Log-rank test

About: Log-rank test is a research topic. Over the lifetime, 592 publications have been published within this topic receiving 21037 citations.

A class of rank test procedures for censored survival data

Abstract: SUMMARY A class of linear rank statistics is proposed for the k-sample problem with rightcensored survival data. The class contains as special cases the log rank test (Mantel, 1966; Cox, 1972) and a test essentially equivalent to Peto & Peto's (1972) generalization of the Wilcoxon test. Martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered, and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses. A class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution. Some Monte Carlo results are displayed which present small sample behaviour.

A new prognostic score for survival of patients with chronic myeloid leukemia treated with interferon alfa. Writing Committee for the Collaborative CML Prognostic Factors Project Group.

Abstract: BACKGROUND: Interferon alfa is a conservative and widely used alternative to bone marrow transplantation in treatment of patients with early chronic myeloid leukemia (CML). A meta-analysis was conducted to develop a reliable prognostic scoring system for estimation of survival of patients with CML treated with interferon alfa. METHODS: Patients treated in prospective studies, including major randomized trials, were separated into learning and validation samples. Cox regression analysis and the minimum P-value approach were used to identify prognostic factors for patient survival and to discover groups in the learning sample with the greatest differences in survival. These findings were then validated by applying the new scoring system to patients in the validation sample. RESULTS: We collected data on 1573 patients who were participants in 14 studies involving 12 institutions; 1303 patients (learning sample, n = 981; validation sample, n = 322) were eligible for inclusion in this analysis, and their median survival time was 69 months (range, 1-117 months). Because two previously described prognostic scoring systems failed to discriminate risk groups satisfactorily, we developed a new scoring system that utilizes the following covariates: age, spleen size, blast count, platelet count, eosinophil count, and basophil count. Among 908 patients with complete data in the learning sample, three distinct risk groups were identified (median survival times of 98 months [n = 369; 40.6%], 65 months [n = 406; 44.7%], or 42 months [n = 133;14.6%]; two-sided logrank test, P< or =.0001). The ability of the new scoring system to discriminate these risk groups was confirmed by analysis of 285 patients with complete data in the validation sample (two-sided logrank test, P = .0002). CONCLUSIONS: A new prognostic scoring system for estimating survival of patients with CML treated with interferon alfa has been developed and validated through use of a large dataset.

The logrank test.

Abstract: We often wish to compare the survival experience of two (or more) groups of individuals. For example, the table shows survival times of 51 adult patients with recurrent malignant gliomas1 tabulated by type of tumour and indicating whether the patient had died or was still alive at analysis—that is, their survival time was censored.2 As the figure shows, the survival curves differ, but is this sufficient to conclude that in the population patients with anaplastic astrocytoma have worse survival than patients with glioblastoma? View this table: Weeks to death or censoring in 51 adults with recurrent gliomas1 (A=astrocytoma, G=glioblastoma) Fig 1 Survival curves for women with glioma by diagnosis We could compute survival curves3 for each group and compare the proportions surviving at any specific time. The weakness of this approach is that it does not provide a comparison of the total survival experience of the two groups, but rather gives a comparison at some arbitrary time point(s). In the figure the difference in survival is greater at some times than others and eventually becomes …

Survival Analysis Part I: Basic concepts and first analyses

Abstract: Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is time until an event occurs. Because of censoring–the nonobservation of the event of interest after a period of follow-up–a proportion of the survival times of interest will often be unknown. It is assumed that those patients who are censored have the same survival prospects as those who continue to be followed, that is, the censoring is uninformative. Survival data are generally described and modelled in terms of two related functions, the survivor function and the hazard function. The survivor function represents the probability that an individual survives from the time of origin to some time beyond time t. It directly describes the survival experience of a study cohort, and is usually estimated by the KM method. The logrank test may be used to test for differences between survival curves for groups, such as treatment arms. The hazard function gives the instantaneous potential of having an event at a time, given survival up to that time. It is used primarily as a diagnostic tool or for specifying a mathematical model for survival analysis. In comparing treatments or prognostic groups in terms of survival, it is often necessary to adjust for patient-related factors that could potentially affect the survival time of a patient. Failure to adjust for confounders may result in spurious effects. Multivariate survival analysis, a form of multiple regression, provides a way of doing this adjustment, and is the subject the next paper in this series.