gms | German Medical Science

Background: In adaptive group sequential designs (AGSD), statistical testing is performed at an interim stage k after a group of observations. In comparison to classical single-stage designs with no statistical interim analyses, AGSD enable more economical and ethical studies because of the possibility of an early stopping for efficacy or futility in case of an overwhelmingly large or small effect, respectively. Hence, they facilitate to save time and money and reduce the patients' risk of an inferior treatment. In case the study is continued to the next consecutive stage, sample size re-estimation based on conditional power of the current trend of the data can be performed. Though a growing number of researchers increasingly recognize interim analyses, quite often difficulties arise during the a priori planning phase and the application of these highly sophisticated statistical procedures.

Research Objective: We clearly outline the concise application of these statistical procedures including sample size reassessment based on conditional power during the conduct of the ongoing study. Therefore, we provide a succinct workflow chart for the potentially tricky part of the planning phase and sample size re-estimation and reassessment.

Method: For the sake of demonstration of the application, we focus only on the dependent variable patient satisfaction assessed with a standardized questionnaire, applied on randomly sampled psychiatric real-world data.

Study Design: The study is conducted as a prospective cohort study of mental health services. We explain how such a study with an AGSD can be planned using the group sequential approach by Wang and Tsiatis [1] with K = 2 stages and power parameter Delta = .25, and the adaptive inverse normal combination test by Lehmacher and Wassmer [2]. Additionally, we also outline the case of testing the null hypothesis against a two-sided alternative, though adaptive designs have been initially designed and are mostly applied only in one-sided testing scenarios.

Data Collection: The data are sampled at two different psychiatric hospitals in Germany. In the workflow chart, we also introduce to the exact sample size estimation including the correction by the sample size inflation factor of the chosen group sequential approach, which is necessary for the application of interim analyses.

Data Analysis: Data analysis has been performed with the statistics and programming software R and IBM SPSS Statistics, Version 23 (SPSS: only for the independent two sample t-test).

Results: The workflow chart provides all parts for the concise application of AGSD in health services research. It displays the detailed workflow process of the following (greatly reduced) steps:

1.

Design the AGSD: Choose the group sequential and adaptive approach, and all statistical parameters, respectively;

2.

Sample size estimation with sample size inflation factor for each group;

3.

Data sampling for Stage 1;

4.

Statistical interim analysis after Stage 1;

5.

Test decisions based on the inverse normal method (INM);

6.

If not stopped after Stage 1: Sample size re-estimation and reassessment based on conditional power;

7.

Data sampling for Stage 2;

8.

Statistical analysis and test decision based on the INM;

This is exemplified by the application on the data of two psychiatric hospitals.

Discussion: The carefully chosen example for the demonstration of the concise application of AGSD evidently underpins the well-known strengths of interim analyses and mid-trial design modifications. The benefits of enabling well-powered studies in case of no early stopping but a continuation to the next planned stage, or saving time and money in case of an early stopping for efficacy or futility after Stage 1, clearly outweigh the slightly more effort in the planning phase. Thus, these methods outperform on average over many studies traditional single-stage designs with no interim analyses.

Practical Implications: Our provided workflow chart dramatically eases the many necessary steps during the planning phase and the application of these highly sophisticated AGSDs, especially focusing on sample size reassessment based on conditional power. Hence, the chart bridges the gap between theory and application for saving on average limited resources, while facilitating more ethical studies in mental health services research.