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Definition Of Exponential Distributions

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A resulting straight line through the graph of H(t) would suggest that an exponential distribution would be the favoured choice for these data, while a straight line through the graph of log H(t)would suggest a weibull distribution for the data. Figure~\ref{HazCumHaz}, for patients who filled in a Home Care or both a Home Care and a Contact Assessment, does not support either distributions. Part results for outputs from the exponential and weibull distributions for these data are shown in Appendix~\ref{AppendixB}. These results confirm the evidence from Figure~\ref{HazCumHaz} and show that neither distributions fit the data well. Therefore, formal modelling for the 3525 patients who filled in either a Home Care assessment alone, or …show more content…

Further, stepwise regression is also known to pick smaller models than desired~footnote{http://www.biostat.jhsph.edu/~iruczins/teaching/jf/ch10.pdf}. The criteria used in the step-wise variable selection process for this study was the Akaike information criterion (AIC). AIC estimates the quality of each model, relative to each of the other models by estimating the information lost when a model is used to represent the data. In doing so, it deals with the trade-off between the goodness of fit of the model and the number of parameters used. When using the AIC criterion, the model with the least is the preferred model. After using the AIC selection process, any insignificant variables which were selected by step-wise regression were manually removed from the model. There was also a need to consider the practicality of the model. Some highly significant variables resulted in coefficients that were very small for any practical use. For instance, if a variable resulted in a coefficient of $0.04$ then this coefficient would be $0.04 \times$ the baseline hazard. This would consequently increase mortality by a factor of $e^{0.04}$ days; which is $~1.04 \times$ baseline number of days. The resulting increase is very insignificant and could be ignored. Table~\ref{LowCoeffs} consists of 63 variables that were removed from

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