^{ 1}Department of Medical Oncology, GROWSchool for Oncology and Developmental Biology, Maastricht University Medical Center, Maastricht, The Netherlands
^{ 2}Radboud Institute for Health Sciences, Department for Health Evidence, Radboud University Medical Center, Nijmegen, The Netherlands
^{ 3}Institute of Epidemiology and Preventive Medicine, National Taiwan University, Taipei, Taiwan
^{ 4}Dutch Expert Centre for Screening, Nijmegen, The Netherlands
^{ 5}Wolfson Institute of Preventive Medicine, Barts and The London School of Medicine and Dentistry, Queen Mary University of London, London, UK
©2022, Korean Society of Epidemiology
This is an openaccess article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
^{} CONFLICT OF INTEREST
The authors have no conflicts of interest to declare for this study.
^{} FUNDING
None.
This study was conducted under the research project “Research and Development on Integrated Surveillance System for Early Warning of Infectious Diseases” (RISEWIDs).
^{} AUTHOR CONTRIBUTIONS
Conceptualization: Geurts SME, Aarts AMWM, Verbeek ALM, Broeders MJM, Duffy SW. Data curation: Geurts SME, Aarts AMWM, Verbeek ALM, Broeders MJM, Duffy SW. Formal analysis: Geurts SME, Aarts AMWM, Verbeek ALM, Broeders MJM, Duffy SW. Funding acquisition: None. Methodology: Geurts SME, Aarts AMWM, Verbeek ALM, Broeders MJM, Duffy SW. Writing – original draft: Geurts SME, Aarts AMWM, Verbeek ALM, Broeders MJM, Duffy SW. Writing – review & editing: Geurts SME, Aarts AMWM, Verbeek ALM, Broeders MJM, Duffy SW, Chen THH.
Term  Definition  Reference 

PCDP duration  The time interval between the start of the PCDP and the time when the cancer manifests clinically (in the absence of screening); The starting point of the PCDP depends upon characteristics of the screening test, notably its sensitivity  [26] 
Sensitivity  The proportion of people with a positive screening test among those who have a cancer in the preclinical detectable phase; Sensitivity is usually considered to be a constant throughout the PCDP, but this is likely to be only approximately true; Intuitively, sensitivity would be lower for smaller tumors earlier in the PCDP and higher for larger tumors later in the PCDP  [1] 
Lead time  The duration by which the diagnosis of a cancer is moved forward in time due to detection during a screening examination rather than being detected clinically; In other words, the PCDP duration is the “potential time” a diagnosis of a cancer is moved forward, while lead time is the actual time; Under the assumption of an exponential PCDP distribution, the mean PCDP duration can also be an estimate of the expected lead time for an individual cancer  [20] 
Screendetected cancers  Cancers diagnosed by a screening examination, whereas interval cancers are clinically diagnosed between screening examinations  [12] 
Length time bias  Length bias occurs because slowly growing tumors with a favorable prognosis have a longer preclinical detectable phase, and are thus more frequently detected at screening than rapidly growing tumors with an unfavorable prognosis  [1] 
Overdiagnosis  The diagnosis of cancer at screening that would never have caused any symptoms or problems during an individual’s lifetime  [41] 
Mathematical approach to estimation 
Data source 


Screened and unscreened populations^{1}  Screened population  
Prevalencetoincidence ratio  Hutchinson 1968 (breast) [13]  Launoy 1997 (colorectal) [18]^{2} 
Zelen 1969 (breast) [6]  Brenner 2011 (colorectal) [19]  
Shapiro 1974 (breast) [14]  
Albert 1978 (cervix) [15,16]  
Louis 1978 (cervix) [17]  
Maximum likelihood estimation  Walter 1983 (breast) [20]  Brookmeyer 1986 (cervix) [24]^{3} 
Day 1984 (breast) [7]  Brookmeyer 1987 (cervix) [25]^{3}  
Alexander 1989 (breast) [21]  Launoy 1997 (colorectal) [18]^{2}  
Shen 2005 (breast) [23]  Straatman 1997 (breast) [26]  
Shen 1999 (breast) [27]  
Pinsky 2001 (colorectal) [28]  
Hsieh 2002 (breast) [29]  
Pinsky 2004 (lung) [22]  
Wu 2005 (breast) [30]^{2}  
Cong 2005 (breast) [31]  
Jiang 2016 (breast [12]  
Shen 2019 (breast) [32]  
Expectationmaximization algorithm  Etzioni 1997 (breast) [33]  
Regression of observed on expected  Chen 1996 (breast) [34]  Paci 1991 (breast) [8] 
Chen 1997 (breast) [35]  Duffy 1995 (breast) [11]  
Duffy 1997 (breast [36]  
Chen 2000 (breast) [37]  
Bayesian Markovchain Monte Carlo simulation  Myles 2003 (breast) [39]  Launoy 1997 (colorectal) [18]^{2} 
Wu 2005 (breast) [30]^{2}  
Kim 2015 (breast, lung) [40]  
Shen 2017 (lung) [38] 
^{} Values arre presented as author, year (cancer type used as an example).
^{1} The unscreened population is considered as a control group, and may include the control arm of a randomized controlled trial or a historical control group from the time period before screening.
^{2} Studies that describe multiple mathematical approaches to estimate the PCDP duration.
^{3} The study design of these articles was casecontrol.
Study 
Model assumptions 


Author, year  Screening round (first and/or subsequent)  Screening data used for estimation (screendetected and/or interval cancers)  Underlying incidence of cancer (estimated within the model, observed from the control group, observed from registry data or not included)  Assumed distribution(s) of the preclinical detectable phase duration  Lead time modeled (yes, no) and its assumed distribution  Confidence interval or standard error around estimate (yes, no)  Test sensitivity (estimated within the model, assumed 100%, observed from the literature, or not included)  Tumor regression modeled (yes, no), estimates corrected for length time bias and/or overdiagnosis  
Prevalence to incidence ratio  
Hutchinson, 1968 [13]  First  Screendetected cancer data  Observed from the control group  Constant  Yes, constant  No  Assumed 100%  No, no  
Zelen, 1969 [6]  First  Screendetected cancer data  Observed from the control group  Exponential  Yes, exponential  No  Assumed 100%  Yes, length time correction  
Shapiro, 1974 [14]  First  Screendetected and interval cancer data  Observed from the control group (corrected for selfselection)  Exponential  No, NA  No  Assumed 100%  No, no  
Albert, 1978 [15,16]  First  Screendetected cancer data  Observed from the control group  Exponential, gamma  Yes, exponential  No  Not included  Yes, length time and overdiagnosis correction  
Louis, 1978 [17]  
Launoy, 1997 [18]^{1}  First  Screendetected and interval cancer  Observed from registry data  Not reported  No, NA  Yes  Estimated within the model  No, no  
Brenner, 2011 [19]  First  Screendetected cancer data  Observed from registry data  Exponential  No, NA  Yes  Assumed 100%  No, no  
Maximum likelihood estimation  
Walter, 1983 [20]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential, lognormal, step function  Yes, NA  Yes  Estimated within the model  No, length time correction  
Day, 1984 [7]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential  Yes, exponential  Yes  Estimated within the model  No, length time correction  
Brookmeyer, 1986 [24]  First and subsequent  Screendetected and interval cancer data  Not included (canceled out the model)  Exponential, piecewise exponential, Weibull, lognormal  No, NA  Yes  Estimated within the model  No, no  
Brookmeyer, 1987 [25]  First and subsequent  Screendetected and interval cancer data  Not included (canceled out the model)  Exponential  No, NA  Yes  Estimated within the model  Yes, overdiagnosis correction  
Alexander, 1989 [21]  First and subsequent  Screendetected and interval cancer data  Observed from the control group (corrected for selfselection)  Exponential  Yes, exponential  No  Estimated within the model  No, no  
Launoy, 1997 [18]^{1}  First  Screendetected and interval cancer data  Observed from registry data  Not reported  No, NA  Yes  Estimated within the model  No, no  
Straatman, 1997 [26]  First and subsequent  Screendetected cancer data  Estimated within the model  Exponential  Yes, exponential  No  Estimated within the model  No, no  
Shen, 1999 [27]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Estimated within the model  No, no  
Pinsky, 2001 [28]  First  Screendetected and interval cancer data  Observed from registry data  Exponential, gamma & Weibull  Yes, not reported  Yes  Estimated within the model  No, length time and overdiagnosis correction  
Hsieh, 2002 [29]  First and subsequent  Screendetected cancer data  Estimated within the model  Weibull and piecewise exponential  No, NA  Yes  Assumed 100%  No, no  
Pinsky, 2004 [22]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential, Weibull  Yes, not reported  Yes  Estimated within the model  No, overdiagnosis correction  
Shen, 2005 [23]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Piecewiseconstant  No, NA  No  Estimated within the model  No, no  
Wu, 2005 [30]1  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Loglogistic  No, NA  No  Estimated within the model  No, no  
Cong, 2005 [31]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Estimated within the model  No, no  
Jiang, 2016 [12]  First and subsequent  Screendetected and interval cancer data  Not included (assumed constant)  Exponential  No, NA  Yes  Estimated within the model  No, no  
Shen, 2019 [32]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Observed from literature  Yes, no  
Expectationmaximization algorithm  
Etzioni, 1997 [33]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  NA  No, NA  No  Estimated within the model  No, no  
Regression of observed on expected  
Paci, 1991 [8]  First and subsequent  Interval cancer data  Estimated within the model  Exponential  Yes, exponential  Yes  Estimated within the model  No, no  
Duffy, 1995 [11]  First and subsequent  Interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Assumed 100%  No, no  
Chen, 1996 [34]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential  No, NA  Yes  Estimated within the model  No, no  
Chen, 1997 [35]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential  No, NA  Yes  Assumed 100% or observed from the literature  No, no  
Duffy, 1997 [36]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Estimated within the model  No, no  
Chen, 2000 [37]  First and subsequent  Screendetected cancer data  Estimated within the model  Not reported  No, NA  Yes  Assumed 100% or estimated within the model  No, no  
Bayesian Markovchain Monte Carlo simulation  
Launoy, 1997 [18]^{1}  First  Screendetected and interval cancer data  Observed from registry data  Not reported  No, NA  Yes  Estimated within the model  No, no  
Myles, 2003 [39]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Poisson  No, NA  Yes  Estimated within the model  No, no  
Wu, 2005 [30]1  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Nonparametric  No, NA  Yes  Estimated within the model  No, no  
Kim, 2015 [40]  First and subsequent  Screendetected interval cancer data  Estimated within the model  Loglogistic  No, NA  Yes  Estimated within the model  No, no  
Shen, 2017 [38]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Assumed 100% or estimated within the model  Yes, overdiagnosis correction 
Term  Definition  Reference 

PCDP duration  The time interval between the start of the PCDP and the time when the cancer manifests clinically (in the absence of screening); The starting point of the PCDP depends upon characteristics of the screening test, notably its sensitivity  [26] 
Sensitivity  The proportion of people with a positive screening test among those who have a cancer in the preclinical detectable phase; Sensitivity is usually considered to be a constant throughout the PCDP, but this is likely to be only approximately true; Intuitively, sensitivity would be lower for smaller tumors earlier in the PCDP and higher for larger tumors later in the PCDP  [1] 
Lead time  The duration by which the diagnosis of a cancer is moved forward in time due to detection during a screening examination rather than being detected clinically; In other words, the PCDP duration is the “potential time” a diagnosis of a cancer is moved forward, while lead time is the actual time; Under the assumption of an exponential PCDP distribution, the mean PCDP duration can also be an estimate of the expected lead time for an individual cancer  [20] 
Screendetected cancers  Cancers diagnosed by a screening examination, whereas interval cancers are clinically diagnosed between screening examinations  [12] 
Length time bias  Length bias occurs because slowly growing tumors with a favorable prognosis have a longer preclinical detectable phase, and are thus more frequently detected at screening than rapidly growing tumors with an unfavorable prognosis  [1] 
Overdiagnosis  The diagnosis of cancer at screening that would never have caused any symptoms or problems during an individual’s lifetime  [41] 
Mathematical approach to estimation  Data source 


Screened and unscreened populations^{1}  Screened population  
Prevalencetoincidence ratio  Hutchinson 1968 (breast) [13]  Launoy 1997 (colorectal) [18]^{2} 
Zelen 1969 (breast) [6]  Brenner 2011 (colorectal) [19]  
Shapiro 1974 (breast) [14]  
Albert 1978 (cervix) [15,16]  
Louis 1978 (cervix) [17]  
Maximum likelihood estimation  Walter 1983 (breast) [20]  Brookmeyer 1986 (cervix) [24]^{3} 
Day 1984 (breast) [7]  Brookmeyer 1987 (cervix) [25]^{3}  
Alexander 1989 (breast) [21]  Launoy 1997 (colorectal) [18]^{2}  
Shen 2005 (breast) [23]  Straatman 1997 (breast) [26]  
Shen 1999 (breast) [27]  
Pinsky 2001 (colorectal) [28]  
Hsieh 2002 (breast) [29]  
Pinsky 2004 (lung) [22]  
Wu 2005 (breast) [30]^{2}  
Cong 2005 (breast) [31]  
Jiang 2016 (breast [12]  
Shen 2019 (breast) [32]  
Expectationmaximization algorithm  Etzioni 1997 (breast) [33]  
Regression of observed on expected  Chen 1996 (breast) [34]  Paci 1991 (breast) [8] 
Chen 1997 (breast) [35]  Duffy 1995 (breast) [11]  
Duffy 1997 (breast [36]  
Chen 2000 (breast) [37]  
Bayesian Markovchain Monte Carlo simulation  Myles 2003 (breast) [39]  Launoy 1997 (colorectal) [18]^{2} 
Wu 2005 (breast) [30]^{2}  
Kim 2015 (breast, lung) [40]  
Shen 2017 (lung) [38] 
Study 
Model assumptions 


Author, year  Screening round (first and/or subsequent)  Screening data used for estimation (screendetected and/or interval cancers)  Underlying incidence of cancer (estimated within the model, observed from the control group, observed from registry data or not included)  Assumed distribution(s) of the preclinical detectable phase duration  Lead time modeled (yes, no) and its assumed distribution  Confidence interval or standard error around estimate (yes, no)  Test sensitivity (estimated within the model, assumed 100%, observed from the literature, or not included)  Tumor regression modeled (yes, no), estimates corrected for length time bias and/or overdiagnosis  
Prevalence to incidence ratio  
Hutchinson, 1968 [13]  First  Screendetected cancer data  Observed from the control group  Constant  Yes, constant  No  Assumed 100%  No, no  
Zelen, 1969 [6]  First  Screendetected cancer data  Observed from the control group  Exponential  Yes, exponential  No  Assumed 100%  Yes, length time correction  
Shapiro, 1974 [14]  First  Screendetected and interval cancer data  Observed from the control group (corrected for selfselection)  Exponential  No, NA  No  Assumed 100%  No, no  
Albert, 1978 [15,16]  First  Screendetected cancer data  Observed from the control group  Exponential, gamma  Yes, exponential  No  Not included  Yes, length time and overdiagnosis correction  
Louis, 1978 [17]  
Launoy, 1997 [18]^{1}  First  Screendetected and interval cancer  Observed from registry data  Not reported  No, NA  Yes  Estimated within the model  No, no  
Brenner, 2011 [19]  First  Screendetected cancer data  Observed from registry data  Exponential  No, NA  Yes  Assumed 100%  No, no  
Maximum likelihood estimation  
Walter, 1983 [20]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential, lognormal, step function  Yes, NA  Yes  Estimated within the model  No, length time correction  
Day, 1984 [7]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential  Yes, exponential  Yes  Estimated within the model  No, length time correction  
Brookmeyer, 1986 [24]  First and subsequent  Screendetected and interval cancer data  Not included (canceled out the model)  Exponential, piecewise exponential, Weibull, lognormal  No, NA  Yes  Estimated within the model  No, no  
Brookmeyer, 1987 [25]  First and subsequent  Screendetected and interval cancer data  Not included (canceled out the model)  Exponential  No, NA  Yes  Estimated within the model  Yes, overdiagnosis correction  
Alexander, 1989 [21]  First and subsequent  Screendetected and interval cancer data  Observed from the control group (corrected for selfselection)  Exponential  Yes, exponential  No  Estimated within the model  No, no  
Launoy, 1997 [18]^{1}  First  Screendetected and interval cancer data  Observed from registry data  Not reported  No, NA  Yes  Estimated within the model  No, no  
Straatman, 1997 [26]  First and subsequent  Screendetected cancer data  Estimated within the model  Exponential  Yes, exponential  No  Estimated within the model  No, no  
Shen, 1999 [27]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Estimated within the model  No, no  
Pinsky, 2001 [28]  First  Screendetected and interval cancer data  Observed from registry data  Exponential, gamma & Weibull  Yes, not reported  Yes  Estimated within the model  No, length time and overdiagnosis correction  
Hsieh, 2002 [29]  First and subsequent  Screendetected cancer data  Estimated within the model  Weibull and piecewise exponential  No, NA  Yes  Assumed 100%  No, no  
Pinsky, 2004 [22]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential, Weibull  Yes, not reported  Yes  Estimated within the model  No, overdiagnosis correction  
Shen, 2005 [23]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Piecewiseconstant  No, NA  No  Estimated within the model  No, no  
Wu, 2005 [30]1  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Loglogistic  No, NA  No  Estimated within the model  No, no  
Cong, 2005 [31]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Estimated within the model  No, no  
Jiang, 2016 [12]  First and subsequent  Screendetected and interval cancer data  Not included (assumed constant)  Exponential  No, NA  Yes  Estimated within the model  No, no  
Shen, 2019 [32]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Observed from literature  Yes, no  
Expectationmaximization algorithm  
Etzioni, 1997 [33]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  NA  No, NA  No  Estimated within the model  No, no  
Regression of observed on expected  
Paci, 1991 [8]  First and subsequent  Interval cancer data  Estimated within the model  Exponential  Yes, exponential  Yes  Estimated within the model  No, no  
Duffy, 1995 [11]  First and subsequent  Interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Assumed 100%  No, no  
Chen, 1996 [34]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential  No, NA  Yes  Estimated within the model  No, no  
Chen, 1997 [35]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Exponential  No, NA  Yes  Assumed 100% or observed from the literature  No, no  
Duffy, 1997 [36]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Estimated within the model  No, no  
Chen, 2000 [37]  First and subsequent  Screendetected cancer data  Estimated within the model  Not reported  No, NA  Yes  Assumed 100% or estimated within the model  No, no  
Bayesian Markovchain Monte Carlo simulation  
Launoy, 1997 [18]^{1}  First  Screendetected and interval cancer data  Observed from registry data  Not reported  No, NA  Yes  Estimated within the model  No, no  
Myles, 2003 [39]  First and subsequent  Screendetected and interval cancer data  Observed from the control group  Poisson  No, NA  Yes  Estimated within the model  No, no  
Wu, 2005 [30]1  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Nonparametric  No, NA  Yes  Estimated within the model  No, no  
Kim, 2015 [40]  First and subsequent  Screendetected interval cancer data  Estimated within the model  Loglogistic  No, NA  Yes  Estimated within the model  No, no  
Shen, 2017 [38]  First and subsequent  Screendetected and interval cancer data  Estimated within the model  Exponential  No, NA  Yes  Assumed 100% or estimated within the model  Yes, overdiagnosis correction 
Factors  Summary of findings 

Type of mathematical estimation approach  Prevalencetoincidence ratio models tend to give shorter estimates, and regression of observed on expected tends to give longer estimates of the PCDP duration and higher test sensitivities than other mathematical estimation approaches 
Data used  The use of only prevalence screening data tends to give shorter estimates, whereas the use of only interval cancer data tends to give longer estimates of the PCDP durations than using both 
Test sensitivity  Shorter durations of the PCDP are observed if 100% test sensitivity is assumed (these studies were predominated by the Health Insurance Plan study data with a younger population and 1960s film technology mammography) than when test sensitivity was estimated within the model 
Underlying incidence  No impact on the PCDP duration 
PCDP, preclinical detectable phase.
Values arre presented as author, year (cancer type used as an example).
The unscreened population is considered as a control group, and may include the control arm of a randomized controlled trial or a historical control group from the time period before screening.
Studies that describe multiple mathematical approaches to estimate the PCDP duration.
The study design of these articles was casecontrol.
correctionNA, not available.
Articles that described multiple methods to estimate the preclinical detectable phase duration.
PCDP, preclinical detectable phase.