Medically assisted reproduction in the context of time
Scholten, I.
Publication date
2015
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Final published version
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Citation for published version (APA):
Scholten, I. (2015). Medically assisted reproduction in the context of time.
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Natural conception:
The importance of repeated
predictions
In progress
Nan van Geloven Irma Scholten Raissa I. Tjon-Kon-Fat Fulco van der Veen Jan-Willem van der Steeg Pieternel Steures Peter G.A. Hompes Ben W.J. Mol Marinus J. Eijkemans Egbert R. Te Velde
ABSTRACT
Study question
How can we predict natural pregnancy chances repeatedly at different time points in the same couple? Summary answer
We developed a dynamic prediction model that can make repeated predictions over time for the same couple.
What is known already
The most frequently used prediction model for natural conception (the “Hunault model”) is able to estimate the probability of a natural conception only once per couple, after the completion of the fertility work-up. The model cannot be used for a second or third time in the same couple.
Study design, size, duration
We studied couples who participated in a prospective cohort study of subfertile couples 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 x 106 were excluded.
Participants/materials, setting, methods
The primary endpoint was a natural ongoing pregnancy. Time to pregnancy was censored when treatment was started, or at the last date of contact during follow up.
A new dynamic prediction model was developed using the same predictors as in the Hunault model: female age, duration of subfertility, subfertility being primary or secondary, sperm motility and referral status. The performance of the repeated predictions from the model was evaluated in terms of calibration, discrimination and relative error reduction.
Main results and the role of chance
Of the 4,996 couples in the cohort, 1,086 (22%) women reached a naturally conceived ongoing pregnancy within a mean follow up of 10 months (range 1-70 months). The pregnancy prognosis in the first year after completion of the fertility workup was 26%. If pregnancy did not occur in this first year, the chance of conceiving in the next year was 13%. The yearly chance lowered to 8% after 2 years of unsuccessful expectant management. Discrimination and calibration of the repeated predictions was fair up to 3 years after the fertility workup. The relative error reduction interpretable as the amount of variation explained by the predictors lowered from 24% in the first year to 5% in the third year. 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 enables to re-assess the natural pregnancy chances after different periods of unsuccessful expectant management. This gives valuable information for treatment
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INTRODUCTION
Approximately 10% of all couples who want to have a child do not conceive within the first year of trying (1–3). In about 50% of these couples the subfertility is more or less unexplained because no major underlying cause is found (4). The prognosis for these couples is still quite good. Demographic studies have shown that 30-60% are expected to conceive within the second year of trying (2,5). There is huge variation in the pregnancy chances of these couples; some couples may take much longer or never conceive (6,7).
A pressing question for unexplained subfertile couples is whether they should continue their attempts of conceiving naturally or start treatment with medically assisted reproduction (MAR). The recent NICE guideline on Fertility suggests that in vitro fertilisation (IVF) should be offered to couples with unexplained subfertility after two years of unfulfilled child wish (8). This general recommendation does not match the need of a personalized approach in which a couples’ prognosis determines whether or not treatment adds value (9). Couples prefer to be informed about their personal chances (10,11). Several prediction models have been developed that can provide patient-specific predictions, of which the synthesis model developed by Hunault has reached the phase of clinical implementation (12,13). This model can be used to estimate the probability of a natural pregnancy within the first year after a couple seeks medical advice in a fertility clinic after absolute causes of subfertility such as anovulation, azoospemia and bilateral tubal pathology have been excluded. 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 center by a general practitioner or gynaecologist.
A major shortcoming is that the Hunault model can only be used once, i.e. after the results of the fertility work-up are known. When couples who agreed on a period of expectant management do not conceive and return to the fertility clinic, the need to assess the natural pregnancy chance becomes even more compelling as these couples often perceive the additional unsuccessful period as evidence that further waiting is senseless. Calculation of the chances a second time for the same couple by simply updating the couples’ characteristics (raise female age and duration of child wish) and then using Hunault’s model a second time as if they came for the first time, results in erroneous estimates. Such predictions are systematically too optimistic because the couple with a longer period of unsuccessful natural attempts belongs to a selection of the population with lower fertility potential and the Hunault model was not developed for such a negatively selected subgroup. To make such temporal updated predictions correctly, we need a dynamic prediction model. Unlike ‘one time only’ models that can only predict pregnancy chances at one fixed moment in time, a dynamic prediction model can reassess pregnancy chances repeatedly for the same couple at different time points in the future (14,15).
Such a dynamic prediction model is currently not available. A mathematical model that has proven to match the dynamics of pregnancy chances over time in the general population and has been used in the demographic literature is the beta-geometric model (16,17). Here we use the beta-geometric model to make dynamic predictions of natural pregnancy for couples with unexplained subfertility that repeatedly seek counselling about whether still to continue attempting natural conception or to embark on MAR.
METHODS
The data for our analysis were collected in a prospective cohort study performed in 38 hospitals in The Netherlands, between January 2002 and February 2004. The study, of which the detailed study protocol has been described elsewhere (18), was designed to validate the Hunault model. The information obtained during the fertility work-up of consecutive couples was recorded and after completion of the workup couples were followed until natural conception leading to an ongoing pregnancy occurred. Ongoing pregnancy was defined as the presence of foetal cardiac activity at transvaginal sonography at a gestational age of at least 12 weeks. If no pregnancy occurred, time to pregnancy was censored when treatment started, or at the last date of contact during follow up. For the current analysis we selected couples with regular cycle (cycle length between 23 and 35 days), at least one patent tube (women with two sided occlusion on hysterosalpingography, diagnostic laparoscopy or on transvaginal hydrolaparoscopy were excluded) and sufficient sperm quality (total
motile sperm count > 1 x 106). Patients in whom tubal status was only assessed by a Chlamydia
antibody titre test during the fertility workup were retained in the analysis, regardless of the outcome. Missing data and data description
Missing patient factors were imputed using a single imputation technique. Although in general a multiple imputation approach might better capture the uncertainty associated with unmeasured data values, we here chose to adhere to the approach used in previous analysis of the same data set.
Numerical variables are described as mean with 5th and 95th percentile and categorical variables as
frequency with percentage. The beta-geometric model
The beta-geometric model focusses on the pregnancy probability per menstrual cycle. This probability differs considerably between couples, but we assumed that for one couple, the probability remains stable during the follow up time of the study. This means that there are couples with higher and lower pregnancy chances per cycle, who cannot be identified at the start of follow up. After several cycles, the
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couples with the higher pregnancy chances are more likely to have become pregnant. The remaining couples are likely to have lower chances. This selection process is modelled by assuming that the per cycle pregnancy probability varies among couples according to a beta distribution, leading to a beta-geometric distribution of the number of cycles to pregnancy (17). The model can be characterized by two parameters: the mean and the variance of the probability of pregnancy in the first cycle after completion of the basic fertility workup. The distribution of the pregnancy probabilities in subsequent cycles follows from these two parameters and the assumed selection process.
As the model focusses on the probability per cycle, we discretized the time to pregnancy into number of cycles, by dividing time to pregnancy by the average 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 6 menstrual cycles is denoted as half a year.
Overall model fit of the beta-geometric model without covariates was assessed visually by comparing the cumulative predictions from the model to Kaplan-Meier estimates on the discretized data. This was first done for the cumulative predictions in the full cohort over maximum three years of follow up, and thereafter, to assess the dynamic fit, for cumulative within one year predictions in couples not yet pregnant after half a year, one and two years of expectant management.
The dynamic prediction model
We incorporated the five known predictors of pregnancy, i.e., female age at completion of workup, duration of subfertility at completion of 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 pregnancy probability as a linear function of the covariates. This results in covariate effects interpretable as odds ratios. The predictions following from the model were expressed in a prediction formula in which the duration of expectant management and the prediction window, i.e. the time period ahead over which you want to predict the pregnancy chance, can both be chosen. Also, to facilitate the estimation of prognosis without complex computation, a nomogram was created for the one year pregnancy chances after completion of the workup, after half a year, after one year and after two years of expectant management.
Model validation
We evaluated the performance of the predictions from the dynamic prediction model on four fixed time intervals: chances of pregnancy within one year after completion of the fertility workup, after half a year, after one year and after two years of unsuccessful expectant management.
The overall predictive performance was measured by the Brier prediction error score, i.e. the squared difference between the predictions and the observed pregnancy outcomes (14). To obtain a score that is comparable over the different evaluated time intervals, the Brier score was expressed relatively to the Brier score of the null model: the beta-geometric model without covariates that assigns to all couples an equal prediction per time interval. This relative Brier score is referred to as the relative error reduction and can be interpreted as the amount of variation that is explained by the predictors, ranging from 0% when the model is no better than assigning all patients an equal probability per time point to 100% when the model predicts perfectly (14). This measure naturally combines the two most important aspects of model evaluation in reproductive medicine: calibration and variability in predicted probabilities (19). A well calibrated model will give a good Brier score. However, if the predictions have low variability, the model will not show much gain over the Brier score of the null model. The relative error reduction in that case will be moderate.
We also assessed calibration and discrimination of the model separately. The degree of agreement between observed and predicted pregnancy rates, i.e. calibration, was assessed visually by comparing the mean predicted one year pregnancy chances with the observed fraction of pregnancies at one year estimated by the Kaplan-Meier method. Again for optimizing comparability of the evaluation on the four different time intervals, this was done in risk groups of fixed size (about 200 couples per risk group). The visual assessment was additionally quantified as the mean distance per risk group between the predicted chances and the observed rate. 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 (20). Models are typically considered reasonable when the c-index is higher than 0.7 and strong when the c-index exceeds 0.8 (21).
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 to predictions obtained from an alternatively fitted semi-parametric Cox prediction model. The parameters of the beta-geometric models were estimated by optimizing the log-likelihood of the observed data, 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).
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RESULTS
Data from 4,996 couples matching our inclusion criteria were available. Mean female age was 32.5 (24.9-39.4) years, the mean duration of subfertility was 1.9 (1.0-4.7) years, both evaluated at the time of completing the fertility work-up. There were 3,205 (62%) women who had not been pregnant before, while 555 (11%) were referred to the fertility clinic by a gynaecologist. Mean cycle length was 28.2 (24.4-33.2) days and mean semen total motile count was 84 (2.4-280) per million.
Pregnancy outcomes and the beta-geometric model
An ongoing pregnancy after natural conception occurred in 1,086 couples after a mean follow-up of 10 months. The cumulative ongoing pregnancy chances after the completion of fertility workup on are depicted in figure 1, panel A. Cumulative chances for ongoing pregnancy according to the Kaplan-Meier estimates within one, two and three years were 26%, 35% and 40% respectively. The beta-geometric model without covariates estimated a mean pregnancy probability in the first menstrual cycle of 3.6%, decreasing over time to 1.4% per cycle after one year of unsuccessful expectant management and to 0.6% per cycle after three years. The cumulative chances according to this beta-geometric model have been added to figure 1, panel A and show that the model fits the data well.
For couples not yet pregnant after half a year, one year and two years of expectant management, the probability of conceiving in the coming year is estimated at 18%, 13% and 8% respectively (Figure 1, panel B). The dotted line again represents the estimates from the beta-geometric model without covariates and shows that the model matches the data well.
The dynamic prediction model
Incorporating the five known predictors of pregnancy into the beta-geometric model led to the prediction formula in the Appendix. This formula enables to calculate the individual probability of natural pregnancy after any number of unsuccessful cycles since the completion of the fertility workup for a chosen number of future cycles. Figure 2 shows the prediction nomogram for four fixed time intervals: the probability to conceive within one year after completion of the workup, after half a year, after a year and after two years of unsuccessful expectant management. To help demonstrate the utility of the nomogram the pregnancy predictions for an example couple are shown in Figure 3. Internal validation of the dynamic prediction model
The effect of the patient characteristics in the beta-geometric model are depicted in Table 1 as odds ratios together with 95% confidence intervals. The calibration plots and performance indices for the four evaluated time intervals are presented in Figure 4. Calibration of the model seems acceptable over the full three year follow up by visual inspection: the absolute difference between the mean
Figure 1. Cumulative pregnancy rates after completion of fertility workup (panel A) and updated cumulative one year
pregnancy rates after half a year, one year and two years of unsuccessful expectant management (panel B)
predictions and the observed fractions of pregnancies, i.e. distance between the dots and the 45 degree reference line, was on average 3 percent points in risk groups of 200 couples. The relative error reduction by the model was 24% in the first year after the workup, decreasing to 5% after two years of expectant management. As the population becomes more homogeneous at later time points, this decrease is understandable: although at the correct level, the predictions do not vary much anymore at the later time points and for that reason are less useful than the earlier predictions (19). The discriminative ability of the model was moderate to reasonable, ranging over time from a c-index of 0.67 in the first year to a c-index of 0.73 in the third year. This suggests that the model does
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a bit better job in distinguishing couples with relatively lower prognosis from couples with relatively higher prognosis at later time points, presumably due to a bigger impact at the later time points of the subgroup of patients with nearly zero chances who are relatively easily distinguishable.
The sensitivity analysis showed that the first year predictions from the beta-geometric model were highly comparable to predictions from an alternatively fitted Cox model. The per couple predictions differed at maximum 2 percent points and the performance indices coincided.
Figure 2. Nomogram of the dynamic prediction rule.
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 75 points at age 44 and duration varies from 0 at 1 year duration to 100 at 5 year duration. Add up all points of the predictors; the more points the lower the chance of a natural pregnancy.
Lower panel: The sum of all points can be used to obtain the pregnancy chance of an individual couple. The lines represent the chances within one year after completion of the workup, after half a year, after a year and after 2 years of unsuccessful expectant management
Figure 3. Example estimation of the pregnancy chances for a couple with female age 26, 2 years duration of subfertility
(both at completion of workup), secondary subfertility, 50% motile sperm referred to the fertility center by a gynaecologist. The upper panel of the nomogram shows that the weights of the five predictors add up to a sum of 94 points. In the lower panel one can read that the chance of a pregnancy within one year is 21% after completion of the workup, 17% after half a year, 14% after a year and 10% after two years of unsuccessful expectant management (EM).
Table 1. Estimated effects of patient factors in the beta geometric model
OR 95% CI
Female age
per year below 31 0.97 (0.94-1.00)
per year above 31 0.92 (0.90-0.95)
Duration child wish/year 0.62 (0.58-0.67)
Subfertility
secondary ref
primary 0.71 (0.63-0.81)
Semen per % motile sperm 1.008 (1.005-1.011)
Referral
GP or other specialism ref
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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 0 0. 2 0. 4 0. 6after fertility workup (n=4996)
predicted probability beta-geometric model
obs
er
ved f
rac
tion
rel err reduc 24% av abs diff= 0.03 c-index 0.67 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 0 0. 2 0. 4 0. 6
after 6 months expectant management (n=2815)
predicted probability beta-geometric model
obs
er
ved f
rac
tion
rel err reduc 15% av abs diff= 0.03 c-index 0.68 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 0 0. 2 0. 4 0. 6
after one year expectant management (n=1354)
predicted probability beta-geometric model
obs
er
ved f
rac
tion
rel err reduc 10% av abs diff= 0.03 c-index 0.72 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 0 0. 2 0. 4 0. 6
after two years expectant management (n=443)
predicted probability beta-geometric model
obs
er
ved f
rac
tion
rel err reduc 5% av abs diff= 0.01 c-index 0.73
Figure 4. Calibration of the predictions of the dynamic prediction rule: predicted versus observed one year pregnancy
rates at four time points. In case zero pregnancies were observed in a certain risk group, no confidence interval could be calculated. Rel err reduc = relative error reduction
DISCUSSION
The newly developed dynamic prediction model is able to estimate the chance of a natural pregnancy repeatedly for the same couple and in addition can predict chances for any chosen time period ahead. In an internal validation, the calibration of the repeated predictions seemed acceptable during the whole three year follow up period. Although seemingly on the correct level, the predictions at the later time points may be less useful than the more early predictions of the model due to lower variability (19). Discrimination was moderate to reasonable, as is to be expected for these kind of models (19). It is well known that apparent model performance in an internal validation overestimates the performance in external data. The generalizability of the developed dynamic model needs to be confirmed in an external dataset before implementation in clinical practice can be advised.
The dynamic prediction model can be used several times for calculating predictions for the same couple. Such predictions cannot be made with currently available models like the Hunault model. For example when a couple referred by a general practitioner with one year primary subfertility, total motile sperm 50% and female age 28 at completion of the fertility workup that was advised expectant management based on a 40% pregnancy chance in the first year after the workup, returns to the clinic after that year and still is not pregnant, erroneously reusing Hunault’s model would suggest a remaining chance of 34% in the second year, which may be a reason to continue the expectant policy. When using the new dynamic prediction model for this couple, the prediction for the second year would more realistically be estimated at only 28%, which may be a reason to consider starting treatment with MAR.
In the development of the dynamic model several choices were made that merit some discussion. We subdivided the time axis into three periods: the duration of subfertility until completion of the diagnostic workup, the time span of expectant management since the diagnostic workup and the prediction window. The model was targeted at calculating the pregnancy chance over the latter period (prediction window) given the duration of the first two periods. This matched the way our dataset was collected: inclusion at fertility workup and prospective pregnancy follow up from completion of the workup on. This implies that our model cannot be used before completion of the diagnostic workup in a fertility clinic, whilst couples probably already want to know their prediction in an earlier phase. For this a model would be needed that can calculate pregnancy chances for any duration of subfertility, irrespective of whether or not couples seek or get medical advice in a clinic. This would either require new data collected in an earlier phase or strong assumptions about the selection of patients that reach the milestone of completion of the workup compared to patients not starting or not finishing the workup. The potential of such an approach should be explored in future research. The exact moment of completion of the workup can vary largely depending on the local
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rapidly after assessing tuba pathology with a Chlamydia antibody titer test, others took more time making more elaborate investigation with for instance a diagnostic laparoscopy. This variation seems inevitable when collecting a large multicenter dataset.
A technical modelling choice was the use of the parametric beta-geometric model while other semi-parametric methods such as (sliding) landmark approaches could also have been used to develop dynamic predictions (14,22). Our choice was prompted by the desire to make one fixed prediction formula that is applicable to several time periods, which is not possible when using semi-parametric approaches. The beta-geometric model has proven to match fecundity data well in the general population and thus seemed a good candidate for our analyses. We must realize however that we here apply the beta-geometric model in a different setting, especially on a much more homogeneous subfertile population compared the general population. We observed that the beta distribution of pregnancy chances estimated in our subfertile population 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 (zero pregnancy chances) (7). Our model did not explicitly account for such a potential infertile subgroup. A third argument for our choice of the beta-geometric model was the decreasing numbers at risk 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, this seems more robust than strict land marking methods that only use those patients still at risk at later time points in the estimates for those periods.
Another potential limitation of our model is that we did not explicitly account for reproductive ageing. In our model we assume that the age at completion of workup matches with a constant pregnancy chance in the next three years. The influence of ageing could be studied more extensively by for instance assuming a fixed age at which menopause occurs (23). Neglecting ageing effects in an analysis has been shown to lead to limited (one or two cycles) overestimation of the number of elapsed cycles before the remaining subgroup of patients has a certain low pregnancy profile (5). We therefore do not expect this to have largely impacted our results.
Dynamic predictions can give valuable input to individualized treatment decisions. When and over which future time horizon to predict can be maximally tailored to the couple’s situation. This tailoring is known to help patients recognize that predictions raised by a doctor actually apply to their situation and can add to an evidence based shared decision process.
Ultimately, for making treatment decisions we not only need an individualized prediction of a couple’s natural pregnancy prognosis, but also of their chances after treatment. So far, no study has been able to assess both of these within the same patient population. In the absence of such studies, the only alternative is to calculate natural pregnancy chances and pregnancy chances after treatment by using
separate models that have been developed in different patient cohorts. Our dynamic model for natural conception can optimize the comparability of such separately obtained predictions. The prediction can be rendered at the exact moment one considers starting treatment and for a number of menstrual cycles ahead matching the time period necessary for the alternatively considered treatment.
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APPENDIx PREDICTION FORMULA
After m unsuccessful expectant management cycles since the completion of fertility workup, the predicted cumulative probability P of natural conception within the next j cycles is:
With
μ = mean pregnancy chance in first cycle
PI = prognostic index = –1.64 – 0.03 * female age years below 31 –0.08 * female age years above 31
–0.47 * duration of child wish –0.34 * primary subfertility +0.008 * percentage of motile sperm –0.74 * referred by gynaecologist
The ∏ sign in the formula indicates replicated multiplication for i’s within the range m+1 to m+j. We will illustrate the formula with two examples.
Example 1 For a couple referred to the fertility clinic by their general practitioner with primary subfertility, VMC 20, duration of subfertility 1.5 years, female age 30 at completion of the fertility workup, the probability of conceiving naturally within the next 3 cycles is calculated as follows:
As no cycles have passed yet since the fertility workup, m=0. We want to calculate the probability for the next 3 cycles, so j=3. The multiplication then has to be done for i=1, i=2 and i=3:
Example 2 If the couple does not conceive within these three months, and returns to the fertility clinic, the probability for another 3 months can be calculated as follows. The parameter remains the same (note that age and duration should not be adjusted!). The m is now 3 and the j is also 3, so the multiplication has to be done for i=4, i=5 and i=6:
𝑃𝑃 = 1 − ∏𝑖𝑖=𝑚𝑚+𝑗𝑗1 − 𝜇𝜇 + 𝑖𝑖 ∗ 0.061 + 𝑖𝑖 ∗ 0.06 𝑖𝑖=𝑚𝑚+1 = 1 + 𝑒𝑒𝑒𝑒𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃𝑃𝑃 = −1.64 − 0.03 ∗ 30 − 0.08 ∗ 0 − 0.47 ∗ 1.5 − 0.34 ∗ 1 + 0.008 ∗ 20 − 0.74 ∗ 0 = −3.4 𝜇𝜇 =1 + 𝑒𝑒𝑒𝑒−3.4−3.4= 0.03 𝑃𝑃 = 1 − (1 − 0.03 + 1 ∗ 0.061 + 1 ∗ 0.06 ) ∗ (1 − 0.03 + 2 ∗ 0.061 + 2 ∗ 0.06 ) ∗ (1 − 0.03 + 3 ∗ 0.061 + 3 ∗ 0.06 ) = 1 − 0.972 ∗ 0.973 ∗ 0.975 = 0.08 = 8% 𝑃𝑃 = 1 − (1 − 0.03 + 4 ∗ 0.061 + 4 ∗ 0.06 ) ∗ (1 − 0.03 + 4 ∗ 0.061 + 4 ∗ 0.06 ) ∗ (1 − 0.03 + 4 ∗ 0.061 + 4 ∗ 0.06 ) = 1 − 0.976 ∗ 0.977 ∗ 0.978 = 0.07 = 7%
