Accelerated failure time model

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  

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. 

The dataset used in this example comprised two phase III placebo-controlled studies used in the license application for oseltamivir (Tamiflu ). See Patel, Kay and Rowell (2006) for further details. Pre-defined symptoms consisted of cough, nasal congestion, headache, sore throat, fatigue, myalgia and feverishness and each of these was assessed on an ordinal scale none, mild, moderate, severe. Alleviation was recorded as the day on which all symptoms 

Term Estimated coefficient Standard error p-value 

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Table 13.1 Accelerated failure time model for flu data...

The sample size methodology above depends upon the assumption of proportional hazards and is based around the logrank test as the method of analysis. If this assumption is not appropriate and we do not expect proportional hazards then the accelerated failure time model may provide an alternative framework for the... 

Quantitative ATs are used to obtain information about the failure-time distribution and degradation in a relatively short period of time (usually weeks or months) by accelerating the use environment. In most cases a model to describe the relationship between failure mechanism and accelerating variables already exists. They are also well-suited for finding dominant failure mechanisms and are usually performed on individual assemblies rather than full systems. In order to set up a quantitative AT, severd different parameters must be known, for example test length, number of samples, desired confidence intervals, field and test environment, stress-life relationship and distribution model. 

The development of thermomechanical models typically involves (a) the development of constitutive models for the solder alloy and other materials in the packaging assembly, (b) the development of geometry models to represent the solder interconnects and the packaging assembly, and (c) the development of failure predictive models for the various material systems in the assembly. The thermomechanical models, when subjected to thermal excursions seen dixring accelerated qualifications or during field-use, will identify the location of failure, mode of failixre, and time to failure in various parts of the packaging assembly. Prior to usage, the models should be validated with experimental test data. 

Bcl-2. Human oncoprotein that plays a role in tissue development and maintenance by preventing apoptosis of specific cell types. Animal models suggest that failure to induce normal levels of apoptosis due to overexpression of Bcl-2 may contribute to the development of lymphoproliferative disorders and acceleration of autoimmunity. The role in human autoimmunity is not clear at this time. 

FOMis/FOMj/c is 11750 times larger than the ratio FOM /FOMa/c- Notice that for the LS method even though the determination of the sampling important direction a (Section 3.2) and the calculations of the conditional one-dimensional failure prohahihty estimates P (F) k = 1,2,..., Nt (equation (3) in the Appendix) require much more than Nf system analyses by the model, this is significantly overweighed hy the accelerated convergence rate that can he attained by the LS method with respect to SS. 

Information on the natural weathering behaviour of joints is very useful. By combining this information with data from accelerated laboratory tests, some realistic predictions of service-lifetime may be made. Theoretical models of the pattern of bondline saturation of joints as a function of time of environmental exposure provide a useful appreciation of the possible extent of problems (e.g. Fig. 4.21). The process of joint failure, as observed in practice or in the laboratory, is frequently non-diagnostic i.e. it rarely reveals the true cause, or the series of stages, leading to deterioration or failure. 

Design tests based on the acceleration models and accepted sampling procedures. Using the acceleration model and the service environment and life, select test conditions and test times that simulate the life of the product in a much shorter period of time. The sample size must be large enough that it is possible to determine whether the reliability goal (acceptable number of failures over the service life) has been met. Ideally, the life distribution in the accelerated test should be determined, even when the test period must be extended to do so. 

Determine life distribution from accelerated life distribution. The accelerated life distribution should be determined by fitting the data with the appropriate statistical distribution, such as the Weibull or log-normal distribution. The life distribution in service can be determined by transforming the time axis of the life distribution using the acceleration model. This predicted life distribution in service can then be used to estimate the number of failures in the specified service hfe. 

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