Sage Journals: Discover world-class research

Abstract

Objectives

In addition to invasive breast cancer, mammography screening often detects preinvasive ductal carcinoma in situ (DCIS) lesions. The natural progression of DCIS is largely unknown, leading to uncertainty regarding treatment. The natural history of invasive breast cancer has been studied using screening data. DCIS modeling is more complicated because lesions might progress to clinical DCIS, preclinical invasive cancer, or may also regress to a state undetectable by screening. We have here developed a Markov model for DCIS progression, building on the established invasive breast cancer model.

Methods

We present formulas for the probability of DCIS detection by time since last screening under a Markov model of DCIS progression. Progression rates were estimated by maximum likelihood estimation using BreastScreen Norway data from 1995–2002 for 336,533 women (including 399 DCIS cases) aged 50–69. As DCIS incidence varies by age, county, and mammography modality (digital vs. analog film), a Poisson regression approach was used to align the input data.

Results

Estimated mean sojourn time in preclinical, screening-detectable DCIS phase was 3.1 years (95% confidence interval: 1.3, 7.6) with a screening sensitivity of 60% (95% confidence interval: 32%, 93%). No DCIS was estimated to be non-progressive.

Conclusion

Most preclinical DCIS lesions progress or regress with a moderate sojourn time in the screening-detectable phase. While DCIS mean sojourn time could be deduced from DCIS data, any estimate of preclinical DCIS progressing to invasive breast cancer must include data on invasive cancers to avoid strong, probably unrealistic, assumptions.

Keywords

DCIS breast cancer statistical models cancer screening

Introduction

Breast cancer is the most prevalent women’s cancer worldwide,¹ with early detection by mammography screening being a common health service. In addition to invasive breast cancers, mammography screening detects preinvasive ductal carcinoma in situ (DCIS) lesions.^2,3 DCIS detection by mammography screening varies, typically constituting 10–25% of all mammography detected lesions.⁴ The natural progression of DCIS is largely unknown and optimal treatment is uncertain.⁵ In practice, treatment of screen-detected DCIS is usually similar to that of invasive cancer, to avoid progression to invasive breast cancer.^2,6 While DCIS detection might contribute to reduced breast cancer mortality,^7–9 it may also result in substantial overdiagnosis and overtreatment.¹⁰

Ultimately, results from ongoing randomized active surveillance trials of low-grade DCIS might provide information about optimal DCIS treatments, but the trials are hampered by slow recruitment.^11,12 DCIS progression models based on screening data report varying results.^13–16 These variations might be partly due to a wide range of modeling assumptions. We here propose a new DCIS natural history model without complex model assumptions, to study the basic DCIS progression paths.

Methods

Population and data

Between 1995 and 2004, the Norwegian government initiated a population-based breast cancer screening program,¹⁷ BreastScreen Norway, organized by the Cancer Registry of Norway. BreastScreen Norway started with analog film-based mammography before they gradually changed to digital mammography between 2000 and 2011. Under BreastScreen Norway all women aged 50–69 received a written invitation biennially. Two view screening mammograms were independently evaluated by two readers. At initial screening until 2002, the program collected questionnaires on time since the last mammogram before entering the program (Table 1). We used these questionnaire data from 1995–2002 with varying time since previous mammography, combined with the corresponding screening results, to estimate DCIS progression. During this period, 78% of invited women attended screening, resulting in 364,731 being screened. Among them, 333,304 answered a question about former mammography experience. Of these 333,304 women, DCIS was detected in 399 women.. Time since the last mammography was categorized as 0–1, 1–3, 3–5, or 5+ years (Table 2). As numeric values were needed for the estimation, 0.67, 2, 4, and 6.5 years were chosen as representative points for each interval, as shown in Weedon-Fekjær et al.¹⁸

Table 1.

Description of the applied BreastScreen Norway data.

Target age range (years)	50–69
Attendance rate	78%
Screening test	Two view mammograms independently evaluated by two readers
Study data:
Area	Norway except Oslo^a
Time period	1995–2002
Screened women	333,304
% Digital screening	3.7%
% Below 56 years of age	49%
Invasive cancers	1937^b
DCIS cases	399

Oslo was excluded due to its gradual implementation of digital mammography.

Estimated based on Weedon-Fekjær et al. ¹⁸ with adjustment for observed person years.

Table 2.

Norwegian DCIS detection at screening by time since last mammogram.

Time since last mammogram	Number of DCIS detected (number of screened women)	Relative risk (standard error)
No earlier screening	169 (114,627)	1.0 (Reference)
5 Years+	74 (47,790)	1.10 (1.15)
3–5 Years	45 (43,379)	0.74 (1.18)
1–3 Years	84 (91,765)	0.66 (1.15)
0–1 Year	27 (35,743)	0.54 (1.23)

DCIS: ductal carcinoma in situ

Note: Summarized basic data and Poisson regression estimates of relative risks (adjusted for age, county of residence, and digital versus analog mammography). Data are based on questionnaire data from first screening attendance in BreastScreen Norway between 1995 and 2002.

Natural progression of DCIS and its arrest by screening

As DCIS natural progression is not directly observable, it is studied indirectly using detection rates from repeated mammography. If DCIS progression is slower, with a long sojourn time in the screening-detectable phase, a larger drop in detection rate from initial to subsequent screenings is expected, as many potential cases at subsequent screening have already been detected at the initial screening. At subsequent screening examinations, there will be a combination of new cases, who have progressed to the screening-detectable phase since the previous examination, and old cases overlooked at previous screenings. In practice, the reservoir of overlooked DCIS cases with a longer sojourn time will gradually decline by screening round. Hence, a lower DCIS detection rate will give a larger drop from second to third screening, as fewer earlier overlooked DCIS cases will be available for each added screening round. Overall, the relative DCIS frequencies for subsequent screening rounds contain important information about DCIS progression and screening test sensitivity. While ordinary screening programs have fixed time intervals between screening examinations, our Norwegian questionnaire data, with varying intervals between screening examinations, are especially suited for evaluating models of DCIS progression.

A DCIS progression model

For invasive cancer progression, Markov models are often used to estimate the time tumors spend in the mammography-detectable phase.^19–21 DCIS progression models become more complicated, as preclinical screening-detectable DCIS lesions might progress to clinical DCIS, preclinical invasive breast cancer, or possibly regress to a state not visible on later mammograms. To avoid limiting the potential natural history pathways, our initial model includes all three potential progression pathways in addition to some non-progressive DCIS (Figure 1). However, if some of these progression options are not present, its estimated probability would tend to zero. In practice, this could guide an exclusion of some progression paths.

Figure 1.

Model of DCIS (ductal carcinoma in situ) progression. Given the limited mortality in the study’s age range, other cause mortality was not modelled. We have assumed that all invasive cancers go through an undetectable DCIS phase, but this is not a key modeling assumption as progression in and out of this phase is not estimated.

Formulas for estimating mean sojourn time and screening sensitivity (assuming only progressive tumors)

Markov models characterize cancer progression by modeling the sojourn time in the preclinical screening-detectable phase.^19,22,23 For invasive breast cancer, a constant progression rate by time, equaling exponentially distributed sojourn times, has given a good model fit.^19,21,22 Assuming a (locally) stable disease model, the rate leaving the preclinical screening-detectable phase equals the rate of entering the preclinical screening-detectable phase. Given a mean sojourn time of $1 / λ$ and incidence of cases leaving the preclinical screening-detectable phase of $INC$ , the prevalence of being in the preclinical phase at initial screening becomes $INC \times (1 / λ)$ . This expression represents cases passing through the preclinical screening-detectable DCIS phase with a rate of $INC$ and staying with a mean time of $1 / λ .$ ^18,19 Then, the expected number of screen-detected cases among $N$ initially screened, with a screening test sensitivity of $β$ , is $INC \times (1 / λ) \times N \times β$ . Invasive breast cancers are traditionally considered progressive, making the rate leaving the preclinical screening-detectable phase observable through the incidence of clinical invasive breast cancer prescreening.¹⁹ For DCIS, the rate of leaving the preclinical DCIS phase is not directly observable, and data on repeated screening exams is needed for modeling progression rates. Based on Zelen and Feinleib’s¹⁹ formulas for the probability of detecting invasive cancer at screening, Weedon-Fekjær et al.¹⁸ formulated expressions for the expected detection rate on repeated mammograms by time since last screening. We will here adopt these formulas and extend to DCIS progression, allowing for progression to invasive cancer, progression to clinical DCIS, and regression to a state not visible on repeated mammograms (Figure 1).

Given a mean sojourn time of $\frac{1}{λ}$ , the combined transition rate out of the preclinical screening-detectable DCIS phase to invasive cancer, clinical DCIS and regression becomes $λ$ . Letting INC be the probability of developing a new preclinical DCIS each year, the probability of preclinical screening-detectable DCIS at the initial screening, $A_{1}$ , becomes

A_{1} = P (“ DCIS detectable at screening ” | “ No earlier screening ”) = INC * \frac{1}{λ}

(1)

With a screening test sensitivity of $β$ , the probability of screening-detected DCIS at the initial screening exams is expressed as

P (“ DCIS detected at screening ” | “ No earlier screening ”) = β * A_{1} = β * INC * \frac{1}{λ}

(2)

At second screening, the pool of screening-detectable DCIS is a sum of (i) earlier overlooked DCIS cases still in preclinical screening-detectable phase and (ii) new preclinical DCIS cases which have entered the screening-detectable phase after initial screening. Following the exponential distribution, $e^{- λ * t_{1}}$ of DCIS cases missed at screening $t_{1}$ years ago are still expected to be in the preclinical screening-detectable DCIS phase at the second screening

P (“ Earlier overlooked DCIS still in screening detectable phase ” | “ One screening t_{1} years ago ”) = A_{1} - A_{1} * β * [e^{- λ * t_{1}}] = A_{1} * (1 - β) * e^{- λ * t_{1}} = INC * \frac{1}{λ} * (1 - β) * e^{- λ * t_{1}}

(3)

Assuming a locally stable disease model, the probability of a preclinical screening-detectable DCIS is $INC * \frac{1}{λ}$ in the absence of screening, of which ${1 - e}^{- λ * t_{1}}$ of the DCIS cases are expected to have entered the preclinical phase in the last $t_{1}$ years. As these new post initial screening cases are not impacted by the earlier screening, we have a probability of INC * $\frac{1}{λ} * (1 - e^{- λ * t_{1}})$ of a new post initial screening case being present at first subsequent screening

\begin{array}{l} P (\{\begin{matrix} “New screening detectable DCIS, \\ not detectable t1 years ago” \end{matrix}\}) \\ = INC * \frac{1}{λ} * (1 - e^{- λ * t_{1}}) \end{array}

(4)

Hence, putting equations (2) and (3) together, the probability of being in the preclinical screening-detectable DCIS phase at second screening, $A_{2}$ , $t_{1}$ years after first initial screening, becomes

A_{2} = P (“ DCIS in preclinical screen detectable phase ” | “ One screening t_{1} years ago ”) = P (“ Earlier overlooked DCIS still in screening detectable phase ” | “ One screening t_{1} years ago ”) + P (“ New screening detectable DCIS, not detectable t_{1} years ago ”) = [A_{1} * {(1 - β) * e}^{- λ * t_{1}}] + [A_{1} * (1 - e^{- λ * t_{1}})] = [INC * \frac{1}{λ} * {(1 - β) * e}^{- λ * t_{1}}] + [INC * \frac{1}{λ} * (1 - e^{- λ * t_{1}})]

(5)

Thus, the probability of DCIS detection at second screening becomes

P (“ DCIS detected at screening ” | “ One screening t_{1} years ago ”) = β * ([INC * \frac{1}{λ} * (1 - β) * e^{- λ * t_{1}}] + [INC * \frac{1}{λ} * (1 - e^{- λ * t_{1}})]) = β * [INC * \frac{1}{λ} * (1 - β) * e^{- λ * t_{1}}] + β * [INC * \frac{1}{λ} * (1 - e^{- λ * t_{1}})]

(6)

Then based on equations (2) and (6), the expected relative DCIS detection rate at second versus first screening becomes

\frac{β * [INC * \frac{1}{λ} * (1 - β) * e^{- λ * t_{1}}] + β * [INC * \frac{1}{λ} * (1 - e^{- λ * t_{1}})]}{β * INC * \frac{1}{λ}} = (1 - β) * e^{- λ * t_{1}} + (1 - e^{- λ * t_{1}}) = 1 - β * e^{- λ * t_{1}}

(7)

As progression rates of Markov models are constant by time, Markov models have no memory and the frequency of DCIS available at the third screening will only depend on the number of cases missed at the previous screening exam, time since previous screening exam, and number of new preclinical DCIS since previous screening exam. In practice, formulas for repeated screening exams become recursive. Hence, for a third screening, $t_{2}$ years after second screening, the expected probability of DCIS detection becomes

β * ([A_{2} * {(1 - β) * e}^{- λ * t_{2}}] + [INC * \frac{1}{λ} * (1 - e^{- λ * t_{2}})])

(8)

Hence, resulting in a relative DCIS frequency at third versus initial screening of

\{(1 - β) * e^{- λ * t_{1}} + (1 - e^{- λ * t_{1}})\} * \{(1 - β) * e^{- λ * t_{2}}\} + (1 - e^{- λ * t_{2}}) = (1 - β * e^{- λ * t_{1}}) * (e^{- λ * t_{2}} - β * e^{- λ * t_{2}}) + 1 - e^{- λ * t_{2}}

(9)

Note that both $t_{1}$ , time from initial to second screening, and $t_{2}$ , time from second to third screening, might vary across one dataset. Hence, the detection rate ratios between initial and subsequent screening examinations can be expressed as a function of $t$

\frac{Expected (“ DCIS detection rate at initial screening ”)}{Expected (“ DCIS detection rate at subsequent screening t years after initial screening ”)} = 1 - β * e^{- λ * t}

(10)

With the exponential sojourn times, the rate going out of the preclinical screening-detectable state is constant (“non-memory”). It is, however, possible that the transitions rates might vary by the time spent in the preclinical screening-detectable DCIS state. For the initial and subsequent screening, changing the sojourn time distribution only requires updating the exponential distribution term, $e^{- λ * t_{1}}$ , in equations (3) and (4).

Expanding the model with non-progressive DCIS

The basic model for DCIS progression might be extended, allowing for some non-progressive DCIS being present at initial screening. If we assume a prevalence $A_{nonprog}$ of non-progressive tumors at first screening, an incidence of $A_{nonprog} * β$ should be added to the expected incidence at initial screening, given the same screening sensitivity $β$ as for progressive DCIS. Analogously, an incidence of $A_{nonprog} * {(1 - β)}^{n} * β$ should be added to n^th subsequent screening to account for any non-progressive DCIS not detected at previous screens. Based on this, the proportion of non-progressive DCIS at first screening, $η = \frac{A_{nonprog}}{{A_{1} + A}_{nonprog}}$ , might be estimated. Non-progressive cancers might also appear between screening examinations, but given our data being from only two screening examinations, progressive and non-progressive DCIS appearing after initial screening might not be uniquely separated.

Estimation of transition probabilities

The transition rate from preclinical screening-detectable DCIS to clinical DCIS, $I d (t)$ , can be estimated directly using the incidence of clinical DCIS in the absence of screening (Figure 1) Similar to sojourn times, the transition rate into preclinical screening-detectable DCIS, $W d (t)$ , must be evaluated indirectly. Assuming a steady phase of cancers transiting through preclinical screening-detectable DCIS phase, the expected prevalence, $A_{1}$ , equals the transition rate multiplied by mean sojourn time¹⁹

A_{1} = W d (t) \times (1 / λ)

(11)

Hence, expected incidence, $I_{scr 1}$ , at initial screening becomes

I_{scr 1} = β \times A_{1} = β \times W d (t) \times (1 / λ)

(12)

leading to a transition rate of

W d (t) = \frac{I_{scr 1}}{β \times (1 / λ)} = (I_{scr 1} \times λ) / β

(13)

Three possible progression paths exist for DCIS leaving preclinical screening-detectable DCIS phase, each with different progression rates in our applied Markov model: Progression to clinical DCIS, $I d (t)$ , progression to invasive cancers, $W p (t)$ , and regression to a state not visible on repeated mammograms, $W e (t)$ . The transition rate $I d (t)$ can be directly estimated from prescreening observation data. The other transition rates, $W p (t)$ and $(t)$ , have no unique impact on observed DCIS frequency, and cannot be estimated separately without jointly modeling DCIS and invasive cancers.

Estimation of mean sojourn time and screening sensitivity using maximum likelihood estimation

Based on the expected and observed number of DCIS at screening, model parameters can be estimated by maximum likelihood estimation. Available data from screening registries are, however, an unbalanced mixture of age groups, mammography modalities, and Norwegian counties. DCIS is less frequent than invasive cancer so subgroup analysis used for invasive cancer is not suitable.^21,22 Aiming for a single overall average estimate across the diverse data, we added a Poisson regression step. The data were first analyzed by Poisson regression to adjust for differences in baseline DCIS frequency across different age groups, counties of residence (Akershus, Hordaland, and Rogaland vs. all other study counties), and mammography modalities (digital vs. analog film mammography). The Poisson regression estimates and their covariance were then used in a maximum likelihood estimation, utilization that Poisson regression parameters are asymptotically normal distributed. Given a set of $n$ estimated relative incidences at subsequent screenings, $t_{1}, t_{2}, \dots, t_{n}$ years after initial screening, the likelihood becomes

L (data| | MST, STS) = \prod_{i = 1}^{i = n} f (\overset{{R R}_{t_{i}}}{}| | μ = E ({R R}_{t_{i}}), σ = S E (\overset{{R R}_{t_{i}}}{}))

(14)

where

$\overset{{R R}_{t_{i}}}{}$ is estimated incidence at subsequent screening i relative to initial screening

$E ({R R}_{t_{i}})$ is expected incidence at subsequent screening i relative to initial screening

$S E (\overset{{R R}_{t_{i}}}{})$ is standard error of the $\overset{{R R}_{t_{i}}}{}$ estimate

and

$f (x || μ = μ^, σ = σ^)$ is the normal distribution density at x given mean $μ^$ and standard derivation $σ^$

In practice, maximum likelihood estimates are obtained by maximizing the log-likelihood function

\log \{L (data || MST, STS)\} = \sum_{i = 1}^{i = n} \log \{f (\overset{{R R}_{t_{i}}}{}| | μ = E ({R R}_{t_{i}}), σ = S E (\overset{{R R}_{t_{i}}}{})\}

(15)

Statistical uncertainties associated with both estimation steps were evaluated jointly by bootstrap replications. For the bootstrap, regression coefficients were sampled from a multivariate normal distribution based on the estimated Poisson regression coefficients and their covariance. Based on 10,000 bootstrap replications, 95% percentile bootstrap confidence intervals were calculated. The R statistical package was used for all data management, analysis, and figures.²⁴ Estimating routines were double-checked by testing on simulated data. R code for estimating parameters under the DCIS Markov model with only progressive DCIS is given in the Supplemental Material and on Github (https://haraldwf.github.io/Rmarkdown-pub/DcisProg-EstMet.html), including an example with the Poisson regression estimates from the here given analysis.

Input for estimating model parameters

The Poisson regression adjustment included data regarding age, county of residence, and digital vs. analog mammography (Table 2). Data from Oslo were excluded because of the gradual implementation of digital mammography. County of residence was defined as Akershus, Hordaland, and Rogaland vs. all other study counties, to adjust for higher DCIS rates in the counties where screening was first disseminated.

For estimating the transition rate from preclinical screening-detectable DCIS to clinical DCIS, $I d (t)$ , we applied data on DCIS incidence before screening, from January 1993 to November 1995. Data were analyzed by Poisson regression adjusting for age and county of residence (Akershus, Hordaland, and Rogaland vs. all other study counties), with $I d (t)$ given for the reference group of women 60 years old not living in Akershus, Hordaland, and Rogaland counties.

Results

Model fit and DCIS progression estimates

All preclinical DCIS lesions are estimated to progress or regress, with no non-progressive DCIS present at initial screening (Table 3, model I). Applying the proposed model with no non-progressive DCIS to Norwegian data, we obtained a very good model fit (Figure 2(a)), with a model deviance of 2.16 under 2 degrees of freedom (equaling a chi-square goodness of fit p-value of 0.34). Estimated sojourn time in preclinical DCIS phase before progression or regression was 3.1 years (95% confidence interval; 1.3, 7.6) and mammogram sensitivity was 60% (95% confidence interval; 35%, 93%) (Table 3, model II).

Table 3.

Estimated DCIS progression through preclinical screening with 95% confidence intervals.

Model	Mean sojourn time (in years)	Screening test sensitivity	Rate of clinical DCIS^a	Proportion progressing to clinical DCIS	Proportion non progressive
I	3.1 (1.1, 7.4)	60% (35%, 98%)	8.2 (6.1, 10.4)	0.10% (0.04%, 0.22%)	0.00% (0.00%, 0.14%)
II	3.1 (1.3, 7.6)	60% (35%, 93%)	8.2 (6.0, 10.4)	0.10% (0.04%, 0.22%)	–

DCIS: ductal carcinoma in situ.

Per 100,000 person years.

Figure 2.

Fit of Markov model (II) to Norwegian DCIS data. (a) Observed data with 95% confidence intervals and model fit. (b) Joint 50%, 75% and 95% confidence regions for estimates of DCIS mean sojourn time and screening sensitivity (based on 10,000 bootstrap replications, evaluated on a 20 × 20 square grid using a two-dimensional bivariate normal density kernel).

Generally, mean sojourn time and sensitivity estimates were highly correlated, with long sojourn times coinciding with low sensitivity and vice versa (Figure 2(b)).

To explore beyond the exponential distribution assumption, decreased or increased variance (overdispersion) was added, extending the exponential sojourn time distribution using a gamma distribution.²⁵ Variations in sojourn time distributions had a moderate effect on our estimated mean sojourn time and screening test sensitivity. Best fit was found with a mean sojourn time of 3.7 years, screening test sensitivity 44%, and an estimated 50% lower variation of sojourn times than seen in the exponential distribution (Table 4). Relative to the number of model parameters, the simpler baseline exponential model gave best fit with the lowest Akaike information criterion (AIC).

Table 4.

DCIS progression Markov model (II) with varying degree of spread in sojourn times, using a gamma distribution extension of the basic exponential distribution.

Overspread compared with baseline model	Model deviance (degrees of freedom)	AIC	Mean sojourn time (in years)	Screening test sensitivity (%)
0.4	1.58 (2)	1.71	4.0	41
0.5	1.57 (2)	1.69	3.7	44
0.6	1.62 (2)	1.75	3.6	47
1.0	2.16 (3)	0.29	3.1	60
1.5	2.57 (2)	2.70	2.3	87
2.0	3.11 (2)	3.24	2.5	100

AIC: Akaike information criterion.

Maximum likelihood estimation was fairly straightforward for the Markov model, but as the applied quasi-Newton optimizing method (“L-BFGS-B” in R) needs initialization values, a grid search was conducted confirming the reported estimates.

Estimating mean sojourn time and mammogram sensitivity without Poisson regression adjustment, mean sojourn time was 3.8 years (95% confidence interval; 1.8, 10) and sensitivity 63% (95% confidence interval; 39%, 95%).

For a reference group with a digital mammography screening taken at 60 years of age, in one of the last 15 counties to enter the screening program, progression rates were estimated. The rate of clinical DCIS, $I_{d} (t)$ , was estimated to be 8.2 per 100,000 woman years (95% confidence interval: 6.0, 10.4). Assuming a locally stable DCIS model by age, the rate into the preclinical screening-detectable DCIS phase, $W_{d} (t)$ , would equal the sum of the transition rates leaving the preclinical screening-detectable DCIS phase $W_{e} (t) + W_{p} (t) + I_{d} (t)$ . This transition rate, $W_{d} (t) = W_{e} (t) + W_{p} (t) + I_{d} (t)$ , was estimated as 83 per 100,000 woman years (95% confidence interval: 38, 188). Overall, 10% (95% confidence interval: 4%, 22%) of preclinical screening-detectable DCIS was estimated to progress to clinical DCIS in the absence of screening, with the remainder progressing to invasive cancer or regressing to a state not visible on repeated mammograms.

Discussion

We propose a DCIS progression model with few model assumptions, avoiding complex and uncertain natural history assumptions. As DCIS data usually are much sparser than invasive breast cancer data, we combined Poisson regression and Markov models to adjust for relevant covariables in sparse datasets. To the best of our knowledge, this is the first application of the combined procedure. Applying the model to Norwegian data, the sojourn time distribution was evaluated using six separate data points giving good model fit. We found no evidence of non-progressive DCIS. Estimated mean sojourn time in the preclinical DCIS state was 3.1 years (95%) confidence interval: 1.3, 7.6) with a screening sensitivity of 60% (95%) confidence interval: 35%), 93%).

As an early phase preinvasive condition, DCIS might be considered as slowly progressing. Our estimated mean sojourn time of 3.1 years showed, however, that sojourn time for preclinical DCIS is likely to be short to moderate. This is not very different from the estimated mean sojourn time of 3.9 to 7.9 years for invasive breast cancer based on the same BreastScreen Norway data.^18,21 The few other available estimates of DCIS sojourn time also indicate it to be relatively short,²⁶ with de Gelder et al. estimating a sojourn time of 2.6 years.²⁷ It is possible that sojourn time might be longer in older women or a cohort only screened by digital mammography.^10,18 However, the sparseness of DCIS data does not allow for subgroup analysis. This result implies that moderate screening intervals are needed if we want to detect many DCIS cases. The model also estimated screening test sensitivity. However, Markov model test sensitivity estimates for cancer screening models should be interpreted with caution since no reference tests exist and screening sensitivity is only an internal variable related to the corresponding sojourn time estimate.²¹ Our estimates have wide confidence intervals, even with a moderate number of model parameters. This is in line with general uncertainties associated with DCIS modeling.²⁶

Interestingly, we found no evidence of non-progressive DCIS. There is a possibility that non-progressive DCIS appears in older age, but this is not likely as our data partly cover women up to 69 years of age. Thus, we project that non-progressive DCIS is uncommon.

The progression rate from screening-detectable DCIS to invasive breast cancer, $W p (t)$ , is of high clinical importance as these DCIS lesions should be treated before reaching invasive breast cancer. $W p (t)$ can potentially be estimated by evaluating the long-term incidence of invasive breast cancer after screening introduction, assuming no regressive invasive breast cancers. A high rate of progression to invasive breast cancer implies that many invasive breast cancers go through a screening-detectable DCIS phase, with the possibility of detection as DCIS cases. Hence, following a screening program over time, a lower-than-expected cumulative incidence of invasive breast cancer after screening introduction indicates substantial progression through the screening-detectable DCIS phase. Estimating $W p (t)$ does, however, require large datasets of both invasive breast cancer and DCIS to be followed over time, with and without screening. Some studies suggest that invasive cancers might regress,^28–31 preventing separation of regressive DCIS from regressive invasive breast cancer based on population data. Estimating progression from screening-detectable DCIS to invasive breast cancer, $W p (t)$ , is outside the scope of this work, but the models we have developed might be extended to this setting in future work.

Optimally, our model parameters should be estimated based on randomized trials, but those data are not yet available for DCIS.^11,12 In the absence of randomized data, our Norwegian screening data with mandatory reporting³² on several levels³ is probably an excellent data source. The questionnaire data are, however, more uncertain. Some women will not remember the date of their last mammogram, and there might be substantial variations in mammography frequency across DCIS risk factors. The higher DCIS incidence seen among women with more than five years since last mammogram, compared to women with no earlier mammography, may indicate some selection bias limiting the estimated proportion of non-progressive DCIS. However, the high number of mammograms taken before the public screening program began indicates that also women outside selected risk groups had mammograms taken before the official program. Opportunistic screening might also have affected the observed DCIS incidence before screening.³³ Our questionnaire data indicate substantial levels of opportunistic screening,³³ while incidence trends before screening show moderate signs of screening before the official program began.^18,34

Extending the modeling to DCIS grade and hormonal status would be useful for clinical decision-making. However, this is challenging as there are no suitable data to evaluate the DCIS progression by subtypes. With the currently available data, DCIS modeling by subtype would entail stricter, more questionable, model assumptions, leading to uncertainties regarding the estimated model parameters. Since we were not able to separate DCIS regression from progression to invasive breast cancer, we could not draw a firm conclusion on the extent of DCIS overdiagnosis. However, a relatively short sojourn time in the preclinical screening-detectable DCIS phase indicates that most DCIS lesions progress or regress within a moderate timeframe. In practice, this potentially suggests a moderate duration of follow-up time if active surveillance will be considered for screening-detected DCIS lesions.

Conclusions

Most preclinical DCIS lesions probably progress or regress, with a moderate mean sojourn time estimated to be 3.1 years.

Footnotes

Acknowledgements

The authors are very grateful for deceased professor Marvin Zelen for his guidance on natural history modeling of breast cancer. The study has used data from the Cancer Registry of Norway. The interpretation and reporting of these data are the sole responsibility of the authors, and no endorsement by the Cancer Registry of Norway is intended nor should be inferred. The authors want to thank Ragnhild Falk for thoroughly reading the manuscript and providing helpful comments.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Institutes of Health under National Cancer Institute Grants R01CA165301 and U01CA199218. The funding agreement ensured the authors’ independence in designing the study, interpreting the data, writing, and publishing the report.

ORCID iD

Harald Weedon-Fekjær

Supplemental material

Supplemental material for this article is available online.

References

IARC. GLOBOCAN, https://gco.iarc.fr/ (2012, accessed 18 July 2020).

Burstein

Polyak

Wong

, et al. Ductal carcinoma in situ of the breast. N Engl J Med 2004; 350: 1430–1441.

Sorum

Hofvind

Skaane

, et al. Trends in incidence of ductal carcinoma in situ: the effect of a population-based screening programme. Breast 2010; 19: 499–505.

Lynge

Ponti

James

, et al. Variation in detection of ductal carcinoma in situ during screening mammography: a survey within the International Cancer Screening Network. Eur J Cancer 2014; 50: 185–192.

Allegra

Aberle

Ganschow

, et al. National Institutes of Health State-of-the-Science Conference statement: diagnosis and management of ductal carcinoma in situ September 22–24, 2009. J Natl Cancer Inst 2010; 102: 161–169.

Sagara

Mallory

Wong

, et al. Survival benefit of breast surgery for low-grade ductal carcinoma in situ: a population-based cohort study. JAMA Surg 2015; 150: 739–745.

Tabar

Vitak

Chen

, et al. Swedish two-county trial: impact of mammographic screening on breast cancer mortality during 3 decades. Radiology 2011; 260: 658–663.

Berry

Cronin

Plevritis

, et al. Effect of screening and adjuvant therapy on mortality from breast cancer. N Engl J Med. 2005; 353: 1784–1792.

Weedon-Fekjær

Romundstad

Vatten

LJ.

Modern mammography screening and breast cancer mortality: population study. BMJ 2014; 348: 8.

10.

de Gelder

Fracheboud

Heijnsdijk

, et al. Digital mammography screening: weighing reduced mortality against increased overdiagnosis. Prev Med 2011; 53: 134–140.

11.

Hwang

Comparison of operative versus medical endocrine therapy for low risk DCIS: The COMET Trial, http://www.pcori.org/research-results/2016/comparison-operative-versus-medical-endocrine-therapy-low-risk-dcis-comet (2016, accessed 15 July 2020).

12.

Francis

Thomas

Fallowfield

, et al. Addressing overtreatment of screen detected DCIS; the LORIS trial. Eur J Cancer 2015; 51: 2296–2303.

13.

van Luijt

Heijnsdijk

Fracheboud

, et al. The distribution of ductal carcinoma in situ (DCIS) grade in 4232 women and its impact on overdiagnosis in breast cancer screening. Breast Cancer Res 2016; 18: 47.

14.

Ryser

Worni

Turner

, et al. Outcomes of active surveillance for ductal carcinoma in situ: a computational risk analysis. J Natl Cancer Inst 2016; 108: djv372.

15.

Gunsoy

Garcia-Closas

Moss

SM.

Modelling the overdiagnosis of breast cancer due to mammography screening in women aged 40 to 49 in the United Kingdom. Breast Cancer Res 2012; 14: R152.

16.

Seigneurin

Francois

Labarere

, et al. Overdiagnosis from non-progressive cancer detected by screening mammography: stochastic simulation study with calibration to population based registry data. BMJ 2011; 343: d7017.

17.

Hofvind

Vacek

Skelly

, et al. Comparing screening mammography for early breast cancer detection in Vermont and Norway. J Natl Cancer Inst 2008; 100: 1082–1091.

18.

Weedon-Fekjaer

Lindqvist

Vatten

, et al. Estimating mean sojourn time and screening sensitivity using questionnaire data on time since previous screening. J Med Screen 2008; 15: 83–90.

19.

Zelen

Feinleib

On the theory of screening for chronic diseases. Biometrika 1969; 56: 601–614.

20.

Day

Walter

SD.

Simplified models of screening for chronic disease: estimation procedures from mass screening programmes. Biometrics 1984; 40: 1–14.

21.

Weedon-Fekjaer

Vatten

Aalen

, et al. Estimating mean sojourn time and screening test sensitivity in breast cancer mammography screening: new results. J Med Screen 2005; 12: 172–178.

22.

Prevost

Launoy

Duffy

, et al. Estimating sensitivity and sojourn time in screening for colorectal cancer: a comparison of statistical approaches. Am J Epidemiol 1998; 148: 609–619.

23.

Paci

Duffy

SW.

Modelling the analysis of breast cancer screening programmes: sensitivity, lead time and predictive value in the Florence District Programme (1975–1986). Int J Epidemiol 1991; 20: 852–858.

24.

Team RC. R: a language and environment for statistical computing. R foundation for statistical computing. Vienna, Austria, 2017.

25.

Gamma distribution (Wikipedia), https://en.wikipedia.org/wiki/Gamma_distribution (accessed 15 July 2020).

26.

van Ravesteyn

van den Broek

, et al. Modeling ductal carcinoma in situ (DCIS): an overview of CISNET model approaches. Med Decis Making 2018; 38: 126S–139S.

27.

de Gelder

Heijnsdijk

van Ravesteyn

, et al. Interpreting overdiagnosis estimates in population-based mammography screening. Epidemiol Rev 2011; 33: 111–121.

28.

Zahl

Gotzsche

Maehlen

Natural history of breast cancers detected in the Swedish mammography screening programme: a cohort study. Lancet Oncol 2011; 12: 1118–1124.

29.

Zahl

Maehlen

Welch

HG.

The natural history of invasive breast cancers detected by screening mammography. Arch Intern Med 2008; 168: 2311–2316.

30.

Fryback

Stout

Rosenberg

, et al. The Wisconsin Breast Cancer Epidemiology Simulation Model. J Natl Cancer Inst Monogr 2006; 2006: 37–47.

31.

Plevritis

Sigal

Salzman

, et al. A stochastic simulation model of U.S. breast cancer mortality trends from 1975 to 2000. J Natl Cancer Inst Monogr 2006; 86–95.

32.

Larsen

Smastuen

Johannesen

, et al. Data quality at the Cancer Registry of Norway: an overview of comparability, completeness, validity and timeliness. Eur J Cancer 2009; 45: 1218–1231.

33.

Lynge

Braaten

Njor

, et al. Mammography activity in Norway 1983 to 2008. Acta Oncol 2011; 50: 1062–1067.

34.

Weedon-Fekjaer

Bakken

Vatten

, et al. Understanding recent trends in incidence of invasive breast cancer in Norway: age-period-cohort analysis based on registry data on mammography screening and hormone treatment use. BMJ 2012; 344: e299.

Estimating the natural progression of non-invasive ductal carcinoma in situ breast cancer lesions using screening data

Abstract

Objectives

Methods

Results

Conclusion

Keywords

Introduction

Methods

Population and data

Natural progression of DCIS and its arrest by screening

A DCIS progression model

Formulas for estimating mean sojourn time and screening sensitivity (assuming only progressive tumors)

Expanding the model with non-progressive DCIS

Estimation of transition probabilities

Estimation of mean sojourn time and screening sensitivity using maximum likelihood estimation

Input for estimating model parameters

Results

Model fit and DCIS progression estimates

Discussion

Conclusions

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

Supplemental material

References