Subject: Statistics
Paper: Biostatistics
Module 20: Sequential Clinical Trials I
Development Team
Principal investigator: Dr. Bhaswati Ganguli,Professor, Department of Statistics, University of Calcutta
Paper co-ordinator: Dr. Sugata SenRoy,Professor, Department of Statistics, University of Calcutta
Content writer: Dr.Atanu Bhattacharjee, Assistant Professor, Centre for Cancer Epidemiology, The Advanced Centre for Treatment, Research and Education in Cancer (ACTREC) Tata Memorial Centre
Content reviewer: Department of Statistics, University of Calcutta
Sequential Clinical Trials
Sequential Clinical Trials
There is an increasing need for innovative clinical trial designs that allow effective agents to be identified more efficiently compared with the standard designs.
Group sequential designs
The flexibility to use cumulated information to modify the subsequent course of the trial is supported by Group sequential designs.
Sequential Clinical Trials
Monitoring in a sequential trial
Monitoring a group sequential clinical trial is a dynamic process.
The time of performing an interim analysis in a group sequential trial is a natural time to update and combine the information from prior experience and accumulated data.
The decision-theoretic approach has the potential ability to concurrently consider efficacy, futility and cost (Berry,1994).
Sequential Clinical Trials
Monitoring in a sequential trial
Monitoring a group sequential clinical trial is a dynamic process.
The time of performing an interim analysis in a group sequential trial is a natural time to update and combine the information from prior experience and accumulated data.
The decision-theoretic approach has the potential ability to concurrently consider efficacy, futility and cost (Berry,1994).
Sequential Clinical Trials
Monitoring in a sequential trial
Monitoring a group sequential clinical trial is a dynamic process.
The time of performing an interim analysis in a group sequential trial is a natural time to update and combine the information from prior experience and accumulated data.
The decision-theoretic approach has the potential ability to concurrently consider efficacy, futility and cost (Berry,1994).
Introduction
Monitoring in a sequential trial
During the monitoring in clinical trial it is obvious that multiple testing problem will occur. It generates the false positive and false negative conclusion.
Adaptive Design and random sample size
However, this issue may be avoided by selecting the sample size in random manner through adaptive design.
Introduction
Monitoring in a sequential trial
During the monitoring in clinical trial it is obvious that multiple testing problem will occur. It generates the false positive and false negative conclusion.
Adaptive Design and random sample size
However, this issue may be avoided by selecting the sample size in random manner through adaptive design.
Introduction
Stopping Rule in Sequential Trial
The stopping rule in any clinical trial is based on the loss function that reflects the evidence of operation characteristics at interim analysis.
The maximum sample size is sequentially determined using interim data.
The overall type I error rate can be controlled by choosing related designing parameters.
Introduction
Stopping Rule in Sequential Trial
The stopping rule in any clinical trial is based on the loss function that reflects the evidence of operation characteristics at interim analysis.
The maximum sample size is sequentially determined using interim data.
The overall type I error rate can be controlled by choosing related designing parameters.
Introduction
Stopping Rule in Sequential Trial
The stopping rule in any clinical trial is based on the loss function that reflects the evidence of operation characteristics at interim analysis.
The maximum sample size is sequentially determined using interim data.
The overall type I error rate can be controlled by choosing related designing parameters.
Introduction
False Postive and False Negative
In Sequential trial testing the decision about the false-positive and false negative can be measured by loss structure.
But it can be concluded that in sequential setting the type I error rate is often smaller than the specified significance level.
Moreover, the procedures that are based on the non-sufficient statistics may increase the type II error rate with or without the decreased type I error rate.
Challenge in Sequential Trial
Challenge in Sequential Trial
It is difficult to get unbiased estimator through sequential trial because the sample size is random in nature.
Example in Sequential Trial
Example
Consider a clinical trial that compares a new treatmentT with a controlC, where the individual treatment response isXT and the individual control response isXC. For notation simplicity, we assume a design with equal randomization, which can be easily extended to more general two-arm trials.
Example in Sequential Trial
Example
The block size at each stage is2Bi, i= 1,2, ...., whereBi for each treatment arm is fixed before the trial starts, but the maximum number of blocks is not predetermined and is determined using interim data.
Example in Sequential Trial
Example
LetX¯Ti andX¯C1 be the observed mean responses in the ith block.
Given the parameter of interest,θ, which is a measure of the treatment difference, let
Xi = ¯XTi−X¯Ci ∼Fi(.|θ),andθ= Z ∞
−∞
xdFi(x|θ) (1)
Introduction
Hypothesis Test
The one-sided hypothesis to be tested is
H0 ≤0 versusH1 :θ >0 (2) The termθ can be assumed with prior distributionπ with
E(θ|π) =δ.
Decision Rule
It is expected that a loss structure consisting of the respective cost of making a false-positive conclusion, a false-negative conclusion, and the cost of the total sample, in which the risk and benefit of the new agent under investigation should be balanced via these cost parameters.
Introduction
Decision Rule
LetDbe the decision of either accepting (A) or rejecting(R) null hypothesis. At the jth interim analysis, the loss function is defined by
L(θ, D, j) =L(θ, D) + 2K2
j
X
i=1
Bi (3)
where
L(θ, D) =K0h0(θ)I{≤0, D=R}+K1h1(θ)I{θ >0, D=A}
(4) K0 is a constant and positive penalty for each unit of h0(θ) when H0 is incorrectly rejected, andK1 is a positive penalty for each unit ofh1(θ) when H0 is incorrectly accepted.
Introduction
Decision Rule
Here,h0(.)and h1(.) are positive and continuous functions, and the positive loss may change with the actual value ofθ. One sensible choice is to allow the loss function to change with the magnitude ofθ, such as h0(θ) =h1(θ) =|θ|w+c with c≥0and w >0.
Introduction
Decision Rule
The loss to accept the null hypothesis increases as the distance of a positiveθ to zero gets larger. Similarly, the loss to rejectH0
increases as a negativeθdeviates from zero further. The unit cost of each sample,K2, is relative to K0 and K1, which should be much smaller thanK0 andK1.
Another special case for the type of loss functions is the commonly used0−Ki loss, withh0(θ) =h1(θ) = 1. Following a common convention that making a false-positive conclusion leads to a more severe penalty than making a false-negative conclusion, we let K0 > K1.
Decision Rule
Decision Rule
LetXj ={X1, ...., Xj}be the accumulated data up to step j, whereXj represents data from thejth block. At each interim analysis the study will be terminated for futility or for efficacy if the evidence is strong enough. Otherwise, the study will continue to(j+ 1)th block.
The loss function related to the above two decisions at the jth interim analysis is defined as the expected loss of stopping the trial and accepting the null hypothesis, that is,
LA(Kj) =E{L(θ, A, j)|Kj}, (5)
Decision Rule
Decision Rule
Lcont(Kj) =E[minD+AorRE()|Kj+1}|Kj] (6) It is possible to achieve the targeted power while minimizing the total sample sizeas monitoring rules. This type of the group sequential designs motivated by internal reasons in view of the interim data towards treatment effect comparison.
