1 Biostatistics Branch, MD A3-03, National Institute of Environmental Health Sciences, PO Box 12233, Research Triangle Park, NC 27709, 2 Institute for Reproductive Health, Georgetown University, Washington, DC, USA and 3 Department of Statistics, University of Padua, Padua, Italy
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Abstract |
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Key words: Bayesian/cervical secretions/fecundability/fertile interval/natural family planning
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Introduction |
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Many couples practising periodic abstinence to avoid pregnancy do not use the ovulation or symptothermal methods, or use them incorrectly, possibly due to the complexity and extensive teaching process needed. The TwoDay Algorithm has been proposed as a simple alternative to these methods (Sinai et al., 1999). The TwoDay Algorithm predicts a woman to be fertile on a given day if she notices secretions on that day or the day before, where secretions are broadly defined to include symptoms of dampness without noticeable mucus or discharge, noticeable mucus without discharge, or visible vaginal discharge, excluding that attributable to menstruation, intercourse or known occurrence of disease. The woman using the TwoDay method does not need to distinguish among types of secretions, but merely to note whether or not she has any.
The aim of this article is to assess the relationship between secretions and day-specific fecundability in order to evaluate the theoretical effectiveness of the TwoDay Algorithm. The efficacy of natural family planning (NFP) methods, which rely on mucus characteristics, is thought to be due to accurate prediction of the fertile days through prediction of impending ovulation. Our hypothesis is that the presence of secretions is predictive of not only impending ovulation, but also of the day-specific pregnancy probabilities within the fertile interval defined relative to ovulation. Using data from a large multinational European fecundability study (Colombo and Masarotto, 2000), we estimate (i) the day-specific probabilities that secretions were present on a particular day within the fertile interval or on the day before; (ii) the day-specific probabilities of conception conditional on secretion status for couples having intercourse on a given day relative to a basal body temperature (BBT)-based proxy for ovulation; and (iii) the day-specific probabilities that the TwoDay Algorithm fails to predict fertility for a given day in the fertile interval and that intercourse on that day results in a pregnancy.
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Materials and methods |
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In each menstrual cycle, women kept daily records of BBT, cervical mucus symptoms and coitus. Cycles in which some form of contraception was used (e.g. condom) were excluded from the analysis. For our purposes, the daily mucus symptom data described in Table I are used to classify each day as covered or not covered by the TwoDay Algorithm. The daily BBT data are used to estimate the day of ovulation within each menstrual cycle (for cycles in which sufficient BBT data are available) using the three over six rule (Marshall, 1968
) as described by Colombo and Masarotto (Colombo and Masarotto, 2000
). We use a BBT-based proxy for ovulation day instead of the cervical mucus peak, since the daily mucus symptom measurements may be informative about measurement error in the peak, causing bias in evaluation of the effects of secretions on the day-specific probabilities of conception. Out of 7288 menstrual cycles of data, there is sufficient information to identify a BBT reference day in 5860 cycles. A total of 2832 cycles remained after excluding cycles with no reported intercourse acts within an 11 day window beginning eight days prior to and ending two days after (8,2) the identified ovulation day. Out of the remaining cycles, there were 434 detected pregnancies.
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Estimating the day-specific probabilities of coverage
In order for the TwoDay Algorithm to cover a given day relative to ovulation (say day k), there must be noticeable secretions on that day (k) or the day before (k1). We were interested in obtaining estimates of the probabilities of coverage for different days in an 11 day (8,2) fertile window around the identified ovulation day. Although we could simply calculate the proportion of cycles covered on day k, for k = 8,7,...,1,2, binomial standard errors and confidence limits are not valid in the presence of heterogeneity among women and among different menstrual cycles from a given woman. Such heterogeneity can result from differences between women and cycles in the frequency of days with secretions. To account for and obtain information about dependency in the coverage indicators, we fitted a multilevel probit model (Chib and Greenberg, 1998; Dunson, 2000
) with vague priors chosen for the parameters as Spiegelhalter et al. have described (Spiegelhalter et al., 1996
).
Modelling the probability of pregnancy
We were also interested in assessing the relationship between the presence of noticeable secretions and the daily probabilities of pregnancy in cycles with intercourse on a given day relative to ovulation. Since the specific intercourse act responsible for a pregnancy cannot be determined with certainty in cycles having multiple days with intercourse, a statistical model is used to relate the intercourse pattern relative to ovulation to the probability of pregnancy. This approach has been used previously for incorporating information from cycles with multiple intercourse acts in estimating day-specific pregnancy probabilities (Barrett and Marshall, 1969; Wilcox et al., 1995
; Colombo and Masarotto, 2000
).
Most analyses of this type have used either the Barrett and Marshall or the Schwartz et al. models (Barrett and Marshall, 1969; Schwartz et al., 1980
). These models are based on the assumption that batches of spermatozoa introduced into the reproductive tract on different days mingle and then compete independently in attempting to fertilize the ovum. A complication of the ESDF data set (and of most data sets of this type) is that the majority of couples contribute multiple menstrual cycles of data and there is evidence of heterogeneity among couples in biologic fecundability, defined here as the probability of pregnancy in a menstrual cycle conditional on intercourse behaviour. Also, as low concentrations of cervical mucins result in impaired sperm motility (Eriksen et al., 1998
), we expect that cervical secretions are positively correlated with fecundability even when adjustment is made for the timing of intercourse relative to ovulation.
To account for these important features of our data, we have used the following model for the probability of pregnancy in a menstrual cycle:
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where Ai is the cycle viability probability for couple i, which is the probability that the aggregate of all factors not related to timing of intercourse or days of cervical secretions are favourable to pregnancy; Cijk and Xijk are indicators of secretions (defined by having secretions that day or the day before, the TwoDay Algorithm) and of intercourse respectively, on day k of cycle j from couple i; pk is interpretable as the probability that pregnancy would occur with intercourse only on day k if the cycle were viable and day k met the criterion for secretions; and R accounts for a multiplicative change in the day-specific pregnancy probabilities due to the absence of secretions on a given day or the day before. The probability of pregnancy for couple i in a cycle with intercourse on only day k is Aipk if day k meets the criterion for secretions, and is otherwise AipkR. If the occurrence of secretions conveys an increased likelihood that intercourse on a particular day results in a clinical pregnancy, then R should be <1. By accounting for differences in the day-specific pregnancy probabilities between days covered and those not covered by the TwoDay Algorithm, this model extends an approach proposed in earlier work (Dunson and Zhou, 2000).
Following Dunson and Zhou, we used a probit mixture model for the couple-specific cycle viability probability Ai (Dunson and Zhou, 2000). Informative prior distributions were chosen for the parameters in this probit model and for the day-specific pk based on results from an analysis (Dunson and Weinberg, 2000a
) of the Wilcox et al. data (Wilcox et al., 1995
). Since, to our knowledge, there are no previous data relating the occurrence of secretions directly to changes in day-specific fecundability, we chose a vague (i.e. non-informative) prior for R. We used an MCMC algorithm (Dunson and Zhou, 2000
) to fit the model, after incorporating a Metropolis-Hastings step (Hastings, 1970
) for the parameter R and a data augmentation step (Tanner and Wong, 1987
) for imputing the coverage indicators for days on which coverage data are unavailable (e.g. due to missing secretion information).
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Results |
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Discussion |
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The primary goal of this article was to assess the relationship between secretions and the daily probabilities of pregnancy in order to evaluate the theoretical effectiveness of the TwoDay Algorithm. We focused our evaluation on the sensitivity of the TwoDay Algorithm and not on the specificity, since estimates of the average number of days identified as fertile (9.0) and of the probabilities of misclassification for days outside the fertile interval have been reported (Sinai et al., 1999). In addition, although the data from the ESDF are extremely informative about the association between fecundability and the occurrence of secretions within the fertile interval, other data sets are more appropriate for evaluation of the distributions of mucus characteristics across the cycle.
We found that the days relative to ovulation on which intercourse has a non-negligible probability of resulting in a pregnancy are typically predicted to be fertile by the TwoDay Algorithm. In addition, we found that intercourse on any given day relative to ovulation is significantly more likely to result in a pregnancy if the TwoDay Algorithm predicts that day to be fertile; that is, if there were noticeable secretions on that day or the day before. Finally, we found that if typical women use the TwoDay Algorithm, their estimated probability of becoming pregnant will be low; though the acceptability of the approach among users and providers of natural family planning methods remains to be fully evaluated. In addition, it appears that secretion data are informative about not only the timing of the fertile days in the cycle but also the probability of pregnancy on a given day relative to ovulation.
Although the efficacy of methods that use mucus and secretion data to identify the fertile days of the menstrual cycle has long been recognized (Guido et al., 1997), to our knowledge these are the first data demonstrating a relationship between secretions and day-specific fecundability adjusting for the timing of intercourse relative to the identified ovulation day. Considering the imprecision and subjectivity inherent in classifying a day as having detectable secretions, the magnitude of the difference in the probabilities of pregnancy between days covered and those not covered by the TwoDay Algorithm is striking. Intercourse on a particular day is ~half as likely to result in a pregnancy if there were no noticeable secretions on that day or the day before. Our data provide further evidence of the important link between mucus and vaginal moisture and human fertility. These results have important implications for clinicians treating couples attempting pregnancy. It appears that couples can increase their chance of achieving pregnancy by simply timing intercourse on days with noticeable secretions. This simple approach may even outperform use of expensive urinary LH kits, which can miss the majority of the fertile interval occurring one or more days prior to ovulation (Dunson et al., 1999).
The estimated day-specific probabilities of pregnancy presented in Figure 2 based on the European data follow a similar pattern to that seen in the North Carolina Early Pregnancy Study (Wilcox et al., 1998
). For the European study, the day of ovulation was estimated from the last day of hypothermia preceding the post-ovulatory rise in BBT. The North Carolina study instead estimated ovulation day from the rapid decline in the ratio of oestrogen to progesterone that accompanies luteinization of the ovarian follicle, based on urinary hormone metabolites (Baird et al., 1991
). For both data sets, the estimated day-specific pregnancy probabilities peak two days prior to the identified ovulation day and are low outside of the six day interval ending on the estimated day of ovulation. The Baird et al. approach used in the North Carolina study to estimate ovulation day has been shown to be highly accurate in a recent validation study that used ultrasound to document directly the time of follicular rupture for a large number of menstrual cycles (Baird et al., 1991
; Rene Ecochard, personal communication). Thus, the similarity between the day-specific estimates in the European and North Carolina studies suggests that bias caused by measurement error in the BBT-based marker of ovulation may be low. Although measurement error may have contributed to the non-zero pregnancy rates estimated from the European data for intercourse outside the six day fertile interval (Dunson et al., 1999
; Dunson and Weinberg, 2000b
), these non-zero estimates may also reflect the much larger number of cycles and pregnancies in the European data set.
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Acknowledgements |
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Notes |
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References |
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Barrett, J.C. and Marshall, J. (1969) The risk of conception on different days of the menstrual cycle. Pop. Studies, 23, 455461.[ISI]
Chib, S. and Greenberg, E. (1998) Analysis of multivariate probit models. Biometrika, 85, 347361.[Abstract]
Colombo, B. and Masarotto, G. (2000) Daily fecundability: first results from a new data base. Demographic Research, 3, 5.
Dunson, D.B. (2000) Bayesian latent variable models for clustered mixed outcomes. J. R. Statist. Soc. B., 62, 355366.[ISI]
Dunson, D.B. (2001) Bayesian analyses of epidemiological data: Some practical advantages. Am. J. Epidemiol., 153, 12221226.
Dunson, D.B. and Weinberg, C.R. (2000a) Accounting for unreported and missing intercourse in human fertility studies. Statist. Med., 19, 665679.[ISI]
Dunson, D.B. and Weinberg, C.R. (2000b) Modeling of human fertility in the presence of measurement error. Biometrics, 56, 288292.[ISI][Medline]
Dunson, D.B. and Zhou, H. (2000) A Bayesian model for fecundability and sterility. J. Am. Statist. Ass., 95, 10541062.[ISI]
Dunson, D.B., Baird, D.D., Wilcox, A.J. and Weinberg, C.R. (1999) Day-specific probabilities of clinical pregnancy based on two studies with imperfect measures of ovulation. Hum. Reprod., 14, 18351839.
Eriksen, G.V., Carlstedt, I., Uldbjerg, N. and Ernst, E. (1998) Cervical mucins affect the motility of human spermatozoa in vitro. Fertil. Steril., 70, 350354.[ISI][Medline]
Frank-Herrmann, P., Freundl, G., Baru, S. et al. (1991) Effectiveness and acceptability of the symptothermal method of natural family planning in Germany. Am. J. of Obstet. Gynecol., 165, 20522054.
Guida, G.A., Tommaselli, M., Pellicano, S. et al. (1997) An overview on the effectiveness of Natural Family Planning. Gynecol. Endocrinol., 11, 203219.[ISI][Medline]
Gurrin, L.C., Kurinczuk, J.J. and Burton, P.R. (2000). Bayesian statistics in medical research: an intuitive alternative to conventional data analysis. J. Eval. Clin. Pract., 6, 193204.[ISI][Medline]
Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97109.[ISI]
Lilford, R.J. and Braumholtz, D. (2000) Who's afraid of Thomas Bayes? J. Epidemiol. Community Health, 54, 731739.
Marshall, J. (1968) A field trial of the basal-body-temperature method of regulating births. Lancet, 2, 810.[ISI][Medline]
Schwartz, D., MacDonald, P.D.M. and Heuchel, V. (1980) Fecundability, coital frequency, and the viability of ova. Pop. Studies, 23, 455461.
Sinai, I., Jennings, V. and Arévalo, M. (1999) The TwoDay Algorithm: a new algorithm to identify the fertile time of the menstrual cycle.Contraception, 60, 6570.[ISI][Medline]
Spiegelhalter, D.J., Thomas, A., Best, N.G. and Gilks, W.R. (1996) BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.50, Cambridge, UK: MRC Biostatistics Unit.
Stanford, J.B., Lemaire, J.C. and Thurman, P.B. (1998) Women's interest in natural family planning. J. Fam. Pract., 46, 6571.[ISI][Medline]
Tanner, M.A. and Wong, W.H. (1987) The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc., 82, 528550.[ISI]
Tierney, L. (1994) Markov chains for exploring posterior distributions. Ann. Statist., 22, 17011762.[ISI]
Trussel, J. and Grummer-Strawn, L. (1990) Contraceptive failure of the ovulation method of periodic abstinence. Fam. Plan. Perspect., 22, 6575.[ISI][Medline]
Wilcox, A.J., Weinberg, C.R. and Baird, D.D. (1995) Timing of sexual intercourse in relation to ovulationeffects on the probability of conception, survival of the pregnancy, and sex of the baby. N. Engl. J. Med., 333, 15171521.
Wilcox, A.J., Weinberg, C.R. and Baird, D.D. (1998) Post-ovulatory ageing of the human oocyte and embryo failure. Hum. Reprod., 13, 394397.[ISI][Medline]
Submitted on January 15, 2001; accepted on June 14, 2001.