Estimation of mean sojourn time for lung cancer by chest X-ray screening with a Bayesian approach

Estimating Transition Probabilities Across the Alzheimer's Disease Continuum Using a Nationally Representative Real-World Database in the United States

INTRODUCTION

Clinical Alzheimer's disease (AD) begins with mild cognitive impairment (MCI) and progresses to mild, moderate, or severe dementia, constituting a disease continuum that eventually leads to death. This study aimed to estimate the probabilities of transitions across those disease states.

METHODS

We developed a mixed-effects multi-state Markov model to estimate the transition probabilities, adjusted for 5 baseline covariates, using the Health and Retirement Study (HRS) database. HRS surveys older adults in the United States bi-annually. Alzheimer states were defined using the modified Telephone Interview of Cognitive Status (TICS-m).

RESULTS

A total of 11,292 AD patients were analyzed. Patients were 70.8 ± 9.0 years old, 54.9% female, and with 12.0 ± 3.3 years of education. Within 1 year from the initial state, the model estimated a higher probability of transition to the next AD state in earlier disease: 12.8% from MCI to mild AD and 5.0% from mild to moderate AD, but < 1% from moderate to severe AD. After 10 years, the probability of transition to the next state was markedly higher for all states, but still higher in earlier disease: 29.8% from MCI to mild AD, 23.5% from mild to moderate AD, and 5.7% from moderate to severe AD. Across all AD states, the probability of transition to death was < 5% after 1 year and > 15% after 10 years. Older age, fewer years of education, unemployment, and nursing home stay were associated with a higher risk of disease progression (p < 0.01).

CONCLUSIONS

This analysis shows that the risk of progression is greater in earlier AD states, increases over time, and is higher in patients who are older, with fewer years of education, unemployed, or in a nursing home at baseline. The estimated transition probabilities can provide guidance for future disease management and clinical trial design optimization, and can be used to refine existing cost-effectiveness frameworks.

Estimating the Length of the Preclinical Detectable Phase for Open-Angle Glaucoma

Importance

A 50% reduction of glaucoma-related blindness has previously been demonstrated in a population that was screened for open-angle glaucoma. Ongoing screening trials of high-risk populations and forthcoming low-cost screening methods suggest that such screening may become more common in the future. One would then need to estimate a key component of the natural history of chronic disease, the mean preclinical detectable phase (PCDP). Knowledge of the PCDP is essential for the planning and early evaluation of screening programs and has been estimated for several types of cancer that are screened for.

Objective

To estimate the mean PCDP for open-angle glaucoma.

Design, Setting, and Participants

A large population-based screening for open-angle glaucoma was conducted from October 1992 to January 1997 in Malmö, Sweden, including 32 918 participants aged 57 to 77 years. A retrospective medical record review was conducted to assess the prevalence of newly detected cases at the screening, incidence of new cases after the screening, and the expected clinical incidence, ie, the number of new glaucoma cases expected to be detected without a screening. The latter was derived from incident cases in the screened age cohorts before the screening started and from older cohorts not invited to the screening. A total of 2029 patients were included in the current study. Data were analyzed from March 2020 to October 2021.

Main Outcomes and Measures

The length of the mean PCDP was calculated by 2 different methods: first, by dividing the prevalence of screen-detected glaucoma with the clinical incidence, assuming that the screening sensitivity was 100% and second, by using a Markov chain Monte Carlo (MCMC) model simulation that simultaneously derived both the length of the mean PCDP and the sensitivity of the screening.

Results

Of 2029 included patients, 1352 (66.6%) were female. Of 1420 screened patients, the mean age at screening was 67.4 years (95% CI, 67.2-67.7). The mean length of the PCDP of the whole study population was 10.7 years (95% CI, 8.7-13.0) by the prevalence/incidence method and 10.1 years (95% credible interval, 8.9-11.2) by the MCMC method.

Conclusions and Relevance

The mean PCDP was similar for both methods of analysis, approximately 10 years. A mean PCDP of 10 years found in the current study allows for screening with reasonably long intervals, eg, 5 years.

Multistate models for the natural history of cancer progression

BACKGROUND

Multistate models can be effectively used to characterise the natural history of cancer. Inference from such models has previously been useful for setting screening policies.

METHODS

We introduce the basic elements of multistate models and the challenges of applying these models to cancer data. Through simulation studies, we examine (1) the impact of assuming time-homogeneous Markov transition intensities when the intensities depend on the time since entry to the current state (i.e., the process is time-inhomogenous semi-Markov) and (2) the effect on precancer risk estimation when observation times depend on an unmodelled intermediate disease state.

RESULTS

In the settings we examined, we found that misspecifying a time-inhomogenous semi-Markov process as a time-homogeneous Markov process resulted in biased estimates of the mean sojourn times. When screen-detection of the intermediate disease leads to more frequent future screening assessments, there was minimal bias induced compared to when screen-detection of the intermediate disease leads to less frequent screening.

CONCLUSIONS

Multistate models are useful for estimating parameters governing the process dynamics in cancer such as transition rates, sojourn time distributions, and absolute and relative risks. As with most statistical models, to avoid incorrect inference, care should be given to use the appropriate specifications and assumptions.

Low positive predictive value of computed tomography screening for lung cancer irrespective of commonly employed definitions of target population

Screening for lung cancer (LC) by low-dose computed tomography (LDCT) has been demonstrated to reduce LC mortality in randomized clinical trials (RCTs), and its implementation is in preparation in many countries. However, definition of the target population, which was based on various combinations of age ranges and definitions of heavy smoking in the RCTs, is subject to ongoing debate. Using epidemiological data from Germany, we aimed to estimate prevalence of preclinical LC and positive predictive value (PPV) of LDCT in potential target populations defined by age and smoking history. Populations aged 50 to 69, 55 to 69, 50 to 74 and 55 to 79 years were considered in this analysis. Sex-specific prevalence of preclinical LC was estimated using LC incidence data within those age ranges and annual transition rates from preclinical to clinical LC obtained by meta-analysis. Prevalence of preclinical LC among heavy smokers (defined by various pack-year thresholds) within those age ranges was estimated by combining LC prevalence in the general population with proportions of heavy smokers and relative risks for LC among them derived from epidemiological studies. PPVs were calculated by combining these prevalences with sensitivity and specificity estimates of LDCT. Estimated prevalence of LC was 0.3% to 0.5% (men) and 0.2% to 0.3% (women) in the general population and 0.8% to 1.7% in target populations of heavy smokers. Estimates of PPV of LDCT were <20% for all definitions of target populations of heavy smokers. Refined preselection of target populations would be highly desirable to increase PPV and efficiency of LDCT screening and to reduce numbers of false-positive LDCT findings.

Sensitivity of chest X-ray for detecting lung cancer in people presenting with symptoms: a systematic review

BACKGROUND

Despite increasing use of computed tomography (CT), chest X-ray remains the first-line investigation for suspected lung cancer in primary care in the UK. No systematic review evidence exists as to the sensitivity of chest X-ray for detecting lung cancer in people presenting with symptoms.

AIM

To estimate the sensitivity of chest X-ray for detecting lung cancer in symptomatic people.

DESIGN AND SETTING

A systematic review was conducted to determine the sensitivity of chest X-ray for the detection of lung cancer.

METHOD

Databases including MEDLINE, EMBASE, and the Cochrane Library were searched; a grey literature search was also performed.

RESULTS

A total of 21 studies met the eligibility criteria. Almost all were of poor quality. Only one study had the diagnostic accuracy of chest X-ray as its primary objective. Most articles were case studies with a high risk of bias. Several were drawn from non-representative groups, for example, specific presentations, histological subtypes, or comorbidities. Only three studies had a low risk of bias. Two primary care studies reported sensitivities of 76.8% (95% confidence interval [CI] = 64.5 to 84.2%) and 79.3% (95% CI = 67.6 to 91.0%). One secondary care study reported a sensitivity of 79.7% (95% CI = 72.7 to 86.8%).

CONCLUSION

Though there is a paucity of evidence, the highest-quality studies suggest that the sensitivity of chest X-ray for symptomatic lung cancer is only 77% to 80%. GPs should consider if further investigation is necessary in high-risk patients who have had a negative chest X-ray.

Test sensitivity of mammography and mean sojourn time over 40 years of breast cancer screening in Nijmegen (The Netherlands)

Objectives

We investigated whether changes in mammographic technique and screening policy have improved mammographic sensitivity, and elongated the mean sojourn time, since the introduction of biennial breast cancer screening in Nijmegen, the Netherlands, in 1975.

Methods

Maximum likelihood estimation, non-linear regression, and Markov Chain Monte Carlo simulation were used to estimate test sensitivity, mean sojourn time, and underlying breast cancer incidence in four time periods, covering 40 years of breast cancer screening in Nijmegen (1975–2012).

Results

Maximum likelihood estimation generated an estimated test sensitivity of approximately 90% and a mean sojourn time around three years, while the estimates based on non-linear regression and Markov Chain Monte Carlo simulation were 80% and four years, respectively. All three methods estimated a rise in the underlying breast cancer incidence over time, with approximately one case more per 1000 women per year in the final period compared with the first period.

Conclusions

The three methods showed a slightly higher mammographic sensitivity and a longer mean sojourn time in the last period, after the introduction of digital mammography. Estimates were more realistic for the more sophisticated methods, non-linear regression and Markov Chain Monte Carlo simulation, while the simple closed form approximation of maximum likelihood estimation led to rather high estimates for sensitivity in the early periods.

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.

Sojourn time and lead time projection in lung cancer screening

OBJECTIVES

We investigate screening sensitivity, transition probability and sojourn time in lung cancer screening for male heavy smokers using the Mayo Lung Project data. We also estimate the lead time distribution, its property, and the projected effect of taking regular chest X-rays for lung cancer detection.

METHODS

We apply the statistical method developed by Wu et al. [1] using the Mayo Lung Project (MLP) data, to make Bayesian inference for the screening test sensitivity, the age-dependent transition probability from disease-free to preclinical state, and the sojourn time distribution, for male heavy smokers in a periodic screening program. We then apply the statistical method developed by Wu et al. [2] using the Bayesian posterior samples from the MLP data to make inference for the lead time, the time of diagnosis advanced by screening for male heavy smokers. The lead time is distributed as a mixture of a point mass at zero and a piecewise continuous distribution, which corresponds to the probability of no-early-detection, and the probability distribution of the early diagnosis time. We present estimates of these two measures for male heavy smokers by simulations.

RESULTS

The posterior sensitivity is almost symmetric, with posterior mean 0.89, and posterior median 0.91; the 95% highest posterior density (HPD) interval is (0.72, 0.98). The posterior mean sojourn time is 2.24 years, with a posterior median of 2.20 years for male heavy smokers. The 95% HPD interval for the mean sojourn time is (1.57, 3.35) years. The age-dependent transition probability is not a monotone function of age; it has a single maximum at age 68. The mean lead time increases as the screening time interval decreases. The standard error of the lead time also increases as the screening time interval decreases.

CONCLUSION

Although the mean sojourn time for male heavy smokers is longer than expected, the predictive estimation of the lead time is much shorter. This may provide policy makers important information on the effectiveness of the chest X-rays and sputum cytology in lung cancer early detection.

Modeling progression in radiation-induced lung adenocarcinomas

Quantitative multistage carcinogenesis models are used in radiobiology to estimate cancer risks and latency periods (time from exposure to clinical cancer). Steps such as initiation, promotion and transformation have been modeled in detail. However, progression, a later step during which malignant cells can develop into clinical symptomatic cancer, has often been approximated simply as a fixed lag time. This approach discounts important stochastic mechanisms in progression and evidence on the high prevalence of dormant tumors. Modeling progression more accurately is therefore important for risk assessment. Unlike models of earlier steps, progression models can readily utilize not only experimental and epidemiological data but also clinical data such as the results of modern screening and imaging. Here, a stochastic progression model is presented. We describe, with minimal parameterization: the initial growth or extinction of a malignant clone after formation of a malignant cell; the likely dormancy caused, for example, by nutrient and oxygen deprivation; and possible escape from dormancy resulting in a clinical cancer. It is shown, using cohort simulations with parameters appropriate for lung adenocarcinomas, that incorporating such processes can dramatically lengthen predicted latency periods. Such long latency periods together with data on timing of radiation-induced cancers suggest that radiation may influence progression itself.

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.