arXiv subjects

Huw Llewelyn

Publications and source records attributed to Huw Llewelyn.

5 recordsLinked to original sources

arXiv2026

Understanding statistics for biomedical research through the lens of replication

Clinicians and scientists have traditionally focussed on whether their findings will be replicated and are very familiar with the concept. The probability that a replication study yields an effect with the same sign, or the same statistical significance as an original study depends on the sum of the variances of the effect estimates. On this basis, when P equals 0.025 one-sided and the replication study has the same sample size and variance as the original study, the probability of achieving a one-sided P is less than or equal to 0.025 a second time is only about 0.283, consistent with currently observed modest replication rates. A higher replication probability would require a larger sample size than that derived from current single variance power calculations. However, if the replication study is based on an infinitely large sample size and thus has negligible variance then the probability that its estimated mean is same sign is 1 - P = 0.975. The reasoning is made clearer by changing continuous distributions to discretised scales and probability masses, thus avoiding ambiguity and improper flat priors. This perspective is consistent with Frequentist and Bayesian interpretations and also requires further reasoning when testing scientific hypotheses and making decisions.

stat.AP↗

arXiv2025

Adding variances of independent probability distributions to estimate probabilities of replication

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a Bayesian prior distribution can be estimated), that prior probability distribution will be uniform. It would follow that a Gaussian probability distribution and a Gaussian likelihood distribution based on the same data set are identical. Replication involves doing two independent studies and is thus modelled by adding the variance of the probability distribution based on the observed data to the variance of the expected probability distribution of the replicating study based on its proposed sample size. This allows an estimate to be made of the probability that the P value will be less than or equal to 0.05 two sided (or any other specified value) in any replicating study. The same model can be used to estimate sample sizes when planning the required power of the initial study. If this requires doubling the variance, then this will require double the sample size estimated using current power calculations, suggesting that studies using current methods are underpowered. These considerations might be used to explain the replication crisis.

stat.ME↗

arXiv2023

Clinical dichotomania: A major cause of over-diagnosis and over-treatment?

Introduction: There have been many warnings that inappropriate dichotomisation of results into positive or negative, high, or normal etc., during medical research could be very damaging. The aim of this paper is to argue that this is the main cause of over-diagnosis and over-treatment. Methods: Illustrative data were taken from a randomised control trial (RCT) that compared the frequency of nephropathy within 2 years in those on treatment with an angiotensin receptor blocker and a control and on patients in whom the numerical value of the albumin excretion rate (AER) was available on all patients before they are randomised. Results: When the RCT results were divided into AER ranges, a negligible proportion developed nephropathy within 2 years and benefited from treatment in the range 20 to 40mcg/min in which 36% of currently treated patients fall (and are thus over-diagnosed and overtreated). Above an AER of 40mcg/min, there was a gradual increase in proportions with nephropathy in each range, with fewer developing nephropathy in each range on irbesartan 150mg daily than on control and fewer still developing nephropathy on 300mg daily. Interpretation: When logistic regression functions were fitted to the data and calibrated, curves were created that allowed outcome probabilities and absolute risk reductions to be estimated for use in shared decision making (illustrated by application to an example patient). This could avoid much overdiagnosis and overtreatment. Conclusion: Careful attention to disease severity by interpreting each numerical diagnostic result provides better application of the principles of diagnosis and treatment decisions that can prevent over-diagnosis and over-treatment.

q-bio.OT↗

arXiv2022

The probabilities of an outcome on intervention and control can be estimated by randomizing subjects to different testing strategies, required for assessing diagnostic tests, test trace and isolation and for natural randomisation

The efficacy of an intervention can be assessed by randomizing patients to different diagnostic tests instead of directly to an intervention and control. This principle is applied by allocating individuals to intervention if the test result is positive (or on one side of a threshold) but allocating individuals to a control if the result is negative (or on the other side of the threshold). This can also be done with different dichotomizing thresholds for one test. The frequencies of the outcome in those with each of the four resulting observations are then used to calculate the risk ratio (RR) for the marginal probabilities by solving simultaneous equations. This assumes that the RR due to intervention compared to control is the same in both test groups created by randomization. The calculations are illustrated by using data from a randomized controlled trial (RCT) that assessed the efficacy of an angiotensin receptor blocker (ARB) in lowering the risk of diabetic nephropathy in patients conditional on urinary albumin excretion rates (AERs). The calculations are also illustrated with simulated data for assessing the effectiveness of test, trace and isolation to reduce transmission of the SARS-Cov-2 virus by randomizing to RT-PCR or LFD tests. This approach allows the probabilities of outcomes, their RRs and odds ratios (OR) conditional on the results of covariates to be determined, also suggesting a way forward for natural as opposed to active randomization.

stat.AP↗

arXiv2018

Replacing P values with frequentist posterior probabilities - as possible parameter values must have uniform base-rate prior probabilities by definition in a random sampling model

Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values conditional solely on actual study observations. If the likelihood probability distribution of a random selection is modelled with a symmetrical continuous function then the frequentist posterior probability of something equal to or more extreme than the null hypothesis will be equal to the P-value; otherwise the P value would be an approximation. An idealistic probability of replication based on an assumption of perfect study methodological reproducibility can be used as the upper bound of a realistic probability of replication that may be affected by various confounding factors. Bayesian distributions can be combined with these frequentist distributions. The idealistic frequentist posterior probability of replication may be easier than the P-value for non-statisticians to understand and to interpret.

stat.OT↗