The analysis of survival data

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. 

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. 

Jager T, Kooijman SALM. 2005. Modeling receptor kinetics in the analysis of survival data for organophosphorus pesticides. Environ Sci Technol 39 8307-8314. 

The combination of censoring and differential follow-up creates some unusual difficulties in the analysis of such data that cannot be handled properly by standard statistical methods. Thus, a different approach called survival analysis or censored survival analysis was developed for the analysis of such data. 

A sterilization process may thus be developed without a full microbiological background to the product, instead being based on the ability to deal with a worst case condition. This is indeed the situation for official sterilization methods which must be capable of general application, and modem pharmacopoeial recommendations are derived firm a careful analysis of experimental data on bacterial spore survival following treatments with heat, ionizing radiation or gas. 

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. 

Due to the issues surrounding the analysis of archived samples, most microarray-based oncology studies have relied on prospective analyses—running samples as they become available, rather than retrospective analyses—running archived samples. While the prospective analysis tends to provide excellent-quality data, the associated clinical data from archived samples tends to be of greater value. In particular, in obtaining archived samples, it is possible to concentrate on those patients for which outcome information is known (e g., survival rates, recurrence, treatment success, and so on). 

In a fashion similar to the discussion presented on organic chemicals, Baas et al. (2007) applied the 1-compartment model without TK interactions for the analysis of-time series survival data for the springtail Folsomia Candida exposed to binary mixtures of heavy metals. It must be stressed that no internal concentrations were measured in these experiments instead, the toxicokinetics parameters were solely determined from the survival pattern in time. In this case, the toxicity data were well described without assuming interactions, which stresses that even though we know that interactions on toxicokinetics can occur, this does not mean that they will significantly influence toxicity for every metal mixture in each organism. 

Significantly different from controls at the 5% level (analysis of variance). Data on development time and survival did not show any significant effect of 8 3 SC dose. Development time data were subjected to an analysis of variance and survival data to a test of independence using the G-statistic. 

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