Estimating Sensitivity and Sojourn Time in Screening for Colorectal Cancer: A Comparison of Statistical Approaches

American Journal of Epidemiology Copyright O 1998 by Trie Johns Hopkins University School of Hygiene and Public Health All rights reserved Vol. 148, No. 6 Printed In U.SA Estimating Sensitivity and Sojourn Time in Screening for Colorectal Cancer A Comparison of Statistical Approaches T. C. Prevost,1 G. Launoy,2 S. W. Duffy,1 and H. H. Chen3 colorectal neoplasms; mass screening; models, statistical; sensitivity and specificity BACKGROUND practice in screening programs is the average sojourn time over all disease cases, usually referred to as the mean sojourn time. A long mean sojourn time indicates a good potential for screening. The shorter the sojourn time, the more frequently screening has to take place in order to be effective. If the mean sojourn time is very short, screening may not be worthwhile at all. Note that this parameterization of the problem is a simplification of the biologic process. One would expect screen-detectability, as measured by sensitivity, to increase continuously with time, as the tumor grows, with varying rates of increase for different individuals. Under the mean sojourn time/sensitivity model as traditionally used, we approximate this by a screen-detectability which is zero up to the beginning of the preclinical screen-detectable period and is equal to constant sensitivity throughout the preclinical screen-detectable period. The length of the preclinical screen-detectable period is variable between individuals in this model. This is illustrated in figure 1. The sigmoid curve shows the true detectability and the rectangle the approximation which is traditionally assumed. This paper uses the rectangular assumption throughout for the sake of simplicity, and because it has previously been found to give a reasonable fit (1). However, the reader should bear in mind that it is a simplification. Screening for occult disease can be carried out for three major purposes: to eliminate those already infected as part of the strategy of an immunization program; to identify and quarantine carriers of an infective agent; and to advance the stage of disease at diagnosis to facilitate curative treatment. Screening for cancer falls into the last category. In this case, two crucial elements are the sojourn time and the sensitivity of the screening test. The former is defined as the duration of the preclinical screen-detectable period, that period during which a person is asymptomatic but the disease is detectable by a screening tool. The latter is the probability that any given case who is subjected to the screening method during this period will have his or her disease detected by it. For any given disease, one would expect the sojourn time to vary between cases, in that tumors grow at varying rates, depending on numerous pathologic and host factors. Therefore, the parameter estimated in Received for publication September 4, 1997, and accepted for publication February 19, 1998. 1 1nstitute of Public Hearth, University Forvie Site, Cambridge CB2 2SR, United Kingdom. 2 Registre des cancers digestifs du Calvados, INSERM, Avenue Cdte de Nacre, 14033 Caen cedex, France. 3 Graduate Institute of Epidemiology, College of Public Health, National Taiwan University, Taipei, Taiwan. 609 Downloaded from http://aje.oxfordjournals.org/ at Universidad del Republica on January 3, 2017 The effectiveness of cancer screening depends crucially on two elements: the sojourn time (that is, the duration of the preclinical screen-detectable period) and the sensitivity of the screening test. Previous literature on methods of estimating mean sojourn time and sensitivity has largely concentrated on breast cancer screening. Screening for colorectal cancer has been shown to be effective in randomized trials, but there is little literature on the estimation of sojourn time and sensitivity. It would be interesting to demonstrate whether methods commonly used in breast cancer screening could be used in colorectal cancer screening. In this paper, the authors consider various analytic strategies for fitting exponential models to data from a screening program for colorectal cancer conducted in Calvados, France, between 1991 and 1994. The models yielded estimates of mean sojourn time of approximately 2 years for 45- to 54-year-olds, 3 years for 55- to 64-year-olds, and 6 years for 65- to 74-year-olds. Estimates of sensitivity were approximately 75%, 50%, and 40% for persons aged 45-54, 55-64, and 65-74 years, respectively. There is room for improvement in all models in terms of goodness of fit, particularly for the first year after screening, but results from randomized trials indicate that the sensitivity estimates are roughly correct. Am J Epidemiol 1998; 148:609-19. 610 Prevost et al. 1.0Tiue O8- O60.4- 02/ 0J0- Time A considerable body of literature on estimation of mean sojourn time and sensitivity has been built up over the years (for reviews, see Stevenson (1) and van Oortmarssen et al. (2)). The seminal work in the field was carried out by Zelen and Feinleib (3), Prorok (4), and Day and Walter (5). Mathematical modeling has been used in the context of cervical cancer (6-8), lung cancer (9), and colorectal cancer (10). Many of the applications, however, have been in the field of screening for breast cancer, partly because of the data sets available from the large number of randomized trials of breast cancer screening (11). The major requisite of estimation is data on screening for the disease, including data on interval cancers, those which are diagnosed clinically after a negative screen. Clearly, if screening is sensitive and if mean sojourn time is reasonably long, there should be relatively few such cancers. Observation of the rate at which the incidence of interval cancers approaches the incidence observed in the absence of screening is essential to determination of the mean sojourn time. Much of the work carried out in the past has involved exponential models of time to clinical disease, since Walter and Day have shown it to give a good fit to breast cancer screening data (12). In addition, it is a mathematically easy distribution with which to work, fitting in well with available Poisson regression computer programs (13). This is relevant, because in this field the available data often dictate that simplifying assumptions be made. These include distributional forms like the exponential, the assumption of a constant sensitivity and a single parameter for mean sojourn time (in turn necessitating several analyses in different strata), and the use of a fixed uniform underlying incidence estimated from randomized or historical control data (3, 5, 13). A technique of estimation which permits analysis of data of complex structure and multiparameter estima- DATA A single round of mass screening for colorectal cancer using fecal Hemoccult testing was conducted in Calvados, France, between April 1991 and May 1994. A total of 71,307 people between the ages of 45 and 74 yea (...truncated)