Bayesian Estimation of the Three Key Parameters in CT for the National Lung Screening Trial Data

Abstract

In this study cancer screening likelihood method was used to analyze the CT scan group in the National Lung Screening Trial (NLST) data. Three key parameters: screening sensitivity, transition probability density from disease free to preclinical state, and sojourn time in the preclinical state, were estimated using Bayesian approach and Markov Chain Monte Carlo simulations. The sensitivity for lung cancer screening using CT scan is high; it does not depend on a patient's age, and is slightly higher in females than in males. The transition probability from the disease-free to the preclinical state has a peak around age 70 for both genders, which agrees with the fact that the highest lung cancer incidence rate appears between age 65 and 74. The posterior mean sojourn time is around 1.5 years for all groups, and that explains why screening only have a short time interval to catch lung cancer. Accurate estimation of the three key parameters is critical for other estimations such as lead time and over-diagnosis, because these quantities are functions of the three key parameters. Journal of Biometrics & Biostatisticsandwhere t represents age and x is the sojourn time in the preclinical state S p . We associate the sensitivity β with age t by a logistic link, m is the average age at entry in the whole study group, in this data, m=61.4 years. If b_ 1 >0, then β(t) will be a monotone increasing function of age t. The lognormal distribution was chosen for w(t) with an upper limit of 30%. According to the NIH SEER database, the lifetime risk of lung cancer for the general population is about 7% for both genders [2]. Since participants in the NLST were heavy smokers, the risk would be higher than that, besides the fact that not all people in the preclinical state will progress into clinical cancer. This research proposes 30% as a reasonable upper limit for w(t). A more detailed description of the parametric models can be found in Wu et al. [5,6]. We choose a different sojourn time distribution than Wu et al. [5], where the previous research used log logistic, and we use Weibull distribution here, both share the same property of mathematical simplicity, and both are stable with 2 parameters. However, Weibull is more flexible in that the n-th moments always exist. ResultsThe six unknown parameters θ=(b 0 , b 1 , μ, σ 2 , λ, α) were estimated based on the NLST data CT arm. We split the data into three groups: male, female and overall. Theoretically, the parameters have a domain of either (-∞,+∞) or (0,+∞). The practical meaning of these parameters will limit them to a finite range. As was described in [5,7], the range for each parameter can be identified as: 0<b_ 0 <4, -0.1<b_ 1 <0.1, 4.0<μ<4.5, 0.01<σ 2 <0.05, 0.01<λ<0.5, and 1.5<α<4.0.Markov Chain Monte Carlo (MCMC) was used to draw posterior samples with non-informative Uniform priors. We partitioned the posterior simulation into three subchains, sampling the posterior for (b 0 , b 1 ), (μ, σ 2 ), (λ, α) separately. Two simulations were carried out with different i...

Inference of Sojourn Time and Transition Density using the NLST X-ray Screening Data in Lung Cancer

“…[10] Wu et al demonstrated that the 95% highest posterior density (HPD) interval for sensitivity is (0.72, 0.98) with a posterior mean 0.89 on the Mayo Lung Project. [7] The sensitivity estimated in the study of Liu et al [11] using the NLST low dose CT group data was around 0.95 for all male-female groups, confirming that low dose CT scan improves lung cancer screening sensitivity greatly. Three previous studies had reported sensitivity of chest X-ray and that had a low risk of bias and, the sensitivity estimates for these studies were: 79.3% (95% CI = 67.6 to 91.0%), 76.8% (95% CI = 64.5 to 84.2%), and 79.7% (95% CI = 72.7 to 86.8%).…”

Lead time distribution for individuals with a screening history

“…and the same parametric models for the w(t), q(x) and Q(x) as in Equations ( 14)- (16). The six unknown parameters θ = (b 0 , b 1 , μ, σ 2 , λ, α) were estimated using Markov Chain Monte Carlo (MCMC) and a likelihood function based on the NLST-LDCT data [22]: two Markov Chains were simulated with overdispersed initial values. Each chain ran 130,000 iterations, with 30,000 burn-in steps; after the burn-in, the posteriors were sampled every 200 steps, providing 500 posteriors θ * from each chain.…”

Sampling-based Markov regression model for multistate disease progression: Applications to population-based cancer screening program

“…Although our proposed non-standard case-cohort design can be applied to any continuous-time Markov process with states defined by each study, for the ease of presentation without loss of generality, the conventional three-state Markov model is applied to elucidating the multistate natural history of BC and CRC, commencing from the disease-free status (state 0), asymptomatic status without clinical symptom but can be detected by the screening method (state 1) defined as the preclinical detectable phase (PCDP), and symptomatic status showing clinical symptoms and signs (state 2) defined as the clinical phase (CP). While the proposed Markov processes were applied to population-based screening data as shown in several our and other previous studies, 7,8,11,22–27 they should be calibrated to accommodate three major issues, including censoring, truncation related to length-bias, and imperfect sensitivity. Lacking of calibration for these issues often led to biased estimates even when a sampling-based Markov process is applied.…”