Related papers: The case for balanced hypothesis tests and equal-t…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
Suppose you are told that taking a statin will reduce your risk of a heart attack or stroke by 3% in the next ten years, or that women have better emotional intelligence than men. You may wonder how accurate the 3% is, or how confident we…
In clinical studies upon which decisions are based there are two types of errors that can be made: a type I error arises when the decision is taken to declare a positive outcome when the truth is in fact negative, and a type II error arises…
Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In…
A confidence sequence (CS) is a sequence of confidence intervals that is valid at arbitrary data-dependent stopping times. These are useful in applications like A/B testing, multi-armed bandits, off-policy evaluation, election auditing,…
Under the null hypothesis, the marginal probability of the positive response is symmetric at any specified correlated coefficient, and the discordance probability is also symmetric to the positive response probability. The marginal…
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…
Binary endpoints are common in clinical trials and conditional odds ratios have traditionally been used to assess treatment effects. However, the interpretation of odds ratios is difficult, they are non-collapsible and rely on strong…
In clinical trials studying paired parts of a subject with binary outcomes, it is expected to collect measurements bilaterally. However, there are cases where subjects contribute measurements for only one part. By utilizing combined data,…
Nonlinear longitudinal proportional effect models have been proposed to improve power and provide direct estimates of the proportional treatment effect in randomized clinical trials. These models assume a fixed proportional treatment effect…
The difference-in-differences (DID) research design is a key identification strategy which allows researchers to estimate causal effects under the parallel trends assumption. While the parallel trends assumption is counterfactual and cannot…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
By the modified directed likelihood, higher order accurate confidence limits for a scalar parameter are obtained from the likelihood. They are conveniently described in terms of a confidence distribution, that is a sample dependent…
Adaptive experiment designs can dramatically improve statistical efficiency in randomized trials, but they also complicate statistical inference. For example, it is now well known that the sample mean is biased in adaptive trials.…
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…
Despite its common practice, statistical hypothesis testing presents challenges in interpretation. For instance, in the standard frequentist framework there is no control of the type II error. As a result, the non-rejection of the null…
Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value $P_C$ is introduced here. It is closely related to the…
Hybrid controlled trials (HCTs), which augment randomized controlled trials (RCTs) with external controls (ECs), are increasingly receiving attention as a way to address limited power, slow accrual, and ethical concerns in clinical…
Constructing nonasymptotic confidence intervals (CIs) for the mean of a univariate distribution from independent and identically distributed (i.i.d.) observations is a fundamental task in statistics. For bounded observations, a classical…
In a randomised clinical trial, when the result of the primary endpoint shows a significant benefit, the secondary endpoints are scrutinised to identify additional effects of the treatment. However, this approach entails a risk of…