Survival analysis origins

Modern survival analysis, an important tool of statistical analysis in drug development today, can be regarded as having its origins in the work of De Witt, Halley, de Moivre and Simpson and other mathematicians of the 17th and 18th centuries who worked on life tables and annuities. 

Proportional hazards model. Generally, a regression model used in survival analysis whereby it is assumed that the hazard functions of individuals under study are proportional to each other over time. (This is equivalent to assuming that the log-hazard functions differ by a constant.) More specifically, and in the form originally proposed by Cox (1972), no further definite assumption is made about the hazard functions themselves. One of the most commonly used statistical techniques in survival analysis. 

By 1977, Piver and colleagues (8) had enrolled 148 patients in this study, and they published an updated analysis that included 117 of these patients. In this update, the authors did not provide an overall survival comparison but reported comparative survival rates in a number of subsets from the original study. 

Sarcomas are tumors of mesenchymal origin, arising in skeletal tissues and extra-skeletal connective tissues including the nerves. They are very rare and mainly effect a younger population. Sarcomas of soft tissues are relatively insensitive to drug treatment and are therefore not discussed in detail in this chapter. A systematic review of fourteen trials of doxorubicin-based adjuvant chemotherapy for the treatment of soft tissue sarcomas involving 1568 patients concluded Doxorubicin-based adjuvant chemotherapy appears to significantly improve time to local and distant recurrence and overall recurrence-free survival in adults with localised resectable soft tissue sarcoma. There is some evidence of a trend towards improved overall survival (see Sarcoma Meta-analysis Collaboration, 1999). 

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. 

We mentioned earlier, in Section 13.1, that if we did not have censoring then an analysis would probably proceed by taking the log of survival time and undertaking the unpaired t-test. The above model simply develops that idea by now incorporating covariates etc. through a standard analysis of covariance. If we assume that InT is also normally distributed then the coefficient c represents the (adjusted) difference in the mean (or median) survival times on the log scale. Note that for the normal distribution, the mean and the median are the same it is more convenient to think in terms of medians. To return to the original scale for survival time we then anti-log c, e, and this quantity is the ratio (active divided by control) of the median survival times. Confidence intervals can be obtained in a straightforward way for this ratio. 

By itself, the discovery of pesticides in rainfall, however, provides no evidence that the origin of the pesticides was local or distant. The analysis of dust, whose origin has been documented by meteorological evidence, does prove that pesticides can be transported over great distances via the atmosphere, that the pesticides can survive the photochemical processes of high altitude, and, finally, that these pesticides can be deposited over land surfaces remote from their application. 

Although CHI 3, and several other iodinated compounds, were readily identified by both n.m.r. and m.s. analysis of the crude oil obtained from A. taxiformis, many of the original iodine-containing compounds were found not to survive the chromatographic separation. Carbonyl diiodide was therefore postulated as an artefact that results from the decomposition of CHI 3 during the chromatographic process. Clearly, further work is required to substantiate or refute the possible formation of this compound, as this remains the only claim of its existence in the literature. 

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