Trade-off between benefits, harms and economic efficiency of low-dose CT lung cancer screening: a microsimulation analysis of nodule management strategies in a population-based setting

Background In lung cancer screening, a nodule management protocol describes nodule assessment and thresholds for nodule size and growth rate to identify patients who require immediate diagnostic evaluation or additional imaging exams. The Netherlands-Leuvens Screening Trial and the National Lung Screening Trial used different selection criteria and nodule management protocols. Several modelling studies have reported variations in screening outcomes and cost-effectiveness across selection criteria and screening intervals; however, the effect of variations in the nodule management protocol remains uncertain. This study evaluated the effects of the eligibility criteria and nodule management protocols on the benefits, harms and cost-effectiveness of lung screening scenarios in a population-based setting in Germany. Methods We developed a modular microsimulation model: a biological module simulated individual histories of lung cancer development from carcinogenesis onset to death; a screening module simulated patient selection, screening-detection, nodule management protocols, diagnostic evaluation and screening outcomes. Benefits included mortality reduction, life years gained and averted lung cancer deaths. Harms were costs, false positives and overdiagnosis. The comparator was no screening. The evaluated 76 screening scenarios included variations in selection criteria and thresholds for nodule size and growth rate. Results Five years of annual screening resulted in a 9.7–12.8% lung cancer mortality reduction in the screened population. The efficient scenarios included volumetric assessment of nodule size, a threshold for a volume of 300 mm3 and a threshold for a volume doubling time of 400 days. Assessment of volume doubling time is essential for reducing overdiagnosis and false positives. Incremental cost-effectiveness ratios of the efficient scenarios were 16,754–23,847 euro per life year gained and 155,287–285,630 euro per averted lung cancer death. Conclusions Lung cancer screening can be cost-effective in Germany. Along with the eligibility criteria, the nodule management protocol influences screening performance and cost-effectiveness. Definition of the thresholds for nodule size and nodule growth in the nodule management protocol should be considered in detail when defining optimal screening strategies. Electronic supplementary material The online version of this article (doi:10.1186/s12916-017-0924-3) contains supplementary material, which is available to authorized users.

: Parameters for the long-term survival probability and the Weibull distributions for time period from clin ical diagnosis to lung cancer death by cell type and stage at diagnosis 7

Modules of the microsimulation model
The model is of modular design and comprises of the following structural modules: Population, Natural History, Clinical Detection and Survival, Screening and Life History.

Population module
Population module creates a screening population with the given demographic structure and smoking patterns.
The individuals in the simulated population were characterized by gender, age at model entry point and then defined by the age at the point of initial smoking, age at smoking cessation and the average number of cigarettes consumed per day. Smoking history determines the exposure to cigarette smoke (first hand), which along with age and gender governs age of death from other causes.
Smoking behaviour data were obtained from two national health surveys conducted between 2008 and 2012: the German Health Interview and Examination Survey for Adults (DEGS) and the German Health Update (GEDA) 1 .
Due to the data availability, the demographic structure was taken from the year of 2012 2 . Based on the smoking behaviour data and demographic structure, the population for the simulation was obtained via bootstrapping 10% of the German population. Smoking behaviours of current smokers were extrapolated over the course of a lifetime and during the modelled years the current smokers could quit smoking. The smoking cessation age was calculated by using the smoking cessation probabilities , which were assigned according to estimates obtained based on the data from the national health surveys.

Other-cause mortality
In the Population module an individual age of death from other causes than lung cancer is simulated based on age at entry the model, gender and the smoking status: never-, current-or former smoker. Five-year survival probabilities across age, gender and the smoking status were constructed based on the estimates obtained by Woloshin et al 3 and extrapolated using the recent life tables for the German population 2 . Other-cause mortality was introduced into the model as a competing risk and computed by applying the probability estimates and two random numbers (for each individual) which defined a five-year age interval in which the person may die from other causes and then the exact age of death within this interval.

Natural History module
The Natural History module simulates the development of lung cancer during individual life course. The sequence of events starts with onset of the first malignant cell, evolves through the progressive stages of lung cancer and ends with the death from the cancer.
The onset of the first malignant cell is simulated by using the biological two-stage clonal expansion (TSCE) model described by Moolgavkar and Luebeck 4 , where age, gender and personal exposure to cigarette smoke are translated into the piecewise constant parameters of the hazard functions. Onset lung cancer is modelled as a competing risk between four histological types: small cell-, large cell-, squamous cell-and adenocarcinomas. For each histological type, we drew an individual age at onset of carcinogenesis from a respective survival function.
The histologic type that develops first is defined as the active cancer. We assume that 20% of adenocarcinomas are of type adenocarcinoma in situ 5 . Additionally, if the onset of cancer takes place, we assume a single malignant nodule per person.
The progression of the cancer is characterised by its growth, nodal involvement and occurrence of distant metastases. Threshold values of tumour volumes at the stages of nodal involvement and distant metastases depend on the histologic cancer type and are rand omly drawn from log-Normal distributions. We applied a Gompertz function to model tumour growth over time 5 . This function determines the individual age at every stage of disease progression given the respective threshold volumes are reached (see section Modelling details of the Natural History, Clinical detection and Survival modules ).

Clinical detection and Survival module
Clinical detection and Survival module simulates symptomatic detection of lung cancer, which includes age and tumour volume at the time of diagnosis, and age of death from lung cancer. The distribution of the tumour volumes at time of diagnosis is given by the log-Normal distribution; age at the time of diagnosis is analogously calculated by using the tumour growth function. Persons with clinical detection undergo diagnostic procedures which include PET CT, EBUS bronchoscopy and head MRI 6 . The diagnosis is assigned according to the TNM Classification of Malignant Tumours (TNM) by the Union for International Cancer Control (UICC). Treatment is not explicitly modelled, however, its effects are implicitly included in lung cancer survival function. The survival depends on the histological class and stage at the time of diagnosis and follows the Weibull distribution 7 (see Table 1). It is assumed that death from lung cancer occurs after the time of clinical diagnosis. Onset of the first malignant cell of each histological class is expressed by the biological two-stage clonal expansion (TSCE) model. The hazard rates and the survival probabilities are given by the equations below which were adopted from an R package "MIcrosimulation Lung Cancer (MILC) model" by Chrysanthopoulou AS. 8 Hazard function for the development of the first malignant cell is described by 8 : where X is total number of normal cells, υ is the normal cell initiation rate, μ is the malignant transformation rate, γ and B are piecewise constant parameters which are determined by: where α the cell division rate and β is the rate of programmed cell death.
For the hazard function, a cumulative hazard function than is constructed and given by 8 : where q ( t ) is the average number of cigarettes consumed per day at age t and α 0 and γ 0 represent coefficients for never smokers. The parameters are given in Table 2.  Table  2 for CPS-II cohort. The life course is segmented into periods which are defined by age, gender and smoking status. Table 3 describes the division. The periods are bounded by age given by a and b, 0 < a < b< , where depicts the age of death. Over these periods the survival functions are differently parameterized to express differences in the risk of onset of carcinogenesis. The parameters for the survival functions are given in Table 4 and are constant over the given period.  Depending on the smoking status an individual life course can be divided into periods as follows. The periods are denoted by T 1 , T 2, T 3 and T 4 .

Never smoker:
For never smokers a life course is divided into three periods in which the survival function is parametrized with different malignant conversion rates (Table 4).
with T 1 = and T 1 =

Current smoker:
For current smokers a life course is divided into four periods which are defined by the age boundaries (as for never smokers) and age at start smoking. The age at smoking initiation can fall into any of the three periods and alter the parameterization for the hazard and survival functions over the periods following the time at smoking initiation as follows: with T is age at start smoking, 0 < < < ; 0 < T < , and:

Former smoker:
For former smokers a life course is divided into five periods given by the age boundaries (as for non-smokers), age at smoking initiation and age at smoking cessation. The hazard and survival functions are respectively parameterized over the pre-smoking, smoking and post-smoking periods.
The survival functions for former smokers are described as follows: with age at initial cigarette smoking and age of cessation, 0 < < < ; 0 < < < , and:

Tumour growth
The following Gompertz function for tumour growth is applied: Where 0 and ( ) represent initial tumour volume and ( ) tumour volume at time , and are the location and scale parameters of the Gompertz distribution.
Maximum tumour volume V max in the Gompertz function is given by: With a given , the volume of the tumour developed over time is expressed by: and time needed to reach volume ( ) can be computed as: where is the growth rate which is drawn from lognormal distributions parameterized according to the histological class (see Table 5) 5 .
Relationship between and a set diameter is described by: where D is a given diameter.
Limits of diameters for are fixed to 277 mm for all histological types except adenocarcinoma in situ for which the limit of diameter for is set to 30 mm.

Modelling regional and distant stages of the disease progression
The disease progression is featured via tumour growth, nodal involvement (regional stage) and metastases (distant stage). It has been previously shown that with a Gompertzian tumour growth function, the disease progression through advanced stages over time are characterized by specific tumour volumes, location and presence of metastases can be well described by applying log-Normal distributions 8 .
Threshold tumour volumes for regional and distant stages are drawn from log -Normal distributions constructed for each histological class ( = 1,2,3,4) and stage ( =regional, distant, clinical diagnosis) as lognormal( , , , 2 ). If a person's threshold volume exceeds computed for her , the corresponding cancer stage will not be reached during the lifetime of this person.
The threshold volumes across the histological classes and progression stages are given in the Table 6 below. The log-Normal distributions are constructed by transforming these volumes to mean and standard deviations of the lognormal( , , , 2 ) distributions.

Screening module
Screening module contains several structural components: eligibility assessment, screen -detection, nodule management (includes follow-up), diagnostic work-up and lung cancer survival.

Eligibility assessment
The eligibility criteria include qualifying age range, accumulated pack-years and number of years since cigarette cessation. Once eligible an individual undergoes a screen chest exam with LDCT.

Screen-detection
The probability of a screen-detection of a nodule depends on the presence of lung cancer and the sensitivity of the LDCT-test. The sensitivity of CT varies with nodule size and its location ( Table 7). The location is considered of two types, central and peripheral, and varies with histological classes 5 . In the case of screendetection of a nodule, the person proceeds through the nodule management algorithm. In the case of no detection, the person is scheduled for the next screening round.

Nodule management algorithms
The

Diagnostic work -up
The diagnostic work-up component models a one-month long period when a patient undergoes a CT-supported biopsy to determine malignancy of the nodule and a head MRI (magnetic resonance imaging) and proceed with diagnosis. Screen-detected nodules are staged according to the TNM system based on the tumour diameter/volume and the progression state at time of diagnosis. During the diagnostic work-up a complication (pneumothorax) may occur, which is modelled as an age-dependent probability (see Table 7).

Lung cancer survival
Description is given in the main text.
where ∆ is time in days between the initial screening and the follow-up exams, 1 is the nodule volume at the time of initial screening, and 2 is the volume at the follow-up

Life history module
For the screening and no screening scenarios , the Life History module calculates the final life scenario for each individual, providing the chronological sequence of events and final age of death along with the cause of death.
The module also calculates events of false-positive cases, overdiagnosed cases, interval cancers and radiation induced cancer and deletes obsolete cases. induce pneumothorax as a complication with the age-dependent probability (see Table 7). The false-positive findings are retroactively included into the model.

Overdiagnosed cases
A case of overdiagnosis is defined as an individual whose lung cancer is expected to be clinically diagnosed after her age of death from other causes but whose cancer is screen -detected before this age (de Koning, Harry J. et al. 2014).

Interval lung cancer
Interval lung cancer is defined as a cancer which is not initially screen -detected but is diagnosed in the time between scheduled screening exams 14 . The module incorporates two sources of interval lung cancer occurrence.
The first is false-negative screening results, which can occur due to the nodule size-dependent sensitivity of CT scan. The second is the truly interval lung cancer, which develops and is diagnosed within the time interval between two screenings.

Radiation-induced cancer
Radiation-induced cancer death may occur in a 10-20-year period after the screening program. The risk is calculated as one radiation-induced cancer death per 2500 screened individuals who received 8 mSv in a 3-year period; these estimates are obtained based on the NLST trial 15 .

Screening scenarios
Based on Table 1 in the main paper, name of a scenario contained specified population, nodule management protocol, thresholds for nodule size and nodule growth. The scenarios were additionally numbered from 1 to 76.
The scenarios that simulated NELSON-like and NLST-like nodule management protocols were 50-75-15-9-NELSON-VDT400-V500 and 55-74-30-15-NLST-GR10-D10.  17 Long-term survival probability for stages I and II in the case the patients would die from lung cancer in the no screening scenario 0.4 7 *people at regional stage of cancer progression can be diagnosed either with stage II or stage III of T NM system.

Model calibration
The calibration process was performed in two steps. Firstly, for each lung cancer type mean and standard deviation of the log-Normal distributed threshold volumes of lymph nodes involvement (regional), distant metastases (distant) and clinical diagnosis were simultaneously calibrated to fit the German UICC data on diseases stage at time of diagnosis 11 . The parameters for the log-Normal distribution of the tumour volumes at time of clinical diagnosis differed depending on the disease stage progression: before and after the lymph nodes involvement (regional stage). Table 6 (section 1.1.4.3) presents the applied parameters in the columns "diagnosis before the regional stage" and "diagnosis after the regional stage". Data limitations allowed for the calibration of a limited number of parameters per cancer type. Therefore, we assumed that the mean and standard deviations of the threshold volumes are equal (see "Tumour growth" section).
Secondly, we simultaneously calibrated the age-and cancer type-dependent malignant conversion rates and age boundaries of the survival functions (derived from the hazard functions, see section 1.1.4.1). The outcomes of the microsimulation model (no screening scenario) were fitted to German age and cancer type specific annual incidental lung cancer cases of the period 2010-2012 11 . The second calibration step was done separately for males and females.
The Nelder-Mead Simplex method implemented in the R package "FME" 18 was used to minimize squared residuals in both calibration steps.

Health economics
The costs per unit were obtained using EBM (Unit assessment scale applied in the German healthcare) or DRG (Diagnosis Related Groups) codes and are summarized in Table 8. The model includes CT-guided needle biopsy-induced pneumothorax as a complication that leads to increased costs of the staging tests.  23 . The same calculations were performed for each of the six evaluated scenarios and scenarios of the sensitivity analys is.

Sensitivity analysis
Parameter uncertainty: We varied the nodule size-dependent sensitivity parameters of LDCT exam within a range of ±20%. The long term survival probability for the screened individualswho were diagnosed at screening with lung cancer in stage I or II and who would die of the cancer in the non-screening scenariowas tested for the range of values: 20%, 30%, 50% and 60%. We decreased adherence for the next years after the initial screening to 85%.

Additional scenarios:
We prolonged the period of the screening program and simulated ten years of annual screening for each of the evaluated scenarios. The cost per LDCT unit varied across three different scenarios (Table 8). Additionally, the total costs were analyzed for a hypothetical scenario (scenario 4) when staging tests at screening were the same as at clinical settings in no screening scenario.
Because treatment costs are based on different assumptions we tested possible impacts of the treatment costs in the sensitivity analyses. In the pessimistic scenario the costs for Stage I and II are based on the ratio of costs between stage IV and I (see Table 9, example is given for 50-75-15-9-NELSON-VDT400-V500). In the last years a few cost inducing pharmaceutical drugs for lung cancer treatment have been developed and introduced to the market 25 . It is possible that they were not taken into the calculations by Mc Guirre et al. To account for that we added the third scenario with lifetime costs for the patients with the advanced cancer of 77,702€ 26 (see Table   9).