Bayesian versus frequentist statistical inference for investigating a one-off cancer cluster reported to a health department

Background. The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods. This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results. Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion. In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit

The effects of custodial vs. non-custodial sentences on re-offending: A systematic review of the state of knowledge

As part of a broad initiative of systematic reviews of experimental or quasiexperimental evaluations of interventions in the field of crime prevention and the treatment of offenders, our work consisted in searching through all available databases for evidence concerning the effects of custodial and non-custodial sanctions on reoffending. For this purpose, we examined more than 3,000 abstracts, and finally 23 studies that met the minimal conditions of the Campbell Review, with only 5 studies based on a controlled or a natural experimental design. These studies allowed, all in all, 27 comparisons. Relatively few studies compare recidivism rates for offenders sentenced to jail or prison with those of offenders given some alternative to incarceration (typically probation). According to the findings, the rate of re-offending after a non-custodial sanction is lower than after a custodial sanction in 11 out of 13 significant comparisons. However, in 14 out of 27 comparisons, no significant difference on re-offending between both sanctions is noted. Two out of 27 comparisons are in favour of custodial sanctions. Finally, experimental evaluations and natural experiments yield results that are less favourable to non-custodial sanctions, than are quasi-experimental studies using softer designs. This is confirmed by the meta-analysis including four controlled and one natural experiment. According to the results, non-custodial sanctions are not beneficial in terms of lower rates of re-offending beyond random effects. Contradictory results reported in the literature are likely due to insufficient control of pre-intervention differences between prisoners and those serving “alternative” sanctions