A Guide to Adaptive Randomization based on a Patient's Characteristics

Clinical Trial Design

The most common design used for Phase II and Phase III clinical trials is the randomized controlled trial design. In randomized controlled trials, the probability of being assigned the study treatment or the control treatment is fixed throughout the trial and is normally 50%, so that each treatment is given to the same number of patients. This approach leads to a high‑chance of identifying if one treatment is significantly better than the other. The fact that 50% of the trial population is assigned to the control treatment is not a particular issue in common diseases such as cardiovascular disease. For example, of the 7 million people in the United Kingdom (UK) with cardiovascular disease, if 200 of them are involved a clinical trial, then 99.9% of the overall cardiovascular disease population will benefit from the results of the clinical trial^[1].

However, in rare diseases such as cystinosis, which only affects an estimated 660 people in the UK, if 200 patients are involved in a clinical trial, only 70.0% of the population will benefit from the results of the clinical trial. In cases of rare diseases, there should be a greater emphasis on the health of the clinical trial population than on the general population^[2]. For this reason, response-adaptive clinical trials are a more suitable design for clinical trials in rare diseases.

Randomized Clinical Trials Vs. Response Adaptive Clinical Trials

Randomized controlled trials give no possibility to change a treatment allocation probability. For example, if one treatment is shown to be better halfway through the trial, then, in order to treat as many patients as successfully as possible, all later patients should be assigned to the estimated ʽbestʼ treatment. However, this option is not a possibility in a randomized clinical trial. An alternative to using a randomized clinical trial in this scenario would be to use a response‑adaptive clinical trial design. This type of trial allows the treatment allocation probability to vary throughout the clinical trial^[3].

Response-adaptive clinical trials use information gained from previous patients to alter the allocation probability for all treatments. These clinical trials vary the treatment allocation probability in order to favour the treatment estimated to be more effective, in order to maximize the number of successful outcomes in patients^[4].

Another downside to randomized controlled trials is that they assume that every patient given the same treatment will react in exactly the same way. This is not the case. Many patients will react differently to a treatment due to their specific characteristics (also known as covariates). These characteristics could include a continuous covariate (e.g., age or weight), a binary covariate (e.g., gender or presence of a certain gene), or a categorical covariate (e.g., blood type). There are some response‑adaptive trial designs that include a patient's covariate value(s) into their treatment allocation probability calculation^[5], such that the allocation probability to each arm depends on the covariate(s) of the individual patient.

Personalized Medicine

Personalized medicine is a step away from the ʽone-size-fits-allʼ medical approach and instead tailors the treatment to an individual to produce the best response and ensure more effective medical care. Since the 2003 human genome project, human DNA can be mapped out and it is feasible to individualize medicine so that it targets a certain gene. As described by Vogenberg^[6], personalized medicine usually targets groups of patients who do not respond well to regular treatment due to certain characteristics such as age, genetics and environmental exposure.

When using a response‑adaptive clinical trial design, these patient characteristics can be used to allocate patients to a certain treatment. If one treatment is identified as working better for a patient with certain characteristics, then the probability of allocating that treatment to the next person can be adjusted depending on the next patient’s characteristics. This approach leads to improved outcomes for patients included in the clinical trial.

For example, when using response‑adaptive clinical trial design, if Treatment A is shown to be more effective in patients who are aged < 30 years, then the allocation probability for Treatment A should be larger for a patient who arrives into the clinical trial aged 26 years than for a patient who is aged 40 years. In this way, response‑adaptive trial designs will allocate more patients to the ʽbestʼ treatment for the individual patient, due to their specific characteristics, than a randomized clinical trial would.

Covariates and Biomarkers

There are multiple trials where the impact of a covariate value on the outcome of a treatment has been shown. These include `Effectiveness of antibiotics for acute sinusitis in real-life medical practice'<sup>[7]</sup>and `K-ras Mutations and Benefit from Cetuximab in Advanced Colorectal Cancer'^[8].

There is a specific type of covariate called a biomarker. A biomarker is defined as ʽa characteristic that is objectively measured and evaluated as an indicator of normal biologic processes, pathogenic processes or pharmacological responses to a specified therapeutic interventionʼ^[9]. Biomarkers are further separated into two subgroups: prognostic and predictive.

A prognostic biomarker supplies information about a patient’s outcome, irrespective of which treatment they are given. For example, a patient who is blood type A might have a better outcome than a patient who is blood type O if both patients are given Treatment A, or if they are both given Treatment B during a clinical trial. Hence, in this scenario, blood type is a prognostic biomarker. In contrast, a predictive biomarker provides information on the outcome of a patient if given a specific treatment. For example, a patient might have a certain gene which means they have a better outcome than a patient without the particular gene if they are both given Treatment A during a clinical trial. However, the same 2 patients may have the same outcome if they are both given Treatment B. Thus, the presence of the gene is a predictive biomarker^[9].

Proposed Adaptive Trial Design

Assume we have K ≥ 2 treatments and a total of N patients in our clinical trial. Each patient arrives into the clinical trial sequentially, such that the outcome of a patient (patient n) is known before the next patient (patient n+1) enters the clinical trial. Here we assume that each patient only receives 1 treatment.

Yang^[10] assumes each treatment within the clinical trial has an unknown probability of producing a positive outcome in each patient. This probability, which is dependent on the covariates of the patient, can be estimated using information from previous patients.

When a patient arrives into the clinical trial, a covariate value, x, is observed for each patient. This covariate could be binary (e.g., gender) or it could be continuous (e.g., weight), or it could even represent multiple covariate values being observed. This patient’s covariate value, along with information from previous patients, will then be used to assign this patient to a treatment.

We have slightly altered the algorithm proposed by Yang^[10]. This altered algorithm is shown below:

1. Allocate the first 5 × K patients who enter the clinical trial to each of the K treatments equally.
2. Estimate the probability of each treatment producing a successful outcome in a patient, based on information from the previous patients.
3. Given we know the covariate, x of the next patient n+ 1, find the treatment with the highest probability of producing a successful outcome in that patient.
4. Select currently the best treatment with high probability and select each of the other treatments with low probability.
5. Given we now know the outcome of patient n + 1, update the probability estimate of that treatment producing a successful outcome in a patient.
6. Repeat Steps 3‑5 for the next patients n + 2, n + 3, ..., N

This algorithm selects the currently estimated ʽbestʼ treatment for patient n with high probability; therefore, it will produce more successful outcomes in patients than a randomized controlled trial with the same treatments. Thus, patients are more likely to join the clinical trial as they are more likely to have successful outcomes. Hence, recruitment for the clinical trial is expected to be easier and quicker than in an equal randomized controlled trial.

However, the algorithm still gives a small probability of allocating a patient to one of the ‘worse’ treatment. Therefore, it maintains a good chance of identifying any significant differences between treatments. So, when the study treatment is proven to be the better treatment, it can be moved to the next phase of clinical development with a high certainty that it is better than the control treatment. When the study treatment is proven to be worse, the clinical trial can be stopped as we know with a high certainty that it will not pass the next phase of clinical trial. Taking this approach allows pharmaceutical companies to save money by only investing in and progressing the best study treatments to the next phase of clinical development.

At the start of the clinical trial, when little information is known about any of the treatments, the difference in probability of being assigned the estimated ʽbestʼ treatment and ʽworseʼ treatment is small. However, as information on the treatments is accumulated, the estimates of each treatment producing a successful outcome in the next patient become more certain. Hence, as more patients enter the clinical trial, the probability of being given the estimated ʽbestʼ treatment increases and the probability of being given the estimated ʽworseʼ treatment decreases.

Real‑world Example

A Phase II/III clinical trial investigated the effect of catumaxomab in the treatment of malignant ascites (ClinicalTrials.gov Identifier: NCT00836654). Malignant ascites are the fluid build‑up between a patient's abdominal wall and their organs and is caused by a cancer^[11]. This study showed that the treatment of malignant ascites due to different epithelial cancers was improved by the use of catumaxomab plus paracentesis. This treatment prolonged puncture‑free survival (PuFS) when compared with paracentesis alone (median PuFS: 46 days vs. 11 days, p < 0.0001). In the original study, PuFS was the primary endpoint and overall survival (OS) was a secondary endpoint. The treatment catumaxomab plus paracentesis versus paracentesis alone also showed an improvement in OS; however, the improvement was not statistically significant (median OS: 72 days vs. 68 days, p = 0.0846).

Catumaxomab was further investigated by Heiss^[12], in regards to the effect of biomarkers on treatment. Heiss et al performed a post‑hoc analysis on the impact of several biomarkers, which found that two predictive biomarkers were significant. Patients who had a relative lymphocyte count (RLC) > 13% and a Karnofsky index (KI) ≥ 70% were shown to have an increased OS if given catumaxomab treatment instead of the control treatment, while no treatment effect was observed in the complementary groups.

Kaplan‑Meier curves for each subset of patients based on simulated data using the results from the post‑hoc analysis^[12] show that the treatment effect varies depending on which subgroup the patient is in (Figure 1, Figure 2, Figure 3 and Figure 4). It can be seen from the plots that the two biomarkers, RLC and KI, are predictive. Therefore; this is a situation where a response‑adaptive trial (using a patient’s covariate values to calculate a treatment allocation probability) could be used.

In this scenario, an effective response‑adaptive trial design will assign a greater number of patients to the catumaxomab treatment instead of the control treatment if they have RLC > 13% and KI ≥70%, RLC > 13% and KI < 70%, or RLC ≤ 13% and KI ≥ 70%. This is due to the catumaxomab treatment resulting in a greater survival rate than the control treatment for these subgroups of patients. The response‑adaptive trial design will also allocate a similar number of patients to the control treatment and the catumaxomab treatment if the patients have RLC ≤ 13% and KI < 70%, as there is a very small difference between the two treatments in this subgroup of patients. The response‑adaptive trial design should allocate more patients to their ʽbestʼ treatment, but still allocate enough patients to their lesser treatment in order to give a good indication of which treatment is best for each subgroup of patients. Thus, the response‑adaptive trial design will still produce a high power.

In order to include a method to allocate patients depending on their RLC and KI values, the design of the clinical trial must include some prior information about which covariates are significant and at what value the continuous covariates would be split. Therefore, a response‑adaptive trial design would be useful in this situation, but only if it was hypothesised that RLC and KI were significant biomarkers above 13% and 70%, respectively, before the trial began.

The ability to predict response to cancer therapy is an important area of clinical research and there have been many attempts to identify biomarkers that correlate to positive outcomes for a patient^[12]. Therefore, identified biomarkers could be used to choose patients who will benefit most from the treatment and, hence, guide treatment decision making for personalized medicine.

Quanticate's statistical consultants are among the leaders in their respective areas enabling the client to have the ability to choose expertise from a range of consultants to match their needs. Our team would be happy to provide support and guidance for your Adaptive Trial Design. If you have a need for these types of services please Submit a RFI and member of our Business Development team will be in touch with you shortly.

Related Blogs:

• The What, Why and How of Adaptive Clinical Trials
• 7 Frequently asked Questions on Clinical Study Design
• Complex Randomization in Clinical Trials Need Not Be Complex

References

[1] (2019, January 23). Retrieved from British Heart foundation: https://www.bhf.org.uk/what-we-do/our-research/heart-statistic

[2] (2019, January 23). Retrieved from What is cystinosis?: https://www.cystinosis.org.uk/learn-more/what-is-cystinosiss/

[3] Villar Sofia S, Bowden Jack and Wason James. Multi-armed bandit models for the optimal design [Journal] // Statistical science: a review journal of thes. - [s.l.] : Statistical science: a review journal of the Institute of Mathematical Statistics, 2015. - Vol. 30. - p. 199.

[4] Cheung, Y. (2006). Continuous Bayesian adaptive randomization based on event times with covariates. Statistics in Medicine, 55-70.

[5] Villar Sofia S and Rosenberger William F. Covariate-adjusted response-adaptive randomization for [Journal] // Biometrics. - [s.l.] : Statistics in Medicine, 2018. - Vol. 74. - pp. 49-57.

[6] Vogenberg, F. R. (2010). Personalized medicine: part 1: evolution and development into theranostics. . Pharmacy and therapeutics, 560.

[7] Blin Patrick [et al.]. Effectiveness of antibiotics for acute sinusitis in real-life medical practice [Journal] // British Journal of clinical Pharmacology. - [s.l.] : British journal of clinical pharmacology, 2010. - Vol. 70. - pp. 418-428.

[8] Karapetis Christos [et al.]. K-ras Mutations and Benefit from Cetuximab in Advanced Colorectal Cancer [Journal] // The New England Journal of Medicine. - [s.l.] : The New England Journal of Medicine, 2008. - Vol. 359. - pp. 1757-1765.

[9] Oldenhuis C N. A. M. [et al.]. Prognostic versus predictive value of biomarkers in oncology [Journal]. - [s.l.] : European journal of cancer, 2008. - 7 : Vol. 44.

[10] Yang, Y. (2002). Randomized allocation with nonparametric estimation for a multiarmed. The annals of Statistics, 100-121.

[11] Becker Gerhild, Galandi Daniel and Blum Hubert E. Malignant ascites: Systematic review and guideline for treatment [Journal] // European Journal of Cancer. - [s.l.] : European Journal of Cancer, 2006. - Vol. 42. - pp. 589-597.

[12] Heiss Markus M [et al.]. The Role of Relative Lymphocyte Count as a Biomarker for [Journal] // Clinical Cancer Research. - [s.l.] : Clinical Cancer Research, 2014. - Vol. 20. - pp. 3348-3357.