Confidence intervals survival data

CREATE 95% CONFIDENCE INTERVAL AROUND THE ESTIMATE AND RETAIN PROPER SURVIVAL ESTIMATE FOR TABLE. data survivalest set survivalest ... 

Within each visit window, the number of deaths, survival probability, and associated confidence intervals are obtained whenever a death occurs. The values are retained and are output to the data set once per visit at the last record, where the number of subjects remaining at risk is captured in the left variable from the ProductLimitEstimates data set. 

Figure 1 The relative 6-year mortality hazard ratios are shown for reported usual sleep hr from 2-3 hr/night to 10 or more hr/night, relative to 1.0 assigned to the hazard for 7 hr/night as the reference standard. The solid line with 95% confidence interval bars shows results from a 32-covariate Cox proportional hazards survival model, as reported previously (3). The dotted lines show data from models that excluded subjects who were not initially healthy, i.e., who died within the first year or whose questionnaires reported any cancer, heart disease, stroke, chronic bronchitis, emphysema, asthma, or current illness (a yes answer to the question are you sick at the present time ). The dot-dash lines with X symbols show models controlling only for age, insomnia, and use of sleeping pills. Data were from 635,317 women and 478,619 men. The thin solid lines with diamonds show the percent of subjects with each reported sleep duration (right axis).

A practical challenge of Bayesian meta-analysis for rare AE data is that noninformative priors may lead to convergence failure due to very sparse data. Weakly informative priors may be used to solve this issue. In the example of the previous Bayesian meta-analysis with piecewise exponential survival models, the following priors for log hazard ratio (HR) (see Table 14.1) were considered. Prior 1 assumes a nonzero treatment effect with a mean log(HR) of 0.7 and a standard deviation of 2. This roughly translates to that the 95% confidence interval (Cl) of HR is between 0.04 and 110, with an estimate of HR to be 2.0. Prior 2 assumes a 0 treatment effect, with a mean log(HR) of 0 and a standard deviation of 2. This roughly translates to the assumption that we are 95% sure that the HR for treatment effect is between 0.02 and 55, with an estimate of the mean hazard of 1.0. Prior 3 assumes a nonzero treatment effect that is more informative than that of Prior 1, with a mean log(HR) of 0.7 and a standard deviation of 0.7. This roughly translates to the assumption that we are 95% sure that the HR... 

If the total population is known and, therefore, also the true mean fi and the standard deviation A, to infer the value that corresponds to a given percent of survival is rather an easy game. Assuming that a normal distribution holds, what shall be done is to evaluate the number k of standard deviation A to subtract to the true mean ji. But when the true mean is not known because the population of data is to large with respect to the sample size (see Eq. 4.1) and the mean available x is just the sample mean, the question arises as to how close or far we really are from the true one. The question can be answered only in terms of confidence interval C. In general terms, if a population parameter is not known, for instance the true mean it can always be estimated using observed sample data. Estimated actually means that its value will never be exactly determined, but it may be included in a range of values whose size depends on the confidence we want to know it. As the... 

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