The authors have declared that no competing interests exist.
Colorectal adenoma are precursor lesions on the pathway to cancer. Their removal in screening colonoscopies has markedly reduced rates of cancer incidence and death. Generic models of adenoma growth and transition to cancer can guide the implementation of screening strategies. But adenoma shape has rarely featured as a relevant risk factor. Against this backdrop we aim to demonstrate that shape influences growth dynamics and cancer risk. Stochastic cell-based models are applied to a data set of 197,347 Bavarian outpatients who had colonoscopies from 2006-2009, 50,649 patients were reported with adenoma and 296 patients had cancer. For multi-stage clonal expansion (MSCE) models with up to three initiating stages parameters were estimated by fits to data sets of all shapes combined, and of sessile (70% of all adenoma), peduncular (17%) and flat (13%) adenoma separately for both sexes. Pertinent features of adenoma growth present themselves in contrast to previous assumptions. Stem cells with initial molecular changes residing in early adenoma predominantly multiply within two-dimensional structures such as crypts. For these cells mutation and division rates decrease with age. The absolute number of initiated cells in an adenoma of size 1 cm is small around 103, related to all bulk cells they constitute a share of about 10−5. The notion of very few proliferating stem cells with age-decreasing division rates is supported by cell marker experiments. The probability for adenoma transiting to cancer increases with squared linear size and shows a shape dependence. Compared to peduncular and flat adenoma, it is twice as high for sessile adenoma of the same size. We present a simple mathematical expression for the hazard ratio of interval cancers which provides a mechanistic understanding of this important quality indicator. We conclude that adenoma shape deserves closer consideration in screening strategies and as risk factor for transition to cancer.
The incidence of colorectal cancer has been markedly reduced by removal of adenoma in screening colonoscopies. Adenoma contain precancerous cells which have already accumulated initial molecular changes on the pathway to cancer. Whereas adenoma size has long been recognized as a major cancer risk factor, the role of adenoma shape has not been studied intensively. Cell-based models ascribe the detected adenoma number and size in large screening cohorts to biological processes of early mutation, cell division, inactivation and transformation to cancer. They link different levels of biological organization which cannot be provided by mere statistical association. With biologically-based modeling we investigate shape-specific features of adenoma development. Model results reveal that adenoma of sessile, peduncular and flat shape exhibit differential growth dynamics, tendency of regression and carcinogenic potential.
Colorectal cancer ranks third in the list of worldwide cancer incidence and is the third leading cause of cancer death in Germany [
Cell-based growth models are closer to biological reality and have been applied to assess the efficiency of different screening approaches or to predict colorectal cancer risk from adenoma detection [
The majority of screening studies were not interested in adenoma shape as a risk factor which determines differential time patterns of growth and transition to cancer. Against this backdrop we hypothesize that consideration of adenoma shape has an impact on screening efficiency. We apply stochastic cell-based growth models and a simple model for transition to cancer to screening data of 197,437 Bavarian outpatients with colonoscopies in the years 2006–2009. We perform combined and separate investigations for sessile, peduncular and flat adenoma of both sexes. For the growth analysis we rely on the mathematical implementation of Dewanji et al. [
By descriptive evaluation of screening data Corley et al. [
Finally, we are investigating a data set out of clinical practice with sufficient detail to prevent the development of colorectal cancer by screening colonoscopy. It was not designed to meet our research aims and therefore has some limitations. Nevertheless, we strive to exploit the available information adequately with MSCE models to characterize the formation of colorectal adenoma and their transition to cancer. Wherever practicable we relate important model results to biological measurements and underline the clinical relevance.
We analyze a subset of 258,116 records from outpatient colonoscopies which were performed by endoscopists as members of the Bavarian Association of Statutory Health Insurance Physicians (BASHIP or Kassenärztliche Vereinigung Bayerns) from January 2006 to December 2009 [
Adenoma counts were reported in three categories of 1, 2–4 or ≥ 5. In the count categories 2–4 and ≥ 5 the number of adenoma was set to 2 and 5, respectively. These are the most probable values under the assumption of Poisson-distributed counts. Under the same assumption the categorical means are estimated to about 2.1 and 5.2 from the recorded data. They came out similar for all shapes so that the bias from estimating counts in categories 2–4 and ≥ 5 can be neglected.
Linear size of adenoma has been grouped into four categories < 0.5, 0.5 − 1, 1 − 2 and > 2 cm. If more than one adenoma was detected only the category of the most advanced adenoma has been reported. Usually the most advanced adenoma acquired the largest size and we make this assumption in the present study. For the remaining adenoma (1 in count category 2–4 and 4 in count category ≥ 5) a size between the detection limit and the upper size bound of the largest adenoma must be assumed.
For the shape-specific analysis we assign the shape of the most advanced adenoma to all reported adenoma in count categories 2–4 and ≥ 5. Here we introduce a miss-classification bias which affects about 13% of patients with higher adenoma counts. We could have avoided miss-classification by analyzing the size distribution of the most advanced adenoma only. But in this case our models would overestimate the adenoma size. Since we are interested in a realistic size for cancer risk estimation we decided to keep miss-classification.
Records with negative adenoma diagnosis have been added to preserve the dependency of the adenoma detection rate (ADR) on age and sex [
In Fig A in
Colorectal cancer cases have been recorded between 2006–2008 and are shown in Table C in
The dominant molecular pathway in 70–80% of colon carcinoma is initiated by mutations in the APC gene [
In other pathways adenoma cells remain diploid with wild-type KRAS status. But they show more diverse molecular changes such as micro-satellite instability (MSI) and epigenetic silencing of the MLH1 gene from DNA methylation [
Colorectal adenoma are pre-neoplastic lesions which originate from
The implementation of the conceptual models is based on the mathematical framework and notation of Dewanji et al. [
The growth model of Dewanji et al. [
The stochastic growth model tracks probabilities for cell numbers per adenoma which accumulate with age, but is not concerned with the spatial distribution of cells. In the present study the unknown cell numbers are uniquely linked to adenoma size
Reference cell numbers
The number of recorded cancer cases in Table C in
Model selection has been based on the three conceptual models for
To identify the preferred models a systematic selection protocol has been executed on three levels. Level I started with estimation of three (
model version | parameter | |||
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Poisson strength/(pre-)initiation [yr−1] | net growth [yr−1] | initiation [-] | ||
- | ||||
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a approximation
b
c unit yr−2
In levels II and III parameter estimates for constant
Since for analysis of ADR and adenoma per colonoscopy (APC) the shape covariable is of lesser clinical importance the results are derived for the model fitted to all shapes combined. The analysis of adenoma size and related cancer risk is presented separately for each shape. CIs from parameter uncertainties in growth models have been omitted for all calculated quantities because they came out generally small.
All analysis has been performed with packages of the R software suite [
Not all biological parameters of the conceptual models from
For fixed attained age the model parameters remain still constant. Since attained age ranges between 55–94 yr and data have been recorded in a short interval for calendar years 2006–09 the age dependences of
Dewanji et al. [
Model parameters are estimated
To speed up the likelihood calculation in categories with more than one adenoma count the approximations of Eq. (S42) were applied. Individual records have been combined for each year of attained age, and for categories of adenoma size and number. Depending on shape the original sex-specific data sets of some 100,000 records shrunk to about 400–500 records without any loss of information. Statistical significance of model parameters were stated based on their p-values on the 95% level.
The deviance
To estimate the two parameters of the transformation rate
Compared to CIs for quantities from the growth models, CIs for cancer hazards from the simple cancer risk models are much larger and are shown where appropriate. For the crude rates 95% CI have been derived by simulation based on the assumption of Poisson-distributed count statistics.
For all three shapes combined and separately models with
Level III models have been further optimized by adjusting the cell number of the detection limit. Goodness-of-fit and model parameters for the preferred level III models of 2d growth are given in Tables G—J in
Parameter age trends are defined in
Results pertaining to APC, ADR and adenoma counts in categories have been derived from the model with
Fig E in
Measured mean number of adenoma per colonoscopy (APC) (top panels) and adenoma detection rate (ADR) (bottom panels) (open circles for 5 yr age groups with 95% CI) compared to the age dependence of APC and ADR (solid lines) expected by the preferred models for women (left panels) and men (right panels), dashed lines for age < 55 yr are model predictions.
Fig F in
Median number of cells per adenoma (top panels) and median adenoma size in cm (bottom panels) for women (left panels) and men (right panels), dashed lines for age < 55 yr are model predictions.
For sessile and flat adenoma 30 initiated cells were identified as the optimal lower bound for the smallest size category of detectable adenoma. With
The extinction of clones with
Shape-specific probability of extinction for clones of initiated cells present at age 60 yr for waiting time ≤ 10yr, clones correspond to adenoma with linear size 0.25, 0.5 and 1 cm for women (top panels) and men (bottom panels).
Parameter estimates and 95% CI for the transformation rate (
Age dependence of the shape-specific hazard from the simple cancer risk model, hazard for all shapes as sum of shape-specific functions (with shaded 95%CI) compared to crude rates for all shapes (point estimates with 95% CI) for women (top panel) and men (bottom panel).
Eq. (S49) defines the transition probability of an adenoma to cancer under the simplified assumption of an age-dependent transformation rate
Shape-specific probability of transition to cancer for adenoma present at age 60 yr with size 0.5, 1 and 2 cm and waiting time up to 10 yr for women (top panels) and men (bottom panels).
Interval cancers are diagnosed during time interval Δ
The expression is valid under the assumption of negligible cancer risk from adenoma created
The product
Comparison of hazard ratios
Shape-specific division rates
Tomasetti and coworkers relate the deceleration in cell division rates to decreasing cancer incidence rates at old age. But they also point to the contribution of ‘weeding out of the susceptible’. We would interpret this contribution as a frailty effect which is an intrinsic feature of MSCE models [
On the other hand, we would not assign the increase in the transformation rate
Estimates of age-dependent APC reproduce the measurements closely in the top panels of
Due to a compensation effect in the two lowest count categories APC estimates reflect the recorded data well. Given the good agreement of the model-expected ADR with more reliable autopsy studies [
Size categories are reported only for the most advanced adenoma. Thus, a comparison of observed and expected size for all adenoma independent from count classification is not possible (Table A in
By demanding biologically feasible division rates
Since the load of precancerous cells in an adenoma influences the risk of transition to cancer a determination of this quantity is of direct clinical relevance. Measurements of low cell numbers with distinct molecular signatures (see Komor et al. [
The extinction probability is considerable for small adenoma of all shapes, but with increasing size extinction becomes nearly impossible (
The shape-specific hierarchy in cancer hazard (
Our models predict transition probabilities proportional to size
Kaminski et al. [
Age dependences of the ADR were very similar for outpatients from Bavaria and California with colonoscopies in overlapping periods of calendar years 2006 to 2008 [
We have presented a comprehensive characterization of adenoma growth and cancer transition risk with shape-specific analysis of screening colonoscopy data. Based on goodness-of-fit MSCE models with modifications tailored to meet the data format for Bavarian outpatients yielded important insights which are summarized below.
Initiated cells in early adenoma of sessile and peduncular shape grow predominantly in 2d areal structures such as crypts. For flat adenoma this issue could not be resolved by goodness-of-fit and growth in 3d structures is equally possible.
In line with measurements from Ki67 staining experiments cell division rates decelerate by about 20–40% for age 55–90 yr. Reduced proliferation might contribute to the attenuation of cancer incidence at old age.
The number of stem cells with initial molecular damage is small in an adenoma. For linear size 1 cm we expect some 103 initiated cells representing a share in the order of 10−5 related to all adenoma cells. These model expectations are supported by marker experiments and can be further validated by molecular measurements.
Early adenoma grow markedly slower than colorectal tumors. The net clonal growth rates in 2d remain < 0.08 yr−1 whereas typical growth rates from fits to cancer incidence data are about twice as high.
The risk for adenoma transiting to cancer shows a pronounced shape dependence. Compared to flat and peduncular adenoma the transition probability for sessile adenoma is about twice as high for the same linear size. For most adenoma transition probabilities increase with squared size.
The hazard ratio for interval cancer serves as a screening quality criterion and has been previously quantified by statistical association. We now provide a mathematical expression based on a simple dependence on mean adenoma number and size which provides a mechanistic explanation.
Biologically-based modeling of adenoma growth and transition to cancer establishes a quantitative link between different levels of biological organization, which in this form cannot be provided by mere statistical association. Macroscopic measurements of adenoma size and number are explained by cell-based processes of molecular damage accumulation, cell division and clonal expansion. Depending on adenoma shape these processes proceed differently. Thus, we conclude that adenoma shape deserves closer consideration in screening strategies and as risk factor for transition to cancer.
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We thank Giorgios T Stathopoulos for making us aware of techniques to measure altered copies of specific genes at low frequencies. Clone size simulations were based on an algorithm developed by Markus Eidemüller. The Bavarian Association of Statutory Health Insurance Physicians (BASHIP) generously supported our study by providing their Bavarian screening data set.