Statistics interim analysis

Timing of any interim analysis Reason for sample size Power of clinical study Level of significance Criteria for termination of study Procedure for missing and imused data Reporting procedures for deviations from statistical plan... 

Finally, it is, in principal, possible to increase the sample size based on the observed treatment difference at an interim stage without affecting the type I error, but great care needs to be taken with regard to dealing with this statistically. Evidence to date suggests that such procedures offer no real advantages over and above a standard interim analysis plan. 

Clinical trials, with almost no exception, are longitudinal (Chow and Liu, 2004). This means that data are accumulated sequentially over time. From the perspective outlined so far in the book, the statistical analysis takes place once the number of subjects stated in the study protocol have been enrolled, randomized, and completed their participation in the trial. This approach can be called the Fixed design or fixed sample design approach. Another design of interest in clinical trials is the group sequential design, in which interim analysis plays a crucial role. 

In the fixed sample clinical trial approach, one analysis is performed once all of the data have been collected. The chosen nominal significance level (the Type I error rate) will have been stated in the study protocol and/or the statistical analysis plan. This value is likely to be 0.05 As we have seen, declaring a finding statistically significant is typically done at the 5% p-level. In a group sequential clinical trial, the plan is to conduct at least one interim analysis and possibly several of them. This procedure will also be discussed in the trial s study protocol and/or the statistical analysis plan. For example, suppose the plan is to perform a maximum of five analyses (the fifth would have been the only analysis conducted had the trial adopted a fixed sample approach), and it is planned to enroll 1,000 subjects in the trial. The first interim analysis would be conducted after data had been collected for the first fifth of the total sample size, i.e., after 200 subjects. If this analysis provided compelling evidence to terminate the trial, it would be terminated at that point. If compelling evidence to terminate the trial was not obtained, the trial would proceed to the point where two-fifths of the total sample size had been recruited, at which point the second interim analysis would be conducted. All of the accumulated data collected to this point, i.e., the data from all 400 subjects, would be used in this analysis. 

Intuitively, it might be the case that you would put more faith in the results of an analysis conducted on 1,000 subjects, somewhat less in the results of an analysis conducted on 800 subjects, and decreasingly less faith in the results of the other three analyses, respectively. Therefore, there are two statistical considerations to be addressed in the case of interim analyses. First, the fact that more than one analysis may be done increases the probability of a Type I error, and it is therefore appropriate to adjust the a-level in a more conservative direction. Second, it is usual to place more faith in an analysis conducted on a larger sample than on a smaller sample. While there are many statistical approaches to the issue of interim analysis, one notable strategy was suggested by O Brien and Fleming (see Ellenberg et al., 2003). 

Hwang, I.K. and Lan, K.K.G., 2006, Interim analysis and adaptive design in clinical trials. In Buncher, C.R. and Tsay, J-Y. (Eds), Statistics in the pharmaceutical industry, 3rd Edition, Chapman Hall/CRC, 245-284. 

A description and analysis of each controlled clinical study pertinent to the biologic s proposed use, including the protocol and a description of the statistical analyses used to evaluate the study. If the study report is an interim analysis, this must be noted and a projected completion date provided. Controlled clinical studies that have not been analyzed in detail for any reason (e.g., because they have been discontinued or are incomplete) should be provided, including a copy of the protocol and a brief description of the results and status of the study. 

The FDA s statisticians expect that each clinical protocol submitted will include a description of any planned interim analyses of the data, including the anticipated monitoring procedures, the variables to be analyzed, and the statistical methods to be applied. The latter includes the choice of significance level for each interim analysis, the frequency of analysis, and a declaration of the circumstances under which the study would be terminated before the planned number of patients have been entered into the study. 

Interim efficacy analyses usually make a mess These analyses require either that the overall size of the trial has to be greater than if no interim analysis was performed, or that a smaller a must be accepted as indicating statistical significance at the end of the whole study. 

The code will be broken and data will be analyzed when the 12-mo follow-up has been completed for all patients. At that time, DHA therapy will be offered to all patients who desire to receive it. Clinical and laboratory studies will be monitored by an independent data and safety monitoring committee. This committee will also perform an interim analysis when 30 patients have completed assessment and has permission to terminate the study if there are significant favorable findings or unanticipated adverse outcomes. A determination of statistical power indicates that this sample size is sufficient to detect a major effect (0.862 standard deviations). With a more modest effect of 25%, however, the statistical power diminishes to 60%. The study has been approved by the Institutional Review Board at the Johns Hopkins Medical Institutions and is supported by a research grant from the Office of Orphan Products Development at the Food and Drug Administration. Fifty-two patients are enrolled in the study at this time. The code has not yet been broken. No adverse effects attributable to the medication have been observed. 

Demets DL, Lan KKG (1994) Interim Analysis - the alpha-spending function approach. Statistics in Medicine 13 1341-1352. 

Essentially, there are two separate issues involved in performing an interim analysis a statistical issue, and an administrative or trial management issue. The statistical issue is very similar to the multiplicity issue discussed in the previous paragraph, and it applies to the reasons (1), (2) and (3) above. If we perform an interim inferential test, the overall error probability is inflated. Therefore, if one contem-... 

O Neill RT (2006) A regulator perspective on data monitoring and interim analysis. In Buncher CR, Tsay J-Y (eds) Statistics in the pharmaceutical industry, 3rd edn. Chapman Htill/CRC, Boca Raton, pp 285-293... 

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