Survival data

Thiols must be added before or within a very short time after irradiation to protect against ceU killing. This is apparent from conventional cell survival data (9) but is even better illustrated by kinetic studies showing that 2-mercaptoethanol (see Table 1) protects oxic V79 cells when added just before but not 7 milliseconds after irradiation (5). 

Goldey ES, Tilson HA, Crofton KM. 1995. Implications of the use of neonatal birth weight, growth, viability, and survival data for predicting developmental neurotoxicity A survey of the literature. Neurotoxicol Teratol 17(3) 313-332. 

Note Concentrations shown are in milligrams of toxaphene ingested per kilogram body weight (BW) fatal to 50% of test animals. A single dose was administered orally and survival data gathered over a 14-day posttreatment observation period. 

Soper, K.A. and Clark, R.L. (1990). Exact permutation trend tests for fetal survival data. Proc. 

Crowley, J. and Breslow, N. (1984). Statistical analysis of survival data. Ann. Rev. Public Health 5 385-411. 

The increased importance and interest in the analysis of survival data has not been restricted to toxicology, but rather has encompassed all the life sciences. Those with further interest should consult Lee (1980) or Elandt-Johnson and Johnson (1980), both general in their approach to the subject. 

Lee, E.T. (1980). Statistical Methods for Survival Data Analysis. Lifetime Learning, Belmont, CA. 

Most Phase III studies in a chronic disease will require 1 year of therapy. Most oncology studies will require 12-months survival data. 

The CUA is a form of cost-effectiveness analysis in which the health outcomes are measured in terms of quality-adjusted life-years (QALYs) gained. The QALY is a measure that associates quantity of life (e.g. survival data and life... 

There is no proof currently that MMPIs as a class will prolong the survival of patients with cancer. Currently, three randomized trials of MMPIs have reported survival data BAY 12-9566 vs gemcitabine in locally advanced or metastatic pancreatic cancer (10), marimastat vs gemcitabine in locally advanced or metastatic pancreatic cancer (11), and marimastat vs placebo in locally advanced or metastatic gastric cancer (12). 

Murphy ML, Hultgren HN, Detre K, et al. Treatment of chronis stable angina a preliminary report of survival data of the randomized Veterans Administration Cooperative Study. N Engl J Med 1977 297 621. 

In order to illustrate the kinds of arguments and considerations which are needed in relation to intention-to-treat, the discussion in this section will consider a set of applications where problems frequently arise. In Chapter 13 we will cover methods for the analysis of time-to-event or so-called survival data, but for the moment I would like to focus on endpoints within these areas that do not use the time-point at which randomisation occurs as the start point for the time-to-event measure. Examples include the time from rash healing to complete cessation of pain in Herpes Zoster, the time from six weeks after start of treatment to first seizure in epilepsy and time from eight weeks to relapse amongst responders at week 8 in severe depression. 

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. 

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. 

In Chapter 6 we covered methods for adjusted analyses and analysis of covariance in relation to continuous (ANOVA and ANCOVA) and binary and ordinal data (CMH tests and logistic regression). Similar methods exist for survival data. As with these earlier methods, particularly in relation to binary and ordinal data, there are numerous advantages in accounting for such factors in the analysis. If the randomisation has been stratified, then such factors should be incorporated into the analysis in order to preserve the properties of the resultant p-values. 

The most popular method for analysis of covariance is the proportional hazards model. This model, originally developed by Cox (1972), is now used extensively in the analysis of survival data to incorporate and adjust for both centre and covariate effects. The model assumes that the hazard ratio for the treatment effect is constant. 

The power of a study where the primary endpoint is time-to-event depends not so much on the total patient numbers, but on the number of events. So a trial with 1000 patients with 100 deaths has the same power as a trial with only 200 patients, but with also 100 deaths. The sample size calculation for survival data is therefore done in two stages. Firstly, the required number of patients suffering events is... 

Example 13.4 Sample size calculation for survival data... 

On a final point, for survival data, information is carried through the numbers of patients with events and not the number completing the trial. So for example, if the trial is continuing until we have seen 900 deaths, then the interim analyses would be conducted after, respectively, 300 and 600 deaths. This is what is meant by equally spaced in this case. 

Each trial that is to be included in the meta-analysis will provide a measure of treatment effect (difference). For continuous data this could be the mean response on the active treatment minus the mean response in the placebo arm. Alternatively, for binary data the treatment effect could be captured by the difference in the cure rates, for example, or by the odds ratio. For survival data, the hazard ratio would often be the measure of treatment difference, but equally well it could be the difference in the two-year survival rates. 

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