Exact sequential analysis for multiple weighted binomial end points

Maro

Kulldorff

2021

Statistics in Medicine

Self Cite

In sequential analysis, hypothesis testing is performed repeatedly in a prospective manner as data accrue over time to quickly arrive at an accurate conclusion or decision. In this tutorial paper, detailed explanations are given for both designing and operating sequential testing. We describe the calculation of exact thresholds for stopping or signaling, statistical power, expected time to signal, and expected sample sizes for sequential analysis with Poisson and binary type data. The calculations are run using the package Sequential, constructed in R language. Real data examples are inspired on clinical trials practice, such as the current efforts to develop treatments to face the COVID‐19 pandemic, and the comparison of treatments of osteoporosis. In addition, we mimic the monitoring of adverse events following influenza vaccination and Pediarix vaccination.

“…The authors of Reference 23 proposed a test statistic based on the weighted sum of the outcomes. For this, let

{\vec{C}}_{1}, {\vec{C}}_{2}, \dots

, denote a sequence of

D

‐dimensional random vectors, where

{\vec{C}}_{i} = (C_{i, 1}, \dots, C_{i, D})

, with

i = 1, 2, \dots

, and

C_{i, j} \sim b i n o m i a l (n_{i, j}, p_{j, R R_{j}})

, for

j = 1, \dots, D

.…”

Section: Exact Sequential Testing Backgroundmentioning

confidence: 99%

“…For the

i

th test, consider the test statistic defined as a composite endpoint, denoted by

S_{i}

, constructed as a weighted sum of cumulative outcomes, that is:

S_{i} = \sum_{g = 1}^{i} (w_{1} C_{g, 1} + \dots + w_{D} C_{g, D}),

where

w_{j}

is the weight associated to the

j

th outcome. Flat critical values in the scale of

S_{i}

can be solved under arbitrary significance levels using numeric procedures 23 . That is,

H_{0}

is rejected for the first

n_{i}

such that

S_{i} \geq b_{n_{i}} = c v

, where

n_{i} = \sum_{g = 1}^{i} \sum_{j = 1}^{D} n_{g, j}

.…”

Section: Exact Sequential Testing Backgroundmentioning

confidence: 99%

w_{1} = 0.05

), forearm fracture (

w_{2} = 0.08

), humerus fracture (

w_{3} = 0.09

), serious infection (

w_{4} = 0.11

), and pneumonia (

w_{5} = 0.30

).…”

Section: Data Analysis Examplesmentioning

confidence: 99%

“…Table 8 was extracted from Reference 23. It contains the cumulative sample size at each test in each of the five endpoints (columns 1 to 5), and the test statistic in column 6, denoted by

U = S_{i, A} / S_{i, B}

, which is the ratio of exposure

A

to exposure

B

weighted sums, where exposure

A

is for denosumab treatment and exposure

B

is for bisphosphonates treatment.…”

Section: Data Analysis Examplesmentioning

confidence: 99%

“…Flat critical values in the scale of

can be solved under arbitrary significance levels using numeric procedures. 23 That is,

is rejected for the first

such that

, where

. Otherwise, the analysis is finalized in favor of

for the first test such that

.…”

Section: Exact Sequential Testing Backgroundmentioning

confidence: 99%

See 3 more Smart Citations

Exact sequential test for clinical trials and post‐market drug and vaccine safety surveillance with Poisson and binary data

Maro

Kulldorff

2021

Statistics in Medicine

Self Cite

Bounded-width confidence interval following optimal sequential analysis of adverse events with binary data

Zhuang

2022

Stat Methods Med Res

Self Cite

In sequential testing with binary data, sample size and time to detect a signal are the key performance measures to optimize. While the former should be optimized in Phase III clinical trials, minimizing the latter is of major importance in post-market drug and vaccine safety surveillance of adverse events. The precision of the relative risk estimator on termination of the analysis is a meaningful design criterion as well. This paper presents a linear programming framework to find the optimal alpha spending that minimizes expected time to signal, or expected sample size as needed. The solution enables (a) to bound the width of the confidence interval following the end of the analysis, (b) designs with outer signaling thresholds and inner non-signaling thresholds, and (c) sequential designs with variable Bernoulli probabilities. To illustrate, we use real data on the monitoring of adverse events following the H1N1 vaccination. The numerical results are obtained using the R Sequential package.

Matching ratio and sample size for optimal sequential testing with binomial data

Oliveira

2023

Stat Methods Med Res

Statistical sequential analysis of binary data is an important tool in clinical trials such as placebo-controlled trials, where a total of [Formula: see text] individuals are randomly allocated into two groups, one of size [Formula: see text] receiving the treatment/drug, and the other of size [Formula: see text] for placebo. The ratio [Formula: see text], namely “matching ratio,” determines the expected proportion of adverse events from the treatment group among the [Formula: see text] individuals. Bernoulli-based designs are used for monitoring the safety of post-licensed drugs and vaccines as well. For instance, in a self-control design, [Formula: see text] is the ratio between the risk and the control time windows. Irrespective of the type of application, the choice of [Formula: see text] is a critical design criterion as it determines the sample size, the statistical power, the expected sample size, and the expected time to signal the sequential procedure. In this paper, we run exact calculations to offer a statistical rule of thumb for the choice of [Formula: see text]. All the calculations and examples are performed using the R Sequential package.