Survival data sample size

The types of data available at the end of a clinical trial will depend upon the trial s sample size, duration, and clinical endpoint. There are two categories of clinical endpoints considered in pharmacoeco-nomic analysis intermediate endpoints and final endpoints. An intermediate endpoint is a clinical parameter, such as systolic blood pressure, which varies as a result of therapy. A final endpoint is an outcome variable, such as change in survival, or quality-adjusted survival, that is common to several economic trials, which allows for comparisons of economic data across clinical studies and is of relevance to policy makers. 

In tong term trials there will usually be an opportunity to check the assumptions which underlay the original design and sample size calculations. This may be particularly important if the trial specifications have been made on preliminary and/or uncertain information. An interim check conducted on the blinded data may reveal that overall response variances, event rates or survival experience are not as anticipated. A revised sample size may then be calculated using suitably modified assumptions... ... 

The power of a study where the primary endpoint is time-to-event depends not so much on the total patient numbers, but on the number of events. So a trial with 1000 patients with 100 deaths has the same power as a trial with only 200 patients, but with also 100 deaths. The sample size calculation for survival data is therefore done in two stages. Firstly, the required number of patients suffering events is... 

Example 13.4 Sample size calculation for survival data... 

Despite the high incidence of malnutrition pre-OLT, data supporting a mortality benefit from pre-OLT nutrition support are relatively lacking. Studies thus far have been limited by small sample size, so it is uncertain whether nutritional interventions in these patients truly convey a survival benefit long term. Larger controlled clinical trials are needed. 

As Whitehead (1997) points out, this can even occur with fixed sample size studies of survival analysis. For example, consider a fixed sample size trial with a recruitment over one year. We may have determined to analyse the results once the last patient recruited has been followed up for one year. This means, though, that patients recruited earlier in the trial will have been followed up longer those recruited at the beginning will, in fact, have been followed up for two years. Often this extra information will also be included in the analysis, which thus reflects a mixture of follow-up times from one to two years. However, once this analysis is complete it will still be possible to obtain further data and in a year s time an analysis of patients with 2-3 years follow up could be carried out. I think it is fair to say, however, that it is more likely to be a problem which makes itself known in a sequential rather than a fixed trial framework. Nevertheless, it is a potential feature of all forecasting systems that they are hostages to the future further information which embarrasses us can always arise. 

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... 

Now the reduction for the 99.99 % probability of survival has grown to 10 % from 241.7 MPa down to 216 MPa. As last, the designer wants to know how far or close these 140 samples are from the population size to use the finite population correction (FPC) given by Eq. 4.9. To that purpose he calculates the overall volume of all the work pieces that must be built with that steel to assess N. The overall volume is equal to 2.2 x 10 mm. Since the volume of the traction specimen used is equal to 7,854 mm the number N of specimens of the entire population is N = 2.2 x 10 /7.854 = 280,112. He concludes that 140 specimens represent only a mere 0.05 % of the entire population size and he cannot apply any correction. This simple example evidences the difference that may arise when using a sample of limited size. Statistics results depend on the sample size. We may try, then, to use the Lieberman one-sided tolerance limit. The mean value of the logarithms of experimental data is og au) = 2.717 and 5 = 0.02175 from Table 4.5 we infer that the value of k for a sample of size 140 and a probability of survival of 99.95 % is k = 3.356 therefore ... 

The use of Weibull plots for design purposes has to be handled with extreme care. As with all extrapolations, a small uncertainty in the slope can result in large uncertainties in the survival probabilities, and hence to increase the confidence level, the data sample has to be sufficiently large N > 100). Furthermore, in the Weibull model, it is implicitly assumed that the material is homogeneous, with a single flaw population that does not change with time. It further assumes that only one failure mechanism is operative and that the defects are randomly distributed and are small relative to the specimen or component size. Needless to say, whenever any of these assumptions is invalid, Eq. (11.23) has to be modified. For instance, bimodal distributions that lead to strong deviations from a linear Weibull plot are not uncommon. 

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