One point I stressed a fair
bit in the previous two posts is the importance of calculating the RR using
person years rather than group size where appropriate*. This was a major issue in FMHS, as the RR
derived from age-adjusted person years was substantially different to the RR
derived from group size. While this
should make little difference in large adequately randomised (or stratified)
trials such as MCS, there were still many differences of ~4-5%.
FMHS (Men)
|
RR Using Group
Size
|
RR Using
Age-Adjusted Person Years
|
Relative Difference
to RR Using Person Years
|
Major CHD Events
|
0.331
|
0.330
|
+0.3%
|
Total CHD Events
|
0.548
|
0.557
|
-1.6%
|
CHD Mortality
|
0.374
|
0.469
|
-20.3%
|
CVD Mortality
|
0.498
|
0.608
|
-18.1%
|
Total Mortality
|
0.724
|
0.882
|
-17.9%
|
FMHS (Women)
|
RR Using Group
Size
|
RR Using
Age-Adjusted Person Years
|
Relative
Difference to RR Using Person Years
|
Major CHD Events
|
0.334
|
0.393
|
-15.0%
|
Total CHD Events
|
0.539
|
0.635
|
-15.1%
|
CHD Mortality
|
0.446
|
0.659
|
-32.3%
|
CVD Mortality
|
0.603
|
0.859
|
-29.8%
|
Total Mortality
|
0.703
|
1.064
|
-33.9%
|
MCS (Men)
|
RR Using Group
Size
|
RR Using Person
Years
|
Relative Difference
to RR Using Person Years
|
Major CHD Events
|
0.932
|
0.895
|
+4.1%
|
CHD Mortality
|
1.147
|
1.102
|
+4.1%
|
CVD Mortality
|
0.978
|
0.940
|
+4.0%
|
Total Mortality
|
1.032
|
0.992
|
+4.0%
|
MCS (Women)
|
RR Using Group
Size
|
RR Using Person
Years
|
Relative
Difference to RR Using Person Years
|
Major CHD Events
|
1.306
|
1.317
|
-0.8%
|
CHD Mortality
|
1.037
|
1.097
|
-5.5%
|
CVD Mortality
|
1.021
|
1.029
|
-0.8%
|
Total Mortality
|
1.156
|
1.164
|
-0.7%
|
To look at how this would
affect the overall result in a meta-analysis I put two sets of data into the Review Manager V.5.1 software
(RevMan), provided by the Cochrane Collaboration,
one using person years for MCS and FMHS and one using group size
Unfortunately the RR in RevMan
is calculated automatically using the number of events and group size for each
group and can’t be changed. One option I
had would be to enter the number of person years (age-adjusted for FMHS)
instead of the group size. However, as
the weighting for each trial is determined both by the number of events/deaths
and the group size, that method would affect the weighting. So I used some basic algebra to keep the
total number of participants constant but changed the number of participants in
each group so RevMan could automatically calculate the correct RR
The equation for the RR using person years is (E =
events/death, and PY = person years):
RR = (Eexp / PYexp) / (Econ
/ PYcon)
To not affect the weighting the total number of person
year needs to equal the total number of participants (N):
PYexp + PYcon = Nexp + Ncon
Therefore:
PYexp = (Nexp + Ncon) /
(1 + (RR x Eexp / Econ))
PYcon = (Nexp + Ncon) /
(1 + (Eexp / (Econ x RR)))
For ‘CHD events’ I’m using the
number of major CHD events
CHD Events (Group Size)
CHD Events (Person Years)
CHD Mortality (Group Size)
CHD Mortality (Person Years)
Total Mortality (Group Size)
Total Mortality (Person Years)
RR Using Group
Size
|
RR Using Person
Years
|
|
CHD Events
|
0.90 (0.74-1.10)
|
0.90 (0.74-1.10)
|
CHD Mortality
|
0.83 (0.61-1.13)
|
0.88 (0.70-1.10)
|
Total Mortality
|
0.92 (0.79-1.07)
|
1.00 (0.91-1.09)
|
FMHS was the largest study and
is quite an outlier regarding its results for CHD events and CHD
mortality. The inclusion/exclusion and the
figures used for FMHS explains much of the difference between the meta-analyses
by Hooper, et al, Mozaffarian, et al and Skeaff & Miller
CHD Events
|
CHD Mortality
|
Total Mortality
|
|
0.83
(0.69-1.00)
P = 0.073
|
0.84 (0.62-1.12)
P = 0.335
|
0.88 (0.76-1.02)
P = 0.005
|
|
0.81 (0.70-0.95)
P = 0.008
|
0.80 (0.65-0.98)
P = ???
|
0.98 (0.89-1.08)
P = ???
|
|
(Modified Fat)
|
0.82
(0.66-1.02)
P = 0.073
|
0.92 (0.73-1.15)
P = 0.46
|
1.02 (0.88-1.18)
P = 0.81
|
(Modified +
Reduced Fat)
|
0.77
(0.57-1.03)
P = 0.077
|
0.98 (0.76-1.27)
P = 0.88
|
0.97 (0.76-1.23)
P = 0.78
|
The main differences between
Hooper and Mozaffarian was that Mozaffarian included FMHS (RCOT is too small to
count for much and Hooper didn’t have data for CHD mortality in SDHS). Mozaffarian found a (likely) significant
reduction in CHD mortality whereas Hooper didn’t and both found no difference
in total mortality. This because FMHS is
a large trial and got a very favourable result for CHD mortality (even using
person years), but found little difference in total mortality. Simply excluding FMHS (if you wanted to only
include adequately randomised trials (what a novel idea!)) single-handedly removes
the favourable result for CHD mortality, changing the RR to 0.99 (0.83-1.20)
Despite the included trials
being almost identical to Mozaffarian, Skeaff found no significant difference
in CHD mortality and was the only meta-analysis to find a significant reduction
in total mortality. The lack of
significance for CHD mortality was probably due to them using incorrect and
lower values for CHD mortality from MRCT, ODHS and FMHS and not including CHD
mortality from LAVAT and MCS. With less
than 300 CHD deaths and 57.17% of weighting going to DART (N = 194, RR = 1.00)
it’s hardly surprising that their RR of 0.84 was so underpowered. Regarding total mortality, Skeaff and
Mozaffarian included exactly the same trials and had almost exactly the same
numbers, but Mozaffarian got an RR of 0.98 and Skeaff got an RR of 0.88
(significant). The reason why is that
Mozaffarian calculated the RR using person years, whereas Skeaff did
not
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