Estimation of Lead Time via Low-Dose CT in the National Lung Screening Trial

Abstract

Based on recent reports from the National Lung Screening Trial (NLST), smokers who were screened by low-dose computer tomography (LDCT) had a 20% lower chance of dying from lung cancer than those screened by chest X-rays. However, due to the complexities of lead time bias and over diagnosis, no formal test has been shown to reduce lung cancer mortality. To correctly evaluate survival benefit due to early detection, it is critical to estimate lead time, the length of time that detection of a disease is advanced by screening. We applied a recently developed probability method to estimate lead time, using the LDCT data from NLST, where human lifetime was treated as random and derived from the actuarial life table of the US Social Security Administration. Using Bayesian posterior samples of key parameters extracted from the NLST-LDCT data, simulations on lead time were carried out on 16 hypothetical cohorts with four initial ages (55, 60, 65, and 70) and four future screening intervals (12, 18, 24, and 30 months). For each scenario, the estimated lead time for both screen-detected and interval cases is reported. Results show that the probability of no-early-detection (interval cases) increases monotonically when the screening interval increases for both genders. A male heavy smoker with an initial screening age at 60 has 11.65% (female 6.76%) chance of no-early-detection with annual screenings. This probability increases to 36.35% (female 28.26%) if the screenings were biennial. The mean lead time appears longer for women than for men. The mean lead time decreases when the screening interval increases, but it appears stable across different initial age groups. These results lay a foundation to evaluate survival benefit accurately with LDCT and to schedule future screening exams.

Appendix 1

The posterior samples were generated using the NLST-LDCT data. The data structure is presented in table below. The data we used includes the number of participants in kth screening exam (n_k), the number of kth screening-detected and confirmed cancer cases (s_k), and the number of interval-incident cases (r_k), stratified by initial age.

Age (t0)	n1	s1	r1	n2	s2	r2	n3	s3	r3
⋮
60	1940	18	3	1847	12	1	1807	17	1
61	1886	16	0	1678	15	1	1630	11	3
62	1558	10	1	1452	9	2	1408	12	0
⋮

The likelihood function used to estimate three key parameters was originally derived in Wu et al. [29]. In the NLST study, the initial age of participants enrolled was from 55 to 74 years, and the participants underwent three annual screening exams. Hence, the likelihood function for all groups becomes

$$ L=\prod \limits_{t_0=55}^{74}\prod \limits_{k=1}^3{D}_{k,{t}_0}^{s_{k,{t}_0}}{I}_{k,{t}_0}^{r_{k,{t}_0}}{\left(1-{D}_{k,{t}_0}-{I}_{k,{t}_0}\right)}^{n_{k,{t}_0}-{s}_{k,{t}_0}-{r}_{k,{t}_0}}, $$

(A.1)

where ${D}_{k,{t}_0}$ is the probability that an individual will be diagnosed at the kth scheduled exam given that the person is in preclinical state, and ${I}_{k,{t}_0}$ is the probability of being incident in the kth screening interval. These two probabilities were both functions of three key parameters. The three key parameters can be modeled by parametric functions as shown in Eqs. (8)–(10); therefore, the likelihood function (A.1) can be expressed as a function with unknown parameters θ = (b₀, b₁, μ, σ², λ, α).

The Metropolis-Hastings algorithm was used to generate posterior samples with non-informative Uniform priors (see Liu et al. [27] for details.). The generated 1000 MCMC posterior samples for both genders are in the supplementary material.