After reviewing hits and reading all the relevant looking papers and following citations, the most useful were:
The overall thrust of the meta-analyses is that there is consistent and substantial evidence that regular vitamin D3 supplementation reduces all-cause mortality somewhere in the RR=0.90-1 range, that vitamin D2 may be worse but calcium seems irrelevant, and this effect seems to be general: the observable between-study heterogeneity is very small despite large differences in subject populations by gender, age, and dosage, and subgroup analyses do not find the effect confined to particular demographics or that a reduction in a particular disease is driving the ACM reduction (which while potentially due to lack of power, would be consistent with the generality of benefits in both the correlational and Mendelian Randomization studies).
The meta-analysis itself can be reproduced given Bolland’s forest plot & table, Figure 5.
vitaminD <- read.csv(stdin(), header=TRUE,
colClasses=c("factor","integer","integer","integer","integer","integer","logical"))
Study, Year,E.deaths, E.n, C.deaths, C.n,Calcium
Inkovaara, 1983, 41, 181, 26, 146, FALSE
Corless, 1985, 8, 41, 8, 41, FALSE
Ooms, 1995, 11, 177, 21, 171, FALSE
Lips A, 1996, 223, 1291, 251, 1287, FALSE
Komulainen, 1998, 2, 232, 2, 232, FALSE
Meyer, 2002, 169, 569, 163, 575, FALSE
Bischoff, 2003, 1, 62, 4, 60, FALSE
Cooper, 2003, 0, 93, 1, 94, FALSE
Latham, 2003, 11, 121, 3, 122, FALSE
Trivedi, 2003, 224, 1345, 247, 1341, FALSE
Avenell, 2004, 4, 70, 3, 64, FALSE
Harwood, 2004, 24, 113, 5, 37, FALSE
Aloia, 2005, 1, 104, 2, 104, FALSE
Flicker, 2005, 76, 313, 85, 312, FALSE
Grant, 2005, 438, 2649, 460, 2643, FALSE
Broe, 2007, 5, 99, 2, 25, FALSE
Burleigh, 2007, 16, 101, 13, 104, FALSE
Lappe, 2007, 4, 446, 18, 734, FALSE
Lyons, 2007, 947, 1725, 953, 1715, FALSE
Smith, 2007, 355, 4727, 354, 4713, FALSE
Björkman, 2008, 27, 150, 9, 68, FALSE
Chel, 2008, 25, 166, 33, 172, FALSE
Prince, 2008, 0, 151, 1, 151, FALSE
Zhu, 2008, 0, 39, 2, 81, FALSE
Lips B, 2010, 1, 114, 0, 112, FALSE
Sanders, 2010, 40, 1131, 47, 1125, FALSE
Glendenning, 2012, 2, 353, 0, 333, FALSE
Inkovaara, 1983, 2, 353, 0, 333, TRUE
Chapuy A, 1992, 258, 1634, 274, 1636, TRUE
Dawson-Hughes, 1997, 2, 187, 2, 202, TRUE
Baeksgaard, 1998, 0, 80, 1, 80, TRUE
Krieg, 1999, 21, 124, 26, 124, TRUE
Chapuy B, 2002, 70, 389, 43, 194, TRUE
Harwood, 2004, 17, 75, 5, 37, TRUE
Meier, 2004, 0, 30, 1, 25, TRUE
Brazier, 2005, 3, 95, 1, 97, TRUE
Grant, 2005, 221, 1306, 217, 1332, TRUE
Porthouse, 2005, 57, 1321, 68, 1993, TRUE
WHI trials, 2006, 744, 18176, 807, 18106, TRUE
Bolton-Smith, 2007, 0, 62, 1, 61, TRUE
Zhu, 2008, 0, 39, 2, 41, TRUE
Salovaara, 2010, 15, 1718, 13, 1714, TRUE
library(metafor)
rem <- rma(measure="RR", ai=E.deaths, bi=(E.n-E.deaths), ci=C.deaths, di=(C.n-C.deaths),
data=vitaminD, method="REML"); rem
# Random-Effects Model (k = 42; tau^2 estimator: REML)
#
# tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0015)
# tau (square root of estimated tau^2 value): 0
# I^2 (total heterogeneity / total variability): 0.00%
# H^2 (total variability / sampling variability): 1.00
#
# Test for Heterogeneity:
# Q(df = 41) = 36.5200, p-val = 0.6699
#
# Model Results:
#
# estimate se zval pval ci.lb ci.ub
# -0.0354 0.0186 -1.8990 0.0576 -0.0719 0.0011
## since I^2=0, this is equivalent to a fixed-effect meta-analysis:
fem <- rma(measure="RR", ai=E.deaths, bi=(E.n-E.deaths), ci=C.deaths, di=(C.n-C.deaths),
data=vitaminD, method="FE"); fem
#
# Fixed-Effects Model (k = 42)
#
# Test for Heterogeneity:
# Q(df = 41) = 36.5200, p-val = 0.6699
#
# Model Results:
#
# estimate se zval pval ci.lb ci.ub
# -0.0354 0.0186 -1.8990 0.0576 -0.0719 0.0011
## 'metafor' works in log RR, so convert the log RR estimates back to RRs:
exp(-0.0719); exp(-0.0354); exp(0.0011)
# [1] 0.9306239536
# [1] 0.9652192513
# [1] 1.001100605(Oddly, the per-study deaths/_n_s in the Bolland forest plot/table don’t add up to the claimed totals, but are short by a few dozen each; since the RR calculated by metafor works out to be about the same, I assume it has something to do with how Bolland decided to handle including multiple subgroups from studies and is not important.)