Iterative Multiple Imputation Research Articles

Abstract PO1-17-07: Invasive disease-free survival as a surrogate for overall survival in patients with hormone receptor−positive/human epidermal growth factor receptor 2−negative early breast cancer: a real-world analysis

Abstract Background: Although the goal of treatment is to improve overall survival (OS), in the adjuvant setting, disease-free survival (DFS) is an important endpoint because DFS risk reduction may reduce mortality risk. After introduction of the STEEP criteria, invasive DFS (iDFS) was adopted as an objective, well accepted primary endpoint in early breast cancer (EBC) trials. This analysis evaluated iDFS as a surrogate for OS in the HR+/HER2− EBC adjuvant treatment setting using real-world data. Methods: This retrospective analysis of the ConcertAI Patient360 database contains deidentified electronic medical records of patients (pts) treated at US academic and community oncology clinics from Jan 1, 1995 to Apr 30, 2021. The cohort included pts with AJCC (8th ed.) stage II-III (if IIIB or IIIC, confirmation was required on residual tumor status; pathological and/or clinical staging [pathological stage was prioritized if both existed in the record]) HR+/HER2− EBC who had surgery and initiated adjuvant endocrine therapy (ET); ovarian function suppression was permitted. iDFS (disease recurrence, metastasis, second primary tumor, or death) and OS (death due to any cause) were defined as time between ET start and first qualifying event. Pts not experiencing an event were censored at data cutoff or maximum follow-up (whichever was first) for iDFS and maximum follow-up for OS. Correlation analyses between individual iDFS and OS times were performed using Pearson and Spearman correlations and an iterative multiple imputation (IMI) algorithm. Subgroup analyses were conducted by first ET, menopausal status (imputed as 50 years if missing), stage, nodal status, prior (neo)adjuvant chemotherapy, and prior radiation. Results: In total, 3133 pts were analyzed. Mean (SD) age (index or ET initiation date) was 58.4 (12.4) years; 98.8% of pts were female, 29.9% were premenopausal, 80.9% had stage II disease, 57.1% had nodal involvement, and 41.6% and 48.8% had received (neo)adjuvant chemotherapy and radiation therapy. Overall, 1854 and 653 pts received nonsteroidal aromatase inhibitors and tamoxifen only. The median follow-up time was 55.1 months for iDFS and 68.2 months for OS. The iDFS (1103 events [35.2%]) rates were 88.9% and 73.9% at 2 and 5 years. The OS (554 events [17.7%]) rates were 97.4% and 90.5% at 2 and 5 years. There was a significant and high correlation ( >0.85 based on IQWiG 2011 guidelines) between iDFS and OS in the overall cohort (Pearson 0.91, P< .001; Spearman 0.88, P< .001) with 82% of OS variation explained by iDFS (least square R2=0.82; Table). Results were confirmed by IMI rho (0.83, P< .001), which is interpreted as very strong ( >0.8). Results were consistent among all reported subgroups; Pearson and Spearman correlations exceeded 0.85 and IMI exceeded 0.8, except for pts with stage III disease where correlation remained high (Pearson 0.88, P< .001) or medium/strong (Spearman 0.84, P< .001; IMI 0.79, P< .001) and where most censoring was observed (38.2% of pts). Conclusions: This retrospective cohort analysis demonstrates a very strong pt-level surrogacy between iDFS and OS among pts with HR+/HER2− EBC treated in a real-world, US-based, academic and community setting. The findings complement the trial-level surrogacy from prior analyses using data from randomized controlled trials and support iDFS as a surrogate endpoint for OS in HR+/HER2− EBC trials. Citation Format: Stephanie Graff, Sara Tolaney, Lowell Hart, Pedram Razavi, Wolfgang Janni, Lee Schwartzberg, Andrii Danyliv, Juan Carlos Mora Payan, Ilia Ferrusi, Rishi Rajat Adhikary, Joyce O'Shaughnessy. Invasive disease-free survival as a surrogate for overall survival in patients with hormone receptor−positive/human epidermal growth factor receptor 2−negative early breast cancer: a real-world analysis [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO1-17-07.

Survival outcomes of patients with metastatic non-small cell lung cancer receiving chemotherapy or immunotherapy as first-line in a real-life setting

Treatment of metastatic non-small cell lung cancer (mNSCLC) has been modified due to the development of immunotherapy. We assessed survival outcomes (overall [OS] and progression-free [rwPFS] survivals, time-to-next-treatment [TNT]) in mNSCLC patients after first-line immunotherapy and chemotherapy in real-life settings. Association between rwPFS and TNT, two candidate surrogate endpoints (SE), with OS was assessed. This retrospective multi-center study uses data from patients included in the Epidemio-Strategy Medico-Economic program with mNSCLC over 2015–2019. The impact of treatment on rwPFS/OS was evaluated with Cox models. Individual-level associations between SE and OS were estimated with an iterative multiple imputation approach and joint survival models. The population included 5294 patients (63 years median age). Median OS in immunotherapy group was 16.4 months (95%CI [14.1–NR]) and was higher than in chemotherapy group (11.6 months; 95%CI [11.0–12.2]). Improved OS was observed for the immunotherapy group after 3 months for subjects with performance status 0–1 (HR = 0.59; 95%CI [0.42–0.83], p < 0.01). The associations between rwPFS and TNT with OS were close (uptau=0.57). Results emphasized a survival improvement with immunotherapy for patients in good health condition. There was moderate evidence of individual-level association between candidate SE and OS.

Progression-free survival as a surrogate endpoint of overall survival in advanced biliary tract cancer: A meta-analysis of randomized trials and individual-patient level correlation.

4101 Background: Biliary tract cancer (BTC) is a heterogeneous group of diseases commonly diagnosed at advanced stages. Overall survival (OS) is the gold-standard primary endpoint in randomized controlled trials (RCT). However, the increasing use of subsequent lines of therapies and cross-over designs may confound the treatment effect. We therefore explored the use of progression free survival (PFS) as a surrogate endpoint of OS both at the trial-level and at the patient-level. Methods: For the trial-level correlation, we conducted a systematic review of RCTs in advanced BTC following the PRISMA guidelines. We searched PubMed, the Cochrane Central Register of Controlled Trials and ClinicalTrials.gov from database inception to June 2022 and identified all randomized phase II/III trials testing systemic therapies for advanced BTC. We used a weighted linear regression to measure the correlation of log-transformed hazard ratios (HR) of OS and PFS based on trial size and calculated the surrogate threshold effect (STE). We used the IQWiG framework to define the strength of evidence. For the individual-level analysis, we included patients with advanced BTC treated with first and second line chemotherapy in the real-world RETUD registry. We estimated the correlation via the iterative multiple imputation method. Results: From a total of 1992 studies, we identified 32 RCTs including 70 treatment arms and 5140 patients that fulfilled the inclusion criteria. Twenty-three trials were performed in the first line setting and most were phase II RCTs (N = 23). We found a moderate correlation between OS and PFS ( R= 0.79, 95% CI 0.61-0.89). The slope of the regression line was 0.62±0.08, indicating that a 10% risk reduction in PFS will result in a 6.2%±0.8% improvement in OS. The STE was 0.69, suggesting that in a hypothetical trial of 400 patients, a PFS HR of 0.69 will likely result in a significant improvement on OS. Regarding the individual-level correlation, a total of 593 patients with advanced BTC were included. The median age of patients was 68y (IQR 59-74), most were males (54%) and received platinum-based chemotherapy (73.1%). In the first line setting, the median OS was 9.7 months (95% CI 8.7-10.5) and median PFS was 5 months (95% CI 4.5-5.5). We observed a strong correlation between PFS and OS ( r= 0.84, 95% CI 0.81-0.86). In the second line setting (N = 259), a similar correlation was observed to the first-line setting ( r= 0.76, 95% CI 0.72-0.8). Conclusions: At the trial-level, in this analysis treatment effects on PFS were moderately correlated with OS. A HR &lt; 0.69 in PFS suggested that it would likely lead to a significant OS benefit in a hypothetical trial including 400 patients. At the individual-level, PFS and OS were strongly correlated in a real-world cohort. Future validation in patients treated in the context of randomized trials is warranted.

Correlation between recurrence-free survival and overall survival after upfront surgery for resected colorectal liver metastases.

The role of recurrence-free survival (RFS) as a valid surrogate endpoint for overall survival (OS) in patients who underwent upfront surgery for colorectal liver metastases remains uncertain. The aim of the study was to compare the two survival measures in a nationwide cohort of upfront resected colorectal liver metastasis. Data from patients with colorectal liver metastases without extrahepatic metastases who underwent curative surgery for liver metastases were retrieved from the Japanese nationwide database (data collection 2005-2007 and 2013-2014). RFS, OS, and survival after recurrence were estimated using the Kaplan-Meier method. The correlation (ρ) between RFS and OS was assessed using the rank correlation method combined with iterative multiple imputation, to account for censoring. As a secondary analysis, the correlation was evaluated according to adjuvant chemotherapy regimen. In sensitivity analysis, the pairwise correlation between RFS and OS was calculated. A total of 2385 patients with colorectal liver metastases were included. In the primary analysis, there was a moderately strong correlation between RFS and OS (ρ = 0.73, 95 per cent c.i. 0.70 to 0.76). The strength of the correlation was similar regardless of the adjuvant treatment regimen (oxaliplatin plus 5-fluorouracil: ρ = 0.72, 0.67 to 0.77; 5-fluorouracil alone: ρ = 0.72, 0.66 to 0.76; observation: ρ = 0.74, 0.69 to 0.78). The mean(s.d.) pairwise correlation coefficient between 3-year RFS and 5-year OS was 0.87(0.06). In surgically treated patients with colorectal liver metastases, there was a moderately strong correlation between RFS and OS, which was unaffected by the treatment regimen. Further validation using a trial-level analysis is required.

Intracranial and Extracranial Progression and Their Correlation With Overall Survival After Stereotactic Radiosurgery in a Multi-institutional Cohort With Brain Metastases

Clinical trials for metastatic malignant neoplasms are increasingly being extended to patients with brain metastases. Despite the preeminence of progression-free survival (PFS) as a primary oncologic end point, the correlation of intracranial progression (ICP) and extracranial progression (ECP) events with overall survival (OS) is poorly understood for patients with brain metastases following stereotactic radiosurgery (SRS). To determine the correlation of ICP and ECP with OS among patients with brain metastases completing an initial SRS course. This multi-institutional retrospective cohort study was conducted from January 1, 2015, to December 31, 2020. We included patients who completed an initial course of SRS for brain metastases during the study period, including receipt of single and/or multifraction SRS, prior whole-brain radiotherapy, and brain metastasis resection. Data analysis was performed on November 15, 2022. Non-OS end points included intracranial PFS, extracranial PFS, PFS, time to ICP, time to ECP, and any time to progression. Progression events were radiologically defined, incorporating multidisciplinary clinical consensus. The primary outcome was correlation of surrogate end points to OS. Clinical end points were estimated from time of SRS completion via the Kaplan-Meier method, while end-point correlation to OS was measured using normal scores rank correlation with the iterative multiple imputation approach. This study included 1383 patients, with a mean age of 63.1 years (range, 20.9-92.8 years) and a median follow-up of 8.72 months (IQR, 3.25-19.68 months). The majority of participants were White (1032 [75%]), and more than half (758 [55%]) were women. Common primary tumor sites included the lung (757 [55%]), breast (203 [15%]), and skin (melanoma; 100 [7%]). Intracranial progression was observed in 698 patients (50%), preceding 492 of 1000 observed deaths (49%). Extracranial progression was observed in 800 patients (58%), preceding 627 of 1000 observed deaths (63%). Irrespective of deaths, 482 patients (35%) experienced both ICP and ECP, 534 (39%) experienced ICP (216 [16%]) or ECP (318 [23%]), and 367 (27%) experienced neither. The median OS was 9.93 months (95% CI, 9.08-11.05 months). Intracranial PFS had the highest correlation with OS (ρ = 0.84 [95% CI, 0.82-0.85]; median, 4.39 months [95% CI, 4.02-4.92 months]). Time to ICP had the lowest correlation with OS (ρ = 0.42 [95% CI, 0.34-0.50]) and the longest median time to event (median, 8.76 months [95% CI, 7.70-9.48 months]). Across specific primary tumor types, correlations of intracranial PFS and extracranial PFS with OS were consistently high despite corresponding differences in median outcome durations. The results of this cohort study of patients with brain metastases completing SRS suggest that intracranial PFS, extracranial PFS, and PFS had the highest correlations with OS and time to ICP had the lowest correlation with OS. These data may inform future patient inclusion and end-point selection for clinical trials.

Evaluation of the response assessment criteria in newly diagnosed and recurrent glioblastoma.

2020 Background: The Response Assessment in Neuro-Oncology (RANO) and modified RANO (mRANO) criteria are the two most widely used criteria to evaluate treatment response in glioblastoma (GBM) clinical trials. Unlike RANO, mRANO omits the evaluation of FLAIR sequence and requires a repeat scan to confirm responses. It also uses the post-radiation (RT) MRI as a baseline MRI in the newly diagnosed setting instead of the pre-RT MRI used in RANO. We sought to compare the 2 response assessment criteria and evaluate the differences between them in a large patient population. We also sought to compare them to immunotherapy RANO (iRANO) in patients who received immunotherapy. Methods: We conducted a retrospective review of consecutive patients with newly diagnosed (nGBM) and recurrent (rGBM) IDH wild-type GBM treated at Dana-Farber Cancer Institute from 2014 to 2020. Bidimensional measurements of enhancing disease and evaluation of FLAIR sequences were performed by two independent readers on patients’ brain MRIs obtained before change of treatment, and discrepancies were evaluated by a third reader. Dates of disease progression (PD) were identified using RANO, mRANO, iRANO, and other response assessment criteria variations. Spearman’s correlations between PFS and OS were calculated using an iterative multiple imputation method to account for any right-censoring. Results: 526 and 580 patients were included in the newly diagnosed and recurrent cohorts, respectively. Spearman’s correlations were not significantly different between RANO and mRANO in the nGBM (0.69 [95% CI 0.62 to 0.75] vs. 0.67 [0.60, 0.73]) and rGBM (0.45 [0.37, 0.52] vs. 0.50 [0.42, 0.57]) cohorts. Evaluation of FLAIR sequences did not improve the correlation between PFS and OS in patients who received antiangiogenic therapy. Addition of confirmation scans was associated with stronger Spearman’s correlations only when PD was identified within 12 weeks of completion of RT in the nGBM cohort, but did not affect the Spearman’s correlations in the rGBM cohort. The use of the post-RT MRI as a baseline was associated with a higher Spearman’s correlation in nGBM than the use of pre-RT MRI (0.67 [0.60, 0.73] vs. 0.53 [0.42, 0.62]). Among 98 patients with nGBM and 175 patients with rGBM who received immunotherapy, the Spearman’s correlations (nGBM and rGBM) with iRANO (0.63 [0.44, 0.76] and 0.34 [0.17, 0.49]) were similar to RANO (0.73 [0.60, 0.82] and 0.42 [0.28, 0.54]) and mRANO (0.65 [0.48, 0.77] and 0.43 [0.28, 0.56]). Conclusions: RANO and mRANO demonstrated similar correlation between PFS and OS. The evaluation of FLAIR can be omitted, while confirmation scans appear to be only beneficial in the nGBM settings during the first 12 weeks of completion of RT. There was a nonsignificant trend in favor of the use of post-RT MRI as the baseline scan in the nGBM setting. The application of iRANO criteria did not add significant benefit in patients who received immunotherapy.

Real-World Therapy with Pembrolizumab: Outcomes and Surrogate Endpoints for Predicting Survival in Advanced Melanoma Patients in Germany

Simple SummaryKnowledge on the real-world outcomes of patients with advanced melanoma and the value of different endpoints for evaluating survival benefits is limited. We investigated the outcomes and different surrogate endpoints for overall survival (OS) in 664 pembrolizumab-treated patients with advanced melanoma in Germany. Our findings support the effectiveness of pembrolizumab in real-world clinical practice. The real-world time to next treatment was most strongly correlated with OS, suggesting it as a valuable surrogate endpoint to assess treatment effectiveness. Real-world studies assessing time to next treatment could support clinical and payer decision making.Knowledge on the real-world characteristics and outcomes of pembrolizumab-treated advanced melanoma patients in Germany and on the value of different real-world endpoints as surrogates for overall survival (OS) is limited. A sample of 664 pembrolizumab-treated patients with advanced melanoma from the German registry ADOReg was used. We examined OS, real-world progression-free survival (rwPFS), real-world time to next treatment (rwTtNT), and real-world time on treatment (rwToT). Spearman’s rank and iterative multiple imputation (IMI)-based correlation coefficients were computed between the OS and the rwPFS, rwTtNT, and rwToT and reported for the first line of therapy and the overall sample. The median OS was 30.5 (95%CI 25.0–35.4) months, the rwPFS was 3.9 months (95%CI 3.5–4.9), the rwTtNT was 10.7 months (95%CI 9.0–12.9), and the rwToT was 6.2 months (95%CI 5.1–6.8). The rwTtNT showed the highest correlation with the OS based on the IMI (rIMI = 0.83), Spearman rank correlations (rs = 0.74), followed by the rwToT (rIMI = 0.74 and rs = 0.65) and rwPFS (rIMI = 0.69 and rs = 0.56). The estimates for the outcomes and correlations were similar for the overall sample and those in first-line therapy. The median OS was higher compared to recent real-world studies, supporting the effectiveness of pembrolizumab in regular clinical practice. The rwTtNT may be a valuable OS surrogate, considering the highest correlation was observed with the OS among the investigated real-world endpoints.

Regression multiple imputation for missing data analysis

Iterative multiple imputation is a popular technique for missing data analysis. It updates the parameter estimators iteratively using multiple imputation method. This technique is convenient and flexible. However, the parameter estimators do not converge point-wise and are not efficient for finite imputation size m. In this paper, we propose a regression multiple imputation method. It uses the parameter estimators obtained from multiple imputation method to estimate the parameter estimators based on expectation maximization algorithm. We show that the resulting estimators are asymptotically efficient and converge point-wise for small m values, when the iteration k of the iterative multiple imputation goes to infinity. We evaluate the performance of the new proposed methods through simulation studies. A real data analysis is also conducted to illustrate the new method.

Impact of clinical versus radiographic progression on clinical outcomes in metastatic castration-resistant prostate cancer

ObjectivesUnequivocal clinical progression (UCP)—a worsening of clinical status with or without radiographic progression (RAD)—represents a distinct mode of disease progression in metastatic prostate cancer. We evaluated the prevalence, risk factors and the impact of UCP on survival outcomes.MethodsA post-hoc analysis of the COU-AA-302, a randomised phase 3 study of abiraterone plus prednisone (AAP) versus prednisone was performed. Baseline characteristics were summarised. Cox proportional-hazards model and Kaplan-Meier method were used for survival and time to event analyses, respectively. Iterative multiple imputation method was used for correlation between clinicoradiographic progression-free survival (crPFS) and overall survival (OS).ResultsOf 736 patients with disease progression, 280 (38%) had UCP-only and 124 (17%) had UCP plus RAD. Prognostic index model high-risk group was associated with increased likelihood of UCP (p<0.0001). Median OS was 25.7 months in UCP-only and 33.0 months for RAD-only (HR 1.39; 95% CI 1.16 to 1.66; p=0.0003). UCP adversely impacted OS in both treatment groups. Lowest OS was seen in patients with prostate specific antigen (PSA)-non-response plus UCP-only progression (median OS 22.6 months (95% CI 20.7 to 24.4)). Including UCP events lowered estimates of treatment benefit—median crPFS was 13.3 months (95% CI 11.1 to 13.8) versus median rPFS of 16.5 months (95% CI 13.8 to 16.8) in AAP group. Finally, crPFS showed high correlation with OS (r=0.67; 95% CI 0.63 to 0.71).ConclusionsUCP is a common and clinically relevant phenomenon in patients with metastaticcastration-resistant prostate cancer (mCRPC) treated with AAP or prednisone. UCP is prognostic and associated with inferior OS and post-progression survival. A combination of PSA-non-response and UCP identifies patients with poorest survival. When included in PFS analysis, UCP diminishes estimates of treatment benefit. Continued study of UCP in mCRPC is warranted.

Iterative Multiple Imputation: A Framework to Determine the Number of Imputed Datasets

We consider multiple imputation as a procedure iterating over a set of imputed datasets. Based on an appropriate stopping rule the number of imputed datasets is determined. Simulations and real-data analyses indicate that the sufficient number of imputed datasets may in some cases be substantially larger than the very small numbers that are usually recommended. For an easier use in various applications, the proposed method is implemented in the R package imi.

PUB027 Appropriate Endpoint for Stage I NSCLC: Correlations of Long-Term Survival with Disease-Free and Recurrence-Free Survival

Overall survival (OS) is commonly reported as an optimal endpoint as it incorporates mortality from the cancer itself, from treatment as well as other causes. We hypothesized that in patients who underwent curative-intent resection for stage I NSCLC, reduced recurrence results in improved OS; recurrence is an appropriate endpoint. We examined the correlations between OS, lung-cancer-specific survival (CSS), disease-free survival (DFS) and recurrence-free survival (RFS). Retrospective reviews identified pStage I NSCLC patients who underwent curative-intent resection of primary lung cancer from a single institution (2000-2011). Survival was estimates by the Kaplan-Meier approach. Correlations between pairs of endpoints (ρ) were reported as correlation coefficients from bivariate survival models using 100 iterative multiple imputation. For DFS, recurrence and death without recurrence are both considered events, whereas death without recurrence is censored in RFS. Among 2186 patients, 70.1% were age 65+, 44.3% with >2cm tumors. OS and CSS are 78% and 90%, respectively. In the presence of recurrence, DFS and RFS are 70% and 81%, respectively. The correlation between DFS and OS is 0.926 (95% CI, 0.912, 0.937), indicating excellent correlation between the two endpoints, regardless of tumor size. The correlation between recurrence and OS is slightly lower (ρ=0.812), while the correlation between recurrence and CSS is as high as DFS vs OS (ρ=0.896). The correlation between DFS and OS did not differ by surgery type; however, in recurrence vs OS or CSS, sublobar surgery trended toward lower correlation. Among early stage NSCLC patients receiving surgical interventions, recurrence is an appropriate endpoint with high correlation with long-term outcomes, particularly among lobar surgeries.

Flexible and Robust Method for Missing Loop Detector Data Imputation

This study is primarily focused on missing traffic sensor data imputation for the purpose of improving the coverage and accuracy of traffic analysis and performance estimation. Missing data, whether attributable to hardware failure or error detection and removal, are a constant problem in loop and other traffic detector data sets. As the rate of missingness increases, the treatment of missing values quickly becomes the controlling factor in overall data quality. Previously, several imputation approaches have been developed for traffic data. However, few studies aim at handling the traffic data with large blocks of missing values for networkwide implementation. A proven predictive mean matching multiple imputation method is introduced; it was applied to loop detector volume data collected on Interstate 5 in Washington State. With the use of the iterative multiple imputation by chained equations approach, the spatial correlation between nearby detectors was considered for prediction, and the presence of missing data was effectively dealt with in all predictors. The proposed methodology is shown to perform well on a range of missing data patterns, including missing completely at random, missing days, and missing months. After the imputation method was applied to 20-s data and postimputation aggregation was performed, the results in this study suggest that the proposed method can outperform elementary pairwise regression and produce reliable imputation estimates, even when entire days and months are missing from the data set. Thus the predictive mean matching multiple imputation method can be used as an effective approach for imputing missing traffic data in a range of challenging scenarios.

Estimating the correlation of bivariate failure times under censoring

The analysis of correlations within pairs of survival times is of interest to many research topics in medicine, such as the correlation of survival-type endpoints of twins, the correlation of times till failure in paired organs, or the correlation of survival time with a surrogate endpoint. The dependence of such times is assumed monotonic and thus quantification by rank correlation coefficients appropriate. The typical censoring of such times requires more involved methods of estimation and inference as have been developed in recent years. The paper focuses on semiparametric approaches, and in particular on the normal copula-based estimation of Spearman correlation coefficients. The copula approach, often presented for a mathematically inclined readership, is reviewed from the viewpoint of an applied statistician. As an alternative to the maximum likelihood methodology for the normal copula approach (NCE) we introduce an iterative multiple imputation (IMI) method which requires only about 0.05% of the computing time of NCE, without sacrificing statistical performance. For IMI, survival probabilities at death or censoring times are first transformed to normal deviates. Then, those deviates that relate to censored times are iteratively augmented, by using conditional multiple imputation, until convergence is obtained for the normal scores rank correlation, which is similar to Spearman's rank correlation. Statistical properties of NCE and IMI are compared by means of a Monte Carlo study and by means of three real data sets, which also give an impression of the typical range of applications, and of their problems.