Estimating mean sojourn time and screening sensitivity using questionnaire data on time since previous screening

Non-progressive breast carcinomas detected at mammography screening: a population study

BACKGROUND

Some breast carcinomas detected at screening, especially ductal carcinoma in situ, may have limited potential for progression to symptomatic disease. To determine non-progression is a challenge, but if all screening-detected breast tumors eventually reach a clinical stage, the cumulative incidence at a reasonably high age would be similar for women with or without screening, conditional on the women being alive.

METHODS

Using high-quality population data with 24 years of follow-up from the gradually introduced BreastScreen Norway program, we studied whether all breast carcinomas detected at mammography screening 50-69 years of age would progress to clinical symptoms within 85 years of age. First, we estimated the incidence rates of breast carcinomas by age in scenarios with or without screening, based on an extended age-period-cohort incidence model. Next, we estimated the frequency of non-progressive tumors among screening-detected cases, by calculating the difference in the cumulative rate of breast carcinomas between the screening and non-screening scenarios at 85 years of age.

RESULTS

Among women who attended BreastScreen Norway from the age of 50 to 69 years, we estimated that 1.1% of the participants were diagnosed with a breast carcinoma without the potential to progress to symptomatic disease by 85 years of age. This proportion of potentially non-progressive tumors corresponded to 15.7% [95% CI 3.3, 27.1] of breast carcinomas detected at screening.

CONCLUSIONS

Our findings suggest that nearly one in six breast carcinomas detected at screening may be non-progressive.

Test sensitivity in a prospective cancer screening program: A critique of a common proxy measure

The true sensitivity of a cancer screening test, defined as the frequency with which the test returns a positive result if the cancer is present, is a key indicator of diagnostic performance. Given the challenges of directly assessing test sensitivity in a prospective screening program, proxy measures for true sensitivity are frequently reported. We call one such proxy empirical sensitivity, as it is given by the observed ratio of screen-detected cancers to the sum of screen-detected and interval cancers. In the setting of the canonical three-state Markov model for progression from preclinical onset to clinical diagnosis, we formulate a mathematical relationship for how empirical sensitivity varies with the screening interval and the mean preclinical sojourn time and identify conditions under which empirical sensitivity exceeds or falls short of true sensitivity. In particular, when the inter-screening interval is short relative to the mean sojourn time, empirical sensitivity tends to exceed true sensitivity, unless true sensitivity is high. The Breast Cancer Surveillance Consortium (BCSC) has reported an estimate of 0.87 for the empirical sensitivity of digital mammography. We show that this corresponds to a true sensitivity of 0.82 under a mean sojourn time of 3.6 years estimated based on breast cancer screening trials. However, the BCSC estimate of empirical sensitivity corresponds to even lower true sensitivity under more contemporary, longer estimates of mean sojourn time. Consistently applied nomenclature that distinguishes empirical sensitivity from true sensitivity is needed to ensure that published estimates of sensitivity from prospective screening studies are properly interpreted.

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

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.

A Bayesian model for estimating multi-state disease progression

A growing number of individuals who are considered at high risk of cancer are now routinely undergoing population screening. However, noted harms such as radiation exposure, overdiagnosis, and overtreatment underscore the need for better temporal models that predict who should be screened and at what frequency. The mean sojourn time (MST), an average duration period when a tumor can be detected by imaging but with no observable clinical symptoms, is a critical variable for formulating screening policy. Estimation of MST has been long studied using continuous Markov model (CMM) with Maximum likelihood estimation (MLE). However, a lot of traditional methods assume no observation error of the imaging data, which is unlikely and can bias the estimation of the MST. In addition, the MLE may not be stably estimated when data is sparse. Addressing these shortcomings, we present a probabilistic modeling approach for periodic cancer screening data. We first model the cancer state transition using a three state CMM model, while simultaneously considering observation error. We then jointly estimate the MST and observation error within a Bayesian framework. We also consider the inclusion of covariates to estimate individualized rates of disease progression. Our approach is demonstrated on participants who underwent chest x-ray screening in the National Lung Screening Trial (NLST) and validated using posterior predictive p-values and Pearson's chi-square test. Our model demonstrates more accurate and sensible estimates of MST in comparison to MLE.

A new statistical method for curve group analysis of longitudinal gene expression data illustrated for breast cancer in the NOWAC postgenome cohort as a proof of principle

Background

The understanding of changes in temporal processes related to human carcinogenesis is limited. One approach for prospective functional genomic studies is to compile trajectories of differential expression of genes, based on measurements from many case-control pairs. We propose a new statistical method that does not assume any parametric shape for the gene trajectories.

Methods

The trajectory of a gene is defined as the curve representing the changes in gene expression levels in the blood as a function of time to cancer diagnosis. In a nested case–control design it consists of differences in gene expression levels between cases and controls. Genes can be grouped into curve groups, each curve group corresponding to genes with a similar development over time. The proposed new statistical approach is based on a set of hypothesis testing that can determine whether or not there is development in gene expression levels over time, and whether this development varies among different strata. Curve group analysis may reveal significant differences in gene expression levels over time among the different strata considered. This new method was applied as a “proof of concept” to breast cancer in the Norwegian Women and Cancer (NOWAC) postgenome cohort, using blood samples collected prospectively that were specifically preserved for transcriptomic analyses (PAX tube). Cohort members diagnosed with invasive breast cancer through 2009 were identified through linkage to the Cancer Registry of Norway, and for each case a random control from the postgenome cohort was also selected, matched by birth year and time of blood sampling, to create a case-control pair. After exclusions, 441 case-control pairs were available for analyses, in which we considered strata of lymph node status at time of diagnosis and time of diagnosis with respect to breast cancer screening visits.

Results

The development of gene expression levels in the NOWAC postgenome cohort varied in the last years before breast cancer diagnosis, and this development differed by lymph node status and participation in the Norwegian Breast Cancer Screening Program. The differences among the investigated strata appeared larger in the year before breast cancer diagnosis compared to earlier years.

Conclusions

This approach shows good properties in term of statistical power and type 1 error under minimal assumptions. When applied to a real data set it was able to discriminate between groups of genes with non-linear similar patterns before diagnosis.

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations

There has been increasing awareness in the wider biological community of the role of clonal phenotypic heterogeneity in playing key roles in phenomena such as cellular bet-hedging and decision making, as in the case of the phage-λ lysis/lysogeny and B. Subtilis competence/vegetative pathways. Here, we report on the effect of stochasticity in growth rate, cellular memory/intermittency, and its relation to phenotypic heterogeneity. We first present a linear stochastic differential model with finite auto-correlation time, where a randomly fluctuating growth rate with a negative average is shown to result in exponential growth for sufficiently large fluctuations in growth rate. We then present a non-linear stochastic self-regulation model where the loss of coherent self-regulation and an increase in noise can induce a shift from bounded to unbounded growth. An important consequence of these models is that while the average change in phenotype may not differ for various parameter sets, the variance of the resulting distributions may considerably change. This demonstrates the necessity of understanding the influence of variance and heterogeneity within seemingly identical clonal populations, while providing a mechanism for varying functional consequences of such heterogeneity. Our results highlight the importance of a paradigm shift from a deterministic to a probabilistic view of clonality in understanding selection as an optimization problem on noise-driven processes, resulting in a wide range of biological implications, from robustness to environmental stress to the development of drug resistance.

Women treated with breast conserving surgery do better than those with mastectomy independent of detection mode, prognostic and predictive tumor characteristics

BACKGROUND

Primary breast conserving treatment (BCT) is well known to have similar long-term survival as mastectomy in breast cancer patients. However, recent studies are suggesting better survival among women treated with BCT compared with mastectomy. More knowledge is needed to understand how disease specific survival is influenced by detection mode, prognostic and predictive tumor characteristics. We aimed to investigate this issue among women targeted by the Norwegian Breast Cancer Screening Program.

METHOD

Information about 9547 women aged 50-69 years diagnosed with primary invasive breast cancer without distant metastasis, who underwent either BCT or mastectomy, 2005-2011, were included in the study. Kaplan-Meier plots were used to estimate six years survival, while Cox proportional hazards models were used to estimate the hazard ratio (HR) of breast cancer death associated with surgical treatment. Information about molecular subtype, detection mode, age at diagnosis, tumor size, lymph node involvement, and histologic grade, in addition to radiation treatment, chemotherapy and endocrine therapy were included in adjusted analyses.

RESULTS

BCT was performed among 61.9% of the women included in the study. Women treated with BCT had prognostic and predictive favorable tumor characteristics compared to women treated with mastectomy. Adjusted analyses revealed a 1.7 (95% CI: 1.3-2.4) higher risk of breast cancer death among women who underwent mastectomy compared with BCT.

CONCLUSION

Women treated with BCT have significantly better breast cancer-specific survival and a lower risk of dying from breast cancer compared to women treated with mastectomy, independent of detection mode, prognostic and predictive tumor characteristic.

Overestimated lead times in cancer screening has led to substantial underestimation of overdiagnosis

Background:

Published lead time estimates in breast cancer screening vary from 1 to 7 years and the percentages of overdiagnosis vary from 0 to 75%. The differences are usually explained as random variations. We study how much can be explained by using different definitions and methods.

Methods:

We estimated the clinically relevant lead time based on the observed incidence reduction after attending the last screening round in the Norwegian mammography screening programme. We compared this estimate with estimates based on models that do not take overdiagnosis into account (model-based lead times), for varying levels of overdiagnosis. Finally, we calculated overdiagnosis adjusted for clinical and model-based lead times and compared results.

Results:

Clinical lead time was about one year based on the reduction in incidence in women previously offered screening. When overdiagnosed tumours were included, the estimates increased to 4–9 years, depending on the age at which screening begins and the level of overdiagnosis. Including all breast cancers detected in women long after the end of the screening programme dilutes the level of overdiagnosis by a factor of 2–3.

Conclusion:

When overdiagnosis is not taken into account, lead time is substantially overestimated. Overdiagnosis adjusted for model-based lead time is a function tending to zero, with no simple interpretation. Furthermore, the estimates are not in general comparable, because they depend on both the duration of screening and duration of follow-up. In contrast, overdiagnosis adjusted for clinically relevant tumours is a point estimate (and interpreted as percentage), which we find is the most reasonable method.

Parameter estimates for invasive breast cancer progression in the Canadian National Breast Screening Study

Background:

The aim of screening is to detect a cancer in the preclinical state. However, a false-positive or a false-negative test result is a real possibility.

Methods:

We describe invasive breast cancer progression in the Canadian National Breast Screening Study and construct progression models with and without covariates. The effect of risk factors on transition intensities and false-negative probability is investigated. We estimate the transition rates, the sojourn time and sensitivity of diagnostic tests for women aged 40–49 and 50–59.

Results:

Although younger women have a slower transition rate from healthy state to preclinical, their screen-detected tumour becomes evident sooner. Women aged 50–59 have a higher mortality rate compared with younger women. The mean sojourn times for women aged 40–49 and 50–59 are 2.5 years (95% CI: 1.7, 3.8) and 3.0 years (95% CI: 2.1, 4.3), respectively. Sensitivity of diagnostic procedures for older women is estimated to be 0.75 (95% CI: 0.55, 0.88), while women aged 40–49 have a lower sensitivity (0.61, 95% CI: 0.42, 0.77). Age is the only factor that affects the false-negative probability. For women aged 40–49, ‘age at entry', ‘history of breast disease' and ‘families with breast cancer' are found to be significant for some of the transition rates. For the age-group 50–59, ‘age at entry', ‘history of breast disease', ‘menstruation length' and ‘number of live births' are found to affect the transition rates.

Conclusion:

Modelling and estimating the parameters of cancer progression are essential steps towards evaluating the effectiveness of screening policies. The parameters include the transition rates, the preclinical sojourn time, the sensitivity, and the effect of different risk factors on cancer progression.

Breast cancer mortality in Norway after the introduction of mammography screening

An organized mammography screening program was gradually implemented in Norway during the period 1996-2004. Norwegian authorities have initiated an evaluation of the program. Our study focused on breast cancer mortality. Using Poisson regression, we compared the change in breast cancer mortality from before to during screening in four counties starting the program early controlling for change in breast cancer mortality during the same time in counties starting the program late. A follow-up model included death in all breast cancers diagnosed during the follow-up period. An evaluation model included only breast cancers diagnosed in ages where screening was offered. The study group had been invited for screening one to three times and followed for on average of 5.9 years. In the follow-up model, 314 breast cancer deaths were observed in the study group, and 523, 404 and 638, respectively, in the four control groups. The ratio between the changes in breast cancer mortality between early and late starting counties was 0.93 (95% confidence interval [CI] 0.77-1.12). In the evaluation model, this ratio was 0.89 (95% CI: 0.71-1.12). In Norway, where 40% of women used regular mammography prior to the program, the implementation of the organized mammography screening program was associated with a statistically nonsignificant decrease in breast cancer mortality of around 11%.

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

OBJECTIVE

To quantify the separate contributions of menopausal hormone treatment and mammography screening activities on trends in incidence of invasive breast cancer between 1987 and 2008.

DESIGN

Population study using aggregated data analysed by an extended age-period-cohort model.

SETTING

Norway. Population Norwegian women aged 30-90 between 1987 and 2008, including 50,102 newly diagnosed cases of invasive breast cancer. Main outcomes measures Attributable proportions of mammography screening and hormone treatment to recent incidence of invasive breast cancer, and the remaining variation in incidence after adjustment for mammography screening and hormone treatment.

RESULTS

The incidence of invasive breast cancer in Norway increased steadily until 2002, levelled off, and then declined from 2006. All non-linear changes in incidence were explained by use of hormone treatment and mammography screening activities, with about similar contributions of each factor. In 2002, when the incidence among women aged 50-69 was highest, an estimated 23% of the cases in that age group could be attributed to mammography screening and 27% to use of hormone treatment.

CONCLUSIONS

Changes in incidence trends of invasive breast cancer since the early 1990s may be fully attributed to mammography screening and hormone treatment, with about similar contributions of each factor.

Why mammography screening has not lived up to expectations from the randomised trials

We analysed the relation between tumour sizes and stages and the reported effects on breast cancer mortality with and without screening in trials and observational studies. The average tumour sizes in all the trials suggest only a 12% reduction in breast cancer mortality, which agrees with the 10% reported in the most reliable trials. Recent studies of tumour sizes and tumour stages show that screening has not lowered the rate of advanced cancers. In agreement with this, recent observational studies of breast cancer mortality have failed to find an effect of screening. In contrast, screening leads to serious harms in healthy women through overdiagnosis with subsequent overtreatment and false-positive mammograms. We suggest that the rationale for breast screening be urgently reassessed by policy-makers. The observed decline in breast cancer mortality in many countries seems to be caused by improved adjuvant therapy and breast cancer awareness, not screening. We also believe it is more important to reduce the incidence of cancer than to detect it 'early.' Avoiding getting screening mammograms reduces the risk of becoming a breast cancer patient by one-third.

Mammography activity in Norway 1983 to 2008

BACKGROUND

In Norway, an organized screening mammography program, the Norwegian Breast Cancer Screening Program (NBCSP) started in four counties in 1996 and became nationwide in 2004. We collected data on pre-program screening activity, and in view of this activity we evaluated the potential impact of the program on breast cancer mortality in Norway.

METHODS

We searched data sources on mammography activity in Norway. Three data sources reported on examination activity, and two on self-reported examinations. We aimed at calculating annual number of women examined by mammography from 1983 to 2008, and coverage rate in program and non-program Norwegian counties.

RESULTS

The annual number of women examined increased from 5000 in 1983 to 110,000 in 1993 to reach its maximum of 131,000 in 2002, excluding program examinations. The annual number of women examined in the organized program increased from 1996 to a steady state about 190,000 in 2004. Prior to start of the organized program, 40% of women in target age groups reported to have had mammography examination. During the years 1996-2002, 64% of first participants in the organized program reported to have been examined previously. Assuming that the Norwegian program would in absence of prior screening have decreased breast cancer mortality by 25%, and that the activity in- and outside the organized program were equally effective, the measured effect of the organized program would under actual circumstances be a reduction of 11%.

CONCLUSION

The example of Norway illustrates that although monitoring of screening outcome is highly warranted, this may be seriously jeopardized if use of mammography examinations was widespread prior to implementation of an organized program.

Modelling the impact of changes in sensitivity on the outcomes of the UK breast screening programme

OBJECTIVES

To assess the impact on breast cancer mortality of improving the sensitivity of breast screening programmes.

METHODS

A Markov model was populated with data obtained from published statistics describing the UK National Health Service Breast Screening Programme and the incidence and mortality of breast cancer in the UK. The model was used to study the impact of changes to the sensitivity of screening. The effects on cancer detection rates and breast cancers and total mortality was studied for a cohort of women followed from age 45 to age 89.

RESULTS

Running the model from age 45 to 89, with sensitivity set at the baseline value of 75%, predicts the detection at screening of 44 cancers per thousand of population and the detection outside screening of 82 cancers per thousand of population. Running the model with values of sensitivity from 75% to 95% shows the proportion of cancers detected at screening increasing as screening improves, and deaths from breast cancer falling. The drop in breast cancer deaths is however modest. Increasing sensitivity from 75% to 85% reduces the number of breast cancer deaths from 28 to 27 per thousand.

CONCLUSIONS

Likely achievable improvements in the sensitivity of screening do not have a marked effect on breast cancer mortality.

Estimating screening test sensitivity and tumour progression using tumour size and time since previous screening

As mammography screening aims to improve the prognosis through earlier detection/treatment, tumour progression and screening test sensitivity (STS) represent key parameters in the evaluation of screening programs. We will here study some methods for estimation of tumour progression and STS, and show how previously used methods can be combined and developed to utilise more of the data available in modern screening programs. Weedon-Fekjaer et al. recently suggested a study design using interview data about time since previous screening to estimate tumour progression and STS in a stepwise Markov model. While useful, the approach does not utilise tumour size measurements, nor link tumour progression to tumour size. Hence, we will here propose formulas for estimating tumour progression and STS using a continuous tumour growth model. To estimate tumour progression and STS, tumour growth curves are followed from one screening to the next, and probabilities for all combinations of tumour sizes at repeated screening examinations calculated. Based on the probabilities for screening detection on subsequent screening examinations, maximum likelihood estimates are calculated. Applied to Norwegian data, the new approach gives similar results to previously published results based on interval data, confirming the earlier estimated large variation in tumour growth rates.

Multi-state Markov models in cancer screening evaluation: a brief review and case study

This work presents a brief overview of Markov models in cancer screening evaluation and focuses on two specific models. A three-state model was first proposed to estimate jointly the sensitivity of the screening procedure and the average duration in the preclinical phase, i.e. the period when the cancer is asymptomatic but detectable by screening. A five-state model, incorporating lymph node involvement as a prognostic factor, was later proposed combined with a survival analysis to predict the mortality reduction associated with screening. The strengths and limitations of these two models are illustrated using data from French breast cancer service screening programmes. The three-state model is a useful frame but parameter estimates should be interpreted with caution. They are highly correlated and depend heavily on the parametric assumptions of the model. Our results pointed out a serious limitation to the five-state model, due to implicit assumptions which are not always verified. Although it may still be useful, there is a need for more flexible models. Over-diagnosis is an important issue for both models and induces bias in parameter estimates. It can be addressed by adding a non-progressive state, but this may provide an uncertain estimation of over-diagnosis. When the primary goal is to avoid bias, rather than to estimate over-diagnosis, it may be more appropriate to correct for over-diagnosis assuming different levels in a sensitivity analysis. This would be particularly relevant in a perspective of mortality reduction estimation.