Analytical bias in studies of pregnancy outcome

Analytical

bias in studies of

pregnancy outcome MAUREEN

HENDERSON,

WILLIAM Baltimore,

.4.

REINKE,

M.D. PH.D.

Maryland

T H I s P A P E R describes three examples of bias met in a study of the effect of significant maternal bacteriuria on pregnancy outcome. They are all problems which can arise when a study group is compared to a population or control group and/or when the results of different studies are compared. All three types of bias are probably well recognized by experienced investigators but we failed to anticipate them so we hope these examples may be of help and interest to others. In most prenatal studies, women at different states of pregnancy enter the study at different times. If pregnancy outcome in two groups of patients is compared, the effect of selection on outcome must be anticipated from the beginning. The earlier in pregnancy women are seen in prenatal clinic the greater the opportunity for a premature delivery while in the study. Two selected groups have to register at the same stages of pregnancy before they have the same probability of pregnancy outcome. Table I is an analysis of gestational length by the stage of pregnancy at registration of 4>771 Negro patients. All 4,771 patients registered before their thirty-sixth week of pregnancy in the University Hospital Prenatal Clinic, Baltimore, between Aug. 1, 1961, and April 30, 1965. Table I shows that the proportion being delivered before the thirty-sixth week of gestation was highest for From the Department Medicine, University School of Medicine. This Health

.rtudy war SerrGe

women who came to the clinic before tile twelfth week of pregnancy. The proportion decreased steadily as patients were first setan later and later in pregnancy. Thirty-three per cent of those who registered before 12 weeks compared with 10 per cent of those who registered between the thirty-second and the end of the thirty-fifth week wer’e delivered prematurely. All women who were delivered before the thirty-sixth week whether or not their infants were live born were included (Table I) . Single live births showed the same trentl. Of mothers of live-born infants registerilq before the twelfth week of pregnancy, 33.85 per cent were delivered of premature infants. The proportion fell steadily as womrn registered later in pregnancy, to a figure of 9.5 per cent of women first seen between the thirty-second and the end of the thirty-fifth week of pregnancy. These data show that women who choose to register at different periods of pregnancy have one different characteristic--namel)r. the expected length of gestation calculatr%d from the reported last menstrual period datcl. As there is a significant correlation between birth weight and length of gestation in theyc data, these women also differ in the cxpcctc~cl birth weights of their infants. One can inft.1 that they are likely to be different in o&r personal characteristics. Some of these personal characteristics will probably he those that again affect infant birth weight. We are accustomed to using age adjusted death rates and attack rates in vital statistics. These data show up a need for more general use of adjusted rates. In this context

of Preventive of Marylnnd

.rupported Grant HD

by Public 00.707.

735

736

Henderson

and Reinke

the adjustment would be for gestational age at prenatal registration. This type of adjustment has to be kept in mind when rates of fetal loss, stillbirths, prematurity and infant morbidity are calculated. The second example of bias is also concerned with appropriately adjusted rates. This source of bias arises when women arc so selected that thr number at risk of premature drtli\.ery in one group is propor-

tionately greater than that of women at risk of premature delivery in thr ,qroup usrcl for comparison. The bias arises \vhen patients included at the beginning of thrx stuclv inept’ dropped out of the study later in pre,~nanc-~ ‘l‘he model for this bias is sl~c)\~n irr ‘I‘al)lt~ 1I and III. Table II shops ;I hq~othc~tic~~i iqwncy d delivery at diffrl-ent rtaq:cx ot’ qcstatiorl of 3 thousand l)atic*rlts. lT\\r, ]JI’~c,c.flt of ttrr patients tlelivc~rc~tl bvfotxh L,(l TI r~.l\s: 3 pc~ cent brtwec~n 2i anti 25 : ‘1 jK’1 c‘rllt lrt\~wl~ 26 anti Xl: ;11it1 I? [“‘I

Table I. Duration

of pregnancy by stage of at prenatal registration

pregnancy

IVeeks’ gestationi at prenatd registration

Ixss

i I

than 12 12 - 15 16-19 “I) 2:‘, 22&_ ‘j 28 - 31

h’o. of worm

Per cent deliuered beforr 36 weeks

908

32.69

157

3 0.6 3

911 1.077 1,0x3 7.12

32 - 35

in

Z-L.63

21n.19 10.19

of delivery

by stage of

pregnancy* Per cent delivered

Ge.rtation (weeks) rp

to

20

‘1 - 2.5 26 - 30 31 - 35

1 de::;ed

2

xl

3 5 15

“9 48 13.5

~ ;:,;:ft

980 951 903 7611

768

Table III.

Effect

of random

patient

l~ct\vec~ll

3.5. l‘abl<~ II also ShO\\~

3 1 arld

tlifa

fourth

column

tlir

r~~mtxi~

oi

I~OII~(‘II

who were still pregnant and at risk or txirlg tlcli\.cred within the stlldy tlllriny thr nest .5 week p(4od. At 20 weeks of prqnancv. 20 women had been clrli\ctrcci and 980 \voinctn wire still at risk of drliwq~. 11uriny the nest period of 5 weeks. ‘2 per c’csnt 111 29 of tllese 980 patients \~cre’ delivered: :il the Tad of the periocl 9.51 patients wt*rf’ lx\’ cent or 48 of these 951 \~ornrn wer(* tit*livcred before the thirty-first UYY~~ of prrq11311C) and at 31 weeks 903 1)aticnts wt‘r~’ still at risk of delivery. Fifteen pf’r CCW~ Of‘ 13.5 of these 9011 pati(,Iltc WW(’ (1(.li\,rrcd brtM-ren 31 and 36 \VWLS of prcgnancy. At the beginnirlr: (,i ttlc. thirt),-sixtll wc~k r)l pr~‘qancy, 760 Izttic’nts had noi txzr77 d(~li\.erc~tl. ‘I‘hr prc7riaturity r~rtc~ ioj t Ilc:c, 1 .0(K) patients XVX. thtxrcsfol(T. 2:i2., 1.OO(i a ratr* of 23.2 per cent.

“5.80 26.93

:16:3

Table II. Frequency

c,c*llt.

tht. nurnbcr of women ~.11tr \vrrfs cleli~er~~~i tlurinx the specified x.veeks of pregnarq~ anti

loss on frequency

of drlix.cry

hy stage 01

pregnancy++ ~ No. at bet ginning of gestation j period

Gestation (weeks) up

to

20

1.000

21 -25

971

26 - 30

80 1

31 - 35

647

/

/ Per cent delivered

NO. deliuered

I /

/ NO. left in .ctudy

/ i

Per cent excluded

'1

30

980

s

‘9

.j

40 97

S-L:! 761

1 I5 15

i 5 I)

1i

15

467

i /

No. excluded

j Renmindrr

9 141

971 801

11-l

&Ii

8’;

-lb7

Analytical

The following hypothesis was stated. If a random 1 per cent of these 1,000 patients had been lost from the study before 20 weeks of pregnancy, and a random 15 per cent had been lost or excluded from the study in each of the next 5 week periods, what would have happened to the total prematurity rate? The effect of losing these proportions of patients during the specified times of pregnancy is shown in Table III. Again, we start with 1,030 patients; 2 per cent are delivered before the twentieth week. So by the end of 20 weeks of pregnancy, 20 patients have been delivered leaving 980 in the study. One per cent (9 patients) was lost or excluded-leaving 971 patients at risk of delivery (in the study) after the twentieth week of pregnancy. During the twenty-first through twenty-fifth weeks of pregnancy, 3 per cent or 29 of the 971 patients were delivered, leaving 942 patients. Fifteen per cent or l-11 of these 941 patients were excluded from further analysis within the study. This left 801 patients to be delivered before the study finished. In the twenty-sixth through thirtieth weeks of gestation, 5 per cent or 40 out of the 801 patients were delivered, leaving 761 patients. Another 15 per cent of these 761 patients or 11-l women were excluded from further analysis within the study. This left 647 patients at the beginning of the thirty-first week of pregnancy. Between the thirty-first and thirty-fifth weeks of pregnancy, 15 per cent or 97 of the 647 women were delivered, leaving 550 pregnant women. Fifteen per cent or 83 of these patients were excluded from further analysis. This left 467 women at risk of being delivered after the thirty-fifth week of pregnancy. In this analysis, 186 patients were delivered before 36 weeks of pregnancy. At the end of the study, 653 were available for analysis. The prematurity is? therefore, 186 divided by 653-a rate of 28.5 per cent. In this model the prematurity rate is increased by changing the total number of study patients at risk of delivery during different stages of pregnancy. Table IV shows how the prematurity rate changed

bias

in pregnancy

outcome

studies

737

when random patients were similarly ~‘Iost” from an actual population of 2,576 Negro patients. These patients registered for prcnatal care between Aug. 1, 1961, and July 31, 1963. Their prematurity rate was illcreased from 22.63 to 26.74 per cent by application of a similar random loss of patients. The third problem of bias is that of study end point definition. \$‘hen pregnant women rnter a study at intervals over a period of time, measurements of pregnancy outconrc can be varied by changing the defined study end point. Bias introduced by differences in end point definition is relatively more inrportant in studies of short duration. FCII simplicity this discussion is limited to prosmaturity defined as a pregnancv of less than 36 weeks’ duration. A population of pregnant women can 1~ selected in the following ways: 1. A defined group of patients who register in a prenatal clinic is followed through delivery. These data should not be analyzed until all women who registered have been delivered because deliveries during the first and latter periods of the study will not truly reflect the over-all pattern of results. Women who arc delivered during the first part of any study do so within a relatively short time after registration, and the group includes women who arc delivered early and excludes patients whose pregnancies are particularly long. The last few months of the study will tend to exclude patients who arc delivered early and include relatively more patients whose pregnancies are full-term OI longer. Fig. 1 shows a distribution of births before 28 weeks; between 28 and 35 weeks: and during or after the thirty-sixth week of gestation. This is the distribution of pregnancy durations of the 2,576 Negro patients included in the second example. Fig. 2 shows that the distribution of pregnancies less than 28 weeks is to the left of the other two distributions. The distribution of pregnancies before 36 weeks is also to the left of the curve for pregnancies ending tlurin< or after the thirty-sixth week. 2. The second way of selecting prenatal patients is to include all women between

738

Henderson

and

Reinke

160 cn w a

2 120 i iz

’ 80 a w 2 = 40,

r YAM NUMBER

OF

I

TOTAL

m w

NUMBER NUMBER

DELIVERIES

BY

MONTH

OF

DELIVERY

NUMBER LESS LESS

THAN THAN

36 28

WEEKS WEEKS

GESTATION GESTATION

rLnbCRl”“E

n

A S&

N D J F f416:

OISTRIBUTION

J J

HE WOMEN OELIVEREO EFORE THE 36TH WEEK OF GESTATION

PERCENTAGE OISTRIBUTION BY MONTH OF OELIVERV OF THE 04 WOMEN OELIVEREO BEFORE THE 28TH WEEK OF GESTATION

A SONOJ 1963

Fig. 2.

FM 1964

Analytical

AUGUST, 6.6%

1961 -MARCH, 28.7 “10

1962 I 1962 75 4% 1

DECEMBER,

1962

AUGUST. 1963 0.2% 148%

El lxssi El

-JULY,

1963

-MARCH,

1964 85 0 %

GESTATION

LESS

GESTATION

28-35

GESTATION

36

Fig. 3. Percentage duration of gestation tier 8 month periods.

THAN

28

WEEKS

WEEKS WEEKS

AND

OVER

distribution at deliwry

of deliveries by during consecu-

defined dates of both registration and deli\,ery. In this selection the early bias will be present but will not be compensated by the tail-end of the survey. This group will have a higher prematurity rate than its total cohort. The degree of bias in this case diminishes with the length of the survey. Fig. 3 shows the variation in prematurity rates in consecutive 8 month periods of time in the same population of Negro women. The high Table IVeek

IV.

Prematurity

of gestation at delivery

No. of

Under 20 21 -25 26 - 30 31-35 36 and over Total

No.

at risk delivery

2,576 2,528 2,125 1.728 1,214

of womrn,

?..i76:

tNo. of patients included 443: p~rmatority ratr, 26.74.

Table

rate by random

total

in study

V. Distribution

patient

loss during

NO. delivered

No. still in study

22 29 92 300 1,214

2,554 2,499 2,033 1,428

dcliwted thlou
of pregnancy

before drtircry

36 werk,, (2,576

durations

in pregnancy

-

point

of

study

March 31, 1962 Nov. 30, 1962 Tulv 31. 1963 YDeiiver; of total

registrants

( No, delivered 167 1,134 2,118 2,576

studies

739

NO. excluded

1 15 15 15 prpmatuvilv T

1.6i7:

by variations

)

care*?

Per cent e.rcluded

383; !Jl!?)

prenatal

tat?.

No.

“;4~)‘” 6.6 4.4 3.9 3.3

Remainder

26 371 305 21+

2,528 2,125 1,728 I.?14

L’?.tii.

of thew

\tho

urtc

drlivrtrd

twfurr

‘i6 \\s.eks,

of study end points Duration

End

outcome

proportion of premature deliveries in the first 8 months and the low proportion in the last 8 months are obvious. Table V shows how the results of pregnancy outcome actually varied when analysis was carried out at different defined end points. These are the same delkreries of Negro patients who re,qistered between Aug. I, 1961. and July 31, 1963. After the first 9 months~~~that is, at the end of March, 1962, 6.6 per cent of the patients had been delivered before the twenty-eighth week of preg-nancy; 28.7 per cent had been delivered between the twentyeighth and the thirty-fifth weeks of pregnancy; the remaining 64.7 per cent \\erc delivered during or after the thirty-sixth week. Analyses at this time shelved that 35.3 per cent of patients xvho entered the study had premature deliveries. By Nov. SO. 1962, the study had been in progress fog 16 months and 1.13-l women had been delivered. Four and four-tenths pc-r cent ilad been delivered before 28 weeks of plegthe twerltynancy; 21.8 per cent between eighth and thirty-fifth weeks of pregnancy; and 73.8 per cent during or after the thirtysixth week. The prematurity rate was now 26.2 per cent--9 per cent lower than that of 35.3 per cent observed 8 months earlier.

647%

APRIL, 1962-NOVEMBER, 4% 20 68 %

bias

of

1

gestation

28(~,~ 28.7 21.8 20.5 19.5

(weekA)

/

‘j6 ~~~64.7 73.8 75.6 77.2

740

Henderson

and

Reinke

‘The third end point selected is that of July 31, 1963--2-1 months after the study began- -2,118 women had been delivered b) this time. Three and nine-tenths (4 per cent of them:I were delivered before 28 weeks; 20.5 121 per centj were delivered between 28 and 35 weeks; and 75.6 per cent were delivered during the thirty-sixth wee.k or later. Here we had a prematurity rate of 24.4 per cent. ‘This rate is much closer to the prc\ious rate of 26.2. When all 2.576 registered patients had been delivered, 3.3 per cent had been delivered beforc the twenty-eighth week; 19.5 (20 per cent) were delivered between 28 and 35 weeks; and 77.2 per cent were delivered during or after the thirty-sixth week. .4 total of 22.8 per cent of all registered patients were delivered prematurely. The last patient was delivered in Febru-

Summary

‘l’his report has described thr(a(s tylxs 01 bias introduced into analyses ol studks (11 pregnancy. In each case the hiah C~IIW frour selcsction of patients for final analvsis. ‘1 IIt, application of the examples of bias describ~l is not rpstrictrd to studies of pregnancy oustcome. Anv comparative stud); continued (IL’~‘I an intcr\xl of time is open to sinlilar opportunities for sc‘lection leading to sinlilar prohlerns of bias. It is hoped that this report \%ill rmphasi~c the need to control seicction tltiring thr study or to use adjusted r,~tcs clurlrlrr analysis.