Maternal Nutrition and Lactational Infertility. edited by J. Dobbing. Nestld Nutrition, Vevey/ Raven Press, New York © 1985.

Model for Analysis of the Relationship Between Data and Postpartum Data

J-P. Habicht and K. M. Rasmussen

Division of Nutritional Sciences, Cornell University, Ithaca, New York 14853

To identify likely determinants of postpartum infecundity and to understand their relative importance in free-living populations, data must be collected from many women. Under such circumstances, a battery of biochemical and endocrinological tests is not feasible. One must often be content to collect interview data, and the onset of after parturition, the onset of a new , and the of a next child are the only data available for looking at the effects of age, nutritional intake, parity, and other possible determinants of postpartum infecundity. The data about the onset of menstruation are generally thought to relate more validly to and fecundity than are data about conception and birth of a new child, which are affected by many other factors. Breastfeeding is now known to be the most important influence in prolonging postpartum infecundity in populations where malnutrition is prevalent and severe enough to have a concomitant effect on fecundity. To study the effect of malnutrition on fecundity, one must then be able to control for differences in the breastfeeding characteristics which postpone the return of fecundity. The most common means of controlling for breastfeeding in the analysis of interview data from surveys has been by statistical methods, often by the use of ordinary least squares (OLS) linear multivariate regression analysis. This analysis as used is implicitly based on the assumption that the duration of postpartum amenorrhoea is determined by breastfeeding practices, even when menstruation returns before the ceases. This seemed illogical and is in contradiction to present knowledge in endocrinology. These linear OLS statistical analyses intro- duce biases which make any interpretation about other determinants of menstrua- tion impossible. We therefore tried to develop a statistical procedure (1) which

Editor's note: This was not one of the original papers commissioned for the workshop but arose from Dr. Habicht's precirculated commentary on the chapters by McNeilly et al., by Robyn et al., and by Lunn et al., this volume. The form in which it appears here—as an appendix—like the rest of the book, takes account of the discussion which occurred at the workshop itself. 119 120 APPENDICES was more compatible with modern endocrinological knowledge so as to be able to study the effect of determinants of postpartum amenorrhoea and anovulation other than breastfeeding in breastfeeding populations.

MODEL Figure 1 (ref. 1, Table 3) depicts a model which relates breastfeeding to the duration of postpartum anovulation through an inhibiting influence (//).' At birth, H is at a higher level / than at conception. The inhibition falls more quickly when no breastfeeding occurs (slope n) than when partial (i.e., supplemented) - feeding occurs (slope p). This inhibition falls least rapidly when full (unsupple- mented) breastfeeding occurs (slope/). That is, we hypothesize that n

H/n

1 2 S Months after Parturition FIG. 1. Behaviour of H. f, slope when full breastfeeding; p, slope when partial breastfeeding; n, slope when not breastfeeding = 1.

'H reveals our belief that the inhibition is mediated hormonally. APPLICATION OF MODELS 121 feed will ovulate sooner after a birth (at time 1.2 months in Fig. 1) because her H level declines at rate n and falls most quickly to the ovulatory threshold, O. A woman who first fully, then partially, breastfeeds will experience a longer period of postpartum anovulation, since her H rises with full breastfeeding, /, and then falls at a much slower rate, p, with partial breastfeeding than it does, n, with no breastfeeding. When the inhibition (H) falls below a threshold even lower than O, lactation ceases if it has not been previously stopped for other reasons unrelated to the inhibition. Restriction or cessation of lactation before this physiological limit can occur for many reasons: biological (e.g., maternal illness) and behavioural, vol- untary and involuntary. In this model, the relationships between breastfeeding and postpartum anovulation are independent of these reasons, and neither the physio- logical maximum duration of lactation nor the change in inhibition after ovulation is germane. They are therefore not depicted in Fig. 1. This model has implications for the statistical analysis of the relationships of measures of breastfeeding with those of postpartum anovulation and with birth spacing. The statistical techniques which evolve from these implications are devel- oped and illustrated in Habicht et al. (1). The following results are from this paper.

EMPIRICAL RESULTS FROM MODEL Empirically, we find in Malaysian women interviewed in 1975 the mean behav- iour of the H (Habicht et al., ref. 1) as depicted in Fig. 1 for women who fully breastfed half a month and partially breastfed 2 months. These women resumed ovulation at 3.5 months with a 95% confidence limit of 3.2 to 3.8 months.2 The average duration of postpartum anovulation for women who did not breastfeed was 1.2 months with 95% confidence limits of 0.9 to 1.6 months. Empirically, we also find in these data that increasing age is associated with delayed resumption of ovulation, as depicted in Fig. 2. This is due either to an increased span (/ - O) between the H levels at birth and the threshold for ovulation (P<0.05) or to a slower fall of H during partial breastfeeding (/)<0.05). It is not due to a slower fall of H during full breastfeeding, and it is not due to a combination of any of the above (P>0.05). Further analyses show that it is in fact due to the increasing span (/ — O) with age.

REVIEW OF ASSUMPTIONS UNDERLYING THE MODEL AND QUESTIONS ENTAILED (Where papers or discussions from the meeting answered the questions, this is noted.)

2For any single woman with this breastfeeding behaviour, the 95% confidence limits for postpartum amenorrhoea would be 0 to 10 months. 122 APPENDICES

H/n -

Months after Parturition

FIG. 2. Changes in H at two ages according to two equations: (—) 25-year-old women; (...) 45-year-old women; Eq. I, intercept 1 changes with age; Eq. II, slope p changes with age; f, slope when full breastfeeding; p, slope when partial breastfeeding; n, slope when not breastfeeding = 1.

1. H can be thought of as a mean level of inhibition which declines in the absence of suckling (as in Figs. 1 and 2). We will use H in this sense. However, H could also be graphed upside down as a mean level of deinhibition, so that H rises in the absence of suckling. Does this model correspond to what endocrinol- ogistsfeel is the mechanism? Endocrinologists seem to agree that the mechanism appears to be a chain of suckling, nipple stimulation, neural impulse to the , suppressed pulses of gonadotrophin-releasing , which suppresses the , which arrests follicular interaction, which in turn prevents ovulation and menstrua- tion. The links between arrival of the neural impulse in the hypothalamus and suppression of pulses of gonadotrophin-releasing hormone are uncertain. It may not be mediated through , even though levels of prolactin are determined in major part by nipple stimulation in lactating mothers. Our H could be thought of as an abstract integration of suckling influences. However our model would be more credible if either gonadotrophin-releasing hor- mone pulsatility, or whatever depresses that pulsatility, could be transformed math- ematically into a continuous variable with the characteristics which we describe for//. The above sequence describes a single chain of neuronal and hormonal events linking suckling to postpartum anovulation. This is compatible with our model. Another pathway is mentioned as possible by Robyn (this volume): prolactin, elevated by suckling, directly suppresses ovarian susceptibility to luteinizing hor- mone and thus prevents follicle maturation. But apparently this pathway is unlikely to be important physiologically even if it exists. Even if this pathway were to play an important role, so that ovulation is suppressed by two paths, our model could still be valid if both pathways were highly synchronized in their effects. APPLICATION OF MODELS 123

2. At any given moment, the presence or absence of ovulation occurring within a month depends solely on where H is relative to O, the threshold when ovulation resumes. If H is above O, there is no ovulation or it is less probable (/><50%) than if H is at or below O. What evidence is therefor this model? Our statistical analysis with OLS implies no ovulation until H reaches O, and then full ovulation. We believe that is physiologically unlikely but were unable to develop a satisfactory stochastic model. McNeilly's chapter (this volume) appears to show a decreasing repression of luteinization until there is a threshold when ovulation occurs. This corresponds to our model, but he does not think that either our H or O relate to prolactin. Lunn's chapter (this volume) requires the assumption of a threshold and that prolactin be our H. In that chapter, prolactin thresholds are derived from data on a subsample of Gambian women below which women stochastically begin men- struating and ovulating. The prolactin levels observed in well- and poorly nourished women are observed relative to these thresholds to estimate actual onset of men- struation and ovulation. However, the data from Kivu (Vis's comments) showing that menstruation can occur at different levels of prolactin in different populations reinforces scepticism that prolactin corresponds to our H. If it does not, then comparing prolactin levels to a prolactin threshold may not be a good estimate of the onset of ovulation and menstruation. Given this uncertainty, one needs other information to be sure that there really was a difference in fecundity between Lunn's better and less well nourished women. 3. The span (I-O) of / (level of H at parturition) to O (threshold of H when ovulation resumes) is estimated in our model. The levels of / and of O cannot be estimated separately. The level of/ relative to H* and O is determined at parturition when H = I. (H* refers to any H between / and 0.) Is there any meaning in I after birth? The level of O relative to / and H* is determined when H = O in our OLS model and as H is near O in a stochastic model. If / only has a meaning at parturition, then any changes in (I-O) which may occur after parturition in the span I-O must be due to changes in O. Our model would not usually pick up such changes if they were linearly related to the fall of Hn (H in the absence of suckling). However, the finding that age affects the span (I-O) might have been due to I-O changing over time because age and duration of breastfeeding are correlated in our data. This is in fact not the explanation, because the age effect is identical among mothers who do not breastfeed at all, as it was in the total sample. Is there any evidence for a change of (I-O) with time after parturition? Is there any evidence for a change in (I-O) with maternal age? The questions were not answered by this meeting. It is important to note that in Lunn's Fig. 1 (this volume) the first measurements are not taken at parturition but about a month afterwards, so that no initial level is presented. 4. Rates of change in H depend only on suckling intensity. Is this so? The intensity can rise or fall (our data showed only declines in suckling intensity from full to partial to no breastfeeding, but this is not required by the model). 124 APPENDICES

H can actually rise if suckling intensity is high enough. Is this so? Because there is some disagreement as to what H might be, this is difficult to answer. Prolactin is said by McNeilly to rise if suckling is intense enough (obser- vations in two women), and it certainly rises in Lunn's Gambian data. However, there is some doubt whether prolactin corresponds to H. 5. The model does not identify what aspects of suckling intensity should be measured. It does presume that all of the aspects can be reduced to a single meaningful indicator relating to H. What are aspects of suckling [e.g., (a) frequency of breastfeeding, (b) duration of each suckle, (c) timing of suckle, (d) frequency of sucking during a suckle, (e) force of suck] which affect H? Are some of these aspects of suckling so highly correlated that it doesn't matter which one measures? McNeilly, Robyn, and Vis agree that frequency of feeds is important. McNeilly also feels that duration is important if the frequency of feeds falls below five. McNeilly feels that the timing of suckling is also very important: late afternoon and night sucklings affect H much more than morning suckling. Both McNeilly and Robyn agree that above a certain threshold increased suckling does not increase prolactin levels, certainly not to the high levels described by Lunn. The implications of this discrepancy in prolactin levels are not clear for ovulation because, as said previously, the relationship of prolactin to H is uncertain. Masnick suggested that it may not be the absolute amount of suckling which is important but the rate of change in suckling patterns. This concept is not captured by our model. McNeilly's evidence (2) indicates this is not the case. Menstruational ovulation resumes when suckling frequency and duration fall below a certain level, irrespective of the rate of changes in frequency and duration. 6. The response ofHto equal intensity of suckling is the same no matter how long since birth the suckle occurs. This assumption was tested on the Malaysian data, but these data were not good enough to permit an unambiguous answer. Is there any evidence for or against this assumption? 7. Assumption 6 implies that the response of H to suckling is independent of breastfeeding (suckling) experience since birth. Is there evidence to support or refute this assumption? 8. Assumptions 4 and 5 imply that the response to suckling is independent of the level of H. What evidence is there for or against this? 9. The period right after birth might be an exception to assumption 6. It appears from some reports that if the mother never breastfeeds, she resumes ovulation much earlier than if she breastfeeds for a short time, much earlier than would be expected from assumption 6. This would imply a sharper rise of H with suckling right after birth than thereafter. There is evidence for this in the Malaysian data (in women who menstruate for the first time after the cessation of breastfeeding). Is there any evidence for this exception to assumption 5? If so, how long is "right after birth" ? Is this due to mistakes in assumptions 7 and/or 8, or is this exception due to something else? McNeilly describes how repression of follicle maturation is different in lactation (repression of LH) from that during pregnancy (repression of FSH). If the latter is APPLICATION OF MODELS 125 more rapidly reversed, H will fall more quickly if breastfeeding is not initiated than it falls after cessation of breastfeeding. If this is not built into the model, H will appear to have a spurious rise due to the initiation of lactation. In fact, prolactin does rise at the initiation of lactation, so that the rise in H might not be spurious if the prolactin rise corresponds to some underlying rise in H. With so many possible contingencies the answer to this question is unknown. Robyn and McNeilly agree that suckling behaviour after anovulatory menstrua- tion does affect how soon ovulation will return. This means that the proportions of anovulatory used in Habicht et al. (1) may not be true for the Malaysian population, or any other (see item 12 for further elaboration). 10. Further assumptions were made in our paper to estimate the timing of first postpartum ovulation from data about first menstruation. These are reviewed under this item and item 11. The proportion of first menstruations that were ovulatory in the Malaysian data are assumed to be the same as those reported by Perez et al. (3) in a Peruvian population (ref. 1, Table 2). What evidence supports or refutes this assumption? 11. The time from ovulation to menstruation does not depend on the time since parturition or on previous or concurrent breastfeeding patterns. We used a mean of 9 days. This means that the position of H relative to O is irrelevant for the duration between ovulation and menstruation in both the OLS model and a sto- chastic model. What is the evidence on this subject? The consensus is that there is instead little variability (a few days only) in the time from ovulation to menstruation, even though it is slightly prolonged after the first ovulation. 12. Women whose first menstruation is ovulatory are similar to those whose first menstruation is anovulatory for all characteristics affecting the parameters of the model [(I-O) and declines of H with different breastfeeding patterns]. One may thus eliminate women with anovulatory menstruations from the sample to estimate the parameter of the model. What evidence is there for this assumption? We tried to test an alternative assumption, that anovulatory menstruation pred- icated the return of ovulation. We did this by adding a constant 39 days to the postpartum amenorrhoeic interval for all intervals which were presumed (see item 10) to have an anovulatory menstruation. The statistical model could not estimate any parameters when this constant was added. We believe that this means that the assumption of a mean constant is wrong. However, anovulatory menstruation may still predict ovulation, but the interval between the first anovulatory and the subsequent ovulatory menstruation may not be constant. It may depend on all the determinants of H (e.g., the anovulatory to ovulatory interval is prolonged by greater intensity of breastfeeding). In other words, an alternative assumption is that the probability of anovulatory menstruation depends on the relationship ofHtoO. What evidence is there that this is true? The alternative hypothesis appears from McNeilly's and Robyn's work to be correct. This means one should be talking about a third threshold, A, for initiation 126 APPENDICES of anovulatory menstruation. Threshold A would be higher than the threshold for ovulation, O. In that case, first menstruations which are ovulatory would be so because H has fallen so rapidly past A to O that there was no time for an anovulatory menstruation. The proportion of ovulatory to anovulatory first menstruation would then depend on the rate of change of H, the only occasion when the Masnick hypothesis might hold. 13. The reason that the present title of our paper (1) is unsatisfactory is that we do not address the effects of breastfeeding on fecundity (as defined in demography: physiological potential to produce offspring) after the first ovulation. A number of the papers prepared for this conference contain information on this subject, and our model could be extended to deal with this. To do this the following questions need to be answered:

a. Does the level of H affect the likelihood of ovum fertilization (e.g., by affecting transport down the fallopian tube)? b. Does the level of H affect nidation or the maintenance of pregnancy? c. Does the level of H affect the interovulatory interval? McNeilly's work shows that even after H reaches O and ovulation resumes, H may not be adequate for enough luteinizing hormone to assure adequate luteiniza- tion to sustain pregnancy. This means that there is yet another threshold, F, to which H must fall for a woman to become fecund again. 14. We state in our paper that the level of H may determine both the onset of ovulation (when H = O, the threshold for ovulation) and the physiological limit to the duration of lactation (when H = threshold for milk production). This assumption can be made even narrower by postulating that it is the same H which determines both the duration of postpartum anovulation and the duration of lactation, and that the threshold of H for the cessation in lactation is parallel to the threshold of H for the resumption of ovulation. Is there any evidence to address this issue? This could be modelled if all women breastfed to the physiological limit of the lactating interval and reported the cessation of breastfeeding correctly by excluding sucking on a dry breast. This combination of prerequisites is probably never found, so that for the purposes of data analysis in free-living human populations, it is academic but interesting nevertheless. However, this issue was not addressed at this workshop. 15. By what mechanism does malnutrition affect the duration of lactational infertility? a. It raises or lowers /, the initial levels of H at parturition. b. It raises or lowers O, the threshold of H when ovulation reappears. c. It raises the threshold for cessation of lactation above O, permitting a more rapid return of to malnourished mothers. d. It changes the postpartum fall in H for similar breastfeeding practices. e. Through none of the above but through changes in breastfeeding practices because of the following factors: APPLICATION OF MODELS 127 i. Mothers' milk yield reduced, so that the infant suckles more. ii. Inadequate supplementation for an older infant, so that the infant suckles more. iii. Different breastfeeding practices by malnourished mothers not instigated by the child; for example, mothers may have different working patterns during the hunger season.

REFERENCES 1. Habicht J-P, Da Vanzo J, Butz WP Meyers L. The contraceptive role of breastfeeding. Population Studies (in press). 2. McNeilly AS, Glasier AR, Howie PW, Houston MJ, Cook A, Boyle H. Ferility after childbirth: pregnancy associated with breastfeeding. Clin Endocrinol (Oxf) 1983;18:167-73. 3. Perez A, Vela P, Potter RG, Masnick GS. Timing and sequence of resuming ovulation and menstruation after childbirth. Population Studies, 1971;25:491-503.