One-Step Generalized Estimating Equations With Large Cluster Sizes

<p>Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.</p

Additional file 3: of Factors associated with the use of cognitive aids in operating room crises: a cross-sectional study of US hospitals and ambulatory surgical centers

Association of reported impact with using the tool regularly (more successful vs. less successful implementation). (DOCX 20 kb

Additional file 2: of Factors associated with the use of cognitive aids in operating room crises: a cross-sectional study of US hospitals and ambulatory surgical centers

Composite score component variables tested for unadjusted association with using the tool regularly (more successful implementation) vs. not (less successful implementation). (DOCX 37 kb

Number of childbirth events observed at each period before and after intervention.

<p>Number of childbirth events observed at each period before and after intervention.</p

Changes in rates of delivery of specific childbirth practices before and after intervention; (2a) On admission; (2b) From pushing until delivery; (2c) Soon after birth (within one hour); (2d); Before discharge (*P value = 0.052; all others p≤0.001).

<p>Changes in rates of delivery of specific childbirth practices before and after intervention; (2a) On admission; (2b) From pushing until delivery; (2c) Soon after birth (within one hour); (2d); Before discharge (*P value = 0.052; all others p≤0.001).</p

Observed in-facility mortality before and after intervention.

<p>Observed in-facility mortality before and after intervention.</p

Demographic characteristics of women and newborns before and after intervention.

a<p>Referred to study facility from another facility after labor started.</p>b<p>Attended fewer than 3 antenatal appointments.</p

Average rate of successful delivery of essential childbirth practices before and after intervention (p<0.001).

<p>Average rate of successful delivery of essential childbirth practices before and after intervention (p<0.001).</p

Frequency of initiation of medication therapy before and after intervention (*p<0.05).

<p>Frequency of initiation of medication therapy before and after intervention (*p<0.05).</p

Additional file 2: of Effectiveness of the WHO Safe Childbirth Checklist program in reducing severe maternal, fetal, and newborn harm in Uttar Pradesh, India: study protocol for a matched-pair, cluster-randomized controlled trial

BetterBirth trial SPIRIT checklist. (DOC 121 kb