Log-rank test

Note that the term censor is introduced in the preceding table. The log-rank test (invoked in SAS with PROC LIFETEST) and the Cox proportional hazards model (invoked in SAS with PROC PHREG) allow for censoring observations in a time-to-event analysis. These tests adjust for the fact that at some point a patient may no longer be able to experience an event. The censor date is the last known time that the patient did not experience a given event and the point at which the patient is no longer considered able to experience the event. Often the censor date is the last known date of patient follow-up, but a patient could be censored for other reasons, such as having taken a protocol-prohibited medication. 

Time-to-event analysis in clinical trials is concerned with comparing the distributions of time to some event for various treatment regimens. The two nonparametric tests used to compare distributions are the log-rank test and the Cox proportional hazards model. The Cox proportional hazards model is more useful when you need to adjust your model for covariates. 

Here we assume that the daystodeath variable is the number of days to death or last known date alive for the patient. The deathcensor variable value is 1 if the patient died and 0 if the patient did not die. The p-value variable for the log-rank test is called ProbChiSq in the pvalue data set where the Test variable equals Log-Rank. ... 

These methods are essential when there is any significant degree of mortality in a bioassay. They seek to adjust for the differences in periods of risk individual animals undergo. Life table techniques can be used for those data where there are observable or palpable tumors. Specifically, one should use Kaplan-Meier product limit estimates from censored data graphically, Cox-Tarone binary regression (log-rank test), and Gehan-Breslow modification of Kruskal-Wallis tests (Thomas et al., 1977 Portier and Bailer, 1989) on censored data. 

The Log-Rank Test is a statistical methodology for comparing the distribution of time until the occurrence of the event in independent groups. In toxicology, the most common event of interest is death or occurrence of a tumor, but it could just as well be liver failure, neurotoxicity, or any other event which occurs only once in an individual. The elapsed time from initial treatment or observation until the event is the event time, often referred to as survival time , even when the event is not death . 

The Log-Rank Test provides a method for comparing risk-adjusted event rates, useful when test subjects in a study are subject to varying degrees of opportunity to experience the event. Such situations arise frequently in toxicology studies due to the finite duration of the study, early termination of the animal or interruption of treatment before the event occurs. 

Examples where use of the Log-Rank Test might be appropriate include comparing survival times in carcinogenity bioassay animals which are given a new treatment with those in the control group or comparing times to liver failure for several dose levels of a new NSAID where the animals are treated for 10 weeks or until cured, whichever comes first. 

The idea behind the Log-Rank Test for comparison of two life tables is simple if there were no difference between the groups, the total deaths occurring at any time should split between the two groups at that time. So if the numbers at risk in the first and second groups in (say) the sixth month were 70 and 30, respectively, and 10 deaths occurred in that month we would expect... 

The Log-Rank Test as presented by Peto et al. (1977) uses the product-limit life-table calculations rather than the actuarial estimators shown above. The distinction is unlikely to be of practical importance unless the grouping intervals are very coarse. 

Many variations of the Log-Rank Test for comparing survival distributions exist. The most common variant has the form ... 

Survival and failure times often follow the exponential distribution. If such a model can be assumed, a more powerful alternative to the Log-Rank Test is the Likelihood Ratio Test. 

Approximate Number of Events Required for 80% Power with 5% Two-Sided Log-Rank Test for Comparing Randomized Arms of Design Shown in Fig. 1. Only Marker + Patients Are Randomized. Treatment Hazard Ratio for Marker + Patients Is Shown in First Column. Time-To-Event... 

These and other factors identified as being associated with early stroke risk (Gladstone et al. 2004 Hill et al. 2004) were used to derive the ABCD score, a predictive tool of stroke risk within seven days after TIA (Rothwell et al. 2005). Briefly, all clinical features that had previously been found to be independently predictive of stroke after TIA were tested in a derivation cohort of 209 patients recruited from the Oxfordshire Community Stroke Project (OCSP, Lovett et al. 2003). Any variable that was a univariate predictor of the seven-day risk of stroke with a significance ofp < 0.1 assessed with the log rank test was incorporated into the score. The score was then validated in three further independent cohorts. 

The appeal is the ease of computation and applicability. The resulting statistics or p-values for the chosen filter method are then ranked and a cutoff chosen to select the most significant features. Examples of filter methods are t-tests, Wdcoxon rank-sum or signed-rank tests, Pearson correlation estimates, log-rank tests, and univariate regression techniques such as linear, logistic, or Cox proportional hazards. 

Figure 1. Cumulative incidence of noncontact erection in male rats tested with estrous females upwind (solid lines, n = 20) or downwind (dashed lines, n = 20) from them. In Test 1, males were sexually naive in Test 2, half the males had had two copulatory experiences. Because there were no significant effects of copulatory experience in Test 2, the data were merged into single functions for relative location of male and female. Probability values are based on Log Rank tests. (Figure adapted from Sachs, 1997.)...

MR-guided LITT was performed in 839 patients (mean age 61.6 years) with 2,506 liver metastases of colorectal cancer between 1993 and 2005. The following criteria were analyzed primary tumor and lymph node staging, localization of the primary tumor (rectum, sigmoid, colon), number of liver metastases at first LITT treatment, synchronous (less than 6 months between diagnosis of tumor and first liver metastases) or metachronous metastases, survival rate, and indication for LITT. The Tarone Ware, Breslow, and Log Rank tests were used for statistical significance. 

Fig. 7. Life table analysis in Atm-/- mice. Treatment was as described for 7 (trial 2). Sold line, mice receiving EUK-189 broken line, mice receiving vehicle. By plan, the study was stopped at 150 days of age. All animals were sacrificed to confirm the presence of thymoma. The Cox-Mantel log rank test yielded p = 0.08. Reprinted from reference 61, copyright (2004), with permission from Elsevier.

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