An age dependent stochastic model of periodic screening: Basic properties

An age dependent stochastic model for the periodic screening of a progressive chronic disease is developed in this paper by combining results from previous modeling efforts. The basic concepts used are the random variables describing the disease free state and preclinical state sojourn times and the age at screening or observation, as well as generations of individuals defined according to time of entry into the preclinical state. At discrete time points, the model characterizes the density functions for individuals who are healthy, have preclinical disease, or have clinical disease. The joint density functions of age and sojourn times for cases detected by a periodic screening program and for cases which surface clinically between screens are derived as functions of screening interval, false negative rate, and disease natural history.     

Quantification of length‐bias in screening trials with covariate‐dependent test sensitivity

Length‐biased sampling exists in screening programs where longer duration disease is detected during the preclinical stage because a longer sojourn time (preclinical duration) has a higher probability of being screen detected. By modeling the course of disease, we quantify the effect of length‐biased sampling on clinical duration when cases are subject to periodic screening with variable test sensitivity. We use the highly flexible bivariate lognormal density to jointly model preclinical and clinical durations, and we model screening test sensitivity as a function of the sojourn time and number of previous false negative screens. We show that the mean clinical duration among screen‐detected cases can be up to 40% higher, with shrinking standard deviation, than those among nonscreen‐detected cases, due to biased sampling alone, irrespective of any possible benefit (increased survival time arising from earlier detection or reduction in mortality). These findings will aid in the design and interpretation of screening trials.     

Nonparametric estimation of asymptomatic duration from a randomized prospective cancer screening trial

We propose a nonparametric estimation of preclinical duration distribution in cancer based on data from a randomized early detection trial. In cancer screening studies, the preclinical duration of a disease is of great interest for better understanding the natural history of the disease, and for developing optimal screening strategies. To estimate the sojourn time distribution nonparametrically, we first estimate the distribution of the age at onset of preclinical disease nonparametrically using data from the screening arm in a randomized screening trial, and the distribution for the age at onset of clinical disease from the control arm of the randomized screening trial. Finally, by using deconvolution the two estimated distributions lead to a nonparametric estimate of the distribution for the gap time between the onset of preclinical disease and the onset of clinical disease. We illustrate the methodology using data from a randomized breast cancer screening trial.     

An early- and late-stage convolution model for disease natural history

The standard convolution model of disease natural history posits an asymptomatic (preclinical) and a symptomatic (clinical) state. An augmented model includes, in both the preclinical and clinical states, an early and late stage of disease. In the case of cancer, the early stage would generally correspond to the organ-confined stages before there is evidence of cancer spread. We compute the number of screen-detected (preclinical) and clinical cases in the early and late stages expected under a given screening program and show how the model can be fit to data from a screening trial using maximum likelihood. We also develop expressions for sojourn time, lead time, and overdiagnosis in the context of the model, where each of the above concepts incorporates disease stage. As an example, we fit the model to data from the Mayo Lung Cancer Screening trial.     

Robust modeling in screening studies: estimation of sensitivity and preclinical sojourn time distribution

In early-detection clinical trials, quantities such as the sensitivity of the screening modality and the preclinical duration of the disease are important to describe the natural history of the disease and its interaction with a screening program. Assume that the schedule of a screening program is periodic and that the sojourn time in the preclinical state has a piecewise density function. Modeling the preclinical sojourn time distribution as a piecewise density function results in robust estimation of the distribution function. Our aim is to estimate the piecewise density function and the examination sensitivity using both generalized least squares and maximum likelihood methods. We carried out extensive simulations to evaluate the performance of the methods of estimation. The different estimation methods provide complimentary tools to obtain the unknown parameters. The methods are applied to three breast cancer early-detection trials.     

Screening for squamous cervical cancer: duration of low risk after negative results of cervical cytology and its implication for screening policies. IARC Working Group on evaluation of cervical cancer screening programmes.

A collaborative study of screening programmes in eight countries was performed to estimate the risks of cervical cancer associated with different screening policies. Most of the data came from centrally organised screening programmes. Relative protection was higher in women who had had two or more negative results of screening tests than in those who had had only one negative smear, particularly in the first five years after the last test. There was little difference in the protection afforded by screening every year compared with every three years, but screening only once every five or 10 years offered appreciably less protection. The age of the women did not affect the sensitivity of the test or the sojourn time of the disease (the length of the detectable preclinical phase during which abnormal cytology could be picked up if a smear were taken); invasive cancer in women under 25 was rare. Centrally organised screening programmes were more effective than uncoordinated screening. Screening programmes should be aimed principally at women aged 35-60 but should start some years before the age of 35, and the intervals between screening should be three years or less.     

Estimation of sojourn time in chronic disease screening without data on interval cases

Estimation of the sojourn time on the preclinical detectable period in disease screening or transition rates for the natural history of chronic disease usually rely on interval cases (diagnosed between screens). However, to ascertain such cases might be difficult in developing countries due to incomplete registration systems and difficulties in follow-up. To overcome this problem, we propose three Markov models to estimate parameters without using interval cases. A three-state Markov model, a five-state Markov model related to regional lymph node spread, and a five-state Markov model pertaining to tumor size are applied to data on breast cancer screening in female relatives of breast cancer cases in Taiwan. Results based on a three-state Markov model give mean sojourn time (MST) 1.90 (95% CI: 1.18-4.86) years for this high-risk group. Validation of these models on the basis of data on breast cancer screening in the age groups 50-59 and 60-69 years from the Swedish Two-County Trial shows the estimates from a three-state Markov model that does not use interval cases are very close to those from previous Markov models taking interval cancers into account. For the five-state Markov model, a reparameterized procedure using auxiliary information on clinically detected cancers is performed to estimate relevant parameters. A good fit of internal and external validation demonstrates the feasibility of using these models to estimate parameters that have previously required interval cancers. This method can be applied to other screening data in which there are no data on interval cases.     

Some Obstacles to the Evaluation and Effective Performance of Health Appraisals

Certain obstacles exist in evaluating screening tests and health examinations. When a voluntarily screened group is compared with an unscreened group and when the survival of cases detected in these two groups is compared, self-selection bias, lead-time bias, length bias and overdiagnosis confuse the evaluation and usually make an examination seem better than it really is. A randomized controlled trial overcomes these biases; one group is offered screening, the other is not and the outcomes in both entire groups are observed. Unavoidable crossovers between the groups tend to obscure any benefit of the examination, however. Evaluations of screening tests have tended to emphasize the value of positive results and have neglected the value of negative results. In obtaining maximum benefit from health appraisals, attention needs to be directed at self-selection, nonmedical threats to life and health, risk factors in addition to early disease and tailoring an examination to the needs of individual patients.     

Two-stage models for the analysis of cancer screening data

Methods are proposed for the analysis of the natural history of disease from screening data when it cannot be assumed that untreated preclinical disease always progresses to clinical disease. The methodology is based on a two-stage model for preclinical disease in which stage 1 lesions may or may not progress to stage 2, but all stage 2 lesions progress to clinical disease. The focus is on joint estimation of the total preclinical duration and the sensitivity of the screening test. A partial likelihood is proposed for the analysis of prospectively collected screening data, and an analogous conditional likelihood is proposed for retrospective data. Some special cases for the joint sojourn distribution of the two stages are considered, including the independent model and limiting models where the duration of stage 2 is short relative to stage 1. The methods are applied to a case-control study of cervical cancer screening in Northeast Scotland.     

Mortality modeling of early detection programs

Summary .   Consider a group of subjects who are offered an opportunity to receive a sequence of periodic special examinations for the purpose of diagnosing a chronic disease earlier relative to usual care. The mortality for the early detection group is to be compared with a group receiving usual care. Benefit is reflected in a potential reduction in mortality. This article develops a general probability model that can be used to predict cumulative mortality for each of these groups. The elements of the model assume (i) a four-state progressive disease model in which a subject may be in a disease-free state (or a disease state that cannot be detected), preclinical disease state (capable of being diagnosed by a special exam), clinical state (diagnosis by usual care), and a death state; (ii) age-dependent transitions into the states; (iii) age-dependent examination sensitivity; (iv) age-dependent sojourn time in each state; and (v) the distribution of disease stages on diagnosis conditional on modality of detection. The model may be used to (i) compare mortality rates for different screening schedules; (ii) explore potential benefit of subpopulations; and (iii) compare relative reductions in disease-specific mortality due to advances and dissemination of both treatment and early detection screening programs.     

Estimation and Prediction for Cancer Screening Models Using Deconvolution and Smoothing

The model that specifies that cancer incidence, I, is the convolution of the preclinical incidence, g, and the density of time in the preclinical phase, f, has frequently been utilized to model data from cancer screening trials and to estimate such quantities as sojourn time, lead time, and sensitivity. When this model is fit to the above data, the parameters of f as well as the parameter(s) governing screening sensitivity must be estimated. Previously, g was either assumed to be equal to clinical incidence or assumed to be a constant or exponential function that also had to be estimated. Here we assume that the underlying incidence, I, in the study population (in the absence of screening) is known. With I known, g then becomes a function of f, which can be solved for using (numerical) deconvolution, thus eliminating the need to estimate g or make assumptions about it. Since numerical deconvolution procedures may be highly unstable, however, we incorporate a smoothing procedure that produces a realistic g function while still closely reproducing the original incidence function I upon convolution with f. We have also added the concept of competing mortality to the convolution model. This, along with the realistic preclinical incidence function described above, results in more accurate estimates of sojourn time and lead time and allows for estimation of quantities related to overdiagnosis, which we define here.     

A bayesian random-effects markov model for tumor progression in women with a family history of breast cancer

SUMMARY: It makes intuitive sense to model the natural history of breast cancer, tumor progression from preclinical screen-detectable phase (PCDP) to clinical disease, as a multistate process, but the multilevel structure of the available data, which generally comes from cluster (family)-based service screening programs, makes the required parameter estimation intractable because there is a correlation between screening rounds in the same individual, and between subjects within clusters (families). There is also residual heterogeneity after adjusting for covariates. We therefore proposed a Bayesian hierarchical multistate Markov model with fixed and random effects and applied it to data from a high-risk group (women with a family history of breast cancer) participating in a family-based screening program for breast cancer. A total of 4867 women attended (representing 4464 families) and by the end of 2002, a total of 130 breast cancer cases were identified. Parameter estimation was carried out using Markov chain Monte Carlo (MCMC) simulation and the Bayesian software package WinBUGS. Models with and without random effects were considered. Our preferred model included a random-effect term for the transition rate from preclinical to clinical disease (sigma(2)(2f)), which was estimated to be 0.50 (95% credible interval = 0.22-1.49). Failure to account for this random effect was shown to lead to bias. The incorporation of covariates into multistate models with random effect not only reduced residual heterogeneity but also improved the convergence of stationary distribution. Our proposed Bayesian hierarchical multistate model is a valuable tool for estimating the rate of transitions between disease states in the natural history of breast cancer (and possibly other conditions). Unlike existing models, it can cope with the correlation structure of multilevel screening data, covariates, and residual (unexplained) variation.     

On the use of time constants as estimates of mean lifetimes in single channel data analysis

For Markov models of single channel kinetics, a sojourn time in a class of states has a density function which is usually a linear combination of exponential densities. There are many instances in the single channel literature where the time constants of exponentials fitted to sojourn time data have been used as estimated mean sojourn times in individual states, though the two may be very different. In the present study the nature and magnitude of this difference in the case of a two state class is illustrated analytically and numerically. The time constants should be viewed at best as approximations, possibly poor, to the estimated mean sojourn times. Estimates of kinetic parameters cannot in general be obtained explicitly from the fitted parameters of the density alone. However, this is shown to be possible in some special cases and enables direct estimation of, for example, the channel opening rate constant (or an upper limit to the estimate of in the case of multiple channels) in standard sequential three or four state models of nicotinic receptor kinetics, using only the fitted parameters of the closed-time density. Offprint requests to: R. O. Edeson     

Human papillomavirus DNA and liquid-based cervical cytology cotesting in screening and follow-up patient groups

OBJECTIVE: To compare the use of human papillomavirus (HPV) DNA and cervical cytology cotesting in screening and follow-up of patients with previous cervical abnormalities and to assess the significance of a positive HPV DNA test result in re-screening of cytologically normal cases. STUDY DESIGN: Cellular samples collected in liquid-based fixative were used for both cervical cytology and HPV DNA testing. The cervical cytology slides were manually screened by cytotechnologists followed by rapid re-screening by pathologists. The HPV DNA tests were performed using hybrid capture test kits. Statistical analyses of cervical cytology results and HPV DNA tests for high- and low-risk HPV from both patient groups were carried out. RESULTS: The prevalence of HPV DNA-positive cases was higher in younger patients. There was a poor correlation between cervical cytology results and HPV DNA tests for the screening group (kappa = 0.23), but a fair to good correlation was obtained for the follow-up group (kappa = 0.51). The false negative fraction of cytology negative/HPV DNA positive cases (0.1317), as compared with cytology negative/HPV DNA negative cases (0.0056), was statistically significant (p = 0.000001). CONCLUSION: The prevalence of HPV DNA decreased with increasing age in both the screening and follow-up patient groups. Virus clearance was delayed in the follow-up group as compared with the screening group. There was a poor correlation between cervical cytology and HPV DNA tests in the screening group but a fair to good correlation in the follow-up patient group. Cotesting of HPV DNA and cervical cytology increases the sensitivity and decreases the false negative fraction, suggesting that cotesting could be used to increase the interval of screening.     

A stochastic model for survival of early prostate cancer with adjustments for leadtime, length bias, and over-detection

To compare the survival between screen-detected and clinically detected cancers, we applied a series of non-homogeneous stochastic processes to deal with leadtime, length bias, and over-detection by using full information on detection modes obtained from the Finnish randomized controlled trial for prostate cancer screening. The results show after 9-year follow-up the hazard ratio of prostate cancer death for screen-detected cases against clinically detected cases increased from 0.24 (95% CI: 0.16-0.35) without correction for these biases, to 0.76 after correction for leadtime and length biases, and finally to 1.03 (95% CI: 0.79-1.33) for a further adjustment for over-detection. Adjustment for leadtime and length bias but no over-detection led to a 24% reduction in prostate cancer death as a result of prostate-specific antigen test. The further calibration of over-detection indicates no gain in survival of screen-detected prostate cancers (excluding over-detected case as stayer considered in the mover-stayer model) as compared with the control group in the absence of screening that is considered as the mover. However, whether the model assumption on over-detection is robust should be validated with other data sets and longer follow-up.     

Estimating key parameters in periodic breast cancer screening—Application to the Canadian National Breast Screening Study data

Problem statement: Breast cancer screening in women of younger age has been controversial. The screening sensitivities, transition probabilities and sojourn time distributions are estimated for females aged 40–49 years and 50–59 years separately, using the Canadian National Breast Screening Study (CNBSS) data. The purpose is to estimate the lead time distribution and the probability of not detecting the cancer early. Approach: Within the 40–49-year-old and 50–59-year-old cohorts separately, the age-independent statistical model was applied. Bayesian estimators along with 95% highest probability density (HPD) credible intervals (CI) were calculated. Bayesian hypothesis testing was used to compare the parameter estimates of the two cohorts. The lead time density was also estimated for both the 40–49 and 50–59-year-old cohorts. Results: The screening sensitivity, transition probability of the disease, and mean sojourn time were all found to increase with age. For the 40–49-year-old and 50–59-year-old cohorts, the posterior mean sensitivities were 0.70 (95% HPD-CI: 0.46, 0.93) and 0.77 (0.61, 0.93), respectively. The posterior mean transition probabilities were 0.0023 (0.0018, 0.0027) and 0.0031 (0.0024, 0.0038), while the posterior mean sojourn times were 2.55 (1.56, 4.26) years and 3.15 (2.12, 4.96) years. Bayes factors for the ratio of posterior probabilities that the respective parameter was larger vs. smaller in the 50–59-year-old cohort were estimated to be 2.09, 40.8 and 3.0 for the sensitivity, transition probability, and mean sojourn time, respectively. All three Bayes factors were larger than two, indicating greater than 2:1 odds in favor of the hypothesis that each of these parameters was greater in the 50–59-year-old cohort. The estimated mean lead times were 0.83 years and 0.96 years if the two cohorts were screened annually. Conclusions: The increase in sensitivity corresponds to an increase in the mean sojourn time. Breast cancer in younger women is more difficult to detect by screening tests and is more aggressive than breast cancer in older women. Women aged 50–59 tend to benefit more from screening compared with women aged 40–49.     

Prevalence screening for ovarian cancer in postmenopausal women by CA 125 measurement and ultrasonography.

OBJECTIVE--To assess the performance of the sequential combination of serum CA 125 measurement and ultrasonography in screening for ovarian cancer. DESIGN--The serum CA 125 concentration of each subject was determined and those with a concentration > or = 30 U/ml were recalled for abdominal ultrasonography. If ultrasonography gave abnormal results surgical investigation was arranged. Volunteers were followed up by annual postal questionnaire. SETTING--General practice, occupational health departments, ovarian cancer screening clinic. SUBJECTS--22,000 women volunteers who were postmenopausal and aged over 45 years. MAIN OUTCOME MEASURES--Apparent sensitivity, specificity, positive predictive value, years of cancer detected. RESULTS--41 women had a positive screening result and were investigated surgically. 11 had ovarian cancer (true positive result) and 30 had other disorders or no abnormality (false positive result). Of the 21,959 volunteers with a negative screening result, eight subsequently presented clinically with ovarian cancer (false negative result) and 21,951 had not developed ovarian cancer during follow up (apparent true negative result). The screening protocol achieved a specificity of 99.9%, a positive predictive value of 26.8%, and an apparent sensitivity of 78.6% and 57.9% at one year and two year follow up respectively. The estimated number of years of cancer detected by the prevalence screen was 1.4 years. CONCLUSIONS--This screening protocol is highly specific for ovarian cancer and can detect a substantial proportion of cases at a preclinical stage. Further investigation is required to determine the effect of the screening protocol on the ratio of early to late stage disease detected and on mortality from ovarian cancer.     

Biomarker technology roundup: from discovery to clinical applications, a broad set of tools is required to translate from the lab to the clinic

Biomarkers are being utilized throughout the drug discovery and development process to understand fundamental biological processes and relationships. Specific biomarkers for disease states, prognosis, and response to therapy have been applied to screening tissues and serum, and serve as new tools in the development of therapeutics, to segment the population for specific treatments. The use of specific biomarkers to screen subjects to determine clinical trial eligibility, and for early toxicology studies, holds the potential to decrease drug failure rates in the later phases of the clinical trial process. Traditional research tools have been employed to study the genes, proteins, and metabolites of interest. In addition, new technologies and permutations of existing technologies have been developed particularly for investigation in the preclinical and clinical phases of drug development. More importantly, the transition of a compound from preclinical to clinical is aided by technologies that span both process segments. Identification of biomarkers that can be studied throughout the development process requires technologies that are both feasible and cost-effective for large patient populations.     

Cervical cancers diagnosed after negative results on cervical cytology: perspective in the 1980s.

OBJECTIVES--To assess the magnitude of the problem of interval cancers of the cervix (those that are diagnosed within a short time after negative screening test results) in the 1980s, to compare the nature of interval cancers in younger women with that in older women, and, by reviewing negative cervical smears, to determine the proportion of interval cancers that might represent the development of malignancy anew compared with the proportion that might be associated with difficulties in sampling or errors in reporting. DESIGN--An audit of the interval cases of cervical cancer that had been diagnosed within 36 months of a smear having been reported as negative by the Victorian Cytology Gynaecological Service among women registered with cervical cancer during 1982-6. SETTING--The Victorian Cytology Gynaecological Service, a free public sector cytology laboratory in Victoria, Australia. SUBJECTS--138 Women, all of whom had had cervical cancer diagnosed during the 36 months after having had a negative cervical smear. Subjects were divided into two age groups: younger women, aged less than 35; older women, aged 35-69. INTERVENTIONS--Negative slides were reviewed for evidence of optimal sampling and for the presence of cellular abnormalities that had been missed at the time of the original reporting. MAIN OUTCOME MEASURES--The number of interval cases of cancer of the cervix registered during 1982-6. The proportion of interval cases occurring in younger women and the proportion occurring in older women. Division of women into three risk categories based on clinical history and screening history that broadly corresponded to the probability that a diagnosis of cervical cancer might be expected during the 36 months after the issuing of a negative smear report. RESULTS--138 Of 1044 (13.2%) women who had been registered with cervical cancer during 1982-6 had had one or more negative smears during the 36 months preceding the diagnosis of cancer. Interval cancers comprised a larger proportion of registrations of cervical cancer in women aged less than 35 years than in women aged 35-69 (21.1% v 11.0%, p less than 0.01). Women with interval cancer who had had at least three negative smears during the 10 years before the diagnosis of cancer were commoner in the younger age group than in the older age group (7.0% v 2.5%, p less than 0.01). When, however, the number of observed cases of squamous cell carcinoma was related to the number of expected cases in the absence of screening, no significant difference was found between the two age groups (6.8% v 4.8%, p greater than 0.10). The rate of diagnosis of interval cancer per 100,000 negative tests was lower among younger women than among older women (10/100,000 v 16/100,000). Review of the negative slides showed that 11.9% were again considered to be negative with an optimal sample having been obtained as evidenced by the presence of endocervical cells or metaplastic cells, or both. CONCLUSIONS--Interval cancers might comprise a larger proportion of all registered cases of cervical cancer among younger women owing to the larger proportion of such cancers being prevented in this age group. Among women with interval cancer review of the negative slides showed that most were accounted for by suboptimal sampling or by errors of reporting.     

A two-sample comparison for multiple ordered event data

A longitudinal study is conducted to compare the process of particular disease between two groups. The process of the disease is monitored according to which of several ordered events occur. In the paper, the sojourn time between two successive events is considered as the outcome of interest. The group effects on the sojourn times of the multiple events are parameterized by scale changes in a semiparametric accelerated failure time model where the dependence structure among the multivariate sojourn times is unspecified. Suppose that the sojourn times are subject to dependent censoring and the censoring times are observed for all subjects. A log-rank-type estimating approach by rescaling the sojourn times and the dependent censoring times into the same distribution is constructed to estimate the group effects and the corresponding estimators are consistent and asymptotically normal. Without the dependent censoring, the independent censoring times in general are not available for the uncensored data. In order to complete the censoring information, pseudo-censoring times are generated from the corresponding nonparametrically estimated survival function in each group, and we can still obtained unbiased estimating functions for the group effects. A real application and a simulation study are conducted to illustrate the proposed methods.