R practice: Meta-analysis (2)Minato Nakazawa
7 February 2011
1 History - cntd.
As agricultural studies developed, some classic statistic textbooks started to include the explanation about statistical methods
to integrate the results of several independent studies. For instance, Tippet’s (1931) “The Methods of Staitstics” and Fisher’s(1932) “Statistical Methods for Research Workers” gave such explanations.

1.1 Trials to integrate the results of the effects of treatment
The first study to integrate the results of the effects of treatment was done by Beecher (1955) about the effect of placebo(Table 1.2). In mid-20th century, placebos were administered to patients for various purposes (typically reducing varioussymptoms like pain after surgery, headache, and others).
Table 1.2 Therapeutic effectiveness of placebos in several conditions.
Cond.
Study
Placebo agent
SPOWP
Keats AS, Beecher HK (1950) J. Pharmacol & saline
Exper. Therap., 100: 1-13.

routeiv

No. patients118% relieved
21

SPOWP

Beecher HK et al. (1951) U.S. Armed ForcesM.J., 2: 1269-76.

salinesc2931

SPOWP

Keats AS et al. (1951) JAMA, 1761-3.

saline

iv

3426

SPOWP

Beecher HK et al. (1953) J. Pharmacol & Exper. Therap., 109: 393-400.

lactoseoral

5236444040
263432SPOWP

Lasagna L et al. (1954) Am J Med, 16: 770-9.

saline

sc

1420
15
21
15
1550
37
53
40
40
15

CoughGravenstein JS et al. (1954) J Appl Physiol,
7: 119-39.

lactoseoral

22233643

DIMC

Lasagna L et al. (1955) JAMA, 157: 1006-20.

salinesc20 (normal)
30 (post-addicts)

3030PFAP

Evans W, Hoyle C (1933) Quart J Med, 2:311-38.

Na2 CO3oral6638PFAP

Travell J et al. (1949) Ann NY Acad Sci USA,
52: 345-53.

“placebo”

oral

1926PFAP

Greiner T et al. (1950) Am J Med, 9: 143-55.

lactose

oral

27

38

HeadacheJellinek (1946)

lactose

oral

199

52

Seasickness

Gay and Carliner (1949)

lactose

oral

3358

AT

Wolf S, Pinsky RH (1954) JAMA, 155: 339-41.

lactoseoral

3130Exp. coughHillis (1952)salinesc

1 (many exp.)

37

ColdDiehl HS (1933) JAMA, 191: 2042-9.

lactoseoral

353535.2±2.2%(ave±se)SPOWP: severe post-operative wound pain; DIMC: drug-induced mood changes; PFAP: pain from angina pectoris; AT: anxiety andtension

1110 (acute)48 (subacute)
Summary 1,082 (total)

Beecher randomly picked up 15 clinical trials and calculated the mean and standard error of the proportions of patients
who gained satisfactory results. The result was 35.2 ± 2.2% patients gained satisfactory results by placebo. The title of hispaper was “The Powerful Placebo”*1 .
The calculation of mean and standard error by R is as follows. I (Minato Nakazawa) think that the mean should be weighedby the number of samples, but the auhtor applied simple mean.
¶³
NoPat <- c(118, 29, 34, 52, 36, 44, 40, 14, 20, 15, 21, 15, 15, 22, 23, 20, 30,66, 19, 27, 199, 33, 31, 1, 110, 48)
Satisf <- c(21, 31, 26, 40, 26, 34, 32, 50, 37, 53, 40, 40, 15, 36, 43, 30, 30,38, 26, 38, 52, 58, 30, 37, 35, 35)
Satisf2 <- c(21, 31, 26, 33, 39, 40, 30, 30, 38, 26, 38, 52, 58, 30, 37, 35, 35)sum(NoPat)sum(NoPat*Satisf)/sum(NoPat)mean(Satisf)
sd(Satisf)/sqrt(length(Satisf))mean(Satisf2)
sd(Satisf2)/sqrt(length(Satisf2))µ´
However, the invention of the word “meta-analysis” and enthusiastic studies about its methodology were done in social
scientific fields, amongst education studies. In the field of education studies, there were many methods of education withenourmous papers. Reviewing them for summary tended to be subjective and biased, because the selection and evaluation
largely depended on the specialty and interest of the reviewer.
The word “meta-analysis” was first used by Glass (1976) who was psychologist. As the milestone book in the social sciencefields, Cooper and Hedges (1994) published “The Handbook of Research Synthesis”.
Introduction of meta-analysis into the clinical trial was done by Richard Peto, one of the famous British statistician. It is very
famous that Yusuf et al. (1985) applied the Peto’s design to secondary preventive effect of beta blocker against heartattack.
Table 1.3 shows the result of meta-analysis of 15 RCTs about the preventive effect (reduction of mortality) of long-term
administration of beta-blocker by Peto’s method. In R, it may be supported by metafor package.

*1 Beecher HK (1955) The powerful placebo. JAMA, 159(17): 1602-6.

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