The fit of a regression predictor to new data is nearly always worse than its fit to the original data. Anticipating this shrinkage leads to Stein-type predictors which, under certain assumptions, give a uniformly lower prediction mean squared error than least squares. Shrinkage can be particularly marked when stepwise fitting is used: the shrinkage is then closer to that expected of the full regression rather than of the subset regression actually fitted. Preshrunk predictors for selected subsets are proposed and tested on a number of practical examples. Both multiple and binary (logistic) regression models are considered.

Publication bias is a major problem, perhaps the major problem, in meta-analysis (or systematic reviews). Small studies are more likely to be published if their results are 'significant' than if their results are negative or inconclusive, and so the studies available for review are biased in favour of those with positive outcomes. Correcting for this bias is not possible without making untestable assumptions. In this paper, a sensitivity analysis is suggested which is based on fitting a model to the funnel plot. Some examples are discussed.

Observational data are often analysed as if they had resulted from a controlled study, and yet the tacit assumption of randomness can be crucial for the validity of inference. We take some simple statistical models and supplement them by adding a parameter which re¯ects the degree of non-randomness in the sample. For a randomized study is known to be 0. We examine the pro®le log-likelihood for and the sensitivity of inference to small nonzero values of . Particular models cover the analysis of survey data with item nonresponse, the paired comparison t-test and two group comparisons using observational data with covariates. Some practical examples are discussed. Allowing for sampling bias increases the uncertainty of estimation and weakens the signi®cance of treatment effects, sometimes substantially so.

What works seeks to identify rehabilitative treatments which are successful in reducing the likelihood that offenders will reoffend. A large number of small case±control studies have been reported in the literature, but with con¯icting results. Meta-analysis has been used to reconcile these ®ndings, but again with con¯icting results. We reanalyse one of the published meta-analyses in the corrections literature and argue the importance of speci®cally modelling heterogeneity and selection bias. A sensitivity approach is advocated, suggesting lower average effects and substantially increased measures of uncertainty. The method is tested on a medical example where independent con®rmation from a large controlled trial is also available.