Period estimates of cancer patient survival are more up-to-date than complete estimates even at comparable levels of precision

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1 Journal of Clinical Epidemiology 59 (2006) ORIGINAL ARTICLES Period estimates of cancer patient survival are more up-to-date than estimates even at comparable levels of precision Hermann Brenner a, *, Timo Hakulinen b a Department of Epidemiology, German Center for Research on Aging, Bergheimer Strasse 20, D Heidelberg, Germany b Finnish Cancer Registry, Institute for Statistical and Epidemiological Cancer Research, Liisankatu 21 B, FIN Helsinki, Finland Accepted 25 October 2005 Abstract Background and Objective: Period provides more up-to-date estimates of cancer patient survival than traditional methods, but there is a trade-off between up-to-dateness and precision. Our objective was to compare the performance of period and in terms of up-to-dateness and precision of survival estimates. Study Design and Setting: Five-year relative survival data actually observed for patients diagnosed with 1 of 20 common forms of cancer in Finland in 36 overlapping 5-year periods between and were compared with period estimates and various variants of estimates of 5-year relative survival potentially available during these periods. Results: At comparable levels of up-to-dateness, survival estimates from period were more precise than survival estimates from. At comparable levels of precision, period provided more up-to-date survival estimates than did. Conclusion: These results further encourage more widespread use of period as a standard tool for up-to-date monitoring of cancer patient survival by population-based cancer registries. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Cancer registries; Statistical methods; Survival 1. Introduction Monitoring cancer patient survival is an important task of population-based cancer registries. In the past, monitoring of patient survival was done mostly by the cohort method; that is, survival estimates were derived for cohorts of patients who had been followed for a number of years (e.g., 5 years or 10 years). For example, the recently published 5-year survival rates from the EUROCARE-3 project, a European collaborative project of cancer patient survival, pertain to patients diagnosed in and followed through 1999 [1]. The cohort method is useful for describing the survival experience of well-defined cohorts of patients, but a disadvantage is that the long-term survival estimates can be obtained only for cohorts of patients diagnosed many years ago. These survival estimates may thus be outdated if there has been recent progress in prognosis for cancer patients. * Corresponding author. Tel.: ; fax: address: h.brenner@dkfz-heidelberg.de (H. Brenner). Occasionally, more recently diagnosed patients were also included in previous survival analyses, even though they could not have been under observation for the full period of interest. For example, in the aforementioned EUROCARE-3 project, one might have considered including all patients diagnosed in , even though patients diagnosed in could not have d 5-year at the end of This so-called provides somewhat more up-to-date and also somewhat more precise estimates of survival. Nevertheless, these survival estimates might still be outdated to some extent, because they are still heavily relying on patients diagnosed many years ago. A few years ago, a new method of survival, denoted period, was introduced to provide more up-to-date estimates of cancer patient survival [2]. The principle of this method consists of restricting the to some recent time period through left truncation of all observations at the beginning of that period in addition to right censoring at its end. For example, in the aforementioned data situation, one might have done a period reflecting the survival experience in only of patients diagnosed in /06/$ see front matter Ó 2006 Elsevier Inc. All rights reserved. doi: /j.jclinepi

2 H. Brenner, T. Hakulinen / Journal of Clinical Epidemiology 59 (2006) It has been shown by extensive empirical evaluation that the period survival approach provides yet more upto-date survival estimates than the approach, but may be less precise due to the restriction of the database to the recent period [3 6]. Based on these findings, it is common understanding that application of period vs. might be considered as an issue of up-to-dateness vs. precision. Previous evaluations, however, have compared two very specific types of and period. Our objective was to provide a comparison of the performance of period and with respect to up-to-dateness and precision of cancer survival estimates for a broader range of scenarios. 2. Materials and methods 2.1. Database Our is based on data from the nationwide Finnish Cancer Registry, which is well known for its high levels of ness and data quality [7]. At the time of our, the database encompassed patients diagnosed within half a century, from 1953 to 2002, with a followup with respect to vital status until the end of We included patients aged 15 or older with a first with 1 of 20 common forms of cancer between 1953 and Statistical We first compared the survival rates actually experienced by patients diagnosed in (the most recent cohorts for whom 5-year was by the end of 2002) with the most up-to-date estimates of 5-year survival rates that could potentially have been available at the time of their (i.e., in ) by or by period. The various options of are illustrated in Table 1. The most up-to-date cohort estimate of 5-year survival potentially available in would reflect the survival experience of patients diagnosed in Because our focus here is on comparing and period, no cohort estimates will be presented. A period estimate of 5-year survival could be obtained by exclusive consideration of survival experience in of patients diagnosed in Table 1 and years of included in the various types of analyses for patients diagnosed with any of 20 common forms of cancer in Finland in Type of Observed Cohort Maximum Period Minimum A estimate of 5-year survival could reflect the full survival experience in of patients diagnosed in A estimate derived in this way would necessarily provide somewhat less up-to-date, but also somewhat more precise estimates of 5-year survival than the period for the period, because of additional inclusion of survival experience in years However, this type of (which we refer to here as maximum ) would reflect just one extreme option, in that the maximum number of cohorts are included who would make some contribution to the survival experience in Obviously, could also be restricted to more recently diagnosed patients, which would lead to more up-to-date estimates of survival at the price of some loss in precision. The most extreme option (which we refer to here as minimum ) would be an restricted to the survival experience in of patients diagnosed in (although none of the patients included in this could actually have d 5-year, survival during the 5th year following could nevertheless be estimated from patients diagnosed in 1993, for whom survival experience during the early part of that year was available, assuming that survival experience during this early part is representative for the 5th year as a whole). With this option, a 5-year survival estimate might be obtained that might even be more up-to-date, but less precise than the period estimate. In practice, one would often decide to do a that is somewhere between the two extremes outlined above. In this, however, we derived both extremes of estimates along with the period estimates of 5-year survival, in order to evaluate their relative performance in terms of up-to-dateness and precision for the broadest possible range of options of. Up-to-dateness was evaluated by differences of the various estimates from 5-year survival rates later observed for patients diagnosed in , and precision was evaluated by the standard errors which were derived according to Greenwood s method [8]. We then repeated all analyses for patients diagnosed in 36 overlapping 5-year periods, ranging from to as outlined in Table 2, and we calculated the following summary measures of performance of the various methods across periods: mean difference and mean squared difference of 5-year survival estimates potentially available in each period from 5-year survival later observed for patients diagnosed within the respective period, as well as mean standard errors of the estimates. The mean differences are an indicator of up-to-dateness of estimates, the mean standard errors are an indicator of precision, and the mean squared differences should be lowest when estimates are both up-to-date and precise. Throughout this article, we report relative rather than absolute 5-year survival rates. The former are more commonly reported by population-based cancer registries.

3 572 H. Brenner, T. Hakulinen / Journal of Clinical Epidemiology 59 (2006) Table 2 cancer and years of included in the comparative evaluation of and period for patients diagnosed in 36 consecutive, overlapping calendar periods Observed Maximum Period Minimum Analogous analyses for further 31 intermediate calendar periods They are calculated as the ratios of absolute survival rates and expected survival rates in the absence of cancer, and thus reflect the probability of surviving the cancer of interest rather than the total survival probability [9,10]. Expected survival rates were derived from age, gender, and calendar period specific mortality figures of the general population according to Hakulinen s method [11]. The analyses were performed using the SAS statistical software package (SAS Institute, Cary, NC, USA). The macro periodh was used for all survival analyses [12]. 3. Results As Table 3 shows, 5-year relative survival actually observed for patients diagnosed in strongly varied by cancer site. It ranged from 90.8% for patients with cancer of the thyroid gland to 2.5% for patients with pancreatic cancer. For many forms of cancer, the estimates of 5-year relative survival obtained by maximum based on the data potentially available in were considerably lower than the 5-year relative survival rates later observed for patients diagnosed in that period. With 9.3, 7.0, and 5.0 percentage points, the differences were largest for prostate, cervical, and rectal cancer, respectively. These patterns indicate major improvement in prognosis for patients with these forms of cancer in the 1990s. With few exceptions, the period estimates of 5-year relative survival were closer to the 5-year relative survival later observed for patients diagnosed in than were the maximum estimates. In particular, the Table 3 Complete and period point estimates of 5-year relative survival available in and their difference from the point estimate of true 5-year relative survival later observed for cancer patients diagnosed in that period 5-year relative survival estimates available in year relative survival observed a Maximum Period Minimum Cancer PE SE PE Diff. b SE PE Diff. b SE PE Diff. b SE Oral cavity c Esophagus c 1.7 Stomach c Colon c Rectum c 1.8 Liver c Pancreas c 0.8 Lung c 0.6 Breast c 0.8 Cervix c 3.6 Corpus c Ovaries c Prostate c 1.5 Kidneys c Urinary bladder c 1.9 Melanoma c 1.9 Brain c 1.8 Thyroid gland c Leukemias c Lymphomas c Abbreviations: Diff., difference; PE, point estimate; SE, standard error. a As later observed for patients diagnosed in b Difference from 5-year relative survival later observed for patients diagnosed in c Bold figures indicate which method provides the most accurate prediction.

4 H. Brenner, T. Hakulinen / Journal of Clinical Epidemiology 59 (2006) differences of period estimates from observed relative survival rates were!2.5 percentage points for all cancers except prostate cancer. The minimum estimates showed a similar range of differences; however, their standard errors were much larger than the standard errors of the period estimates. The maximum estimates had the lowest standard errors, but the differences between the standard errors of maximum estimates and period estimates were generally small. Table 4 shows the results of a more comprehensive evaluation, where we calculated the mean difference and the mean squared difference of the various 5-year relative survival estimates potentially available in each of the 36 time windows ranging from to from the 5-year relative survival later observed for patients diagnosed in those periods. The of mean differences indicates once more that the maximum estimates may often be considerably too pessimistic (as indicated by negative values), except for cancers with no or little improvement in prognosis over time, such as pancreatic cancer. The period estimates and the minimum estimates also tended to be on average somewhat too pessimistic, but to a much lesser degree than the maximum estimates. For 12 out of 20 cancers, the period estimates were closest to zerodthat is, they showed the lowest tendency to systematically over- or underestimate prognosis of patients diagnosed in the respective periods. With respect to the mean squared difference, the period estimates fared better (i.e., showed lower values) than the maximum estimates for 19 out of 20 cancers, despite their slightly higher standard errors. The period estimates also fared better than the minimum estimates, which had much higher mean standard errors, for 19 out of 20 cancers. 4. Discussion Here we provide a comparison of the performance of period with for deriving up-to-date estimates of survival. Two extreme forms among a broad range of possible types of were assessed. One of these extreme forms, denoted maximum, generally provided slightly more precise but also less up-to-date estimates of 5-year relative survival than period. These results are in agreement with previous comparative analyses of and period, which had exclusively assessed this specific type of. The other extreme form of, denoted minimum, provided 5-year survival estimates which were similarly up-to-date, but much less precise than those obtained by period. It follows from our results that the choice between and period is not generally a choice of Table 4 Mean difference and mean squared difference of and period estimates of 5-year relative survival available in defined calendar periods a from true 5-year relative survival later observed for cancer patients diagnosed in that period Cancer Mean difference of 5-year relative survival from observed Maximum Period Minimum Mean squared difference of 5-year relative survival from observed Maximum Period Minimum Mean standard error of 5-year relative survival Maximum Period Oral cavity 0.1 b b Esophagus b b Stomach b b Colon b b Rectum b b Liver b b Pancreas b b Lung b b Breast b b Cervix b b Corpus b b Ovaries b b Prostate b b Kidneys b b Urinary bladder b b Melanoma b b Brain b b Thyroid gland b b Leukemias b b Lymphomas b b NOTE. In addition, the mean standard errors of all types of estimates are given. a As illustrated in Table 2. b Bold figures indicate which of the three methods performs best according to each criterion. Minimum

5 574 H. Brenner, T. Hakulinen / Journal of Clinical Epidemiology 59 (2006) precision vs. up-to-dateness. Rather, our analyses point to general advantages of period over. On the one hand, period provides much more precise estimates than if the latter is applied in such a way that both approaches provide comparably up-to-date survival estimates. On the other hand, period would be expected to provide more up-to-date estimates than if the latter is applied in such a way that both approaches yield comparably precise survival estimates (i.e., with an application somewhere close to maximum ). Only if there is no change in survival over time (and, hence, up-to-dateness does not matter at all) would the maximum with its slightly more precise estimates appear to be preferable. Apart from its potential disadvantages with respect to up-to-dateness and precision, other disadvantages of may also be relevant in certain situations. To begin with, the volume of the database varies strongly for different years of. It is largest for the 1st year of and progressively diminishes for the later years of. This may lead to very imprecise estimates of conditional survival for the later years, at least in the case of minimum. For example, in the minimum analyses performed for this paper, the estimates of conditional survival during the 5th year following would be based on some part of the 5th year survival experience of patients diagnosed in one single calendar year only. Because conditional survival estimates are often of particular interest on their own, especially from a clinical point of view, this may be a serious limitation. By contrast, apart from the reduction of the cohorts by prior deaths, a similarly broad database would be available for each year of with period. Furthermore, the unbalanced representation of the survival experience in various episodes of might be of concern for estimates even within years. For example, in the minimum analyses performed in our study, survival experience during the early part of the first year (i.e., from to the end of the calendar year of ) is included from patients diagnosed in 5 consecutive calendar years, whereas survival experience in the later part of that year (i.e., from the beginning of the calendar year following the year of ) is included from patients diagnosed in 4 consecutive calendar years only. If the hazard differs between the early and the late months of the 1st year following (which is likely to be the case for some forms of cancer), the estimates of survival within that year might be distorted. Similar problems might also arise for other years of followup, even though probably to a minor degree due to the generally lower and more homogenous hazards within those years. Again, no such problem arises with period which is based on balanced representations of survival experience within each single year of. In the interpretation of our results the following limitations should be kept in mind. Only one specific form of period was assessed: period for 5-year periods. This specific width of period was chosen because results of population-based monitoring of survival are often reported for 5-year cohorts (e.g., [1]) or for 5-year periods (e.g., [4]). Shorter periods, such as 1-, 2-, or 3-year periods, may sometimes be preferred to provide even more up-todate information on survival [13 16]. Obviously, this comes at the price of some loss in precision which may well be tolerable in very large data sets. Examples for 1- year period analyses include recent analyses of survival of cancer patients in the United States based on the large database of the SEER program [13,14]. In such situations, minimum would be expected to provide less up-to-date, but somewhat more precise estimates than period. We also present results for 5-year relative survival only. Again, this specific outcome measure was chosen because of its widespread use in population-based monitoring of survival. Occasionally, longer term survival rates, such as 10-, 15-, or 20-year survival rates, are also reported. As previously shown, the advantages of period compared to other methods of survival in terms of up-to-dateness are even larger in such situations [3 5,17]. Only two extreme options of pure were assessed. In practice, some interim forms of and cohort (including only patients with some minimum potential time) have more often been used [18,19]. Such interim forms would typically provide survival estimates that are both less precise and less up-to-date than survival estimates from corresponding pure [5]. Even with pure, some interim forms between the two extremes assessed here would often be preferred. In particular, the minimum form of would rarely be applied in this extreme formdeven though the underlying assumption that the survival experience of patients during the early part of the 5th year following is representative for that year is implicitly made in other applications of as well, due to the unbalanced representation of years as outlined above. Nonetheless, assessing the extreme forms allowed us to explore the full range of variation of precision and up-to-dateness of estimates. Up-to-dateness of survival estimates appears to be of particular relevance for monitoring progress in cancer patient survival by population-based cancer registries. Complete, and in particular cohort, may still be the method of choice in situations where the main focus is on evaluation of a specific type of care provided to patients diagnosed during a defined time window (e.g., in a defined clinical setting). In summary, our results provide further evidence for the use of period, which is now applied by an increasing number of population-based cancer registries (e.g.,

6 H. Brenner, T. Hakulinen / Journal of Clinical Epidemiology 59 (2006) [15,16,20 25]), in up-to-date monitoring of cancer patient survival. Depending on the specific type of, period estimates may be more or less precise than estimates. In the former case, the advantage in precision may be obtained without any relevant loss of up-to-dateness. In the latter case, the often minor disadvantage in precision would typically be paid off by a substantial gain in up-todateness. Further advantages of period compared to include a more balanced representation of the various years of. Taken together, these results further encourage more widespread use of period, which may be extended to modeling approaches to adjust for covariates [26], for up-to-date monitoring of cancer patient survival. Acknowledgments The work of Hermann Brenner was supported in part by a grant from the German Cancer Foundation (Deutsche Krebshilfe), Project No Br 5. 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