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Survival Analysis and Cox Regression
Published in K. V. S. Sarma, R. Vishnu Vardhan, Multivariate Statistics Made Simple, 2018
K. V. S. Sarma, R. Vishnu Vardhan
In clinical management of patients, an event like death is non-repairable once it occurs. All interventions are valid only before the occurrence of the event. In such cases we measure the time to occurrence and a simple measure is the Mean Time To Failure (MTTF) which sounds like a warranty period.
Restoration of complete bladder function by neurostimulation
Published in Jacques Corcos, David Ginsberg, Gilles Karsenty, Textbook of the Neurogenic Bladder, 2015
However, no implant can be designed to be completely guaranteed against technical failure. The body is a hostile environment to implanted materials, and patients do not always comply with recommendations of how best to protect an implant. The Finetech–Brindley SARS is extremely well tolerated in the body and has an exceptional life expectancy. Indeed, some patients are still successfully using a device which was implanted over 30 years ago. Technical failures will undoubtedly occur and therefore implants must be designed to enable repair to ensure patients continue to receive benefit. Brindley11 reported on the technical failures of his first 500 implants and found a mean time to failure of 19.6 years which is exceptionally good in terms of implanted devices. The main failures were of cables, receiver blocks, and at the region where the cables enter the intrathecal space. Cable failures are relatively easy to repair as are receiver blocks. The difficulties arise when cable failures occur very close to electrodes. In the case of an intrathecal implant failing near the electrodes, it is possible to replace the device with an extradural implant, especially if a sacral deafferentation has already been performed. If the failure appears to be at the extradural electrode site but not in the appropriate nerves, then it may be possible to access these intact nerves from the anterior side of the sacrum as they exit through the foramina using a recently described laparoscopic technique.12–14
Bayesian Adaptive Designs in Drug Development
Published in Emmanuel Lesaffre, Gianluca Baio, Bruno Boulanger, Bayesian Methods in Pharmaceutical Research, 2020
For time-to-event endpoints, things get a bit more complicated, primarily because posterior distributions may no longer be available in closed form. When one is collecting failure-time data, observations come in pairs for each person, (Ti, δi), where Ti is the observed time on study for the i-th patient, and δi is an indicator of whether or not the patient experienced the event. For example, if overall survival (time from randomization until death) is the primary endpoint for the study, then a patient may die before the data analysis, in which case δi = 1, or the patient may still be alive at the time of analysis and δi = 0. Suppose we assume that the patients’ times until they experience the event of interest follow an Exponential distribution and the distribution’s rate parameter depends on the treatment. The statistical model for the observations is when patient i receives treatment j. If one posits a Gamma distribution prior for λj, then the posterior distribution will also be a Gamma distribution. The form of the posterior for this model is as follows. The parameters in the posterior Gamma distribution are and . If there are two treatments, A and B, say, then the randomization probability for treatment A may simply be the posterior probability that treatment A is better than treatment B with respect to the primary endpoint. For example, one could consider the mean time to failure, , or the median failure time, . For the mean, the probability a patient is assigned treatment A might be . One could use the same sort of computation to make the randomization probability a function of the posterior distributions of the treatment-specific medians. The posterior distributions of the treatment-specific means are available directly from the parameters in the posterior distributions of the treatment-specific hazard functions or of the Exponential distributions’ rate parameters. That is, , where (α′, β′) are the parameters of the posterior Gamma distribution as shown above. If one is using the median as the summary statistic, then one can use an Inverse-Gamma prior distribution for the median (instead of a Gamma distribution as the prior for the rate parameter) and the posterior will again be Inverse-Gamma. Conjugacy follows, since the median is inversely proportional to the rate parameter in the Exponential sampling distribution.
Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications
Published in Journal of Applied Statistics, 2021
M. S. Eliwa, M. El-Morshedy, Sajid Ali
MTTF, MTBF and AvB are reliability terms based on methods and procedures for lifecycle predictions for a product. Customers often must include reliability data when determining what product to buy for their application. MTTF, MTBF and AvB are ways of providing a numeric value based on a compilation of data to quantify a failure rate and the resulting time of expected performance. Also, In order to design and manufacture a maintainable system, it is necessary to predict the MTTF, MTBF and AvB. If 16) when r = 1. The AvB is consider the probability that the component is successful at time x, i.e.
Bias-corrected estimators for proportion of true null hypotheses: application of adaptive FDR-controlling in segmented failure data
Published in Journal of Applied Statistics, 2022
Aniket Biswas, Gaurangadeb Chattopadhyay, Aditya Chatterjee
Now we consider framing of the appropriate hypotheses. We assume that the mileages at failure for the ith segment to be exponentially distributed with mean ith. segment, a quantity similar to mean time to failure (MTTF) in terms of the response variable ‘mileage’, for 5].