Natural conception: repeated predictions over time

Abstract

STUDY QUESTION

How can we predict chances of natural conception at various time points in couples diagnosed with unexplained subfertility?

SUMMARY ANSWER

We developed a dynamic prediction model that can make repeated predictions over time for couples with unexplained subfertility that underwent a fertility workup at a fertility clinic.

WHAT IS KNOWN ALREADY

The most frequently used prediction model for natural conception (the ‘Hunault model’) estimates the probability of natural conception only once per couple, that is, after completion of the fertility workup. This model cannot be used for a second or third time for couples who wish to know their renewed chances after a certain period of expectant management.

STUDY DESIGN, SIZE, DURATION

A prospective cohort studying the long-term follow-up of subfertile couples included in 38 centres in the Netherlands between January 2002 and February 2004. Couples with bilateral tubal occlusion, anovulation or a total motile sperm count <1 × 10⁶ were excluded.

PARTICIPANTS/MATERIALS, SETTING, METHODS

The primary endpoint was time to natural conception, leading to an ongoing pregnancy. Follow-up time was censored at the start of treatment or at the last date of contact. In developing the new dynamic prediction model, we used the same predictors as the Hunault model, i.e. female age, duration of subfertility, female subfertility being primary or secondary, sperm motility and referral status. The performance of the model was evaluated in terms of calibration and discrimination. Additionally, we assessed the utility of the model in terms of the variability of the calculated predictions.

MAIN RESULTS AND THE ROLE OF CHANCE

Of the 4999 couples in the cohort, 1053 (21%) women reached a natural conception leading to an ongoing pregnancy within a mean follow-up of 8 months (5th and 95th percentile: 1–21). Our newly developed dynamic prediction model estimated the median probability of conceiving in the first year after the completion of the fertility workup at 27%. For couples not yet pregnant after half a year, after one year and after one and a half years of expectant management, the median probability of conceiving over the next year was estimated at 20, 15 and 13%, respectively. The model performed fair in an internal validation. The prediction ranges were sufficiently broad to aid in counselling couples for at least two years after their fertility workup.

LIMITATIONS, REASONS FOR CAUTION

The dynamic prediction model needs to be validated in an external population.

WIDER IMPLICATIONS OF THE FINDINGS

This dynamic prediction model allows reassessment of natural conception chances after various periods of unsuccessful expectant management. This gives valuable information to counsel couples with unexplained subfertility that are seen for a fertility workup.

STUDY FUNDING/COMPETING INTEREST(S)

This study was facilitated by grant 945/12/002 from ZonMW, The Netherlands Organization for Health Research and Development, The Hague, The Netherlands. No competing interests.

natural conception, dynamic prediction, prospective cohort, expectant management, spontaneous pregnancy

Introduction

Approximately 10% of all couples who wish to have a child does not conceive within the first year of trying (Gnoth et al., 2003; Wang et al., 2003). In ~50% of these couples, no major underlying cause is found and they are diagnosed with unexplained subfertility, including mild-to-moderate male subfertility, mild endometriosis and cervix factor subfertility (Aboulghar et al., 2009; Brandes et al., 2010). Demographic studies have shown that 30–60% of couples not conceiving in the first year still conceive within the second year of trying, but there is huge variation in the chances of natural conception; some couples may take much longer and some may never conceive at all (te Velde et al., 2000; Sozou and Hartshorne, 2012; van Geloven et al., 2013).

A pressing question for couples with unexplained subfertility is whether they should continue their attempts of conceiving naturally or start with medically assisted reproduction (MAR). The recent National Institute for Health and Care Excellence guideline on Fertility suggests that IVF should be offered to couples with unexplained subfertility after two years of unfulfilled child wish (NICE 2013). This recommendation is not in line with a personalized approach in which the individual couple's prognosis of natural conception is taken into account in the decision whether or not to treat (van den Boogaard et al., 2011). Also, couples do not behave according to, nor identify themselves with the ‘average’ and wish to be informed about their personal prognosis (Dancet et al., 2011, 2014).

Several prediction models have been developed that provide patient-specific predictions, of which the synthesis model of Hunault has reached the phase of clinical implementation (Hunault et al., 2004; Leushuis et al., 2009). This model is used to estimate the probability of natural conception over the next year after a couple has completed the fertility workup. It is based on female age, duration of subfertility, female subfertility being primary or secondary, sperm motility and whether the couple has been referred to the fertility centre by a general practitioner (GP) or by a gynaecologist.

A major shortcoming of the Hunault model is that it can only be used once, i.e. after completion of the fertility workup. Couples who do not conceive after an additional period of expectant management often perceive this unsuccessful period as evidence that further waiting is futile. Reassessment of their chances on natural conception after extended expectant management would be extremely helpful in counselling these patients. Calculation of their chances using the Hunault model a second time or a third time by simply updating the characteristics of the couples, i.e. increased female age and duration of subfertility, results in erroneous estimates. Such predictions are systematically too optimistic because couples with a longer period of unsuccessful natural attempts belong to a selection of the population with lower fertility potential. To make repeated predictions correctly, we need a dynamic prediction model, i.e. a model that can reassess chances as more information is collected over time (van Houwelingen and Putter, 2012; McLernon et al., 2014).

Such a dynamic prediction model is currently not available for natural conception. A mathematical model that has proven to approximate the dynamic process of chances on natural conception over time in the general population is the beta-geometric model (Bongaarts, 1975; Weinberg and Gladen, 1986).

Our aim was to derive a dynamic prediction model that is able to make repeated predictions after a given period of expectant management and is not only able to predict the chances of natural conception over the next year, but also the chances over shorter, e.g. over the next half year, or longer periods, e.g. over one and a half or two years.

Materials and Methods

Study design

We used data from a prospective cohort in 38 hospitals in the Netherlands, between January 2002 and February 2004. That cohort study, of which the detailed protocol has been described elsewhere, was designed to validate the Hunault model (van der Steeg et al., 2007). In short, we recorded information obtained during the fertility workup of consecutive couples. After completion of the workup, we followed couples until natural conception leading to an ongoing pregnancy. We defined ongoing pregnancy as the presence of foetal cardiac activity at transvaginal sonography at a gestational age of at least 12 weeks. If no pregnancy occurred, then we censored follow-up time at the start of treatment or at the last date of contact during follow-up.

For the current study, we selected couples with no major causes explaining the fertility problem, regular menstrual cycles (cycle length between 23 and 35 days), at least one patent fallopian tube and semen analyses with a total motile sperm count >1 × 10⁶. This resulted in a different cohort size compared with the validation study by van der Steeg et al.

We only used results from tubal tests performed in the first 6 months after initiation of the fertility workup and assumed by that time the workup was completed.

Missing data and data description

We accounted for missing data by multiple imputation. All numerical results are based on pooled estimates over 10 imputed data sets using Rubin's Rules (Rubin, 2004). Graphical results are shown based on one randomly selected imputed data set (Vergouwe et al., 2010). We reported descriptive statistics as mean with 5th and 95th percentile and categorical variables as frequency with percentage.

Model development

We used the beta-geometric method to derive a dynamic prediction model. This method focuses on the probability of natural conception per menstrual cycle. This probability differs considerably between couples (Eijkemans et al., 2014). The beta-geometric method assumes that the probability in a couple remains stable over time, which is considered to represent the intrinsic conception rate (Evers, 2002; Stanford et al., 2010; Sozou and Harthshorne, 2012). After several natural cycles, the couples with higher chances are more likely to have become pregnant, while the remaining couples are likely to have lower chances. The model mimics this selection process by assuming that the per cycle probability on natural conception varies among couples according to a beta distribution, leading to a beta-geometric distribution of the number of cycles to natural conception (Weinberg and Gladen, 1986). The model is characterized by two parameters: the mean and the variance of the probability of natural conception in the first cycle after completion of the basic fertility workup. The distribution of the probabilities in subsequent cycles follows from these two parameters and the assumed selection process.

As the model focuses on the probability per cycle, we discretized the observed time to natural conception into number of cycles, by dividing this time to conception by cycle length. We used rounding to the first following whole cycle number for women who conceived and rounding to the nearest whole cycle number for censored observations. In the reporting of results, we assume that a year consists of 13 menstrual cycles, which matches the average cycle length in our cohort (28 days). A period of six menstrual cycles is denoted as half a year.

We assessed overall model fit of the beta-geometric model without covariates visually by comparing the cumulative predictions from the model with Kaplan–Meier estimates. This was first done for the cumulative predictions in the full cohort over a maximum of two and a half years of follow-up. Thereafter, to assess the dynamic fit, this was also done for cumulative predictions over the next year in women not yet pregnant at four fixed time points: directly after the workup, after half a year, after one year and after one and a half years of expectant management.

To protect against data-driven overfitting, i.e. optimism based on own data when selecting predictor variables, we used the known predictors of natural conception from the Hunault model (Harrell et al., 1996). We incorporated these predictors, i.e. female age at completion of the fertility workup, duration of subfertility at completion of the fertility workup, female subfertility being primary or secondary, percentage of motile sperm and referral status, into the beta-geometric model by expressing the logit of the mean natural conception probability as a linear function of the covariates. This results in covariate effects, which are interpretable as odds ratios (ORs). We also corrected for possible overfitting by decreasing the log ORs by a heuristic shrinkage factor pooled over imputation sets and recalibrated the intercept (Van Houwelingen and Le Cessie, 1990; Vergouwe et al., 2010). The predictions following from the model were expressed in a prediction formula in which the elapsed period of expectant management and the time period of interest over which to predict, can both be chosen as any value. Also, to facilitate the estimation of prognosis, we created a user-friendly nomogram that allows assessment of the chances of natural conception over the next year after completion of the workup, after half a year, after one year and after one and a half years of expectant management.

Model validation

We evaluated the performance of the dynamic prediction model for chances of natural conception over the next year at the predefined four fixed time intervals.

We assessed the degree of agreement between observed and predicted natural conception rates, i.e. calibration, by dividing couples in risk groups of equal size (~200 per risk group). We first visually compared the mean predicted chances over the next year with the corresponding observed fraction of achieved conceptions estimated by the Kaplan–Meier method. Second, we calculated the mean of the absolute differences between the predicted and the observed natural conception rates (Hosmer and Lemeshow, 1989).

The ability of the dynamic prediction model to distinguish between women who do and women who do not conceive, i.e. discrimination, was assessed by calculating Harrel's c-index (Harrell et al., 1996). The maximum achievable c-index, considering the distribution of predicted chances in our cohort, is realistically not 1 but most likely between 0.62 and 0.76 (Mol et al., 2005; Cook, 2007; Coppus et al., 2009).

In addition to proper calibration and discrimination, clinical useful models should have sufficient variability in the calculated chances (Coppus et al., 2009). We therefore also assessed the ranges of the chances given by the model at the four evaluated time points, with wider ranges indicating enhanced utility.

Lastly, we assessed the robustness of the parametric assumptions of our model in a sensitivity analysis. To this end, we compared the performance of the first year predictions from the parametric beta-geometric model with predictions obtained from a semi-parametric Cox prediction model fitted on the same data.

We obtained the parameters of the beta-geometric model by direct log-likelihood estimation, using the ‘BFGS’ method of the general optimization procedure optim in the R environment for statistical computing (R Development Core Team 2011), R Foundation for Statistical Computing, Vienna, Austria).

Results

Data from 4999 couples matching our inclusion criteria were available. Mean female age was 32.5 (25.0–39.4) years, the mean duration of subfertility was 2.1 (1.0–4.8) years, both evaluated at the time of completing the fertility workup. There were 3264 (65%) women with primary subfertility, while 512 (10%) were referred to the fertility clinic by another gynaecologist. Mean cycle length was 27.8 (24.4–33.2) days, mean percentage of motile sperm cells was 40 (5.5–73) and mean semen total motile count was 85 (2.4–283) per million. In total, 1.7% of these data was missing and thus imputed.

An ongoing pregnancy after natural conception occurred in 1053 couples after a mean follow-up of 8 months (1–21). The cumulative two and a half years chances after the completion of the fertility workup are depicted in Fig. 1 A using the Kaplan–Meier method.

The dynamic prediction model

The beta-geometric model without covariates estimated a mean probability of natural conception in the first menstrual cycle of 3.6%, decreasing over time to 1.6% per cycle after one year of unsuccessful expectant management and to 0.9% per cycle after two and a half years. Cumulative chances according to the beta-geometric model within one, one and a half, two, and two and a half years were estimated at 27, 33, 38 and 41%, respectively (representing the dotted line in Fig. 1 A). The model seems to fit the observed data, depicted by the solid Kaplan–Meier curve, well.

For couples not yet pregnant after half a year, after one year and after one and a half years of expectant management, the probability of conceiving over the next year was estimated by the beta-geometric model at 20, 15 and 13%, respectively (Fig. 1B). The dotted lines again represent the estimates from the beta-geometric model and show no major deviations from the shape of the solid Kaplan–Meier curves representing the observed data.

Figure 1

Cumulative natural conception rates after completion of fertility workup (A) and updated cumulative one-year rates after half a year, one year and one and a half years of unsuccessful expectant management (B). Percentages are estimates from the beta-geometric model.

The effect of the five known predictors of natural conception after shrinkage by a factor 0.971 is depicted in Table I as OR together with 95% confidence intervals (CIs). For instance, increased female age, especially above 31, has a negative effect on a couple's chance to conceive (OR 0.96 per year when below 31 and 0.93 per year when above) as well as the duration of subfertility (OR 0.79 per year).

Table I

Estimated effects of patient factors in the beta-geometric model after shrinkage.

	OR	95% CI
Female age
Per year older while below 31	0.96	0.94–0.99
Per year older while above 31	0.93	0.90–0.95
Duration subfertility per year	0.79	0.73–0.84
Subfertility
Secondary	Ref.
Primary	0.70	0.61–0.80
Referral
GP or other specialist	Ref.
Gynaecologist	0.52	0.39–0.70
Semen per % motile sperm	1.006	1.003–1.009

CI, confidence interval; GP, general practitioner; OR, odds ratio.

Incorporating these patient characteristics into the beta-geometric model led to the prediction formula in the Supplementary information. This formula enables the reader to calculate the individual probability of natural conception after any number of unsuccessful cycles since the completion of the fertility workup for a chosen number of future cycles. The prediction formula is transformed into a nomogram in Fig. 2 for convenient usage, based on the four fixed time intervals. To help demonstrate the utility of the nomogram, the natural conception predictions for an index couple are shown in Fig. 3.

Figure 2

Nomogram of the dynamic prediction model. Upper panel: Each of the five predictors has a certain weight expressed as points. For example, female age varies from 0 points at age 20 to 100 points at age 44 and duration varies from 0 at one-year duration to 70 at five-year duration. Add up all points of the predictors; the more points the lower the chance of a natural conception. Lower panel: the sum of all points can be used to obtain the natural conception chance of an individual couple. The lines represent the chances over the next year after completion of the workup, after half a year, after a year and after one and a half years of unsuccessful expectant management (EM).

Figure 3

Example estimation of the natural conception chances for a couple with female age 26, one-year duration of subfertility (both at completion of workup), primary subfertility, 25% motile sperm, referred to the fertility centre by their general practitioner (GP). The upper panel of the nomogram shows that the weights of the five predictors add up to a sum of 77 points. In the lower panel, one can read that the chance of a natural conception over the next year is 35% after completion of the workup, 26% after half a year, 20% after a year and 17% after one and a half years of unsuccessful expectant management (EM).

Internal validation of the dynamic prediction model

The calibration plots for the four evaluated time intervals are presented in Fig. 4. The model is fairly well calibrated from completion of the fertility workup up to two and a half years of follow-up based on the general trends in the four plots and the CIs from the observed rates which nearly all cover the ideal 45 degree line. The absolute difference between the mean predicted chances and the observed fractions of natural conceptions per risk group of 200 couples, i.e. the distance between the dots and the 45 degree reference line in Fig. 4, was on average 2.8 percent points and 7.1 percent points at the highest. The mean and maximum differences stratified by the time since the fertility workup are depicted in Table II, showing that the model was equally well calibrated over the four time periods.

Figure 4

Calibration of the predictions of the dynamic prediction model: predicted versus observed one year natural conception rates at four fixed time points.

Table II

Calibration of the dynamic prediction model: mean and maximum of the absolute differences (in percentages) between predicted and observed one year natural conception rates per group of n = 200, stratified by the elapsed period of expectant management (EM).

	Mean difference	Max difference	Number of risk groups
After completion of the workup	2.5	7.1	25
After half a year EM	2.5	6.1	13
After one year EM	2.3	6.4	5
After one and a half years EM	3.7	6.2	2
Total	2.8	7.1	45

The discriminative ability of the model approached the realistic maximum, ranging over time from a c-index of 0.63 (95%CI 0.61–0.65) in the first year, 0.62 (95% CI 0.58–0.65) from half a year, 0.60 (95% CI 0.54–0.66) from a year, to 0.61 (95% CI 0.51–0.71) for a year and a half, all for conceiving in the following year. The discriminative ability of the model was fairly stable over time, with wider CIs at later time points reflecting the lower number of couples in follow-up.

The estimated chances of natural conception over the next year ranged from 0 to 63% after completion of the fertility workup (median: 27%), from 0 to 46% after half a year unsuccessful expect management (median: 20%), from 0 to 36% after a year of unsuccessful expectant management (median: 15%) and from 0 to 26% after a year and a half of unsuccessful expectant management (median: 13%). The prediction range in this last time interval was relatively narrow and may not contribute to relevant prognostic stratification anymore.

The sensitivity analysis showed that the first year predictions from the dynamic prediction model using the beta-geometric method were highly comparable to predictions from a Cox model. The per couple predictions differed at maximum 1.5 percent points and the performance indices coincided (data not shown).

Discussion

The dynamic prediction model we developed is able to estimate the chances of natural conception repeatedly over any chosen time period for couples with unexplained subfertility that are seen for a fertility workup. In an internal validation, the model showed fair calibration and discrimination. The prediction ranges were sufficiently broad to aid in counselling couples for at least two years after their fertility workup.

Our study has some strengths. First, we developed our dynamic prediction model on a large, prospectively collected cohort of 4999 couples that were included in 38 hospitals throughout the Netherlands. Because the Dutch population is a mixture of ethnic groups, this somewhat strengthens generalizability.

Second, we used the parametric beta-geometric method to develop our dynamic model instead of other semi-parametric methods such as (sliding) landmark approaches for repeated predictions (van Houwelingen, 2007; van Houwelingen and Putter, 2012). Our choice was prompted by three arguments, of which the first was our aim to make one fixed prediction formula that is applicable to several time periods, which is not possible when using semi-parametric approaches. The second is that the beta-geometric model has proven to match fecundity data well in the general population and thus seemed the best candidate for our analyses, although we acknowledge that a subfertile cohort is more homogeneous. The third argument for the beta-geometric model was the decreasing numbers of couples in the study at later time points. The selection process estimated by our method is mainly based on the selection observed in the cycles where patient numbers are highest, which gives more robust estimates than strict landmarking methods that only use those couples still at risk at later time points in the estimates for those periods.

Our study has some limitations. First of all, it is well known that performance of a model in an internal validation overestimates the performance in external data. We reduced this overfitting to some extent by only including the known predictors from the Hunault model and by using shrinkage methods. All predictors increased or decreased chances of natural conception in the expected direction and effect estimates were similar to those reported in Hunault et al. Only referral by a gynaecologist had a notably stronger effect in our model compared with Hunault's. A clear biological explanation for the predictive value of referral status remains unclear. The variable probably reflects a concealed selection process: for couples referred by gynaecologists, the time spent in these procedures influences the underlying selection process, which is apparently not fully captured by the duration of subfertility (Hunault et al., 2004). The generalizability of the developed dynamic model needs to be confirmed in an external data set before implementation in clinical practice can be advised.

Second, we subdivided the time axis into three periods: the period of subfertility until completion of the fertility workup, the period of expectant management since the fertility workup and the future time period over which to predict. This matched the way our data set was collected: inclusion at the fertility workup and prospective follow-up from completion of the workup. Consequently, our results apply to couples who have finished the diagnostic workup, acknowledging that the exact moment of completion of such a workup can vary largely depending on local clinic's diagnostic protocols.

Third, we did not explicitly account for reproductive ageing and sterility. In our model, we assume that the chance of natural conception for a couple remains stable during the two and a half years of follow-up, which may not apply to women of advanced age (Eijkemans et al., 2014). However, the effect of accounting for advancing age in a prediction model is moderate and doing so would have severely complicated both the model and its interpretation (Sozou and Hartshorne, 2012). We also assume that each couple has a chance of conception greater than zero. We observed that the estimated beta distribution of natural conception chances peaked at the lower range where chances are close to zero. Possibly, this right skewed shape is caused by a relatively large subgroup of patients with absolute infertility (van Geloven et al., 2013). Our model did not explicitly account for such a potential subgroup with zero chances.

Fourth, our outcome is ongoing pregnancy instead of live birth. This is because live birth greatly increases logistical efforts in large cohorts which may introduce loss to follow-up.

Our dynamic model is able to reassess the chance of natural conception after a certain period of expectant management. For example, when using our model for a couple referred by a GP with one year primary subfertility, female age at the completion of the fertility workup of 26 and a motile sperm percentage of 25, they might be advised expectant management because of their predicted 35% natural conception chance in the first year after the workup. When the couple returns to the clinic after that year, reusing our model with an elapsed period of expectant management of 13 cycles yields a chance of 20% over the second year, which is a realistic decrease in the estimate that may be a reason to consider treatment with MAR.

If, for this same couple, we would use the current ‘one time only’ model developed by Hunault et al. (2004), we would estimate the chance of natural conception over the first year after the fertility workup at 36%. When the couple returns after that year, erroneously reusing Hunault's model would suggest a remaining chance of 30% over the second year, which is an overly optimistic estimate that ignores the process of selection of couples with lower fertility potential. An advice to continue expectant management could therefore be unjust.

Additionally, using the formula in the Supplementary information, prediction of the chances over different time periods are possible instead of the predicted 35% over the first year, e.g. over the first 6 months (22%) or over the first one and a half years (42%) for this couple after the fertility workup. Early treatment in couples that still have high chances of natural conception can thus be avoided, as well as any delay of treatment in couples with poor remaining prospects.

We feel that dynamic predictions can give valuable input to individualized treatment decisions. When and over which future time horizon to predict can be tailored to the couple's situation. This tailoring is known to help couples recognize that predictions raised by a doctor actually apply to their situation and can add to an evidence-based, shared decision process. Ultimately, in making treatment decisions we not only need an individualized prediction of the prognosis of natural conception in a particular couple, but also information of the chances of conception with treatment. So far, no study has assessed this within the same patient population. In the absence of such studies, the only alternative is to calculate chances of conception after treatment by using separate models that have been developed in other cohorts and compare these with the predictions for natural conception generated by our dynamic model.

Authors’ roles

E.R.t.V., N.v.G., M.v.W., I.S., F.v.d.V. and R.T.K.F. were responsible for the concept and design. B.W.M., F.v.d.V. and P.H. initiated the data collection. J.W.v.d.S. and P.S. collected and cleaned the data. N.v.G., E.R.t.V. and M.J.E. designed the statistical analysis plan. R.v.E. analysed the data. N.v.G. and R.v.E. drafted the manuscript. All authors contributed critical revision to the paper and approved the final manuscript.

Funding

This study was facilitated by grant 945/12/002 from ZonMW, The Netherlands Organization for Health Research and Development, The Hague, The Netherlands.

Conflict of interest

None declared.