The reliability of an environmental epidemiology meta-analysis, a case study.

Claims made in science papers are coming under increased scrutiny with many claims failing to replicate. Meta-analyses are questionable when based on data from observational studies which are often unreliable. We examine the reliability of the base studies used in an air quality/heart attack meta-analysis and the resulting meta-analysis. A meta-analysis study that includes 14 observational air quality/heart attack studies is examined for its statistical reliability. We use simple counting to evaluate the reliability of the base papers and a p-value plot of the p-values from the base studies to examine study heterogeneity. We find that the base papers have the potential for massive multiple testing and multiple modeling with no statistical adjustments. Statistics coming from the base papers are not guaranteed to be unbiased, a requirement for a valid meta-analysis. There is study heterogeneity for the base papers with strong evidence for so called p-hacking in some, possibly many, of the studies. We make two observations: there are many claims at issue in each of the 14 base studies so uncorrected multiple testing is a serious issue. We find that some of the base papers exhibit the characteristics of p-hacking and are therefore not reliable; the resulting meta-analysis is not reliable.