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Survival Analysis Part II: Multivariate data analysis – an introduction to concepts and methods
Open accessAbstract
Survival analysis involves the consideration of the time between a fixed starting point (e.g. diagnosis of cancer) and a terminating event (e.g. death). The key feature that distinguishes such data from other types is that the event will not necessarily have occurred in all individuals by the time the study ends, and for these patients, their full survival times are unknown. For instance, in studies that measure the length of survival after diagnosis of cancer, it is common for a proportion of individuals to remain alive and disease-free at the end of the follow-up period, and for these patients, we know only a lower limit on their actual time to event. Thus, special methods are required for these type of data. The explanation and demonstration of some of the methods proposed to analyse such data are the basis of this series.
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“The proportional hazards assumption was assessed using the log(−log(survival)) plot, and those that failed the assumption or that were deemed to be time dependent were entered as continuous time-dependent covariates (Bradburn et al, 2003).”
From Cohort study of adherence to adjuvant endocrine therapy, breast cancer recurrence and mortality (2013) · cites this paper as Bradburn et al, 2003
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Factors Driving Inequality in Prostate Cancer Survival: A Population Based Study
Burns, R., Sharp, L., Sullivan, F. J., Deady, S., Drummond, F. J., & O’Neill, C. (2014) · PLoS ONE · doi:10.1371/journal.pone.0106456 · Cited by 18
“model for survival analysis in cancer have been extensively discussed elsewhere [26–27].”
Diffusion of medication drop-boxes in North Carolina from 2007 to 2016
Egan, K. L., Wolfson, M., Dudley, W. N., Francisco, V. T., Strack, R. W., Wyrick, D. L., & Perko, M. A. (2018) · Addictive Behaviors · doi:10.1016/j.addbeh.2018.03.029 · Cited by 18
Drechsler, W., & Natter, M. (2011) · Journal of Interactive Marketing · doi:10.1016/j.intmar.2011.02.001 · Cited by 18
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BackgroundDySurv: dynamic deep learning model for survival analysis with conditional variational inference
Mesinovic, M., Watkinson, P., & Zhu, T. (2024) · Journal of the American Medical Informatics Association · doi:10.1093/jamia/ocae271 · Cited by 23
“29 Thus, the dataset can be represented as with X i representing the feature matrix of patient i , T being the time-to-event i.e., the minimum of the event and censoring time, y 2 f; ; 1 g being the label for the outcome with ; representing right-censoring, and N samples included.”
Kang, K., Kim, H., Hur, W., Jung, J.-H., Jeong, S. J., Shin, H., Seo, D., Jeong, H., Choi, B. H., Hong, S., et al. (2020) · Molecular & Cellular Proteomics · doi:10.1074/mcp.ra120.002169 · Cited by 18
“The HR was estimated using multivariable Cox regression (36).”
MethodCano, L., Bertani, S., Island, M., Cerapio, J., Ruíz, E., Pineau, P., Monbet, V., Boudjéma, K., Taxa, L., Casavilca-Zambrano, S. A., et al. (2021) · Scientific Reports · doi:10.1038/s41598-021-93369-4 · Cited by 20
Dynamics of beetle-killed snags following mountain pine beetle outbreaks in lodgepole pine forests
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Briolat, E. S., Arenas, L. M., Hughes, A. E., Liggins, E., & Stevens, M. (2021) · BMC Ecology and Evolution · doi:10.1186/s12862-021-01883-w · Cited by 17
“Final survival models were relevelled to provide a hazards ratio (HR) for the effect of being a generalist rather than a specialist, where an HR greater than 1 indicates that the probability of detection increases and an HR below 1 that it decreases with this strategy [81].”
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“The modification in HR value has already been documented previously [35], and this event might be related to the low number of patients as well as to the small contribution of Exo-miR-17-5p in the model compared to Exo-miR-130a- 3p.”
ResultEffects of planting food crops on survival and early growth of timber trees in eastern Panama
Paul, C., & Weber, M. (2015) · New Forests · doi:10.1007/s11056-015-9477-5 · Cited by 17
“Among the various semi-parametric models that can handle such censored data, the Cox proportional hazard model was chosen in order to allow for the incorporation of multiple covariates (Bradburn et al. 2003).”
MethodKalledsøe, L., Dragsted, L. O., Hansen, L., Kyrø, C., Grønbæk, H., Tjønneland, A. M., & Olsen, A. (2018) · Growth Hormone & IGF Research · doi:10.1016/j.ghir.2018.12.003 · Cited by 17
Reis-Pina, P., Sabri, E., Birkett, N., Barbosa, A., & Lawlor, P. G. (2019) · Journal of Pain and Symptom Management · doi:10.1016/j.jpainsymman.2019.06.017 · Cited by 17
Zheng, C., Tang, H., Wang, X., Chen, Z., Zhang, L., Kang, Y., Yang, Y., Chen, L., Zhou, H., Cai, J., et al. (2022) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2022.154872 · Cited by 17
Survival analysis of time‐to‐event data in respiratory health research studies
Kasza, J., Wraith, D., Lamb, K. E., & Wolfe, R. S. (2014) · Respirology · doi:10.1111/resp.12281 · Cited by 17
ABO Incompatibility and Hematopoietic Stem Cell Transplantation Outcomes.
Vaezi, M., Dameshghi, D. O., Souri, M., Setarehdan, S. A., Alimoghaddam, K., & Ghavamzadeh, A. (2017) · Europe PMC (PubMed Central) · Cited by 17
The power of tumor sizes in predicting the survival of solitary hepatocellular carcinoma patients
Yang, A., Xiao, W., Chen, D., Wei, X., Huang, S., Lin, Y., Zhang, C., Lin, J., Deng, F., Wu, C., et al. (2018) · Cancer Medicine · doi:10.1002/cam4.1873 · Cited by 17
Análise de sobrevivência em estudos clínicos e experimentais
Miot, H. A. (2017) · Jornal Vascular Brasileiro · doi:10.1590/1677-5449.001604 · Cited by 17
Evaluation of harvest indices for monitoring cougar survival and abundance
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“Rather, each covariate within the model is assumed to act multiplicatively (i.e., proportionally) on the baseline mortality hazard at each time step (Bradburn et al. 2003): hi(t)¼ h0(t) exp(biXi) such as where h0 refers to the baseline hazard (i.e., the hazard’s value when all covariate values are…”
BackgroundPredicting credit risk in Peer-to-Peer lending with survival analysis
Byanjankar, A. (2017) · IEEE Symposium Series on Computational Intelligence (SSCI) · doi:10.1109/ssci.2017.8280927 · Cited by 16
“A hazard ratio greater than one indicate that as the value of kth covariate increases the event hazard increases and thus results in the decrease in survival period [39].”
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Ćosić, S. J., Sirotković-Skerlev, M., Kulić, A., Jakić‐Razumović, J., Kovač, Z., & Vrbanec, D. (2011) · Tumori Journal · doi:10.1177/030089161109700419 · Cited by 16
Lai, C.-C., Ji, D.-D., Wu, F., Mu, J., Yang, J.-R., Jiang, D. D.-S., Lin, W.-Y., Chen, W.-T., Yen, M.-Y., Wu, H.-S., et al. (2015) · Journal of Epidemiology · doi:10.2188/jea.je20150061 · Cited by 16
Whitworth, L. J., Coxon, J., van Laarhoven, A., Thương, N. T. T., Dian, S., Alisjahbana, B., Ganiem, A. R., van Crevel, R., Thwaites, G. E., Troll, M. A., et al. (2021) · eLife · doi:10.7554/elife.61722 · Cited by 15
“Both studies used, as the primary metric of significance testing, Cox regression modelling, an approach that assumes that the ratio of hazard rates between groups is constant throughout the observed period (Bradburn et al., 2003; Greenland et al., 2016).”
MethodDhanorkar, S., & Siemsen, E. (2021) · Production and Operations Management · doi:10.1111/poms.13479 · Cited by 15
“Other studies have used the Cox model, where the baseline hazard function is estimated nonparame-trically (Bradburn et al. 2003).”
MethodCan sarcopenia predict survival in locally advanced rectal cancer patients?
Gartrell, R., Qiao, J., Kiss, N. K., Faragher, I. G., Chan, S. T. F., Baird, P. N., & Yeung, J. M. C. (2023) · ANZ Journal of Surgery · doi:10.1111/ans.18512 · Cited by 15
“Five-year OS and RFS were estimated with Kaplan–Meier curves and univariate comparisons analysed with log-rank test, followed by multivariate regression and hazard ratio (HR) calculated if proportional hazards assumption was shown; when proportional hazards assumption was not met, log-logistic analysis (with time rati…”
MethodSurvival of Eurasian lynx in the human‐dominated landscape of Europe
Premier, J., Bastianelli, M. L., Oeser, J., Anders, O., Andrén, H., Aronsson, M., Bagrade, G., Belotti, E., Breitenmoser‐Würsten, C., Bufka, L., et al. (2025) · Conservation Biology · doi:10.1111/cobi.14439 · Cited by 15
“Multivariate models are an appropriate way to make statistical inference about individuals’ mortality risk depending on their exposure to multiple time-varying and static factors and treatments (e.g., Bradburn et al., 2003).”
Bayesian bivariate generalized Lindley model for survival data with a cure fraction
Martínez, E. Z., & Achcar, J. A. (2014) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2014.07.011 · Cited by 15
Dong, Y., Liu, Y., Bai, H., & Jiao, S. (2019) · Scientific Reports · doi:10.1038/s41598-019-42345-0 · Cited by 15
Río‐Ospina, L. D., Camargo, M., León, S. C. S., Sánchez, R., Pérez, D. A. M., Patarroyo, M. E., & Patarroyo, M. A. (2020) · Scientific Reports · doi:10.1038/s41598-020-64268-x · Cited by 15
A mediation analysis to explain socio‐economic differences in bladder cancer survival
Russell, B. A., Hemelrijck, M. V., Gårdmark, T., Holmberg, L., Kumar, P., Bellavia, A., & Häggström, C. (2020) · Cancer Medicine · doi:10.1002/cam4.3418 · Cited by 15
Lim, G. B., Kim, Y., Seo, J.-H., Lee, H. J., Gong, G., & Park, S. H. (2020) · BMC Cancer · doi:10.1186/s12885-020-07399-8 · Cited by 15
Epidemiologia explicada - Análise de Sobrevivência
Botelho, F. B., Silva, C., & Cruz, F. (2009) · Cited by 15
Cautionary Note Regarding the Use of CIs Obtained From Kaplan-Meier Survival Curves
Carter, R. E., & Huang, P. (2008) · Journal of Clinical Oncology · doi:10.1200/jco.2008.18.8011 · Cited by 15
Surviving fully Bayesian nonparametric regression models
Hanson, T., & Jara, A. (2013) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199695607.003.0030 · Cited by 15
Hu, M., Babiskin, A. H., Wittayanukorn, S., Schick, A., Rosenberg, M., Gong, X., Kim, M., Zhang, L., Lionberger, R. A., & Zhao, L. Y. (2019) · Clinical Pharmacology & Therapeutics · doi:10.1002/cpt.1479 · Cited by 15
“Other regression-based survival methods 15,16 are also subject to those assumptions.”
BackgroundFleisig, G. S., Slowik, J. S., Wychgram, C., D’Angelo, J. A., Chalmers, P. N., Erickson, B. J., Froom, R. J., Porter, K. M. P., & Curriero, F. C. (2025) · Orthopaedic Journal of Sports Medicine · doi:10.1177/23259671251351339 · Cited by 14
“6 Before modeling, descriptive statistics were compared between pitchers with and without UCL surgery during the follow-up period.”
Kamaruddin, M., Wan‐Arfah, N., Naing, N. N., Hassan, M. R. A., & Chan, H. (2022) · Asian Pacific Journal of Tropical Medicine · doi:10.4103/1995-7645.340568 · Cited by 14
Egilsson, E., Bjarnason, R. G., & Njarðvík, U. (2023) · JMIR mhealth and uhealth · doi:10.2196/45414 · Cited by 15
Hermans, K., Spruytte, N., Cohen, J., Audenhove, C. V., & Declercq, A. (2014) · BMC Geriatrics · doi:10.1186/1471-2318-14-132 · Cited by 15
“A survival analysis deals with time until the occurrence of a particular event [38,39].”
BackgroundTransforming cumulative hazard estimates
Ryalen, P. C., Stensrud, M. J., & Røysland, K. (2018) · Biometrika · doi:10.1093/biomet/asy035 · Cited by 14
“On the other hand, additive models have been criticized because the effect estimates may be harder to understand: Often effect estimates are directly plotted as cumulative hazard curves, which seems to be unsatisfactory to applied researchers [12].”
BackgroundImpact of Quality Factors on Users’ Viewing Behaviors in Adaptive Bitrate Streaming Services
Takahashi, S., Yamagishi, K., Lebreton, P., & Okamoto, J. (2019) · International Conference on Quality of Multimedia Experience (QoMEX) · doi:10.1109/qomex.2019.8743191 · Cited by 14
“In addition, if the proportional hazard model [28] is applied to our dataset in our future modeling, we should consider at least the average bitrate, number of stalling events, and average stalling duration as the external covariates of our model.”
MethodAn explanation of the hazard ratio
Kay, R. (2004) · Pharmaceutical Statistics · doi:10.1002/pst.119 · Cited by 14
“For further reading on the general survival data area, including the comparison of survival curves, the inclusion of covariates through the proportional hazards model and the use of models which are not based on proportionality see [1–5].”
MethodCost–Utility Analysis of Chemotherapy Regimens in Elderly Patients with Stage III Colon Cancer
Lairson, D. R., Parikh, R. C., Cormier, J. N., Chan, W., & Du, X. L. (2014) · PharmacoEconomics · doi:10.1007/s40273-014-0180-8 · Cited by 14
“Given that some stage III colon cancer patients have a long survival and more than 50 % of the study patients were alive at the study end date, a Weibull distribution parametric regression model was applied to estimate the median overall survival [26, 28, 37, 38].”
MethodTime to first treatment interruption in the Chinese methadone maintenance treatment programme
Sullivan, S. G., Wu, Z., & Detels, R. (2013) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2013.06.021 · Cited by 14
Li, M., & Ashuri, B. (2021) · Journal of Construction Engineering and Management · doi:10.1061/(asce)co.1943-7862.0002164 · Cited by 13
Grzesiak, W., Adamczyk, K., Zaborski, D., & Wójcik, J. (2022) · Animals · doi:10.3390/ani12151942 · Cited by 13
“For additional descriptions of cow survivability, regression model parameters were estimated and the values of the hazard ratio (HR) were determined over three successive lactations to identify the predictors most strongly correlated with the survival times of cows in each culling category [16,34,35,37,44,45,51].”
MethodFairness with censorship and group constraints
Zhang, W., & Weiss, J. C. (2023) · Knowledge and Information Systems · doi:10.1007/s10115-023-01842-5 · Cited by 13
“However, their definitions exclude the censoring information when measuring discrimination, which could introduce substantial bias, as censored information might be of importance and cannot simply be ignored [13].”
BackgroundSánchez-Martínez, L. J., Charle‐Cuéllar, P., Gado, A. A., Dougnon, A. O., Sanoussi, A., Ousmane, N., Lazoumar, R. H., Touré, F., Vargas, A., Hernández, C. L., et al. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1253545 · Cited by 13
Hung, Y., Lee, P., Chang, Y., Yang, M., Chiu, C., Chen, M., Lan, K., Lee, I., Hou, M., Chao, Y., et al. (2024) · Alimentary Pharmacology & Therapeutics · doi:10.1111/apt.18403 · Cited by 13
Surgical approach for recurrent inguinal hernias: a Nationwide Cohort Study
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“Characteristics No GF (n = 1,548) Primary GF (n = 13) Secondary GF (n = 69) HLA A, B, DR mismatch 0 1,124 (73) 6 (46) 44 (64) 1 40 (3) 0 2 (3) 2 93 (6) 1 (8) 3 (4) 3 275 (18) 6 (46) 20 (29) ND 15 (1) 0 0 Donor age, yr Median (range) 33 (7–70) 33 (19–68) 35 (5–62) Donor age, yr ≤ 25 327 (21) 3 (23) 14 (20) 26–45 930 (6…”
Case‐control analysis of survival outcomes in sinonasal acinic cell carcinoma
Biron, V. L., Lentsch, E. J., Gerry, D. R., & Bewley, A. F. (2014) · International Forum of Allergy & Rhinology · doi:10.1002/alr.21301 · Cited by 13
Coelho, C. A. S., Firpo, M. Â. F., Maia, A. D. H. N., & MacLachlan, C. (2017) · International Journal of Climatology · doi:10.1002/joc.5010 · Cited by 13
Li, D., Madhoun, H., Roberts, W. N., & Jarjour, W. N. (2018) · Lupus · doi:10.1177/0961203318770534 · Cited by 13
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“In line with traditional multi-variate statistical modeling [17], the key requirement for an automatically derived model is to allow survival to be assessed with respect to several factors simultaneously as well as offer estimates of the strength of effect for each factor.”
BackgroundFrom conference abstract to publication in the conservation science literature
Arregoitia, L. D. V., & González‐Suárez, M. (2019) · Conservation Biology · doi:10.1111/cobi.13296 · Cited by 13
“The null hypothesis was that there was no difference between them (Bradburn et al. 2003).”
BackgroundA time series approach to player churn and conversion in videogames
del Río, A. F., Guitart, A., & Periáñez, Á. (2021) · Intelligent Data Analysis · doi:10.3233/ida-194940 · Cited by 15
An Integrating Immune-Related Signature to Improve Prognosis of Hepatocellular Carcinoma
Zhu, R., Guo, W., Xu, X., & Zhu, L. (2020) · Computational and Mathematical Methods in Medicine · doi:10.1155/2020/8872329 · Cited by 13
“Cox proportional-hazards regression model [34] was used to analyze the correlation between survival time and genes.”
MethodA guide to survival analysis for manual therapy clinicians and researchers
Hancock, M. J., Maher, C. G., Costa, L. D. C. M., & Williams, C. M. (2013) · Manual Therapy · doi:10.1016/j.math.2013.08.007 · Cited by 13
Nagy, M., Schulz–Ertner, D., Bischof, M., Welzel, T., Hof, H., Debus, J., & Combs, S. E. (2009) · Tumori Journal · doi:10.1177/030089160909500308 · Cited by 13
Ben‐Assuli, O., Ramon‐Gonen, R., Heart, T., Jacobi, A., & Klempfner, R. (2023) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2023.104340 · Cited by 12
The unwell patient with advanced chronic liver disease: when to use each score?
Moore, O., Ma, W., Read, S. A., George, J., & Ahlenstiel, G. (2025) · BMC Medicine · doi:10.1186/s12916-025-04185-w · Cited by 12
“The intrinsic strengths of the MELD scores come from their objective construction as a product of multivariate analysis, representing the best method to minimise confounders and increase statistical power [32].”
Steep Decline and Cessation in Seed Dispersal by Myrmica rubra Ants
Bologna, A., & Detrain, C. (2015) · PLoS ONE · doi:10.1371/journal.pone.0139365 · Cited by 12
“In comparison with other survival models such as parametric ones, this Cox model does not make any specific assumption on the statistical distribution of the hazard [52].”
MethodChai‐Adisaksopha, C., Iorio, A., Hillis, C., Lim, W., & Crowther, M. A. (2016) · BMC Hematology · doi:10.1186/s12878-016-0055-7 · Cited by 12
Vey, J. A., Kapsner, L. A., Fuchs, M., Unberath, P., Veronesi, G., & Kunz, M. (2019) · Cancers · doi:10.3390/cancers11101606 · Cited by 12
“Several statistical methods have been developed for survival data analysis [24,25].”
BackgroundMethodGenome Instability Profiles Predict Disease Outcome in a Cohort of 4,003 Patients with Breast Cancer
Lischka, A., Doberstein, N., Freitag‐Wolf, S., Koçak, A. A., Gemoll, T., Heselmeyer‐Haddad, K., Ried, T., Auer, G., & Habermann, J. K. (2020) · Clinical Cancer Research · doi:10.1158/1078-0432.ccr-20-0566 · Cited by 12
Epidemiological Study of Return to Work and Mortality in Lung Cancer Survivors
Yang, Z., Lai, C., Ho, C., & Wang, C. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19010309 · Cited by 12
“Cox regression is a technique for evaluating the association between variables and specific events [21].”
MethodIndividual Fairness with Group Awareness Under Uncertainty
Wang, Z., Dzuong, J., Yuan, X., Chen, Z., Wu, Y., Yao, X., & Zhang, W. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-70362-1_6 · Cited by 13
Determining the statistical significance of survivorship prediction models
Berty, H. P., Shi, H., & Lyons‐Weiler, J. (2010) · Journal of Evaluation in Clinical Practice · doi:10.1111/j.1365-2753.2009.01199.x · Cited by 12
Szadkowski, L., Tseng, A. L.-I., Walmsley, S. L., Salit, I. E., & Raboud, J. (2012) · AIDS Research and Human Retroviruses · doi:10.1089/aid.2012.0018 · Cited by 12
“8 Mixed linear models 9 were used to evaluate the longitudinal CD4 count response to treatment.”
Statistical primer: basics of survival analysis for the cardiothoracic surgeon†
Thuijs, D. J. F. M., Hickey, G. L., & Osnabrugge, R. L. J. (2018) · Interactive Cardiovascular and Thoracic Surgery · doi:10.1093/icvts/ivy010 · Cited by 12
Naseri, P., Baghestani, A. R., Momenyan, N., & Akbari, M. E. (2018) · International Journal of Cancer Management · doi:10.5812/ijcm.62863 · Cited by 12
Peters, J. M., Walter, V., Patterson, A. D., & Gonzalez, F. J. (2019) · npj Precision Oncology · doi:10.1038/s41698-019-0098-x · Cited by 12
Rød, B., Barabadi, A., & Naseri, M. (2020) · Journal of Management in Engineering · doi:10.1061/(asce)me.1943-5479.0000823 · Cited by 12
Risk of inflammatory bowel disease in uveitis patients: a population-based cohort study
Lo, T.-C., Chen, Y., & Chen, H. (2021) · Eye · doi:10.1038/s41433-021-01645-4 · Cited by 11
Pijnenborg, P., Verhoeven, R. H. A., Fırat, M., van Laarhoven, H. W. M., & Genga, L. (2021) · International Conference on Process Mining (ICPM) · doi:10.1109/icpm53251.2021.9576880 · Cited by 11
Assessment of Eurasian lynx reintroduction success and mortality risk in north-west Poland
Skorupski, J., Tracz, M., Tracz, M., & Śmietana, P. (2022) · Scientific Reports · doi:10.1038/s41598-022-16589-2 · Cited by 11
Gu, Y., Wang, M., Gong, Y., Li, X., Wang, Z., Wang, Y., Jiang, S., Zhang, D., & Li, C. (2023) · Future Oncology · doi:10.2217/fon-2023-0736 · Cited by 11
Zhu, R., Wang, X., Sun, F., Zhu, L., & Guo, W. (2024) · Frontiers in Bioscience-Landmark · doi:10.31083/j.fbl2903123 · Cited by 11
Belding, J. N., Bonkowski, J. F., Englert, R. M., Stanfill, A. G., & Tsao, J. W. (2024) · Frontiers in Neurology · doi:10.3389/fneur.2024.1442715 · Cited by 12
Multivariable Regression Models in Clinical Transplant Research
Singh, S. K. S., Kaplan, B. E., & Kim, S. J. (2015) · Transplantation · doi:10.1097/tp.0000000000000996 · Cited by 11
Gligorijević, T., Ševarac, Z., Milovanović, B., Đajić, V., Zdravkovic, M. D., Hinić, S., Arsić, M., & Aleksić, M. (2017) · Complexity · doi:10.1155/2017/8953083 · Cited by 11
“Nevertheless, it is likely that the assumptions required by the Cox model may not be satisfied because the model assumes that the underlying hazard rate is a function of independent variables, instead of the survival time [31].”
BackgroundGenerative Adversarial Networks for Robust Breast Cancer Prognosis Prediction with Limited Data Size
Hsu, T.-C., & Lin, C. (2020) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/embc44109.2020.9175736 · Cited by 11
PlasmiR: A Manual Collection of Circulating microRNAs of Prognostic and Diagnostic Value
Tastsoglou, S., Miliotis, M., Kavakiotis, I., Alexiou, A., Gkotsi, E. C., Lambropoulou, A., Lygnos, V., Kotsira, V., Maroulis, V., Zisis, D., et al. (2021) · Cancers · doi:10.3390/cancers13153680 · Cited by 11
“Prognostic biomarker assessment studies routinely employ log-rank tests and Kaplan–Meier analysis to evaluate significance in survival between cohort subgroups, univariate, or multivariate Cox regression models to evaluate potential biomarkers and adjust for confounders [17,18].”
MethodSurvival Analysis in Modeling the Birth Interval of the First Child in Indonesia
Hidayat, R. S. A., Sumarno, H., & NUGRAHANI, E. H. (2014) · Open Journal of Statistics · doi:10.4236/ojs.2014.43019 · Cited by 11
“Cox Proportional Hazard and Non-Proportional Hazard Model Cox proportional hazard is a model usually used as multivariate approach to analyze the data [12].”
MethodSpecial considerations in prognostic research in cancer involving genetic polymorphisms
Savas, S., Liu, G., & Xu, W. (2013) · BMC Medicine · doi:10.1186/1741-7015-11-149 · Cited by 11
“Interested readers may refer to other articles for further information [6-10].”
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Senescence in the city: exploring ageing patterns of a long‐lived raptor across an urban gradient
Sumasgutner, P., Koeslag, A., & Amar, A. (2019) · Journal of Avian Biology · doi:10.1111/jav.02247 · Cited by 11
Jirásková, L., Ryška, A., Tebbens, J. D., Hornychová, H., Čečka, F., Štaud, F., & Červený, L. (2019) · Cancers · doi:10.3390/cancers11111621 · Cited by 11
“A Cox’s proportional hazards multivariate model was used to corroborate any association of clinical and pathological factors and expression of ENT1/ENT1, NOTCH3, and/or miR-21 with patients’ DSS [19,25,48,84,85].”
MethodPrognostic Models: A Methodological Framework and Review of Models for Breast Cancer
Altman, D. G. (2007) · Translational medicine series · doi:10.3109/9781420019940.002 · Cited by 11
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“modely rizika (hazardu), kterými se však v našem článku nezabýváme (3).”
Zhao, Z., Gao, Y., Tan, F., Xue, Q., Gao, S., & He, J. (2024) · Translational Lung Cancer Research · doi:10.21037/tlcr-24-91 · Cited by 10
Wang, C., Firdi, N. P., Chu, T.-C., Faiz, M. F. I., Iqbal, M. Z., Li, Y., Yang, B., Mallya, M., Bashashati, A., Li, F., et al. (2024) · Medical Image Analysis · doi:10.1016/j.media.2024.103342 · Cited by 10
Cao, S., Liu, L., Yang, L., Li, H., Zhu, R., Yu, G., Jiao, N., & Wu, D. (2025) · International Immunopharmacology · doi:10.1016/j.intimp.2025.114317 · Cited by 10
Investigating key predictors of persistent low back pain: A focus on psychological stress
Carney, K. M. B., Guite, J. W., Young, E. E., & Starkweather, A. R. (2021) · Applied Nursing Research · doi:10.1016/j.apnr.2021.151406 · Cited by 10
Ren, Z., Wang, Z., Gu, D., Ma, H., Zhu, Y., Cai, M., & Zhang, J. (2021) · Frontiers in Cell and Developmental Biology · doi:10.3389/fcell.2021.740455 · Cited by 10
“Multivariate Cox regression is the most widely utilized regression model for analyzing medical survival time and survival status data (Bradburn et al., 2003), and it was used to explore the”
MethodKim, H. H., Ko, C., Park, J. A., Song, I. H., & Park, Y. R. (2022) · JMIR Public Health and Surveillance · doi:10.2196/41261 · Cited by 10
“Variables found to be significant in the univariate analysis were included in the multivariate analysis using the Cox proportional hazards model [43].”
Adverse outcome of AML with aberrant CD16 and CD56 NK cell marker expression
Junge, A., Bacher, U., Mueller, B. U., Keller, P., Solenthaler, M., & Pabst, T. (2018) · Hematological Oncology · doi:10.1002/hon.2516 · Cited by 10
“A multivariate Cox proportional hazard model was used to determine the impact of CD16 and CD56 in comparison to other risk factors.(22) Additional variables included gender and age at diagnosis as well as the NPM1 mutational status.”
MethodUnobserved population heterogeneity and dynamics of health disparities
Zheng, H. (2020) · Demographic Research · doi:10.4054/demres.2020.43.34 · Cited by 10
“Recent methodological developments suggest using an appropriately weighted survival curve (Cole and Hernán 2004; Hernán 2010) or accelerated-failure-time model (Bradburn et al. 2003) to mitigate mortality selection bias.”
Metadata
- Authors
- Bradburn, M. J., Clark, T. G., Love, S. B., & Altman, D. G.
- Affiliations
- Cancer Research UK (GB)
- Corresponding author
- Bradburn, M J
- Venue
- British Journal of Cancer
- Published
- 2003-07-29
- Volume
- 89
- Issue
- 3
- Pages
- 431-436
- ISSN
- 0007-0920 (ISSN-L)
- 1532-1827
- PMC
- PMC2394368
- OpenAlex
- W2107482271
- Cited by
- 741
- References
- 16
- Citations by year
- 2026: 31 · 2025: 55 · 2024: 86 · 2023: 67 · 2022: 54 · 2021: 91 · 2020: 55 · 2019: 41 · 2018: 43 · 2017: 35 · 2016: 26 · 2015: 21 · 2014: 27 · 2013: 15 · 2012: 24
- FWCI
- 7.17
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by-nc-sa
- www.springer.com/tdm (unspecified)
- Locations
- British Journal of Cancer (publishedVersion, cc-by-nc-sa)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (acceptedVersion)
- LSHTM Research Online (London School of Hygiene and Tropical Medicine) (acceptedVersion)
- Funders
- Cancer Research UK
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- survival analysis, multivariate survival data, censored data, time to event, cancer survival, censoring
- MeSH terms
- Clinical Trials as Topic, Humans, Neoplasms, Models, Statistical, Multivariate Analysis, Survival Analysis
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