Kaplan-Meier curve

In the next section we will discuss Kaplan-Meier curves, which are used both to display the data and also to enable the calculation of summary statistics. We will then cover the logrank and Gehan-Wilcoxon tests which are simple two group comparisons for censored survival data (akin to the unpaired t-test), and then extend these ideas to incorporate centre effects and also allow the inclusion of baseline covariates. 

We have mentioned earlier in this chapter that it is not possible to calculate the mean survival time. It is, however, usually possible to obtain median survival times Irom the Kaplan-Meier curves. The median survival time for a particular... 

The Kaplan-Meier curves do not of themselves provide a formal, p-value, comparison of the treatments. This comparison of the survival curves is undertaken using either the logrank test or the Gehan-Wilcoxon test. We will look at these two test procedures in turn. 

The hazard rate can be estimated from data by looking at the patterns of deaths (events) over time. This estimation process takes account of the censored values in ways similar to the way such observations were used in the Kaplan—Meier curves. 

It is worth revisiting the calculation of the Kaplan—Meier curve following on from the discussion of the hazard rate, in order to see, firstly, how censoring is accounted for, and secondly, how the two are linked in terms of the calculation. 

Fig. 25.1. Kaplan-Meier curves showing risks of stroke after carotid endarterectomy (exciuding the 30-day immediate postoperative period). A, any stroke i, any ipsiiaterai ischemic stroke D, disabiing ipsiiaterai ischemic stroke.

Figure 10-5 Percentage of patients who remained continuously on the initially dispensed topical ocular hypotensive. Kaplan-Meier curves are shown separately by diagnostic status at treatment initiation (diagnosed vs. suspect glaucoma) and class of initial glaucoma medication. (Adapted from Nordstrom BL, Friedman DS, Mazaffari E, et al. Am J Ophthalmol 2005 140 598-606.)...

Figure 4.5 Kaplan-Meier curves for survival free of reinfarction in the angioplasty and streptokinase groups during follow-up. The rate of survival free of reinfarction was higher in the group of 194 patients assigned to undergo angioplasty than in the group assigned to receive streptokinase. (From Ref. 65.)...

Details of statistical analyses for potential toxicities that should be explicitly considered for all products and AEs of special interest Aiialyses for these events will in general be more comprehensive than for standard safety parameters. These analyses may include subject-year adjusted rates, Cox proportional hazards analysis of time to first event, and Kaplan-Meier curves. Detailed descriptions of the models would typically be provided. For example, if Cox proportional hazards analysis is specified, a detailed description of the model(s) that will be used should be provided. This would generally include study as a stratification factor, covariates, and model selection techniques. More advanced methods, such as multiple events models or competing risk analyses, should be described if used (as appropriate). It is recommended that graphical methods also be employed, for example, forest plot and risk-over-time plot (Xia et al., 2011). 

Fig. 11.3 CARE-HF Study Kaplan-Meier curve for all cause mortality or an unplanned hospitalization for a major cardiovascular event, whieh was the primary endpoint CRT group had a 37% risk reduction as compared to medical therapy group. (Reprodueed with permission fiom Cleland JGF, Daubert J-C, Erdmann E, et al. N Engl J Med 2005 352 1539-49.)...

Figure 9.3 Kaplan-Meier curves showing faster rate of deterioration in quadriceps muscle strength in s-IBM patients carrying the HLA-DR1/DR3 genotype compared with other HLA-DRBl genotypes.

The Kaplan-Meier estimates produce a step function for each group and are plotted over the lifetime of the animals. Planned, accidentally killed, and lost animals are censored. Moribund deaths are considered to be treatment related. A graphical representation of Kaplan-Meier estimates provide excellent interpretation of survival adjusted data except in the cases where the curves cross between two or more groups. When the curves cross and change direction, no meaningful interpretation of the data can be made by any statistical method because proportional odds characteristic is totally lost over time. This would be a rare case where treatment initially produces more tumor or death and then, due to repair or other mechanisms, becomes beneficial. 

In these analyses, the Kaplan-Meier method was used to generate age-of-onset-curves. Eigure 1 shows not only that the onset distributions were similar across countries, but also that more than 50% of the cases had their first onset before age 20. Even the proportion of individuals with a first manifestation of anxiety disorder before age 10 is remarkably high. After age 40, the risk for... 

Kaplan and Meier (1958) introduced a methodology for estimating, from censored survival data, the probability of being event-free as a function of time. If the event is death then we are estimating the probability of surviving and the resultant plots of the estimated probability of surviving as a function of time are called either Kaplan-Meier (KM) curves or survival curves. 

Figure 13.1 Kaplan-Meier survival curves in placebo and carvedilol groups (Packer M, Coats AJS, Fowler MB, et al. for the Carvedilol Prospective Randomised Cumulative Survival Study Group, Effect of carvedilol on survival in severe chronic heart failure. New England Journal of Medicine, 344, 1651-1658. (2001) Massachusetts Medical Society.)...

Overall survival (Kaplan-Meier survival curve and non-parametric statistical analysis). 

Figure 14 Kaplan-Meier survival curves for SMT-F tumor bearing mice treated with 10 imol/kg PCI-0123 (4). The mice were irradiated 3h (n = 9, ), 5h (n=16, A), 12h (n = 8, ) and 24h (n = 7, O) post injection of PCI-0123 with 150 J/cm 150mW/cm at 732 nm. A matched set of control animals received light irradiation alone (n = 10, ). Tumor volumes were 70 35 mm. All animals at day 40 that were still in the study displayed no evidence of disease at the tumor site. Reproduced from [108] by permission of the American Society of Photobiology...

Figure 10.2.8 Kaplan-Meier Survival Curves for SMT-F-bearing Mice Treated with 10 pmol kg PCI-0123 (Complex 10.4 Acetate Counter Anions).

Figure 44-28 Kaplan Meier survival curves for pulmonary embolism patients without ACS based on cardiac troponin T-positive versus cardiac troponin T-negative serum samples using a cutoff concentration of 0.1 ng/mL. (From Gannitsis , MuUer-Bardorff M, fCurowski Weidtmann B.Wiegond U, Kampmann M, et al. independent prognostic value of cardiac troponin T in patients with confirmed pulmonary embolism. Circulation 2001 102 211-7.)...

Figure 44-29 Kaplan Meier survival curves by baseline cardiac troponin cutoffs. (From Apple FS, Murakami MM, Peorce LA, Herzog CA, et ai Predictive value of cardiac troponin I and T for subsequent death in end-stage renal dfseose. Circulation 2002 106 2941-5.)...

Sometimes, these data are presented in a shorter table that displays only those time points at which an individual had an event or was censored, and thus the only values of time for which the probability of survival changes. It is more common, however, to see analyses of this type displayed graphically. The Kaplan-Meier estimate of the survival distribution is displayed for both groups in Figure 8.3. The survival curves displayed in the figure are termed "step functions" because of their appearance. We return to the interpretation of Figure 8.3 after we have fully specified the survival distribution function. 

Both studies used Kaplan-Meier survival curve analysis (2 19,225) to estimate the ultimate success rate in the NCE cohort under study. 25 Grabowski and Vernon s estimate of R D cash costs is less useful for corroborative purposes than Wiggins estimate because the... 

Figure 110.3 Survival curves in euthyroid cardiac patients and in cardiac patients with subclinical hypothyroidism. Kaplan-Meier survival curves of cardiac patients with normal thyroid function and of cardiac patients with low-T3 syndrome. Events considered cardiac and overall death. Modified from lervasi et al., (2007). Reprinted with permission.

Figure 6 Kaplan-Meier survival curve for patients with initial therapy for grade III and grade IV gliomas treated with BCNU-loaded polymer implants vs. placebo. (From Ref. 96.)...

Figure 7 (Facing page) (A) Kaplan-Meier survival curve for animals treated with intracranial 10 mg 3.8% (w/w) BCNU pCPP SA (20 80) polymers placed on day 5 after 9L gliosarcoma implantation with or without daily oral quinacrine gavages (20mg/kg) starting day 5 and lasting 14 days. (B) Kaplan-Meier survival curve for animals treated with intracranial BCNU polymers placed on day 5 after 9L ghosarcoma implantation with or without intracranial 10 mg 15% (w/w) quinacrine pCPPrSA (20 80) polymers placed on day 3 after tumor implantation. (C) Kaplan-Meier survival curve for animals treated with intracranial BCNU polymers placed on day 5 after 9L gliosarcoma implantation with or without intracranial 10 mg 15% (w/w) quinacrine pCPP SA (20 80) polymers concurrently on day 3 after tumor implantation.

Figure 6. PARP-2" mice are sensitive to ionizing radiation. A) Kaplan-Meier survival curves after 8 Gy of whole body irradiation. Wilcoxon test p(PARP-2 vs PARP-2 ) < 10. (Taken from Minissier-de Murcia et al, with permission). B) Comparison ofy-ray survival curves of wild-type, PARP-T and PARP-2 mouse 3T3 fibroblasts. 10 fibroblasts from mid-log growing subcultures were plated in triplicate in 25 cm flasks and returned to the incubator overnight prior to irradiation. Following treatment, the flasks were supplied with 8 ml fresh medium and grown for exacdy 5 doubling times (relative to mock irradiated cells) with two changes of medium. Cells were harvested by trypsin-EDTA and scored visually under microscope. PARP-1, PARP-T and PARP-2 fibroblasts yielded a convex curve which fitted a linear-quadratic dose-dependent equation, as most usually found among various cell lines, with a pseudo-plateau relating to Cl arrest. PARP-2 fibroblasts showed a concave profile and fitted a double-exponential equation. PARP-2 fibroblasts were clearly the most sensitive ones in the low dose rai of radiation (insert) Bars,SD.

Fig. 5 Mice vaccinated with different formulations (diluent, NiNLP alone, trE-His alone, or NINLP-trE-His) were challenged with 1000 ffu of live WNV NY99 and observed daily for 21 days. Kaplan-Meier survival curves indicate that conjugation of trE-His to NiNLP improved its efficacy and better protects mice from the vims challenge. Eigure reproduced from [55].

This study, described as a randomized double-blind comparison of vitamin C (10 g per day) and a lactose placebo in 100 patients with advanced adenomatous colorectal cancer, gave survival times published only in a Kaplan-Meier figure. We have measured the published curves and produced the semilogarithmic plot shown as Fig. 4. 

---