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Biostatistics in Clinical Trials
Guosheng Yin
Department of Statistics and Actuarial Science The University of Hong Kong
Pokfulam Road, Hong Kong
Biostatistics plays a critical role in all aspects of clinical trials, including study planning and trial design, sample size and power calculation, interim monitoring, patient safety concerns, data analyses, and results reporting and interpretations of findings. With a solid understanding of various statistical concepts, particularly those ambiguous ones, clinicians and trial investigators can improve the implementation, comprehension and quality of clinical trials. This article outlines some fundamental biostatistics skills and several common statistical concerns and pitfalls in clinical trials.
Drug development is of high risk, which starts from thousands of chemical compounds in the lab to reach the clinical usage as an approved drug. It takes over 10 years and millions of dollars for a new drug to be developed. As the first trial on human beings, clinical trials can be classified as phases I, II, III and IV according to different stages of development. Innovative statistical methods can help clinical trials to deliver clear interpretable results using the minimum number of patients in the shortest time possible.
Adaptive Design
Modern adaptive designs in clinical trials include many different types, for example, adaptive dose escalation in phase I dose finding, early termination of trials, dropping or inserting doses, adaptive phase II trial design (including phase IIa and phase IIb), single to multiple arms transition, dropping arms, seamless phase I-II and phase IIa-IIb, early stopping either for futility or success in phase III group sequential designs, adaptive randomization, sample size
re-estimation, conditional power based on interim data.
P-value
In clinical trials, the p-value is often used, which means the probability of obtaining the data or result as or more extreme than the observed one assuming that the null hypothesis is true. If the p-value is low (e.g., <0.05) then either (1) the observation of the data is a rare event, or (2) the null hypothesis is not true. However, researchers are often more interested in the question
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“what is the probability that a hypothesis is true given the data?” To address this question, Bayesian statistics need to be used. Multiple testing issues often arise in clinical trials, which may inflate the type I error rate if the significance level is not properly adjusted for each test. Control of type I error is a vital aid to prevent a flood of false positives into the medical literature. Group sequential methods in phase III clinical trials typically use alpha-spending functions to control the type I error.
Single-to-Double Arm Trial
To expedite the developmental process of new drugs, phase II trials can be launched as a single-to-double arm trial. In the single arm portion, the efficacy of the drug is evaluated with reference to the standard response rate; while in the double arm portion, a control arm is introduced as a concurrent comparator. The hypotheses in such a single-to-double arm trial change from the single stage to double stage. It is critical to control the overall type I error rate.
Superiority Trial vs. Noninferiority Trial
Superiority trials aim to test whether the experimental drug is clinically superior to the standard treatment. Noninferiority trials intend to demonstrate that the therapeutic effect of the experimental treatment is not worse than that of the standard treatment by more than a
prespecified noninferiority margin. In a noninferiority trial, if the 95% confidence interval for the treatment benefit excludes both the noninferiority margin and zero, we may directly claim
superiority without the need to adjust for multiplicity due to the closed testing principle. If a superiority trial fails to reject the null hypothesis, one cannot infer noninferiority as a backup plan.
Proportional Hazards Assumption in Survival Analysis
In survival analysis, when comparing two survival curves, if they cross at some time point, the statistical power is often low due to some cancellation in the rank test statistics. The log-rank test is optimal under the proportional hazards assumption, which is however underpowered if such an assumption is violated as in the crossing curve cases. The partitioned log-rank test first defines the lower and upper components of the test separated by the partitioning time point, and then combines the lower and upper tests after square them (so there is no cancellation of the
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test statistics). The final test statistic takes the supremum over all possible values of the partitioning time points.
In transplantation studies, if there is a strong immune reaction of graft-versus-host disease (GVHD), a reaction of donated stem cells against patients’ own tissues, patients are likely to die soon after the transplantation. Patients may be considered as “cured” if they could survive the risk of the GVHD. Under such circumstances, there is a clear violation of the proportional hazards assumption and thus the usual Cox proportional hazards model cannot be applied. Alternative approaches have been developed such as cure rate models, transformation models, or accelerated failure time models.
Conclusion
There is no shoe that fits all. Different clinical trials may require different types of statistical methods and designs; different types of data may also require different models for analysis and interpretations. Close collaborations between biostatisticians and clinicians are the key to the success of clinical trials.
