Meta-analysis and the reversed Theorem of the Means.

Conventional meta-analysis estimators are weighted means of study measures, meant to estimate an overall population measure. For measures such as means, mean differences and risk differences, a weighted arithmetic mean is the conventional estimator. When the measures are ratios, such as odds ratios, logarithms of the study measures are most frequently used, and the back-transform is a weighted geometric mean, rather than the arithmetic mean. For numbers needed to treat, a weighted harmonic mean is the back-transform. The Theorem of the Means effectively states that unless all of the studies have an equal result, the arithmetic mean must be greater than the geometric mean, which must be greater than the harmonic mean. When the weights are fixed sampling weights, the inequalities are in the expected direction. However, when the weights are the usual reciprocal variance estimates, the inequalities go in the opposite direction. The use of reciprocal variance weights is therefore questioned as perhaps having a fundamental flaw. An example is shown of a meta-analysis of frequencies of two classes of drug-resistant HIV-1 mutations.

Calcineurin inhibitor substitution with sirolimus vs. reduced-dose calcineurin inhibitor plus sirolimus is associated with improved renal dysfunction in heart transplant patients.

Heart transplant (HTx) patients are at risk of developing renal dysfunction. Sirolimus has been used as an alternative for calcineurin inhibitors (CNI) in transplant patients with renal dysfunction. Recent data suggest that the combination of sirolimus with a CNI is associated with a deterioration of renal function in renal transplant patients. The purpose of the present study was to compare the effect on the creatinine clearance (CrCl) of heart transplant (HTx) patients with renal dysfunction (RD) on CNI-based sirolimus-free regimens of conversion to either reduced-dose CNI plus sirolimus or outright substitution of CNI with sirolimus. We retrospectively identified 29 treatment switches for 26 patients with RD defined as a decline in the CrCl > 25% post-HTx. Treatment switches were divided into two groups. Group 1 included 13 switches in 13 patients (four women, nine men, age 62 +/- 10 yr) in whom sirolimus replaced CNI. Group 2 included 16 switches in 15 patients [two women, 13 men (one man underwent two such switches), age 61 +/- 9 yr] in whom CNI dose was reduced and sirolimus was added. Two men appear in both groups. Average follow-up was 10.4 +/- 3.2 months. Overall mortality, rejection, and side-effects rates were comparable between groups. At 12-months post-switch, the mean CrCl had increased from 48 +/- 15 at time of treatment switch to 56 +/- 22 mL/min in group 1 and decreased from 53 +/- 19 to 47 +/- 17 mL/min in group 2 (p = 0.02). In conclusion, substitution of CNI with sirolimus provided improved renal recovery compared with lower-dose CNI plus sirolimus in HTx patients with renal dysfunction.

Statistical analysis of correlated data using generalized estimating equations: an orientation.

The method of generalized estimating equations (GEE) is often used to analyze longitudinal and other correlated response data, particularly if responses are binary. However, few descriptions of the method are accessible to epidemiologists. In this paper, the authors use small worked examples and one real data set, involving both binary and quantitative response data, to help end-users appreciate the essence of the method. The examples are simple enough to see the behind-the-scenes calculations and the essential role of weighted observations, and they allow nonstatisticians to imagine the calculations involved when the GEE method is applied to more complex multivariate data.