by half-life. At its simplest, this model predicts that a single cell of 10 pm will become a tumour of 1 mm in diameter after its volume had doubled 20 times. A further ten doublings will produce a tumour of about 1 cm in diameter and after ten more doublings, the tumour will have a diameter of 10 cm with a total mass of 1 kg. This is shown in Fig. 1. This figure shows how a tumour appears to be small and slow-growing for the majority of its lo-
Diameter
5
(cm)
2
4
6
8 10 12 14 16 18 20 22 Number
Time Fig. 1. The life of a solid tumour. time of 1 month takes 40 months 1 year takes 40 years
2426
of Volume
Time is expressed to reach 10 cm
28
30 3234
36 3840
42 44
Doublings +
as volume doublings. diameter, while another
A tumour with a doubling with a doubling time of
life until it reaches a diagnosable size when it appears to grow very rapidly. In fact, the rate of tumour growth is relatively constant throughout its life and compared with other tissues is rather slow. (The vast majority of cancers grow very much more slowly than a human thumb-nail (Spratt & Spratt 1976).) T umour growth is like the reward demanded in the Arabian legend: one grain of corn for the first square on the chess board, two for the next, four for the next, etc. The amount of grain on the sixty-fourth square exceeds the total world production of corn since the beginning of mankind. Tumour doubling time (Ts) for the.model may be calculated from two diameter measurements separated by a known time or more simply may be derived from Fig. 2. The mathematics of the model are discussed in the appendix. 6 Validation
of the model
This model of tumour
growth can be validated in the following
ways:
Measurement of doubling times. If a tumour grows at a constant exponential rate, then its doubling time will be constant. Doubling times have been calculated for many lung tumours, both primary and secondary, from serial chest radiographs. The vast majority of observations show the doubling times of individual tumours to be constant. Whenever doubling times have been shown to change, they tend to become longer towards the end of the tumour’s life. In other words, the tumour growth rate slows as the tumour gets larger. A review of published series shows that SO-90% of tumours grow exponentially.
3
Natural History of Lung Cancer 10 9a76-
-10
5-
- 7
4-
- 6
- 9 - 8
Diameter (cm)
- 5
Number of Doublings
-. 4
- 1 0
12
24
36 48 Days
60
72
84
0
Fig. 2. Chart for measuring tumour doubling time. Tumour diameter is plotted on a logarithmic scale against time. Using the right-hand scale one volume doubling can be marked on the growth curve and the doubling time read from the time scale
Observations on Wilm’s tumour. This elegant study by Collins et al. (1956) formed one of the corner-stones of their hypothesis of exponential growth. An embryonic tumour must have begun at or after the time of conception of the child. The tumour then took a known length of time to manifest itself clinically. The maximum time from one cell to diagnosis is therefore the age of the child at diagnosis plus nine months. If the tumour is then removed surgically and one cell is left behind, this cell continues to grow at the same, rate as the original tumour. After the same time interval, i.e. age at diagnosis plus nine months, any recurrence will be the same size as the original tumour and should be clinically obvious. If the child is well at this time then he is cured. 206 case histories of children with surgically treated Wilm’s tumour were reviewed. The tumour had recurred in 137 children and in every case this was within their theoretical period of risk. Forty-nine patients had been free of disease for longer than the risk period and none of these suffered a recurrence subsequently. Animal studies. Tumour growth rates have been plotted in animals and show exponential growth with a tendency for slowing of growth as the tumour gets large (Dethlefsen et al. 1968). Acceleration of growth is not seen. Some of the tumours studied are very different from naturally occurring disease in man and so these studies have to be interpreted with caution. Nevertheless, the broad principles of exponential growth are confirmed. Objections to the model There are some objections to the exponential
model:
4
D. M. Geddes
Doubling times may not be constant during the microscopic period of tumour growth. Some tumours have doubling times which are so long that back extrapolation provides the absurd conclusion that the tumour began many years before the individual was conceived. This is probably a reflection of the slowing of tumour growth with size referred to above. This applies to only a few tumours but nonetheless estimates of starting time of a tumour by back extrapolation must be seen as only approximate. This objection is less important for extrapolation forward over a few tumour doublings. Metastases. Can observations on the primary tumours be applied to its metastases? Metastases seem, in general, to grow faster than their primary. The evidence for this is limited and information for primary lung tumours very scanty indeed (Brenner et al. 1967). Nevertheless, variation in growth rates between the primary and metastatic tumour will introduce inaccuracy into any calculations based on the growth of the primary alone. This inaccuracy will be greater for oat-cell tumours, which metastasize widely early, than for squamous and adenocarcinomas. The exponential model then fits the observed facts reasonably well. Exceptions will occur when the centre of a tumour breaks down, when tumours are under hormonal control, as a result of treatment and, rarely, when spontaneous regression occurs. From this model the natural history of a tumour can be calculated by extrapolation. Extrapolating back in time gives an approximate date for malignant change (when the first malignant cell arose) ; while extrapolation forward to a total of 40 doublings, when there will be about 1 kg of tumour, gives an approximate date of death. This is summarized in Table I. Table I. The natural
history
of a solid tumour
Doublings
Cells
Diameter
0 20 30 35 40
1 106 109
10 pm 1 mm 1 cm 3 cm 10 cm
l()lO*5
1012
which
grows exponentially
Microscopic Microscopic Detectable on chest radiograph Average diagnosis Death
Calculating the natuural history To do these calculations, three properties of tumour need to be known: doubling time, size and total tumour mass at death. Doubling time. Reports of doubling times of 228 primary lung cancers in the literature are listed by cell type in Table II. Doubling times show a log-normal distribution and so the geometric mean and standard deviation have been calculated. The distribution of histological types among these 228 reported tumours shows 48% squamous, 26% adeno-, 19% undifferentiated carcinoma and 7% miscellaneous. This distribution is relatively close to the overall incidence of different cell types in lung cancer. Size.
from
Fig. 3 shows the distribution of sizes of peripheral tumours at diagnosis taken four published series. This distribution is log-normal and the mean diameter
Natural History of Lung Cancer Table II. Reports
of doubling
Squamous Brenner et al. 1967 Breur 1966 Chahinian 1972 Garland et al. 1963 and Garland 1966 Meyer 1973 Schwartz 1961 Steele and Buell 1973 Weiss et al. 1966 and Weiss 1974
Log
mean
Mean
Ts
s Figures
A&no
(days) represent
the
primary
lung
UndifSeeventiated
cancer*
Oat
3
2 24
12
12
111
60
42
5
5.084 kO.815 161
4.456 20.596 86
3.362 kO.540 29
number
Other
Total
12
9
7
1
of tumours
4 2 27
3
36 11 10 16
4.476 kO.725 88
TZ
for
1
3 2 21
Total
times
5
3 1 4
60 22 12 67
2
34
10
228
2
23
8
-
4.621 kO.791 102
measured
(geometric) is 3.1 cm. The larger series of Steele and Buell(l973) has not been included because they selected tumours under 6.0 cm in diameter. However, the mean size of the 303 peripheral tumours is 3.0 cm, which agrees well with the other series. Two large surgical series (Slack et al. 1972; Soorae & Abbey-Smith 1977) have reported tumour size and this is given as greatest diameter. These show a mean greatest diameter of 4.0 cm from a total of 1282 cases. Most tumours are not spherical, but wedge-shaped or 24 22 20 18 16 Number of Turnour
14 12 s
10 8 6 4 2 1 2
3
4
5
6
Tumour Fig. 3. Distribution of sizes of 90 primary Meyer (1973), Schwartz (1961) and Weiss
lung tumours (1971)
‘7 8
9 10 11 12 13 14 15
Diameter at diagnosis.
(cm) Data
fromChahinian
(1972),
6
D. M. Geddes
cylindrical, and a cylinder 4 cm by 2 cm has the same volume as a 3 cm sphere. The mean diameter of 3.1 cm from Fig. 3 therefore agrees well with the surgical series. We have taken this distribution of sizes to be reasonably representative of tumours at diagnosis. Tumour mass at death. Direct measurements of total tumour mass are impossible because the total mass of microscopic metastases is unknown. However, from the tumour growth diagram in Fig. 1 it can be deduced that death will occur within a relatively narrow range of doubling times. After 35 doublings, a 4 cm diameter tumour with a total mass of about 30 g is most unlikely to cause death unless it is in some critical site. At the other end of the scale, after 45 doublings, a tumour will have a total mass of 32 kg at which time survival is inconceivable. Death will therefore occur sometime between these two extremes, A total tumour mass of 1 kg has generally been taken to cause death and this is equivalent to 40 tumour doublings. The three series reported which allow the calculation to be made all show the mean time of death to occur very close to 40 doublings (Table III). Obviously, there will be some variation about this mean figure with some patients dying with small critically placed metastases, while others survive with massive intrathoracic tumours. However, the variation in terms of doublings will be small. Table III.
Number
Breur 1966 Schwartz 1961 Spratt and Spratt 1964 Calculation.
of volume
doublings
Lung metastases Lung primary Lung metastases
at death ?a
Mean daub&s to death
79 13 118
39.5 41 39
Na =number of volume doublings to reach a tumour diameter dcm = 10 loglod + 30,. Volume doublings at death = Nd + survival from d&Tz.
We have used these data on doubling times, tumour size and tumour mass at death to calculate the natural history of lung cancer. This is summarized in Table IV. If all the doubling times of lung cancer in the literature are pooled, then the time from malignant change to diagnosis is about 10 years, and following diagnosis, the average time to death is about 18 months. PREDICTED SURVIVAL
The simplest situation is to consider a single tumour with a known doubling time and size. Predicted survival can be calculated from Fig. 4. This shows that both size and doubling time have a profound influence on survival. For example, a tumour with the average doubling time of 100 days will cause death within four months if it is diagnosed when its diameter has reached 8 cm, but the same tumour diagnosed as a 1 cm nodule would not be expected to cause death for nearly three years. Similarly, a 2 cm cancer will cause death in seven months when it has a doubling time of 30 days (e.g. an oat-cell carcinoma) while a patient with the same sized tumour with a doubling time of 300 days (e.g. a slow-growing adenocarcinoma) will survive for over five years without treatment.
Natural Table IV. Natural
History of Lung Cancer history
of untreated
7
lung cancer
Yeavs from malignant Histology
n
Squamous Adenocarcinoma Undifferentiated Miscellaneous All Oat cell
111 60 44 8 228 5
change to
Mean Ts (days)
Earliest Diagnosis (1 cm)
Usual Diagnosis (3 cm)
Death (10 cm)
88 161 86 102 29
7.2 13.2 7.1 8.4 2.4
8.4 15.4 8.2 9.8 2.8
9.6 17.6 9.4 11.2 3.2
Any group of tumours will have a range of sizes and doubling times. Predicted survival curves from time of diagnosis for different sized tumours based on the distribution of doubling times in Table II are shown in Fig. 5. By combining these curves according to the distribution of tumour sizes at diagnosis from Fig. 3 predicted survival curves from diagnosis can be calculated. These are shown in Fig. 6. This represents the survival of an overall group of patients with lung cancer. The curves for different histological
120
0.5cm /
1
P
80 I 70-
Predicted Survival (months)
6050-
/
50 Fig. 4. Predicted predicted survival
lcm /
100 150 200 250 Doubling Time
2cm
3cm
4cm
/
300 350
400
survival for tumours according to size and doubling time. Calculation: to 40 volume doublings is (40- Nd)Tz, i.e., lOT2 (1 - logrod)
The
D. M. Geddes
123456789 Years Fig. 5. Predicted survival To survive to time t,
curves from time of diagnosis
for different
tumour
sizes. CuZcuZution:
t Tz%O(lFrom the distribution of doubling calculated for each value of t
log1od)
times in Table
II, the percentage
with
equal or longer
Ts is
types of tumour show marked differences with adenocarcinomas surviving longer than squamous tumours. Oat-cell carcinomas have been included, but because of the paucity of data, the curve is at best approximate. CLINICAL CORRELATIONS Long latent period This is at first sight surprising but helps to explain some of the puzzling features of the disease. Date of the first abnormal chest radiograph. Direct evidence comes from the study of Rigler et al. (1953) who questioned the relatives and doctors of 264 patients with lung cancer in order to find out how many had had previous chest radiographs. Fifty such patients were identified and the old films were then reviewed. Radiographic abnormalities which long preceded diagnosis were found in most cases. One patient lived nine years from the first radiographic change to operation and another had a peripheral carcinoma visible on radiography more than four years before his first symptom. In the 13 patients with operable disease, the first radiographic abnormality preceded surgery by an average of three years.
Natural
History of Lung Cancer
-
l
-
Adenocarcinoma
-
All
l
9
l
l
-----
Squamous l
l
Undifferentiated (-jat
Percent Survival
1234j6j89 Years Fig. 6. Predicted survival curves from time of diagnosis according to histology. Calculation: survival curves in Fig. 5 were combined according to the distribution of sizes in Fig. 3
The
Age at onset. Table IV suggests that lung cancer is diagnosed on average about 10 years after malignant change has occurred. Since the peak incidence of the disease is at the age of 60, malignant change must occur around the age of 50. Since a smoker usually starts in his teens, he smokes for about 30 years without developing the disease. The long delay between application of the carcinogen and malignant change is puzzling. It suggests that prolonged stimulation is necessary to produce malignancy or that there is some efficient anti-tumour defence system which becomes less effective with age. Increasing inefficiency of immunosurveillance might be responsible. In practice, it means that a young smoker who gives up the habit after 10 years of smoking should have only a very slight risk of developing lung cancer. It is therefore interesting that Doll and Peto (1976) showed no increased risk of the disease in doctors who stopped smoking before the age of 30. Age and aggressiveness of cancer. If two men both develop malignant change at the age of 40 years, and doubling time of one tumour is 30 days and of the other 300 days, then the fast-growing tumour will present after about three years, while the slow-growing tumour will present after 30 years. So one man will have an aggressive cancer at the age of 43 years, while the other will have relatively benign disease at the age of 70 years. This accords well with clinical experience of lung cancer. Steele and Buell (1973) showed that lung cancer in young patients had shorter doubling times. Recurrent cancer after surgery. Usually a patient is considered cured if he is free of disease five years after his operation. However, reports of long follow-up after surgery are
10
D. M, Geddes
littered with ‘second’, and ‘third’ and even ‘fourth’ primaries (Shields & Robinette 1973; Abbey-Smith et al. 1976). Two observations suggest that many second primaries are recurrences. First, the incidence of second ‘primaries’ seems to fall off with time, so that after 10 years, they are almost unknown. This 10 years is the time needed for a single malignant cell left at operation to grow to a diagnosable tumour. Secondly, the later the ‘second primary’ develops, the more benign it appears to be. This is to be expected if the ‘second primary’ is a recurrence: the reason it presents late is precisely because it grows slowly. Table
V.
Lung cancer deaths after stopping
Years after stopping smoking
Deaths in ex-smokers divided by No. expected non-smokers -
Observed* 0 <5 5-9 10-14 215
smoking in
Predicted
15.8
-
16.0 5.9 5.3 2.0
15 11 6 2
i(: Doll and Peto (1976). For 100 deaths occurring at year 0 the number of tumours beginning in each preceding year were calculated from the distribution of doubling times (time to death =40 x T2). For each year after stopping smoking the contribution of the preceding year to total deaths was deleted. Total deaths expected in each year were then compared with those in year 0 and the 16: 1 risk reduced accordingly. For this calculation adenocarcinomas were excluded since they are not associated with smoking. Calculation.
Stopping smoking. After stopping smoking, the risk of lung cancer remains high for some time and is still nearly twice that of life-time non-smokers after 1.5 years (Doll & Peto 1976). Table V shows the increased risk of lung cancer for ex-smokers according to the number of years they have stopped smoking and this is very similar to the increased risk as calculated from doubling times. If malignant change stops as soon as smoking stops, more than 10 years are then needed before all tumours which have just begun are large enough to cause death. Survival curves Fig. 6 shows survival curves for all tumours and for each cell type. These curves give an indication of the survival which might be expected in an untreated group of patients with lung cancer. Detailed comparison between these curves and actual survival curves is probably not justified but they illustrate a number of important points. Correlation of survival with cell type. Oat-cell carcinomas have the shortest prognosis while adenocarcinomas have the longest. Squamous cell and undifferentiated carcinomas,
Natural
History of Lung Cancer
11
other than oat-cell, occupy a middle position. This agrees well with the observations of Hyde et al. (1973) on the natural course of inoperable cancer in 7500 patients. Comparison with observed survival jigures. Five-year survival in lung cancer varies from 5 to 9%. This prognosis is similar to that predicted from growth rates. There are two main differences: the predicted survival figures show less early mortality and then after five years the actual survival figures are better. These differences are partly technical, since the distribution of sizes used is likely to be biased towards small tumours and this will reduce early mortality. Also, the time of death is taken as exactly 40 doubling times when in reality this will be distributed between 35 and 4.5 doubling times. The effect of its variation around 40 will be to increase early and reduce late mortality. After allowing for these technical inaccuracies, the better 5-lo-year survival figures obtained in practice may represent the effect of treatment. Such an effect is, however, obviously very small. Slowing of tumour growth is another explanation. The efSect of staging. Staging selects tumours into groups on the basis of size and spread and is likely to select for doubling time as well. Small slow growing tumours will show good survival figures on the basis of natural history alone and these good figures may be falsely attributed to treatment. This is discussed in more detail in the next section. The important conclusion is that survival figures from staged disease must be interpreted with caution. Treatment Radiotherapy and chemotherapy. Trials with untreated controls have been done for radiotherapy and chemotherapy. This is obviously the best method of assessing any therapy and so predicted survival based on growth rates has little extra to offer. Indeed since these trials show that treatment may actually be harmful (Laing et al. 1975) it is difficult to understand why an untreated control group is not considered obligatory. In the absence of controls, growth rates may have some value. Chahinian and Israel (1969) pointed out that a drug may be effective without necessarily making a tumour disappear. The drug may slow the growth rate and so prolong survival. They therefore suggested the concepts of survival gain and volume gain as mathematical tools to evaluate treatments. In summary, this involves calculating the survival of the patient on treatment over and above that predicted from the growth curve of his tumour. This might help investigators to recognize a potentially valuable drug. The theoretical implication of this model of tumour growth is that a treatment killing 99% of all cancer cells in the body will succeed only in reducing 1012 tumour cells to 1010. This is equivalent to about seven volume doublings. An oat-cell tumour with a doubling time of 20 days will therefore have been set back a mere 4-5 months. A 90% cell kill is equivalent to about three doubling times and so the benefit may be almost unnoticeable. Surgery. There are no trials with an untreated control group, but there are a few reports of ‘operable’ patients who have not had surgery. Smart (1966) showed a 22% five-year survival in such patients treated with radiotherapy which suggests that there may be little difference between the two managements. The obvious untreated ‘control’ patients are those who are considered operable but who refuse or are unfit for operation.
12
D. M. Geddes
Surprisingly, there is very little information on such patients in the literature. Boucot et al. (1967) reported 12 such patients from the Philadelphia pulmonary neoplasm research project with a median survival of 19 months, median survival in 23 patients with curative resections was little better at 22 months. Weiss and Boucot (1977) reported 48 patients with lung cancer originating as round tumours, again from the Philadelphia project. After excluding postoperative deaths, there was no difference in terms of survival between resected and unresected cases. Three of the four patients living longer than five years were in the unoperated group. Both these studies can be criticized, the first because of a high operative mortality, the second because of lack of histology in some patients. However, they raise serious doubts about the role of surgery. Selection of patients for surgery. Surgical patients are inevitably highly selected. Limited disease will select for small tumour mass and so the tumour will be further back on its growth curve. Lack of local invasion or distant metastases are likely to select slow-growing tumours both because fast growers metastasize sooner and also because any metastases will be clinically obvious sooner if they grow fast. The delay between first symptom and surgery will allow fast-growing tumours to invade and become ‘inoperable’ while slower-growing tumours will have changed little. Finally, the general condition of the patient will be a reflection of the doubling time of the tumour. Patients who are symptom-free are likely to have tumours with long doubling times (Chahinian 1972). The effect of selecting for slow-growing tumours will be to improve survival figures. This is shown in Fig. 7. Here we have arbitrarily taken the longest 25% of the doubling times in the literature and calculated a survival curve based on tumour growth. By
1
2
3
4
5
6
7
8
9
Years
Fig. 7. Predicted
survival
curves
for
all tumours
and
for
the
25%
with
longest
doubling
times
Natural
13
History of Lung Cancer
selecting patients in this way, 28% five-year survival and 4% ten-year survival can be achieved. Comparison of predicted with actual survival after surgery. The best way to estimate the true effect of surgery is to compare predicted with actual survival in patients in whom tumour size and doubling time have been recorded before operation. Weiss et al. (1966) have reported 18 such patients from the Philadelphia project and Meyer (1973) reported a further 17. The predicted survival of these patients has been taken from Fig. 4 and is compared with their actual survival in Fig. 8. This graph shows that patients dying from recurrent tumour survive only as long as their tumour growth predicts.* In other words surgery, in spite of removing the obvious tumour mass, has not prolonged survival significantly. If only a few cells were left behind at the operation site, then a long latent 120-
*A
A A
110loo-
80. 70Actual Survival (months)
f30-
50s
10
20
30 40
Predicted *Died of Myocardial A = Alive
Fig. 8.
Survival
following
resection
of lung
50
Survival
cancer.
60 70
80
90
(months)
Infarct, Predicted
tumour and
free actual
figures
compared
by least squares regression is between predicted (x) and actual (y) survival PiO.001). Th e s 1ope is significantly different from 1. Patients dying soon after operation survive a little longer than predicted while those dying more than 40 months after operation tend to die earlier than predicted. This may represent early benefit from removal of tumour mass which is later reversed by the tendency of metastases to grow faster than the primary. However, these few observations do not allow any definite conclusions. * The
correlation
y=16+0.6x
(r=0.76,
14
D. M. Geddes
period would be expected before the recurrent tumour was clinically apparent. Late recurrence with improved survival would then be expected. The fact that there is no improvement in survival suggests that a mass of tumour similar to that removed has been left behind. All these operations were ‘curative’, i.e. as far as the surgeon could tell the tumour had been removed completely. The tumour mass left behind must therefore be in the form of distant metastases. It is difficult to avoid the conclusion that in 27 of these 35 patients with small peripheral tumours, distant metastases were present at the time of operation. Eight patients were still alive at the time of the reports. Seven of these are in the top left-hand quarter of the graph, well separated from the patients who died. These represent surgical cures. It is possible that one cell left behind at operation will still lead to a recurrence and death up to 40 doubling times later and a patient cannot be confidently pronounced cured until this time has passed. Of the eight patients alive, only one has lived this long. This analysis is based upon an exponential model of tumour growth. If any primary lung cancers deviate from exponential growth and grow more slowly as they get older, their natural history will be prolonged and they may not cause death for many years, if at all. Such tumours will tend to be operable and so will contribute to surgical survival figures. It is chastening to realize that if only 5% of all tumours were to behave in this way, the majority of five-year survivors could be expected on tumour natural history alone.
CONCLUSIONS
About seven-eighths of a tumour’s life will have passed when it is diagnosed. The vast majority, and perhaps all tumours, will be disseminated at this time. It is therefore not surprising that treatment is so unsuccessful and in particular that local treatment has so little to offer. How then can the dismal picture of lung cancer be improved? Earlier diagnosis Attempts at population screening by chest radiography to detect cases early have proved both costly and ineffective. Many have largely been abandoned. The best that could be expected from such programmes is to diagnose the tumour a few doubling times earlier. Cancer which has been present some 7-10 years before diagnosis is hardly likely to be affected by bringing that date forward a few months. Some much more sensitive technique would be needed to detect a clump of malignant cells 1 mm in diameter. It is clearly unrealistic to expect this sensitivity from chest radiographs or scans. A more optimistic approach is to identify a circulating specific tumour marker, biochemical or immunological. This might allow much earlier diagnosis, but the problems of establishing the relevance of such a marker in an apparently healthy patient are formidable: once established, it is difficult to see what one would do next. Treatment Systemic treatment is needed to treat disseminated disease. When effective drugs or immunotherapy are discovered, it will be logical to use them as early as possible when
Natural
History of Lung Cancer
15
the tumour mass is smallest. The role of surgery may then need to be redefined as another effective means of reducing tumour mass rather than as curative treatment in its own right. Joseph et al. (1971) h ave reported excellent controlled studies of resection of pulmonary metastases from a range of primary tumours. They showed that resection prolonged survival and this was especially striking for tumours with the longest doubling times. Surgery in some of these patients may be reducing tumour mass so much that the patients’ own immunological defences are capable of controlling the remaining disease. In primary lung cancer the place of surgery as an adjunct to effective systemic therapy must remain uncertain until such therapy is discovered. Prevention Lung cancer is a preventable disease. At present it is virtually untreatable and in view of its natural history may remain so. It is, then, easy to see where the bulk of any research effort should be aimed. How can people be persuaded not to start smoking? Once started, how can they be helped to stop? Are there any innocuous alternatives? Is there an identifiable genetic group predisposed to lung cancer? Is there any form of immunotherapy which would prevent the development of the disease rather than treat it when it is too late? Control of the present lung cancer epidemic lies in the answers to these questions. APPENDIX:
THE MATHEMATICS
OF TUMOUR
GROWTH
Exponential model The volume, V, of a sphere diameter, d, is: V= $3 Where a tumour grows from VO to Vt in time t, the volume at time t can be calculated using the exponential coefficient, b: Vt = VO ebt By expressing the volume in terms of diameter (equation
(2) l), equation 2 becomes:
which is:
solving for b: b=3 ~ log& = -3 log (@/do) t log do t Tumour
doubling
time (Ta) is the time for the tumour vt=2vo :. 2V0 = VO ebTz
(3) volume to double, i.e.:
16
D. M. Geddes
solving for Ts log Z=bTs
substituting
for b (equation
3): Ta=
t log 2
3 log h/do
Thus, Ts can be calculated from two diameter measurements, interval t.
do and dt, separated by
Other models As a result of studies with animal tumours, it is evident that the Gompertzian
function
V= Vo exp [s (l-e-at)] describes tumour growth better (Laird 1964) (u = deceleration parameter ; A = growth parameter). This expression is essentially exponential growth with a tendency to decelerate with time. Tumour growth slows as the tumour enlarges. Another approach is the relationship dM/dt = kMb where M is the tumour mass and b the exponent. When b = 1, this represents exponential growth and b = 0 is linear growth. From a study of many hundreds of mouse mammary tumours, Dethlefsen et al. (1968) found a value of b = 0.72 to describe tumour growth best. There are insufficient data to establish whether these more complicated equations describe tumour growth in man. Certainly an exponential model may oversimplify tumour growth, but for the purposes of this review, the simple relationship is preferred. All the more complicated expressions show a slowing of tumour growth with time. This will tend to prolong predicted survival. ACKNOWLEDGEMENTS
I am particularly grateful to David Brown who performed all the calculations, as well as giving invaluable and intelligible mathematical and statistical advice. I am also greatly indebted to Dr L. D. Hill, Dr S. Spiro and Dr Gordon Steele for detailed and constructive criticism of the manuscript, and to Heather Rolls for the speed and accuracy of her typing. REFERENCES ABBEY-SMITH,
Thorax BOLJCOT,
K.
R., NIGAM, 31, 507. R.,
COOPER,
B. K. & THOMPSON, D.
A. & WEISS,
W.
Archs intern. Med. 120, 168. BRENNER, M. W., HOLSTI, L. R. & PERTOLLA,
(1967)
J. M. The
(1976) role
Second
of surgery
primary in the
lung cure
carcinoma.
of lung
cancer.
Y. (1967) The study of graphical analysis of the growth of human tumours and metastases of the lung. Br. J. Cancer 21, 1. BREUR, K. (1966) Growth rate and radiosensitivity of human tumours. Europ. J. Cancer 2, 157. CHAHINIAN, P. & ISRAEL, L. (1969) Survival gain and volume gain. Mathematical tools in evaluating treatments. Europ. J: Cancer 5, 625.
Natural History of Lung Cancer
17
P. (1972) Relationship between tumour doubling time and anatomoclinical features in 50 measurable pulmonary cancers. Chest 61, 340. COLLINS, V. P., LOEFFLER, R. K. & TIVEY, H. (1956) Observations on growth rates of human tumours Am. J. Roent. rad. Ther. 76, 988. DETHLEFSEN, L. A., PREWITT, J. M. S. & MENDELSOHN, M. 1,. (1968) Analysis of tumour growth curves. J. natn. Cancer Inst. 40, 389. DOLL, P. & PETO, R. (1976) Mortality in relation to smoking: 20 years observations on male British doctors. Br. med. J. 2, 1525. GARLAND, L. H. (1966) The rate of growth and apparent duration of primary bronchial cancer. Am.
CHAHINIAN,
J. Roent. GARLAND, L.
rad.
They.
96,
604.
H., COULSON, W. & WOLLIN, E. (1963) The rate of growth and apparent duration of untreated primary bronchial carcinoma. Cancer, N. Y. 16, 694. HYDE, L., WOOLFE, J., MCCRAKEN, S. YESNER, R. (1973) Natural course of inoperable lung cancer.
Chest 64, 309. JOSEPH, W. L., MORTON,
D. I,. & ADKINS, P. C. (1971) Prognostic significance of tumour doubling time in evaluating operability in pulmonary metastatic disease. J. thorac. cardiovusc. Surg. 61, 23. LAING, A. H., BERRY, R. J., NEWMAN, C. R. & PETO, J. (1975) Treatment of inoperable carcinoma of bronchus. Lancet, 2, 1163. LAIRD, A. K. (1964) Dynamics of tumour growth. Br. J. Cancer 18, 490. MEYER, J. A. (1973) Growth rate versus prognosis in resected primary bronchogenic cancer. Cancer, MILLER, A.
N.Y.
31,
1468.
B., Fox, W. & TALL, R. (1969) MRC comparative trial of surgery and radiotherapy for the primary treatment of oat cell carcinoma of the bronchus. Lancet 2, 979. MORRISON, R., DEELEY, T. J. & CLELAND, W. P. (1963) The treatment of carcinomaof the bronchus. A clinical trial to compare surgery and supervoltage radiotherapy. Lancet 1, 683. RIGLER, L. G., O’LOUGHLIN, B. J. & TUCKER, R. C. (1953) The duration of carcinoma of the lung. Dis. Chest 23, 50. SCHWARTZ, M. (1961)
A biomathematical
approach
to clinical
tumour
growth.
Cancer, N. Y. 14,
1272. T. W. & RORINETTE, C. D. (1973) Long term survivors after resection of bronchial carcinoma. Smgery Gynec. Obstet. 136, 759. SLACK, N. H., CHAMBERLAIN, A. & BROSS, I. D. (1972) Predicting survival following surgery for bronchogenic carcinoma. Chest 62, 433. SMART, J. (1966) Can lung cancer be cured by irradiation alone? r. Am. med. Ass. 195, 1034. SOORAE, A. S. & ABBEY-SMITH, R. (1977) T umour size as a prognostic factor after resection of lung cancer. Thorax 22, 19. SPRATT, J. S. & SPRATT, T. L. (1964) Rates of growth of pulmonary metastases and host survival. Ann. Surg. 159, 161. SPRATT, J. S. & SPRATT, J. A. (1976) The prognostic value of measuring the gross linear radial growth of pulmonary metastases and primary pulmonary cancers. J. thorac. cavdiovasc. Surg.
SHIELDS,
71, 274. STEELE, J. D. & BUELL, Surg. 65, 140.
P. (1973) Asymptomatic
solitary
pulmonary
nodules. J. thorac.
cardiovasc.
WEISS, W. (1971) Peripheral measurable bronchogenic carcinoma: growth rate and period of risk after therapy. Am. Rev. resp. Dis. 103, 198. WEISS, (1974) Tumour doubling time and survival of men with bronchogenic carcinoma. Chest 65, 3. WEISS, W. & BOUCOT, K. R. (1977) Prognosis of lung cancer originating as a round lesion. Am. Rev. resp. Dis. WEISS, W., BOUCOT,
116,
827.
K. R. & COOPER, D. A. (1966) G rowth rate in the detection and prognosis of bronchogenic carcinoma. r. Am. med. Ass. 198, 1246. WEISS, W., BOUCOT, K. R. & COOPER, D. A. (1968) Survival of men with peripheral lung cancer in relation to histologic characteristics and growth rates. Am. Rev. yesp. Dis. 98, 75. 2
Hypothesis THE NATURAL HISTORY A REVIEW BASED ON RATES
OF LUNG CANCER: OF TUMOUR GROWTH
D. M. GEDDES Brompton Hospital, London Out of 100 patients with lung cancer discovered, fewer than 10 will live five years. Eighty will have inoperable disease at the time of diagnosis and most of these will die within three years; only one or two will be alive after five years. The 20 patients with localized disease will have an operation and about six of them will be alive after five years. These statistics have not changed over the past 30 years and this is in spite of many attempts at earlier diagnosis as well as a considerable improvement in operative mortality. In the face of these gloomy statistics there is a surprising lack of information about the natural history of the disease. There are no proper controlled studies of unselected patients in the literature. The few studies which have included an untreated control group have always been done on ‘inoperable’ patients, i.e. those with the most advanced disease. Trials of radiotherapy and chemotherapy show very little, if any, benefit in terms of survival and untreated control patients sometimes do better than those who are treated (Laing et al. 1975). The role of surgery appears at first sight to be better defined. Surgery is better than radiotherapy for squamous but not for oat-cell carcinomas (Morrison et al. 1963 ; Miller et al. 1969). However, since patients with early localized disease are considered to be curable, treatment cannot be withheld in the interests of a controlled trial. The result is that the natural history of limited operable disease is unknown. Radiotherapists and chemotherapists can justifiably complain that their treatment is never given to the patients with the best prospects of cure. Against this background of doubt about the best form of treatment, and certainty that most treatment is ineffective, is the obvious need for a better understanding of the natural history of the disease. Such understanding should help in three ways. First in assessing the true value of existing treatments. Second in judging an individual patient’s prognosis and so in choosing the most appropriate treatment. Third, and most important, in planning a rational search for new and more effective forms of treatment. We have used the considerable literature on tumour growth rates in lung cancer in an attempt to calculate the natural history of the disease. EXPONENTIAL
MODEL
OF TUMOUR
GROWTH
This hypothesis was first suggested by Collins et al. in 1956. The hypothesis assumes a tumour to start from a single cell. This cell then divides to become two cells, each of which divide to become four, eight, sixteen and so on. If this process goes on at a constant rate, then the tumour growth will be exponential and its volume at any time can be easily calculated. The simplest way to describe the growth rate is the volume doubling 1
2
D. M. Geddes
time-the time taken for the tumour volume to double. Exponential tumour growth is analagous to the exponential decay of a radioactive isotope. Growth is described by doubling time where decay is described by half-life. At its simplest, this model predicts that a single cell of 10 pm will become a tumour of 1 mm in diameter after its volume had doubled 20 times. A further ten doublings will produce a tumour of about 1 cm in diameter and after ten more doublings, the tumour will have a diameter of 10 cm with a total mass of 1 kg. This is shown in Fig. 1. This figure shows how a tumour appears to be small and slow-growing for the majority of its lo-
Diameter
5
(cm)
2
4
6
8 10 12 14 16 18 20 22 Number
Time Fig. 1. The life of a solid tumour. time of 1 month takes 40 months 1 year takes 40 years
2426
of Volume
Time is expressed to reach 10 cm
28
30 3234
36 3840
42 44
Doublings +
as volume doublings. diameter, while another
A tumour with a doubling with a doubling time of
life until it reaches a diagnosable size when it appears to grow very rapidly. In fact, the rate of tumour growth is relatively constant throughout its life and compared with other tissues is rather slow. (The vast majority of cancers grow very much more slowly than a human thumb-nail (Spratt & Spratt 1976).) T umour growth is like the reward demanded in the Arabian legend: one grain of corn for the first square on the chess board, two for the next, four for the next, etc. The amount of grain on the sixty-fourth square exceeds the total world production of corn since the beginning of mankind. Tumour doubling time (Ts) for the.model may be calculated from two diameter measurements separated by a known time or more simply may be derived from Fig. 2. The mathematics of the model are discussed in the appendix. 6 Validation
of the model
This model of tumour
growth can be validated in the following
ways:
Measurement of doubling times. If a tumour grows at a constant exponential rate, then its doubling time will be constant. Doubling times have been calculated for many lung tumours, both primary and secondary, from serial chest radiographs. The vast majority of observations show the doubling times of individual tumours to be constant. Whenever doubling times have been shown to change, they tend to become longer towards the end of the tumour’s life. In other words, the tumour growth rate slows as the tumour gets larger. A review of published series shows that SO-90% of tumours grow exponentially.
3
Natural History of Lung Cancer 10 9a76-
-10
5-
- 7
4-
- 6
- 9 - 8
Diameter (cm)
- 5
Number of Doublings
-. 4
- 1 0
12
24
36 48 Days
60
72
84
0
Fig. 2. Chart for measuring tumour doubling time. Tumour diameter is plotted on a logarithmic scale against time. Using the right-hand scale one volume doubling can be marked on the growth curve and the doubling time read from the time scale
Observations on Wilm’s tumour. This elegant study by Collins et al. (1956) formed one of the corner-stones of their hypothesis of exponential growth. An embryonic tumour must have begun at or after the time of conception of the child. The tumour then took a known length of time to manifest itself clinically. The maximum time from one cell to diagnosis is therefore the age of the child at diagnosis plus nine months. If the tumour is then removed surgically and one cell is left behind, this cell continues to grow at the same, rate as the original tumour. After the same time interval, i.e. age at diagnosis plus nine months, any recurrence will be the same size as the original tumour and should be clinically obvious. If the child is well at this time then he is cured. 206 case histories of children with surgically treated Wilm’s tumour were reviewed. The tumour had recurred in 137 children and in every case this was within their theoretical period of risk. Forty-nine patients had been free of disease for longer than the risk period and none of these suffered a recurrence subsequently. Animal studies. Tumour growth rates have been plotted in animals and show exponential growth with a tendency for slowing of growth as the tumour gets large (Dethlefsen et al. 1968). Acceleration of growth is not seen. Some of the tumours studied are very different from naturally occurring disease in man and so these studies have to be interpreted with caution. Nevertheless, the broad principles of exponential growth are confirmed. Objections to the model There are some objections to the exponential
model:
4
D. M. Geddes
Doubling times may not be constant during the microscopic period of tumour growth. Some tumours have doubling times which are so long that back extrapolation provides the absurd conclusion that the tumour began many years before the individual was conceived. This is probably a reflection of the slowing of tumour growth with size referred to above. This applies to only a few tumours but nonetheless estimates of starting time of a tumour by back extrapolation must be seen as only approximate. This objection is less important for extrapolation forward over a few tumour doublings. Metastases. Can observations on the primary tumours be applied to its metastases? Metastases seem, in general, to grow faster than their primary. The evidence for this is limited and information for primary lung tumours very scanty indeed (Brenner et al. 1967). Nevertheless, variation in growth rates between the primary and metastatic tumour will introduce inaccuracy into any calculations based on the growth of the primary alone. This inaccuracy will be greater for oat-cell tumours, which metastasize widely early, than for squamous and adenocarcinomas. The exponential model then fits the observed facts reasonably well. Exceptions will occur when the centre of a tumour breaks down, when tumours are under hormonal control, as a result of treatment and, rarely, when spontaneous regression occurs. From this model the natural history of a tumour can be calculated by extrapolation. Extrapolating back in time gives an approximate date for malignant change (when the first malignant cell arose) ; while extrapolation forward to a total of 40 doublings, when there will be about 1 kg of tumour, gives an approximate date of death. This is summarized in Table I. Table I. The natural
history
of a solid tumour
Doublings
Cells
Diameter
0 20 30 35 40
1 106 109
10 pm 1 mm 1 cm 3 cm 10 cm
l()lO*5
1012
which
grows exponentially
Microscopic Microscopic Detectable on chest radiograph Average diagnosis Death
Calculating the natuural history To do these calculations, three properties of tumour need to be known: doubling time, size and total tumour mass at death. Doubling time. Reports of doubling times of 228 primary lung cancers in the literature are listed by cell type in Table II. Doubling times show a log-normal distribution and so the geometric mean and standard deviation have been calculated. The distribution of histological types among these 228 reported tumours shows 48% squamous, 26% adeno-, 19% undifferentiated carcinoma and 7% miscellaneous. This distribution is relatively close to the overall incidence of different cell types in lung cancer. Size.
from
Fig. 3 shows the distribution of sizes of peripheral tumours at diagnosis taken four published series. This distribution is log-normal and the mean diameter
Natural History of Lung Cancer Table II. Reports
of doubling
Squamous Brenner et al. 1967 Breur 1966 Chahinian 1972 Garland et al. 1963 and Garland 1966 Meyer 1973 Schwartz 1961 Steele and Buell 1973 Weiss et al. 1966 and Weiss 1974
Log
mean
Mean
Ts
s Figures
A&no
(days) represent
the
primary
lung
UndifSeeventiated
cancer*
Oat
3
2 24
12
12
111
60
42
5
5.084 kO.815 161
4.456 20.596 86
3.362 kO.540 29
number
Other
Total
12
9
7
1
of tumours
4 2 27
3
36 11 10 16
4.476 kO.725 88
TZ
for
1
3 2 21
Total
times
5
3 1 4
60 22 12 67
2
34
10
228
2
23
8
-
4.621 kO.791 102
measured
(geometric) is 3.1 cm. The larger series of Steele and Buell(l973) has not been included because they selected tumours under 6.0 cm in diameter. However, the mean size of the 303 peripheral tumours is 3.0 cm, which agrees well with the other series. Two large surgical series (Slack et al. 1972; Soorae & Abbey-Smith 1977) have reported tumour size and this is given as greatest diameter. These show a mean greatest diameter of 4.0 cm from a total of 1282 cases. Most tumours are not spherical, but wedge-shaped or 24 22 20 18 16 Number of Turnour
14 12 s
10 8 6 4 2 1 2
3
4
5
6
Tumour Fig. 3. Distribution of sizes of 90 primary Meyer (1973), Schwartz (1961) and Weiss
lung tumours (1971)
‘7 8
9 10 11 12 13 14 15
Diameter at diagnosis.
(cm) Data
fromChahinian
(1972),
6
D. M. Geddes
cylindrical, and a cylinder 4 cm by 2 cm has the same volume as a 3 cm sphere. The mean diameter of 3.1 cm from Fig. 3 therefore agrees well with the surgical series. We have taken this distribution of sizes to be reasonably representative of tumours at diagnosis. Tumour mass at death. Direct measurements of total tumour mass are impossible because the total mass of microscopic metastases is unknown. However, from the tumour growth diagram in Fig. 1 it can be deduced that death will occur within a relatively narrow range of doubling times. After 35 doublings, a 4 cm diameter tumour with a total mass of about 30 g is most unlikely to cause death unless it is in some critical site. At the other end of the scale, after 45 doublings, a tumour will have a total mass of 32 kg at which time survival is inconceivable. Death will therefore occur sometime between these two extremes, A total tumour mass of 1 kg has generally been taken to cause death and this is equivalent to 40 tumour doublings. The three series reported which allow the calculation to be made all show the mean time of death to occur very close to 40 doublings (Table III). Obviously, there will be some variation about this mean figure with some patients dying with small critically placed metastases, while others survive with massive intrathoracic tumours. However, the variation in terms of doublings will be small. Table III.
Number
Breur 1966 Schwartz 1961 Spratt and Spratt 1964 Calculation.
of volume
doublings
Lung metastases Lung primary Lung metastases
at death ?a
Mean daub&s to death
79 13 118
39.5 41 39
Na =number of volume doublings to reach a tumour diameter dcm = 10 loglod + 30,. Volume doublings at death = Nd + survival from d&Tz.
We have used these data on doubling times, tumour size and tumour mass at death to calculate the natural history of lung cancer. This is summarized in Table IV. If all the doubling times of lung cancer in the literature are pooled, then the time from malignant change to diagnosis is about 10 years, and following diagnosis, the average time to death is about 18 months. PREDICTED SURVIVAL
The simplest situation is to consider a single tumour with a known doubling time and size. Predicted survival can be calculated from Fig. 4. This shows that both size and doubling time have a profound influence on survival. For example, a tumour with the average doubling time of 100 days will cause death within four months if it is diagnosed when its diameter has reached 8 cm, but the same tumour diagnosed as a 1 cm nodule would not be expected to cause death for nearly three years. Similarly, a 2 cm cancer will cause death in seven months when it has a doubling time of 30 days (e.g. an oat-cell carcinoma) while a patient with the same sized tumour with a doubling time of 300 days (e.g. a slow-growing adenocarcinoma) will survive for over five years without treatment.
Natural Table IV. Natural
History of Lung Cancer history
of untreated
7
lung cancer
Yeavs from malignant Histology
n
Squamous Adenocarcinoma Undifferentiated Miscellaneous All Oat cell
111 60 44 8 228 5
change to
Mean Ts (days)
Earliest Diagnosis (1 cm)
Usual Diagnosis (3 cm)
Death (10 cm)
88 161 86 102 29
7.2 13.2 7.1 8.4 2.4
8.4 15.4 8.2 9.8 2.8
9.6 17.6 9.4 11.2 3.2
Any group of tumours will have a range of sizes and doubling times. Predicted survival curves from time of diagnosis for different sized tumours based on the distribution of doubling times in Table II are shown in Fig. 5. By combining these curves according to the distribution of tumour sizes at diagnosis from Fig. 3 predicted survival curves from diagnosis can be calculated. These are shown in Fig. 6. This represents the survival of an overall group of patients with lung cancer. The curves for different histological
120
0.5cm /
1
P
80 I 70-
Predicted Survival (months)
6050-
/
50 Fig. 4. Predicted predicted survival
lcm /
100 150 200 250 Doubling Time
2cm
3cm
4cm
/
300 350
400
survival for tumours according to size and doubling time. Calculation: to 40 volume doublings is (40- Nd)Tz, i.e., lOT2 (1 - logrod)
The
D. M. Geddes
123456789 Years Fig. 5. Predicted survival To survive to time t,
curves from time of diagnosis
for different
tumour
sizes. CuZcuZution:
t Tz%O(lFrom the distribution of doubling calculated for each value of t
log1od)
times in Table
II, the percentage
with
equal or longer
Ts is
types of tumour show marked differences with adenocarcinomas surviving longer than squamous tumours. Oat-cell carcinomas have been included, but because of the paucity of data, the curve is at best approximate. CLINICAL CORRELATIONS Long latent period This is at first sight surprising but helps to explain some of the puzzling features of the disease. Date of the first abnormal chest radiograph. Direct evidence comes from the study of Rigler et al. (1953) who questioned the relatives and doctors of 264 patients with lung cancer in order to find out how many had had previous chest radiographs. Fifty such patients were identified and the old films were then reviewed. Radiographic abnormalities which long preceded diagnosis were found in most cases. One patient lived nine years from the first radiographic change to operation and another had a peripheral carcinoma visible on radiography more than four years before his first symptom. In the 13 patients with operable disease, the first radiographic abnormality preceded surgery by an average of three years.
Natural
History of Lung Cancer
-
l
-
Adenocarcinoma
-
All
l
9
l
l
-----
Squamous l
l
Undifferentiated (-jat
Percent Survival
1234j6j89 Years Fig. 6. Predicted survival curves from time of diagnosis according to histology. Calculation: survival curves in Fig. 5 were combined according to the distribution of sizes in Fig. 3
The
Age at onset. Table IV suggests that lung cancer is diagnosed on average about 10 years after malignant change has occurred. Since the peak incidence of the disease is at the age of 60, malignant change must occur around the age of 50. Since a smoker usually starts in his teens, he smokes for about 30 years without developing the disease. The long delay between application of the carcinogen and malignant change is puzzling. It suggests that prolonged stimulation is necessary to produce malignancy or that there is some efficient anti-tumour defence system which becomes less effective with age. Increasing inefficiency of immunosurveillance might be responsible. In practice, it means that a young smoker who gives up the habit after 10 years of smoking should have only a very slight risk of developing lung cancer. It is therefore interesting that Doll and Peto (1976) showed no increased risk of the disease in doctors who stopped smoking before the age of 30. Age and aggressiveness of cancer. If two men both develop malignant change at the age of 40 years, and doubling time of one tumour is 30 days and of the other 300 days, then the fast-growing tumour will present after about three years, while the slow-growing tumour will present after 30 years. So one man will have an aggressive cancer at the age of 43 years, while the other will have relatively benign disease at the age of 70 years. This accords well with clinical experience of lung cancer. Steele and Buell (1973) showed that lung cancer in young patients had shorter doubling times. Recurrent cancer after surgery. Usually a patient is considered cured if he is free of disease five years after his operation. However, reports of long follow-up after surgery are
10
D. M, Geddes
littered with ‘second’, and ‘third’ and even ‘fourth’ primaries (Shields & Robinette 1973; Abbey-Smith et al. 1976). Two observations suggest that many second primaries are recurrences. First, the incidence of second ‘primaries’ seems to fall off with time, so that after 10 years, they are almost unknown. This 10 years is the time needed for a single malignant cell left at operation to grow to a diagnosable tumour. Secondly, the later the ‘second primary’ develops, the more benign it appears to be. This is to be expected if the ‘second primary’ is a recurrence: the reason it presents late is precisely because it grows slowly. Table
V.
Lung cancer deaths after stopping
Years after stopping smoking
Deaths in ex-smokers divided by No. expected non-smokers -
Observed* 0 <5 5-9 10-14 215
smoking in
Predicted
15.8
-
16.0 5.9 5.3 2.0
15 11 6 2
i(: Doll and Peto (1976). For 100 deaths occurring at year 0 the number of tumours beginning in each preceding year were calculated from the distribution of doubling times (time to death =40 x T2). For each year after stopping smoking the contribution of the preceding year to total deaths was deleted. Total deaths expected in each year were then compared with those in year 0 and the 16: 1 risk reduced accordingly. For this calculation adenocarcinomas were excluded since they are not associated with smoking. Calculation.
Stopping smoking. After stopping smoking, the risk of lung cancer remains high for some time and is still nearly twice that of life-time non-smokers after 1.5 years (Doll & Peto 1976). Table V shows the increased risk of lung cancer for ex-smokers according to the number of years they have stopped smoking and this is very similar to the increased risk as calculated from doubling times. If malignant change stops as soon as smoking stops, more than 10 years are then needed before all tumours which have just begun are large enough to cause death. Survival curves Fig. 6 shows survival curves for all tumours and for each cell type. These curves give an indication of the survival which might be expected in an untreated group of patients with lung cancer. Detailed comparison between these curves and actual survival curves is probably not justified but they illustrate a number of important points. Correlation of survival with cell type. Oat-cell carcinomas have the shortest prognosis while adenocarcinomas have the longest. Squamous cell and undifferentiated carcinomas,
Natural
History of Lung Cancer
11
other than oat-cell, occupy a middle position. This agrees well with the observations of Hyde et al. (1973) on the natural course of inoperable cancer in 7500 patients. Comparison with observed survival jigures. Five-year survival in lung cancer varies from 5 to 9%. This prognosis is similar to that predicted from growth rates. There are two main differences: the predicted survival figures show less early mortality and then after five years the actual survival figures are better. These differences are partly technical, since the distribution of sizes used is likely to be biased towards small tumours and this will reduce early mortality. Also, the time of death is taken as exactly 40 doubling times when in reality this will be distributed between 35 and 4.5 doubling times. The effect of its variation around 40 will be to increase early and reduce late mortality. After allowing for these technical inaccuracies, the better 5-lo-year survival figures obtained in practice may represent the effect of treatment. Such an effect is, however, obviously very small. Slowing of tumour growth is another explanation. The efSect of staging. Staging selects tumours into groups on the basis of size and spread and is likely to select for doubling time as well. Small slow growing tumours will show good survival figures on the basis of natural history alone and these good figures may be falsely attributed to treatment. This is discussed in more detail in the next section. The important conclusion is that survival figures from staged disease must be interpreted with caution. Treatment Radiotherapy and chemotherapy. Trials with untreated controls have been done for radiotherapy and chemotherapy. This is obviously the best method of assessing any therapy and so predicted survival based on growth rates has little extra to offer. Indeed since these trials show that treatment may actually be harmful (Laing et al. 1975) it is difficult to understand why an untreated control group is not considered obligatory. In the absence of controls, growth rates may have some value. Chahinian and Israel (1969) pointed out that a drug may be effective without necessarily making a tumour disappear. The drug may slow the growth rate and so prolong survival. They therefore suggested the concepts of survival gain and volume gain as mathematical tools to evaluate treatments. In summary, this involves calculating the survival of the patient on treatment over and above that predicted from the growth curve of his tumour. This might help investigators to recognize a potentially valuable drug. The theoretical implication of this model of tumour growth is that a treatment killing 99% of all cancer cells in the body will succeed only in reducing 1012 tumour cells to 1010. This is equivalent to about seven volume doublings. An oat-cell tumour with a doubling time of 20 days will therefore have been set back a mere 4-5 months. A 90% cell kill is equivalent to about three doubling times and so the benefit may be almost unnoticeable. Surgery. There are no trials with an untreated control group, but there are a few reports of ‘operable’ patients who have not had surgery. Smart (1966) showed a 22% five-year survival in such patients treated with radiotherapy which suggests that there may be little difference between the two managements. The obvious untreated ‘control’ patients are those who are considered operable but who refuse or are unfit for operation.
12
D. M. Geddes
Surprisingly, there is very little information on such patients in the literature. Boucot et al. (1967) reported 12 such patients from the Philadelphia pulmonary neoplasm research project with a median survival of 19 months, median survival in 23 patients with curative resections was little better at 22 months. Weiss and Boucot (1977) reported 48 patients with lung cancer originating as round tumours, again from the Philadelphia project. After excluding postoperative deaths, there was no difference in terms of survival between resected and unresected cases. Three of the four patients living longer than five years were in the unoperated group. Both these studies can be criticized, the first because of a high operative mortality, the second because of lack of histology in some patients. However, they raise serious doubts about the role of surgery. Selection of patients for surgery. Surgical patients are inevitably highly selected. Limited disease will select for small tumour mass and so the tumour will be further back on its growth curve. Lack of local invasion or distant metastases are likely to select slow-growing tumours both because fast growers metastasize sooner and also because any metastases will be clinically obvious sooner if they grow fast. The delay between first symptom and surgery will allow fast-growing tumours to invade and become ‘inoperable’ while slower-growing tumours will have changed little. Finally, the general condition of the patient will be a reflection of the doubling time of the tumour. Patients who are symptom-free are likely to have tumours with long doubling times (Chahinian 1972). The effect of selecting for slow-growing tumours will be to improve survival figures. This is shown in Fig. 7. Here we have arbitrarily taken the longest 25% of the doubling times in the literature and calculated a survival curve based on tumour growth. By
1
2
3
4
5
6
7
8
9
Years
Fig. 7. Predicted
survival
curves
for
all tumours
and
for
the
25%
with
longest
doubling
times
Natural
13
History of Lung Cancer
selecting patients in this way, 28% five-year survival and 4% ten-year survival can be achieved. Comparison of predicted with actual survival after surgery. The best way to estimate the true effect of surgery is to compare predicted with actual survival in patients in whom tumour size and doubling time have been recorded before operation. Weiss et al. (1966) have reported 18 such patients from the Philadelphia project and Meyer (1973) reported a further 17. The predicted survival of these patients has been taken from Fig. 4 and is compared with their actual survival in Fig. 8. This graph shows that patients dying from recurrent tumour survive only as long as their tumour growth predicts.* In other words surgery, in spite of removing the obvious tumour mass, has not prolonged survival significantly. If only a few cells were left behind at the operation site, then a long latent 120-
*A
A A
110loo-
80. 70Actual Survival (months)
f30-
50s
10
20
30 40
Predicted *Died of Myocardial A = Alive
Fig. 8.
Survival
following
resection
of lung
50
Survival
cancer.
60 70
80
90
(months)
Infarct, Predicted
tumour and
free actual
figures
compared
by least squares regression is between predicted (x) and actual (y) survival PiO.001). Th e s 1ope is significantly different from 1. Patients dying soon after operation survive a little longer than predicted while those dying more than 40 months after operation tend to die earlier than predicted. This may represent early benefit from removal of tumour mass which is later reversed by the tendency of metastases to grow faster than the primary. However, these few observations do not allow any definite conclusions. * The
correlation
y=16+0.6x
(r=0.76,
14
D. M. Geddes
period would be expected before the recurrent tumour was clinically apparent. Late recurrence with improved survival would then be expected. The fact that there is no improvement in survival suggests that a mass of tumour similar to that removed has been left behind. All these operations were ‘curative’, i.e. as far as the surgeon could tell the tumour had been removed completely. The tumour mass left behind must therefore be in the form of distant metastases. It is difficult to avoid the conclusion that in 27 of these 35 patients with small peripheral tumours, distant metastases were present at the time of operation. Eight patients were still alive at the time of the reports. Seven of these are in the top left-hand quarter of the graph, well separated from the patients who died. These represent surgical cures. It is possible that one cell left behind at operation will still lead to a recurrence and death up to 40 doubling times later and a patient cannot be confidently pronounced cured until this time has passed. Of the eight patients alive, only one has lived this long. This analysis is based upon an exponential model of tumour growth. If any primary lung cancers deviate from exponential growth and grow more slowly as they get older, their natural history will be prolonged and they may not cause death for many years, if at all. Such tumours will tend to be operable and so will contribute to surgical survival figures. It is chastening to realize that if only 5% of all tumours were to behave in this way, the majority of five-year survivors could be expected on tumour natural history alone.
CONCLUSIONS
About seven-eighths of a tumour’s life will have passed when it is diagnosed. The vast majority, and perhaps all tumours, will be disseminated at this time. It is therefore not surprising that treatment is so unsuccessful and in particular that local treatment has so little to offer. How then can the dismal picture of lung cancer be improved? Earlier diagnosis Attempts at population screening by chest radiography to detect cases early have proved both costly and ineffective. Many have largely been abandoned. The best that could be expected from such programmes is to diagnose the tumour a few doubling times earlier. Cancer which has been present some 7-10 years before diagnosis is hardly likely to be affected by bringing that date forward a few months. Some much more sensitive technique would be needed to detect a clump of malignant cells 1 mm in diameter. It is clearly unrealistic to expect this sensitivity from chest radiographs or scans. A more optimistic approach is to identify a circulating specific tumour marker, biochemical or immunological. This might allow much earlier diagnosis, but the problems of establishing the relevance of such a marker in an apparently healthy patient are formidable: once established, it is difficult to see what one would do next. Treatment Systemic treatment is needed to treat disseminated disease. When effective drugs or immunotherapy are discovered, it will be logical to use them as early as possible when
Natural
History of Lung Cancer
15
the tumour mass is smallest. The role of surgery may then need to be redefined as another effective means of reducing tumour mass rather than as curative treatment in its own right. Joseph et al. (1971) h ave reported excellent controlled studies of resection of pulmonary metastases from a range of primary tumours. They showed that resection prolonged survival and this was especially striking for tumours with the longest doubling times. Surgery in some of these patients may be reducing tumour mass so much that the patients’ own immunological defences are capable of controlling the remaining disease. In primary lung cancer the place of surgery as an adjunct to effective systemic therapy must remain uncertain until such therapy is discovered. Prevention Lung cancer is a preventable disease. At present it is virtually untreatable and in view of its natural history may remain so. It is, then, easy to see where the bulk of any research effort should be aimed. How can people be persuaded not to start smoking? Once started, how can they be helped to stop? Are there any innocuous alternatives? Is there an identifiable genetic group predisposed to lung cancer? Is there any form of immunotherapy which would prevent the development of the disease rather than treat it when it is too late? Control of the present lung cancer epidemic lies in the answers to these questions. APPENDIX:
THE MATHEMATICS
OF TUMOUR
GROWTH
Exponential model The volume, V, of a sphere diameter, d, is: V= $3 Where a tumour grows from VO to Vt in time t, the volume at time t can be calculated using the exponential coefficient, b: Vt = VO ebt By expressing the volume in terms of diameter (equation
(2) l), equation 2 becomes:
which is:
solving for b: b=3 ~ log& = -3 log (@/do) t log do t Tumour
doubling
time (Ta) is the time for the tumour vt=2vo :. 2V0 = VO ebTz
(3) volume to double, i.e.:
16
D. M. Geddes
solving for Ts log Z=bTs
substituting
for b (equation
3): Ta=
t log 2
3 log h/do
Thus, Ts can be calculated from two diameter measurements, interval t.
do and dt, separated by
Other models As a result of studies with animal tumours, it is evident that the Gompertzian
function
V= Vo exp [s (l-e-at)] describes tumour growth better (Laird 1964) (u = deceleration parameter ; A = growth parameter). This expression is essentially exponential growth with a tendency to decelerate with time. Tumour growth slows as the tumour enlarges. Another approach is the relationship dM/dt = kMb where M is the tumour mass and b the exponent. When b = 1, this represents exponential growth and b = 0 is linear growth. From a study of many hundreds of mouse mammary tumours, Dethlefsen et al. (1968) found a value of b = 0.72 to describe tumour growth best. There are insufficient data to establish whether these more complicated equations describe tumour growth in man. Certainly an exponential model may oversimplify tumour growth, but for the purposes of this review, the simple relationship is preferred. All the more complicated expressions show a slowing of tumour growth with time. This will tend to prolong predicted survival. ACKNOWLEDGEMENTS
I am particularly grateful to David Brown who performed all the calculations, as well as giving invaluable and intelligible mathematical and statistical advice. I am also greatly indebted to Dr L. D. Hill, Dr S. Spiro and Dr Gordon Steele for detailed and constructive criticism of the manuscript, and to Heather Rolls for the speed and accuracy of her typing. REFERENCES ABBEY-SMITH,
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