The Importance of Using Person Years to Calculate Relative Risk

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 = (E_exp / PY_exp) / (E_con / PY_con)

To not affect the weighting the total number of person year needs to equal the total number of participants (N):

PY_exp + PY_con = N_exp + N_con

Therefore:

PY_exp = (N_exp + N_con) / (1 + (RR x E_exp / E_con))

PY_con = (N_exp + N_con) / (1 + (E_exp / (E_con 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
Skeaff & Miller (2009)	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
Mozaffarian, et al (2010)	0.81 (0.70-0.95) P = 0.008	0.80 (0.65-0.98) P = ???	0.98 (0.89-1.08) P = ???
Hooper, et al (2012) (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
Hooper, et al (2012) (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