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Risk and prognostic factors in epidemiological and clinical research are often semicontinuous such that a proportion of individuals have exposure zero, and a continuous distribution among those exposed. We call this a spike at zero (SAZ). Typical examples are consumption of alcohol and tobacco, or hormone receptor levels. To additionally model non-linear functional relationships for SAZ variables, an extension of the fractional polynomial (FP) approach was proposed. To indicate whether or not a value is zero, a binary variable is added to the model. In a two-stage procedure, called FP-spike, it is assessed whether the binary variable and/or the continuous FP function for the positive part is required for a suitable fit. In this paper, we compared the performance of two approaches – standard FP and FP-spike – in the Cox model in a motivating example on breast cancer prognosis and a simulation study. The comparisons lead to the suggestion to generally using FP-spike rather than standard FP when the SAZ effect is considerably large because the method performed better in real data applications and simulation in terms of deviance and functional form.Abbreviations:CI: confidence interval; FP: fractional polynomial; FP1: first degree fractional polynomial; FP2: second degree fractional polynomial; FSP: function selection procedure; HT: hormone therapy; OR: odds ratio; SAZ: spike at zero

In a recent article, Royston (2015, Stata Journal15: 275–291) introduced the approximate cumulative distribution (ACD) transformation of a continuous covariate xas a route toward modeling a sigmoid relationship between xand an outcome variable. In this article, we extend the approach to multivariable modeling by modifying the standard Stata program mfp.The result is a new program, mfpa, that has all the features of mfpplus the ability to fit a new model for user-selected covariates that we call FP1(p1, p2). The FP1(p1, p2) model comprises the best-fitting combination of a dimension-one fractional polynomial (FP1) function of xand an FP1 function of ACD (x). We describe a new model-selection algorithm called function-selection procedure with ACD transformation, which uses significance testing to attempt to simplify an FP1(p1, p2) model to a submodel, an FP1 or linear model in xor in ACD (x). The function-selection procedure with ACD transformation is related in concept to the FSP (FP function-selection procedure), which is an integral part of mfpand which is used to simplify a dimension-two (FP2) function. We describe the mfpacommand and give univariable and multivariable examples with real data to demonstrate its use.

Assessing the instability of a multivariable model is important but is rarely done in practice. Model instability occurs when selected predictors—and for multivariable fractional polynomial modeling, selected functions of continuous predictors—are sensitive to small changes in the data. Bootstrap analysis is a useful technique for investigating variations among selected models in samples drawn at random with replacement. Such samples mimic datasets that are structurally similar to that under study and that could plausibly have arisen instead. The bootstrap inclusion fraction of a candidate variable usefully indicates the importance of the variable. We describe Stata tools for stability analysis in the context of the mfpcommand for multivariable model building. We offer practical guidance and illustrate the application of the tools to a study in prostate cancer.

There is increasing interest in the medical world in the possibility of tailoring treatment to the individual patient. Statistically, the relevant task is to identify interactions between covariates and treatments, such that the patient's value of a given covariate influences how strongly (or even whether) they are likely to respond to a treatment. The most valuable data are obtained in randomized controlled clinical trials of novel treatments in comparison with a control treatment. We describe two techniques to detect and model such interactions. The first technique, multivariable fractional polynomials interaction, is based on fractional polynomials methodology, and provides a method of testing for continuous-by-binary interactions and by modeling the treatment effect as a function of a continuous covariate. The second technique, subpopulation treatment-effect pattern plot, aims to do something similar but is focused on producing a nonparametric estimate of the treatment effect, expressed graphically. Stata programs for both of these techniques are described. Real data for brain and breast cancer are used as examples.

Spline functions provide a useful and flexible basis for modeling relationships with continuous predictors. However, to limit instability and provide sensible regression models in the multivariable setting, a principled approach to model selection and function estimation is important. Here the multivariable fractional polynomials approach to model building is transferred to regression splines. The essential features are specifying a maximum acceptable complexity for each continuous function and applying a closed-test approach to each continuous predictor to simplify the model where possible. Important adjuncts are an initial choice of scale for continuous predictors (linear or logarithmic), which often helps one to generate realistic, parsimonious final models; a goodness-of-fit test for a parametric function of a predictor; and a preliminary predictor transformation to improve robustness.

Abstract: Despite years of research and hundreds of reports on tumor markers in oncology, the number of markers that have emerged as clinically useful is pitifully small. Often initially reported studies of a marker show great promise, but subsequent studies on the same or related markers yield inconsistent conclusions or stand in direct contradiction to the promising results. It is imperative that we attempt to understand the reasons that multiple studies of the same marker lead to differing conclusions. A variety of methodologic problems have been cited to explain these discrepancies. Unfortunately, many tumor marker studies have not been reported in a rigorous fashion, and published articles often lack sufficient information to allow adequate assessment of the quality of the study or the generalizability of study results. The development of guidelines for the reporting of tumor marker studies was a major recommendation of the National Cancer Institute-European Organisation for Research and Treatment of Cancer (NCI-EORTC) First International Meeting on Cancer Diagnostics in 2000. As for the successful CONSORT initiative for randomized trials and for the STARD statement for diagnostic studies, we suggest guidelines to provide relevant information about the study design, pre-planned hypotheses, patient and specimen characteristics, assay methods, and statistical analysis methods. In addition, the guidelines suggest helpful presentations of data and important elements to include in discussions. The goal of these guidelines is to encourage transparent and complete reporting so that the relevant information will be available to others to help them to judge the usefulness of the data and understand the context in which the conclusions apply.

Background: To identify prognostic factors for overall survival in patients with newly diagnosed glioblastoma undergoing radiation therapy. Patients and Methods: From January 1980 to June 2000, we treated 432 consecutive patients with glioblastoma at out institution. 17 patients were excluded from the analysis for various reasons. Mean age of the 415 patients who were included in the study was 59 years (19-81 years), Karnofsky performance status (KPS) was ≥ 70 in 280 patients. 343 patients underwent resection, 72 had a biopsy. Various fractionation schemes were used (conventional fractionation, n = 112; hypofractionation, n = 94; accelerated hyperfractionation, n = 209). Survival probabilities were estimated using the method of Kaplan and Meier. Multivariate analysis was done with a Cox regression model. Results: By July 2001, 406 patients had died. Medial overall survival was 8.2 months. Of ten factors considered in a proportional hazards model stratified for treatment (fractionation scheme and type of surgery), significant variables in a multivariate model were age (50-64 years vs < 50 years [RR 1.35; 95% CI 1.02-1.78], ≥ 65 years vs < 50 years [RR 2.08; 95% CI 1.54-2.81]), performance status (KPS < 70 vs ≥ 70 [RR 1.53; 95% CI 1.23-1.90]), and central tumor location (yes vs no [RR 1.39; 95% CI 1.04-1.87]). Blood hemoglobin (Hb) values were available in 318 patients and serum lactate dehydrogenase (LDH) levels in 234 patients. 89 patients were anemic (Hb men < 13 g/dl, women < 12 g/dl), in 80 patients the LDH level was raised beyond the upper limit of the normal range (> 240 U/l). By including the three significant variables, both parameters had an additional significant effect with an estimated relative risk of about 1.4 in their corresponding subgroups. Conclusion: Besides established prognostic factors, anemia and raised serum LDH levels may negatively influence outcome in glioblastoma patients. Our results from data-dependent modeling have to be confirmed by independent studies. Hintergrund: Die vorliegende Studie untersucht Prognosefaktoren für das Gesamtüberleben bei Patienten, die aufgrund eines neu diagnostizierten Glioblastoms bestrahlt wurden. Patienten und Methodik: Von Januar 1980 bis Juni 2000 wurden 432 Glioblastompatienten an unserer Klinik behandelt. 415 Patienten wurden in die Analyse einbezogen. Das durchschnittliche Alter betrug 59 Jahre (19-81 Jahre), der Karnofsky-Performance-Status (KPS) war bei 280 Patienten ≥ 70. Bei 343 Patienten wurde der Tumor reseziert, bei 72 Patienten biopsiert. Die Strahlentherapie erfolgte konventionell fraktioniert (n = 112), hypofraktioniert (n = 94) oder akzeleriert hyperfraktioniert (n = 209). Die Schätzung der überlebenswahrscheinlichkeiten erfolgte mit der Methode von Kaplan und Meier. Multivariate Analysen wurden mit einem Regressionsmodell nach Cox durchgeführt. Ergebnisse: Bis Juli 2001 waren 406 Patienten verstorben. Das mediane Gesamtüberleben betrug 8,2 Monate. Von zehn Faktoren, die in einem nach Resektionsstatus und Fraktionierungsschema stratifizierten Proportional-Hazards-Modell untersucht wurden, erwiesen sich als signifikant: Alter (50-64 Jahre vs. < 50 Jahre) [RR 1,35; 95%-CI 1,02-1,78], ≥ 65 Jahre vs. < 50 Jahre [RR 2,08; 95%-CI 1,54-2,81]), Allgemeinzustand (KPS < 70 vs. ≥ 70 [RR 1,53; 95%-CI 1,23-1,90]) und zentraler Tumorsitz (ja vs. nein [RR 1,39; 95%-CI 1,04-1,87]). Werte für Hämoglobin (Hb) und Serum-Lactat-Dehydrogenase (LDH) lagen bei 318 bzw. 234 Patienten vor. 89 Patienten waren anämisch (Hb Männer < 13 g/dl, Frauen < 12 g/dl), bei 80 Patienten war der LDH-Wert erhöht (> 240 U/l). Unter Berücksichtigung der drei signifikanten Variablen übten beide Parameter in den jeweiligen Untergruppen einen zusätzlichen Effekt aus mit einem relativen Risiko von etwa 1,4. Schlussfolgerung: Neben bekannten Prognosefaktoren beeinflussen erniedrigte Hb- und erhöhte LDH-Werte das überleben bei Patienten mit Glioblastom negativ.

In 1984 the GBSG started a multicenter randomized trial to compare the effectiveness of 6 cycles of cyclophosphamide, methotrexate and fluorouracil (CMF) with or without radiotherapy (RT) as adjuvant treatment in node-positive breast-cancer patients treated by mastectomy. During 5 years, 199 patients were randomized. After a median follow-up of about 9 years, the treatment groups 6 × CMF and 6 × CMF + RT were compared regarding time to recurrence and death. As the first event of failure, we observed locoregional recurrence in 22 patients, distant metastases in 66 patients, a secondary malignancy in 9 patients and death without previous event in 5 patients. For event-free survival (EFS), no significant difference was observed [relative risk (RR) 6 × CMF + RT vs. 6 × CMF 0.82, 95% confidence interval (CI) 0.55–1.21]. Event-specific analysis showed a significant decreased risk after radiotherapy for locoregional recurrence. The risk for distant metastases was estimated as slightly decreased and the risk for secondary malignancy and for death without previous event was estimated as increased in treatment group 6 × CMF + RT in comparison with treatment group 6 × CMF, but these effects were not significant. For overall survival (OS) and breast-cancer-specific survival (BCS), no significant treatment effect could be demonstrated. There is a beneficial effect of radiotherapy on locoregional recurrence. For EFS and BCS, a tendency in favour of radiotherapy is observed, but this is not significant; for OS, no difference can be demonstrated, but the power of the study is too low to detect small treatment effects. Int. J. Cancer 86:408–415, 2000. © 2000 Wiley-Liss, Inc.

When the role of a new prognostic factor is investigated, careful planning of an appropriate study is required. This includes an assessment of the power of the study in terms of sample sizes. An adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors. With survival time as endpoint this will usually be done with the Cox proportional hazards model. Sample size and power formulae in survival analysis have been developed by Schoenfeld for randomized treatment comparisons. In the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest. In this situation, the existing sample size and power formulae are not valid and may not be applied. In this paper, Schoenfeld's formula is first extended to the situation where a correlated factor is included in the analysis. The validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation. Second, an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor. This extends the formula for independent effects. Finally, the approach is illustrated by an example on the prognostic impact of DNA ploidy and other factors in advanced ovarian cancer. Copyright © 2000 John Wiley & Sons, Ltd.

When the role of a new prognostic factor is investigated, careful planning of an appropriate study is required. This includes an assessment of the power of the study in terms of sample sizes. An adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors. With survival time as endpoint this will usually be done with the Cox proportional hazards model. Sample size and power formulae in survival analysis have been developed by Schoenfeld for randomized treatment comparisons. In the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest. In this situation, the existing sample size and power formulae are not valid and may not be applied. In this paper, Schoenfeld's formula is first extended to the situation where a correlated factor is included in the analysis. The validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation. Second, an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor. This extends the formula for independent effects. Finally, the approach is illustrated by an example on the prognostic impact of DNA ploidy and other factors in advanced ovarian cancer. Copyright © 2000 John Wiley & Sons, Ltd.

Prognostic classification schemes have often been used in medical applications, but rarely subjected to a rigorous examination of their adequacy. For survival data, the statistical methodology to assess such schemes consists mainly of a range of ad hoc approaches, and there is an alarming lack of commonly accepted standards in this field. We review these methods and develop measures of inaccuracy which may be calculated in a validation study in order to assess the usefulness of estimated patient-specific survival probabilities associated with a prognostic classification scheme. These measures are meaningful even when the estimated probabilities are misspecified, and asymptotically they are not affected by random censorship. In addition, they can be used to derive R²-type measures of explained residual variation. A breast cancer study will serve for illustration throughout the paper. Copyright © 1999 John Wiley & Sons, Ltd.

Prognostic classification schemes have often been used in medical applications, but rarely subjected to a rigorous examination of their adequacy. For survival data, the statistical methodology to assess such schemes consists mainly of a range of ad hocapproaches, and there is an alarming lack of commonly accepted standards in this field. We review these methods and develop measures of inaccuracy which may be calculated in a validation study in order to assess the usefulness of estimated patient‐specific survival probabilities associated with a prognostic classification scheme. These measures are meaningful even when the estimated probabilities are misspecified, and asymptotically they are not affected by random censorship. In addition, they can be used to derive R2‐type measures of explained residual variation. A breast cancer study will serve for illustration throughout the paper. Copyright © 1999 John Wiley & Sons, Ltd.

Background. In 1989 it was suggested that the timing of surgery during follicular or corpus luteum phase of the menstrual cycle could substantially influence the survival time in premenopausal breast-cancer patients [1]. Several researchers analysed their data, but in general they could not confirm this observation. Nevertheless, two other reports in that series found some influence of the time of surgery during menstrual cycle on prognosis, although, they suggested different time periods as favourable [8, 9].

The process of model building involved in the analysis of many medical studies may lead to a considerable amount of over-optimism with respect to the predictive ability of the ‘final’ regression model. In this paper we illustrate this phenomenon in a simple cutpoint model and explore to what extent bias can be reduced by using cross-validation and bootstrap resampling. These computer intensive methods are compared to an ad hoc approach and to a heuristic method. Besides illustrating all proposals with the data from a breast cancer study we perform a simulation study in order to assess the quality of the methods. © 1997 John Wiley & Sons, Ltd.

Zusammenfassung: □ Hintergrund: In den letzten Jahren wurden häufig Metaanalysen durchgeführt, wenn anhand mehrerer epidemiologischer Studien eine einheitliche Bewertung von Risikofaktoren nicht möglich war. Die Ergebnisse werden dann insbesondere zur Beurteilung von schwachen Risikofaktoren herangezogen. □ Material und Methode: In unserer Arbeit beschreiben wir methodische Aspekte bei der Durchführung solcher Analysen, und der Unterschied zwischen Metaanalysen aus publizierten Daten und Metaanalysen aus Originaldaten, auch gepoolte Analysen genannt, wird verdeutlicht. Die methodischen Aspekte werden anhand eines Beispiels zum Risiko der oralen Kontrazeption für Brustkrebs demonstriert. Grenzen von Metaanalysen aus publizierten Daten werden aufgezeigt. □ Schlußfolgerung: Gepoolte Neuauswertungen sind zwar wesentlich zeitaufwendiger und kostenintensiver, sie können aber zu zuverlässigeren und glaubwürdigeren Ergebnissen führen.

Both nuclear DNA content and S-phase fraction (SPF) can be helpful in predicting prognosis in certain malignancies. We investigated in a retrospective study the prognostic significance of nuclear DNA content and SPF as measured by flow cytometry of tumor specimens from 162 women with nonpretreated surgically staged FIGO stage I endometrial cancer using clearly defined inclusion criteria. A total of 139 (86%) cases were found to be diploid, whereas 23 (14%) were aneuploid. Ploidy showed a correlation with histologic grade, estrogen as well as progesterone receptor levels, and depth of myometrial infiltration. Univariate analysis of follow-up data showed an increased relative risk (RR) for recurrence-free survival (RFS) for grade 3 tumors (RR = 2.11, ns), for age (RR = 1.04, P = 0.023) as a continuous variable, and for SPF in diploid tumors (RR = 3.10, P = 0.035). In addition, univariate analysis of overall survival revealed similar results with a slightly increased relative risk for ploidy (RR = 1.52, ns). Multivariate analysis of RFS showed age as the only independent prognostic factor. Multivariate analysis of RFS for diploid tumors showed no independently significant factor; however, age as a continuous variable with a relative risk of 1.04 and SPF with a relative risk of 2.94 were of borderline significance. Our results suggest that abnormalities of the nuclear DNA content and SPF in this homogeneous group of patients are associated with clinical and morphological prognosticators; however, ploidy is no independent prognostic factor for RFS. For diploid tumors, SPF might be a possible independent prognostic factor. Copyright 1995, 1999 Academic Press

The purpose of this study was to evaluate the differences of blood supply in benign and malignant breast tumors by color Doppler flow measurements. The study included 471 patients, 133 with carcinomas, 325 with benign breast lesions, and 13 with mastitis. An ATL UM9/HDI was used with an electronic 10-MHz linear array broadband transducer. The following flow data were analyzed: Presence of vascularity; number of tumor arteries; the mean, minimum, maximum RI index, and AB ratio; the mean, minimum, and maximum peak systolic flow velocity and the sum of all peak systolic flow velocities in each tumor. In all cancers and in most benign pathologies vascularity was found. Highly significant differences between benign and malignant were found for all quantitative flow data such as number of tumor arteries and blood flow velocity (P< 0.0001). Flow profiles analyzed by RI index and AB ratio showed a trend for increased flow resistance in malignancies. However, due to the wide overlap between benign and malignant, indices did not allow a sufficient differentiation. The study showed that standardization of the Doppler examination technique and equipment parameters is essential for vascularity assessment of tumors.

CA-125 is an antigenic determinant expressed on ovarian cancer cells and serves as serum marker in patients with ovarian cancer. It has also been detected, however, in serum of healthy women and in patients with benign gynecologic diseases. Previous studies in patients with ovarian hyperstimulation syndrome suggested that the production of CA-125 is correlated with proliferative ovarian activity. In this study, we describe the pattern of CA-125 secretion in 13 healthy women during menstrual cycle and during hormonal contraceptive treatment. That pattern is characterized by an increase of CA-125 serum concentrations parallel to the growth of the dominant follicle. It was not observed during hormonal contraceptive treatment. We conclude that CA-125 serum levels during menstrual cycle seem to be dependent upon the cyclic changes in the female genital tract.

Local recurrence rates play an important role in the evaluation and judgement of local treatment modalities in breast cancer. In the medical literature different methods for the calculation of these rates have been used. In this note we discuss the methods, the observed differences, and the interpretation of the resulting estimates.

The purpose was to evaluate the validity of transvaginal color Doppler sonography for differentiating between benign and malignant ovarian tumors. Color Doppler and Duplex measurements were obtained in 212 (144 benign, 68 malignant) ovarian and tubarian tumors preoperatively. One hundred and thirty-one patients were postmenopausal and 81 premenopausal. An ATL UM9/HDI was used. The following criteria were analyzed: minimum and mean resistance index and pulsatility index, number and distribution of tumor arteries, diastolic notch, and the maximum, minimum, mean, and sum of all peak systolic, maximum enddiastolic, and time-average maximum velocities. Most criteria showed highly significant differences between benign and malignant tumors with variable overlaps. RImingives a sensitivity of 80%, specificity of 69%, and accuracy of 75% for postmenopausal patients and 80, 59, and 67% for pre- and postmenopausal patients, respectively. PImingives equivalent results. The number of tumor arteries and the maximum flow velocities increase the accuracy. The summation of all flow velocities gives the best result with a sensitivity of 93%, specificity of 85%, and accuracy of 87% for postmenopausal and 91, 76, and 80% for pre- and postmenopausal tumors, respectively. Flow data show no relevant differences between low malignant potential tumors and ovarian carcinomas. Serous cystadenomas and benign teratomas show higher differences than mucinous cystadenomas, functional cysts, and endometriomas in comparison to malignancies. A separate analysis of pre- and postmenopausal tumors is important. Differentiation seemed better for post- than for premenopausal tumors. The four flow criteria (RImin, number of tumor arteries, and maximum and sum of all peak systolic velocities) seemed appropriate for tumor differentiation. However, this study confirms that a single measurement is not sufficient to differentiate ovarian lesions. Measurements of flow velocities (e.g., maximum and sum of all peak systolic velocities) are superior compared with RIminand PImin.

The prognostic effect of histological tumor grade was evaluated in 1036 patients with early breast cancer (pT1 pN0 M0) entered into a trial comparing mastectomy and breast preserving treatment. All analyses were adjusted for the factors treatment, patients' age, and tumor size. Tumor grade was defined according to Bloom and Richardson based on the sum of scores assigned to each of three histological features: 1) degree of differentiation, 2) pleomorphism, and 3) mitotic index. The relative importance of these factors with regard to disease-free survival was evaluated. In univariate as well as in multivariate analyses the pleomorphism was the only factor showing a significant effect (univariate: p=0.0024, multivariate: p=0.015). It was investigated how the factors should be combined to define a histological grading score which yields the best possible classification of the patients with respect to prognosis. A new grading system was defined splitting the patients into three groups: 1) pleomorphism 1; 2) pleomorphism 2 or pleomorphism 3 and mitotic index 1; 3) pleomorphism 3 and mitotic index 2 or 3. This yields a good classification of the patients with respect to prognosis (p=0.0004). The prognostic effect of this score was compared with the effects of the grading systems proposed in the literature. According to Bloom and Richardson and in the modified version by Schauer and Weiss, grading is based on the sum of scores of the various histological factors. Therefore, the strong effect of the pleomorphism was diluted in these grading definitions (Bloom and Richardson: p=0.03, Schauer and Weiss: p=0.028). The grading system proposed by Le Doussalet al. consists only of the scores of pleomorphism and mitotic index (p=0.014). In summary, the factor pleomorphism showed a stronger effect on disease-free survival by itself than the grading systems proposed in the literature.

Several prognostic classification schemes in node negative breastcancer are proposed, but only the Nottingham PrognosticIndex (NPI) seems to be sufficiently validated. Validation,which is a prerequisite for a sensible assessment,is not published for two recent proposals accordingto Glick et al. [1] and Rubens [2].The German Breast Cancer Study Group (GBSG) entered662 eligible patients in a prospective observational study.603 of them had complete data for seven’standard‘ prognostic factors and median follow-up is about5 years. As there is no accepted andinformative measure of separation for classification schemes presentlyavailable, we propose a new one and useit additionally to the well known logrank-test andKaplan-Meier estimates to investigate the predictive power ofthe three schemes. Significant differences in survival andrecurrence-free survival could be established for the NPIsubgroups but not for others where even theordering of the groups was different. With theCox model and the classification and regression treeapproach we develop two new proposals for thedifferentiation of subgroups of node negative patients. Asin the NPI, tumor size and grade arethe most important factors, but with a differentweighting scheme. Young age (≤ 40 years) andvery high estrogen receptor values (> 300 fmol)in a small subgroup of patients were associatedwith worse prognosis. The new proposals showed abetter degree of separation, which demonstrates that animprovement seems possible using standard factors. Because themeasures of separation give an overoptimistic impression forthe new proposals, a validation with other studiesis necessary before a general recommendation can begiven.

The process of model building involved in the analysis of many medical studies may lead to a considerable amount of over‐optimism with respect to the predictive ability of the ‘final’ regression model. In this paper we illustrate this phenomenon in a simple cutpoint model and explore to what extent bias can be reduced by using cross‐validation and bootstrap resampling. These computer intensive methods are compared to an ad hocapproach and to a heuristic method. Besides illustrating all proposals with the data from a breast cancer study we perform a simulation study in order to assess the quality of the methods. © 1997 John Wiley & Sons, Ltd.

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