×

Evaluating the effect of optimized cutoff values in the assessment of prognostic factors. (English) Zbl 0875.62567

Summary: In clinical research the assessment of prognostic factors is often based on the division of the patients into two groups: a high risk and a low risk group. A common strategy is to select an optimal cutoff value in the prognostic factor which defines the two groups. The effect is measured as difference between the groups. We provide simple correction formulae for the correct P-value of the selected two-sample statistic. Moreover, we discuss consequences of that optimization on both the estimator of the cutoff point and the estimated effect. An approximate confidence region for both parameters is given. The small sample behaviour is analysed by means of a Monte-Carlo study. The optimization of the cutoff value results in an overestimation of the difference between the prognostic groups. Extensions of our discussion to censored data are given, too. Finally, we apply our approach to an example from oncology.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62F25 Parametric tolerance and confidence regions

Software:

AS 183
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Altman, D. G.: Categorising continuous variables. British J. Cancer 64, 975 (1991)
[2] Altman, D. G.; Lausen, B.; Sauerbrei, W.; Schumacher, M.: Dangers of using ”optimal” cutpoints in the evaluation of prognostic factors. J. national cancer institute 86, 829-835 (1994)
[3] Beasly, J. D.; Springer, S. G.: The percentage points of the normal distribution. Applied statistics algorithms, 188-191 (1985)
[4] Becker, R.; Chambers, J.; Wilks, A.: The new S language. (1988) · Zbl 0642.68003
[5] Breiman, L.; Friedman, J. H.; Olsen, R. A.; Stone, C. J.: Classification and regression trees. (1984) · Zbl 0541.62042
[6] Courdi, A.; Hery, M.; Chauvel, P.: Prognostic value of continuous variables in breast cancer and head and neck cancer: dependence on the cut-off level. British J. Cancer 58, 88-90 (1988)
[7] Cox, D. R.: Regression models and life tables (with discussion). J. roy. Statist. soc. Ser. B 74, 187-200 (1972) · Zbl 0243.62041
[8] Hilsenbeck, S. G.; Clark, G. M.; Mcguire, W. L.: Why do so many prognostic factors fail to pan out?. Breast cancer res. Treatment 22, 197-206 (1992)
[9] Hunter, D.: An upper bound for the probability of a union. J. appl. Probab. 13, 597-603 (1976) · Zbl 0349.60007
[10] Lausen, B.; Schumacher, M.: Maximally selected rank statistics. Biometrics 48, 73-85 (1992)
[11] Mcguire, W.; Hilsenbeck, S.; Clark, G. M.: Optimal mastectomy timing. J. national cancer institute 84, 346-348 (1992)
[12] Miller, R.; Siegmund, D.: Maximally selected chi-square statistics. Biometrics 38, 1011-1016 (1982) · Zbl 0502.62091
[13] Pfisterer, J.; Kommoss, F.; Sauerbrei, W.; Menzel, D.; Kiechle, M.; Giese, E.; Hilgarth, M.; Pfleiderer, A.: DNA flow cytometry in node positive breast cancer: prognostic value and correlation to morphological and clinical factors. Analytical and quantitative cytology and histology (1995)
[14] Schäfer, H.: An application of the bootstrap in clinical chemistry. Bootrapping and related techniques, 213-217 (1992)
[15] Schmoor, C.: Antwort auf den kommentar von L. Edler und C. Quintero. Biometrie und informatik in medizin und biologie 22, 69-76 (1991)
[16] Schumacher, M.; Olschewski, M.; Schmoor, C.: The impact of heterogenity on the comparison of survival times. Statist. med. 6, 773-784 (1987)
[17] Siegmund, D.: Confidence sets in change-point problems. Int. statist. Rev. 56, 31-48 (1988) · Zbl 0684.62028
[18] Sigurdsson, H.; Baldetorp, B.; Borg, A.: Flow cytometry in primary breast cancer: improving the prognostic value of the fraction of cells in the S-phase by optimal categorisation of cut-off levels. British J. Cancer 62, 786-790 (1990)
[19] Tibshirani, R.; Hastie, T.: Local likelihood estimation. J. amer. Statist. assoc. 82, 559-567 (1987) · Zbl 0626.62041
[20] Van Houwelingen, H. C.; Le Cessie, S.: Predictive value of statistical models. Statist. med. 9, 1303-1325 (1990)
[21] Verweij, P. J. M.; Van Houwelingen, H. C.: Crossvalidation in survival analysis. Statist. med. 12, 2305-2314 (1993)
[22] Wichmann, B. A.; Hill, I. D.: An efficient and portable pseudo-random number generator. Applied statistics algorithms, 238-242 (1985)
[23] Worsley, K. J.: Testing for a two-phase multiple regression. Technometrics 25, 35-42 (1983) · Zbl 0508.62061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.