Constant hazard ratio

Even though the individual hazard rates seen in Figure 13.3 are not constant, it would be reasonable to assume, wherever we look in time, that the ratio of the hazard rates is approximately constant. In fact, these hazard rates have been specifically constructed to behave in this way. When this is the case, the ratio of the hazard rates will be a single value, which we call the hazard ratio. We will denote this ratio by X so that X = h /h. ... 

Even if the hazard ratio is not precisely a constant value as we move through time, the hazard ratio can still provide a valid summary provided the hazard rate for one of the treatment groups is always above the hazard rate for the other group. In this case the value we get for the hazard ratio from the data represents an average of that ratio over time. 

However, it is not always the case, by any means, that we see a constant or approximately constant hazard ratio. There will be situations, as seen in Figure 13.4, when the hazard rate for one group starts off lower than the hazard rate for a second group and then as we move through time they initially move closer together, but then a switch occurs. The hazard rate for the first group then overtakes that for the second group and they continue to move further apart from that point on. 

Figure 13.4 Hazard rates for two groups of patients where the hazard ratio is not constant...

In an earlier section we saw two different patterns for two sets of survival curves. In Figure 13.2 a) the survival curves move further and further apart as time moves on. This pattern is consistent with one of the hazard rates (think in terms of death rates) being consistently above the other hazard rate. This in turn corresponds to a fairly constant hazard ratio, the situation we discussed in Section 13.4.1. So a constant hazard ratio manifests itself as a continuing separation in the two survival curves as in Figure 13.2 a). Note that the higher hazard rate (more deaths) gives the lower of the two survival curves. 

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 proportional hazards model, as the name suggests, assumes that the hazard ratio is a constant. As such it provides a direct extension of the logrank test, which is a simple two treatment group comparison. Indeed if the proportional hazards model is fitted to data without the inclusion of baseline factors then the p-value for the test Hg c = 0 will be essentially the same as the p-value arising out of the logrank test. 

As we have already seen, there will be settings where the pattern of differences between treatment groups does not conform to proportional hazards, where the hazard ratio is not a constant, single value. Such situations are best handled by using an alternative model to incorporate baseline factors. The accelerated failure time model is an analysis of variance technique which models the survival time itself, but on the log scale ... 

The TL and MAK values should be used as guides in the control of health hazards. They are not constants that can be used to draw fine fines between safe and dangerous concentrations. Nor is it possible to calculate the TL or MAK values of solvent mixtures from the data in Table A-13, because antagonistic action or potentiation may occur with some combinations. It should be noted that occupational exposure limits such as the TL and MAK values are not intended for use as a comparative measure of one solvent against another. The values set airborne concentration limits on chemical exposure, but do not describe the ease with which that airborne limit is achieved. In addition, the vapour pressure of the solvent must also be considered. The lower the vapour pressure, the lower the airborne concentration. In order to better compare the safety of volatile compounds such as organic solvents, the use of the vapour hazard ratio ( VHR) has been recommended as a feasible measure [175], The vapour hazard ratio is defined as the quotient of the saturation concentration of a solvent (in mg/m at a given temperature and pressure) and its occupational exposure limit (in mg/m e.g. TL or MAK values), according to ... 

Peivaporation, the separation of tw o peilectly mixed liquids (usually w here they cannot he separated by distillation, because they form an azeotropic, constant boiling mixture at a particular concentration ratio - most famously the azeotrope of ethanol and w ater), is easily achieved through a membrane, by virtue of the different diffusion rates of the tw o vapours. It is also used to treat riitse w aters that have become contaminated by VOCs (volatile organic compounds, hazardous to human health), such as solvents, degreasers and petroleum-based mixtures. In either case, 99% contaminant removal can be achieved. 

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