Mean from Median Estimation in Longitudinal Meta-Analysis of Quality of Life in Radiation Oncology Patients

Meta-analysis of longitudinal data, where some of the studies report results with means and standard errors while others use medians and ranges, is a complex analytical problem with several challenges which must be overcome. Existing methods for estimating means from medians and either ranges, interquartile ranges, or both have not previously been evaluated in a longitudinal setting. In this work, a simulation study was used to estimate mean bias, between studies variance bias, and coverage of confidence intervals in a longitudinal setting. A second simulation study estimated the variance of meta-analysis results from a given set of studies that may be attributed to a random subset of those studies reporting medians rather than means. Finally, the methods were used to evaluate a real data set measuring 15 different domains of quality of life for oncology patients undergoing radiotherapy. Mean and between studies variance biases were generally small when underlying data were normally distributed or moderately skewed, but they became more severe as the level of skewness increased and as the proportion of studies reporting medians increased. Similarly, coverage levels were high for normal or moderately skewed data but fell to zero in some instances with highly skewed data and when a high proportion of medians were reported. Within a given set of studies, the variance of mean estimates was low when underlying data were normal or moderately skewed, but increased as the data became more skewed and as the proportion of studies reporting medians increased. Measures in the real data fell into two broad classes: measures of functioning and measures of problems. Among oncology patients, measures of function tended to decrease immediately following radiotherapy before rebounding to levels higher than baseline while measures of problems tended to increase initially before falling to levels at or below baseline values.