Estimating the mean and variance from the median, range, and the size of a sample

BACKGROUND: Usually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial. METHODS: In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data. RESULTS: We found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n ≤ 15). For moderately sized samples (15 <n ≤ 70), our simulations show that the formula range/4 is the best estimator for the standard deviation (variance). For large samples (n > 70), the formula range/6 gives the best estimator for the standard deviation (variance). We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy. CONCLUSION: Using these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported

Randomised phase III trial of carboplatin plus etoposide vs split doses of cisplatin plus etoposide in elderly or poor-risk patients with extensive disease small-cell lung cancer: JCOG 9702

We compared the efficacy and the safety of a carboplatin plus etoposide regimen (CE) vs split doses of cisplatin plus etoposide (SPE) in elderly or poor-risk patients with extensive disease small-cell lung cancer (ED-SCLC). Eligibility criteria included: untreated ED-SCLC; age ⩾70 and performance status 0–2, or age <70 and PS 3. The CE arm received carboplatin area under the curve of five intravenously (IV) on day 1 and etoposide 80 mg m−2 IV on days 1–3. The SPE arm received cisplatin 25 mg m−2 IV on days 1–3 and etoposide 80 mg m−2 IV on days 1–3. Both regimens were given with granulocyte colony-stimulating factor support in a 21–28 day cycle for four courses. A total of 220 patients were randomised. Median age was 74 years and 74% had a PS of 0 or 1. Major grade 3–4 toxicities were (%CE/%SPE): leucopenia 54/51, neutropenia 95/90, thrombocytopenia 56/16, infection 7/6. There was no significant difference (CE/SPE) in the response rate (73/73%) and overall survival (median 10.6/9.9 mo; P=0.54). Palliation scores were very similar between the arms. Although the SPE regimen is still considered to be the standard treatment in elderly or poor-risk patients with ED-SCLC, the CE regimen can be an alternative for this population considering the risk–benefit balance