Abstract

BACKGROUND

It is generally acknowledged that the outcomes of IVF treatments are correlated between repeat cycles in the same couple and that these effects need to be allowed for in the analysis of such treatments. However, there are few studies that have attempted to estimate the magnitude of these effects or their clinical consequences.

METHODS

We use the embryo-uterus model, extended to include inter-cycle correlations in both the embryo and uterine components to estimate these effects in a large data set of 12 480 embryo transfer cycles from 8768 UK IVF patients, including embryo grading parameters. Empirical Bayes estimates are used to predict the consequences of previous cycle failures on the prognosis of future cycles.

RESULTS

Statistically and clinically significant correlations can be detected which amount to a median odds ratio of 2.3 (95% CI: 1.8–2.9) in the chances of an embryo being viable between any two randomly selected patients. These act predominantly through the embryo component of the model. Inclusion of these effects in the embryo model does alter the estimates and predictions, but not dramatically. Around 10 cycle failures are required to reduce the probability of success in future cycles to half that of the initial cycle.

CONCLUSIONS

There are important inter-cycle correlations between embryos transferred across different cycles from the same patients, implying substantial unmeasured prognostic embryo characteristics. The implications for extended culture and cryopreserved embryos need further investigation as well as similar consideration of the other components of treatment, particularly response to stimulation. Although these effects should not be ignored they have limited impact in the development of predictive models for individual cycles, but do need to be accounted for when considering multiple cycle treatment programmes. For individual patients the failure of one or several embryo transfers does not have a big impact on the chances of success in future cycles. The magnitude of the correlations suggests that for any individual couple, previous cycle implantation failures do not imply a greatly reduced prognosis for future cycles.

Introduction

It is widely accepted that the outcomes of multiple infertility treatments for the same couple are not independent (Dias et al., 2008) and this has consequences for the analysis of outcome data from such treatments. These correlations between repeat cycles of treatment in the same couples reflect the fact that the factors affecting prognosis for any individual are not fully known and there are (unmeasured) patient characteristics which affect positively or negatively the outcomes of all treatment cycles for any given couple. The non-independence of cycle outcomes from the same couples can be considered equivalently as a correlation between treatment outcomes or as heterogeneity between patients with similar characteristics. The need to allow for such non-independence in study design and analysis is widely acknowledged, particularly in the context of clinical trials (Vail and Gardener, 2003; Makubate and Senn, 2010).

In clinical practice, treatment failure in a previous cycle is seen as a potential indicator of poorer prognosis for future treatments, independently of other factors. In cross-sectional data, a reduction in treatment success rates is seen with increasing attempt number (e.g. Templeton et al., 1996; Hirst et al., 2011; Nelson and Lawlor, 2011), although these effects are at least in part attributable to patient selection with a complex set of policy, financial, clinical and psychological factors determining which patients receive multiple treatments.

The hypothetical modelling study of Dias et al. (2008) investigated the role of correlations between repeat treatments in determining the success rates of subsequent treatments following one or more failures. Taking a single attempt at achieving pregnancy, this work assumed that individual couples have differing underlying potential success rates and therefore those failing in the first cycles and receiving subsequent cycles would be more likely to be those of poorer prognosis. Thus, the existence of inter-patient heterogeneity in prognosis directly leads to a decrease in success rates across cycles in observed data.

In the analysis of observational data, there have been a few attempts to allow for intra-patient correlations, mainly treating these as nuisance variables (e.g. Templeton et al., 1996; Hirst et al., 2011; Jonsdottir et al., 2011), but more often they are ignored (e.g. Baker et al., 2010) or only one cycle per patient is selected or an argument is made that the effects are small (e.g. Roberts et al., 2010a; Nelson and Lawlor, 2011). It has been argued that the omission of these correlations makes little difference to the model estimates and predictions (Templeton et al., 1996; Roberts et al., 2010a; Nelson and Lawlor, 2011) except where one explicitly needs to predict across multiple cycles from the same individual (e.g. Roberts et al., 2010b; Roberts et al., 2011). For such modelling studies, estimates of the correlations between cycles are needed. Additionally, the magnitude of the effects may illuminate the degree to which there are still unidentified prognostic factors to be identified.

There is very little previous work which attempts to explicitly quantify the magnitude of the correlations between repeat cycles: we are only aware of our own work (Roberts et al., 2010a; Hirst et al., 2011). This is largely due to the fact that these analyses are technically and computationally challenging.

The EU model, although underutilized, provides a rich framework within which to represent the embryo-implantation process. The model explicitly includes prognostic factors that act on the individual embryos and those which act on the recipient patient, with logistic regression sub-models for the two components. Although initially derived based on a specific biological mechanism involving embryo viability and uterine receptivity (Speirs et al., 1983; Zhou and Weinberg, 1998) it has a structure which readily accommodates a wider range of treatment and clinical factors. As such it can be conceived as a multilevel model with factors acting at either the patient or the embryo level whilst allowing for the lack of knowledge of individual embryo fates within multiple embryo transfers. The EU model structure explicitly allows, through the common U component, for correlations between embryos within each cycle, but until recently it has not been possible to include correlations between embryos from the same patients across multiple cycles.

This present work utilizes extensions to the EU model which include correlations between repeat cycles in the same patients by adding inter-patient heterogeneity (in a random intercept form) in either the embryo or the patient sub-model. We utilize a large multicentre UK data set which has sufficient detail and size to allow reliable estimation of the effects (Roberts et al., 2010a). We estimate the magnitude of these effects and their influence on model parameter estimates along with consideration of the implications for prediction of outcomes following one or more treatment failures.

Materials and Methods

The data set has been described previously (Roberts et al., 2010a) and the main characteristics of the data set analysed here are summarized briefly in Table I. It consists of routinely collected data from five UK treatment centres covering the range of UK practice and including NHS, fee-paying and private centres. A total of 12 480 fresh cycles from 8768 couples treated between 2000 and 2005 are included in the analyses presented here. The variables include patient and treatment characteristics and embryo grades of all transferred embryos. Most transfers were of double embryos (83%) with 11% single and 6% triple.

Table I

Patient characteristics of the data set.

Parameter Categories  
Number of patients  8768 
Number of embryo transfers  12 480 
Embryo transfers per couple 6079 (69%) 
1935 (22%) 
>2 754 (9%) 
Numbers of embryos transferred 1328 (11%) 
10 413 (83%) 
739 (6%) 
Female age Mean (SD) [range] 33.8 (4.2) [19, 47] 
Treatment attempta 1st 6791 (54%) 
2nd 2903 (23%) 
≥3rd 2786 (22%) 
IVF or ICSI IVF 6470 (52%) 
ICSI 6017 (48%) 
Tubal diagnosis Yes 3133 (25%) 
PCO diagnosis Yes 1298 (10%) 
Endometriosis Yes 1144 (9%) 
Idiopathic diagnosis Yes 3348 (27%) 
Male factor diagnosis Yes 4667 (37%) 
Outcomes Live birth events 2800 (22.4%) 
Multiple birth rateb 686 (24.5%) 
Parameter Categories  
Number of patients  8768 
Number of embryo transfers  12 480 
Embryo transfers per couple 6079 (69%) 
1935 (22%) 
>2 754 (9%) 
Numbers of embryos transferred 1328 (11%) 
10 413 (83%) 
739 (6%) 
Female age Mean (SD) [range] 33.8 (4.2) [19, 47] 
Treatment attempta 1st 6791 (54%) 
2nd 2903 (23%) 
≥3rd 2786 (22%) 
IVF or ICSI IVF 6470 (52%) 
ICSI 6017 (48%) 
Tubal diagnosis Yes 3133 (25%) 
PCO diagnosis Yes 1298 (10%) 
Endometriosis Yes 1144 (9%) 
Idiopathic diagnosis Yes 3348 (27%) 
Male factor diagnosis Yes 4667 (37%) 
Outcomes Live birth events 2800 (22.4%) 
Multiple birth rateb 686 (24.5%) 

aFresh plus frozen IVF cycles.

bNumber of multiple birth outcomes and percentage of live birth events.

PCO, polycystic ovary syndrome.

The data are fitted using an EU model framework, which comprises two logistic regression sub-models describing the embryo and uterine components of the success. The model requires that for an embryo to develop it must both be viable (positive outcome from the embryo component) and have a receptive uterus (positive outcome from the uterine component). Details of the model and fitting process as used here have been described previously (Roberts, 2007). For the work here, we add a patient-level random effect term to either the embryo or uterus sub-model which can be thought of as representing unmeasured covariates specific to each patient—an individual measure of prognosis. Formally the probability Eijk of embryo k in cycle j for patient i being viable and the corresponding probability of the uterus being receptive, Uij, is given by: 

formula
where forumla and forumla are covariate matrices for the E and U sub-models and forumla and forumla the corresponding parameter vectors. The forumla and forumla are the added random effects which are assumed to be normally distributed with zero mean and variances forumla and forumla. For single embryo transfer, the probability of a live birth in cycle j for patient i is given simply by UijEij1. For double embryo transfer, the probability of a singleton birth is given by forumla and a twin birth by UijEij1Eij2.

The models are fitted by direct maximization of the observed data likelihood using custom-written software implemented using the ml procedure in Stata. Intergration over the random effects utilized Gauss-Hemite quadrature with a minimum of 16 integration points and the results confirmed by increasing the number of points (Stylianou, 2011). We present models without any random effects and with a random effect added to either the U or the E sub-model. Whilst it is possible in principal to fit a model which includes random effects in both sub-models, this is (unsurprisingly) not identified in this data set. Predicted outcomes are presented as both population averages over the patient variability (forumla or forumla) and as empirical Bayes estimates which give predictions for future cycles given the outcomes (in this case negative) of previous cycles.

All the analyses here used live birth (number of babies) as the outcome measure and the covariates included were based on previous work with this data set (Roberts et al., 2010a). In order to simplify the presentation, the full model presented in the earlier work has been somewhat simplified by removing non-significant covariates and using a categorical representation of embryo cell growth and grade rather than a spline representation. The simplified model gives virtually identical results to the full model described earlier. Cell growth is represented as doublings per day [i.e. log2 (cell number)/(days in culture)] and classified as slow (<0.7), normal (0.7–1.0) or fast (≥1.0). Grade was based on Steer et al. (1992). The assignment of prognostic factors to either the E or U sub-model follows that described previously and utilized a combination of clinical knowledge and statistical selection. The model selection procedure of the previous work led to the inclusion of treatment attempt number in the U sub-model. As the effect of attempt number is critical to the understanding of the effects of inter-cycle correlations, we also considered variants of the model in which attempt was fitted in the E, the U or both model components.

The model parameters are shown as odds ratios with 95% CI. The between-patient variances forumla and forumla are shown as median odds ratios (MOR) (Larsen and Merlo, 2005): these estimate the median odds ratio of response between the higher and lower of any two randomly selected patients. Models are compared using the Akiake Information criterion (AIC) which provides a measure of the goodness of fit allowing for the number of parameters fitted. Model fit is quantified using the standard area under the receiver–operator characteristics curve (AUC), with three non-independent values for no birth, singleton and multiple births. Hypothesis tests are based on likelihood ratio tests between appropriately chosen models.

Results

Table II shows the fitted model parameters for the three variants: no correlation between cycles, correlation in the U sub-model and correlation in the E sub-model. The estimates from the model with U sub-model correlations are almost identical to that when the correlation is omitted, with only a very marginal increase in the uncertainty (as shown by the width of the 95% CI). This has been noted before (Templeton et al., 1996; Roberts et al., 2010a; Hirst et al., 2011; Nelson and Lawlor, 2011) based on less sophisticated approaches. There are rather larger differences in the estimates when we allow for correlations in the E sub-model, although these are still rather small on any practical scale.

Table II

Model parameters, expressed as odds ratios (OR) with 95% CI, assuming either no correlation between cycles from the same patients, or a correlation in the U or E sub-model.

 No correlation
 
Correlation in U sub-model
 
Correlation in E sub-model
 
 OR 95% CI OR 95% CI OR 95% CI 
U sub-model 
 Age 
  ≤26 0.85 0.58 1.23 0.84 0.55 1.27 0.74 0.43 1.26 
  27–29 0.85 0.63 1.16 0.85 0.60 1.18 0.76 0.48 1.18 
  30–31 1.06 0.79 1.43 1.08 0.78 1.50 1.01 0.65 1.57 
  32–33 1.10 0.81 1.49 1.12 0.80 1.57 1.08 0.69 1.71 
  34–35       
  36–37 0.80 0.58 1.10 0.78 0.55 1.11 0.79 0.50 1.26 
  38–39 0.85 0.56 1.29 0.83 0.53 1.32 0.87 0.48 1.59 
  40–42 0.48 0.24 0.98 0.44 0.21 0.95 0.55 0.19 1.65 
  ≥43 0.14 0.02 0.77 0.12 0.02 0.72 0.13 0.01 1.46 
 Embryo 
  1 0.60 0.37 0.97 0.56 0.33 0.96 0.55 0.32 0.96 
  2 0.75 0.58 0.98 0.73 0.54 0.98 0.74 0.54 1.02 
  3 0.82 0.64 1.04 0.80 0.61 1.04 0.81 0.61 1.08 
  4 0.89 0.70 1.11 0.87 0.68 1.13 0.87 0.66 1.15 
  5 1.00 0.79 1.26 1.00 0.77 1.29 1.01 0.76 1.34 
  6       
  7–8 1.13 0.92 1.40 1.15 0.90 1.45 1.16 0.89 1.50 
  9–12 1.21 0.98 1.49 1.23 0.97 1.56 1.25 0.97 1.63 
  ≥13 1.31 1.01 1.70 1.35 1.00 1.80 1.38 0.99 1.91 
 Years infertile 
  0–2 1.25 1.03 1.52 1.31 1.05 1.63 1.34 1.05 1.72 
  3 1.05 0.86 1.29 1.06 0.85 1.33 1.08 0.84 1.38 
  4 11       
  5 0.91 0.74 1.12 0.91 0.72 1.14 0.91 0.71 1.16 
  6 0.91 0.73 1.14 0.90 0.71 1.16 0.90 0.69 1.17 
  7–8 0.84 0.68 1.04 0.83 0.65 1.05 0.82 0.64 1.06 
  ≥9 0.85 0.69 1.05 0.84 0.66 1.05 0.82 0.64 1.06 
 Year 1.05 1.00 1.11 1.05 0.99 1.12 1.05 0.97 1.14 
 Tubal diagnosis 0.75 0.66 0.86 0.73 0.63 0.85 0.73 0.62 0.85 
 Endometriosis 1.28 1.06 1.55 1.32 1.06 1.65 1.35 1.05 1.75 
 Attempt 
  1st       
  2nd 0.82 0.71 0.94 0.84 0.72 0.98 0.84 0.71 0.99 
  3rd 0.83 0.69 1.00 0.87 0.70 1.08 0.89 0.70 1.13 
  4 or more attempts 0.71 0.59 0.87 0.77 0.61 0.97 0.77 0.60 1.00 
 Previous birth 1.36 1.17 1.58 1.37 1.15 1.62 1.44 1.18 1.77 
E sub-model 
 Age 
  ≤26 1.65 1.12 2.44 1.63 1.10 2.41 1.79 1.08 2.97 
  27–29 1.57 1.16 2.14 1.55 1.14 2.11 1.68 1.13 2.48 
  30–31 1.39 1.05 1.84 1.38 1.04 1.83 1.46 1.02 2.07 
  32–33 1.12 0.85 1.47 1.11 0.84 1.47 1.14 0.81 1.62 
  34–35       
  36–37 0.99 0.73 1.34 0.99 0.73 1.33 0.95 0.65 1.39 
  38–39 0.74 0.51 1.08 0.74 0.51 1.07 0.70 0.44 1.10 
  40–42 0.56 0.28 1.14 0.56 0.28 1.13 0.43 0.17 1.07 
  ≥43 0.62 0.07 5.29 0.62 0.07 5.28 0.49 0.03 8.97 
 Male diagnosis 1.10 0.98 1.23 1.10 0.98 1.23 1.13 1.00 1.28 
 Year 1.01 0.95 1.06 1.01 0.95 1.06 1.00 0.94 1.08 
 Growth rate 
  <0.7 0.38 0.31 0.47 0.38 0.31 0.47 0.35 0.27 0.44 
  0.7–1.0 0.54 0.44 0.67 0.54 0.44 0.67 0.51 0.41 0.64 
  1.0–1.3       
  >1.3 0.40 0.27 0.58 0.39 0.27 0.58 0.37 0.25 0.57 
 Grade 
  1 0.19 0.13 0.27 0.19 0.13 0.27 0.17 0.11 0.25 
  2 0.57 0.45 0.73 0.57 0.45 0.72 0.54 0.42 0.69 
  3 0.86 0.75 1.00 0.86 0.75 1.00 0.84 0.72 0.98 
  4       
 Embryo transfer 
  1 1.10 0.75 1.60 1.09 0.75 1.59 1.11 0.75 1.63 
  2ET       
  3 0.83 0.66 1.04 0.83 0.66 1.05 0.87 0.68 1.13 
 Correlation parameters 
  σU    0.71 0.25 1.16    
  σE       0.85 0.60 1.10 
MOR    1.96 1.27 3.03 2.25 1.77 2.86 
 No correlation
 
Correlation in U sub-model
 
Correlation in E sub-model
 
 OR 95% CI OR 95% CI OR 95% CI 
U sub-model 
 Age 
  ≤26 0.85 0.58 1.23 0.84 0.55 1.27 0.74 0.43 1.26 
  27–29 0.85 0.63 1.16 0.85 0.60 1.18 0.76 0.48 1.18 
  30–31 1.06 0.79 1.43 1.08 0.78 1.50 1.01 0.65 1.57 
  32–33 1.10 0.81 1.49 1.12 0.80 1.57 1.08 0.69 1.71 
  34–35       
  36–37 0.80 0.58 1.10 0.78 0.55 1.11 0.79 0.50 1.26 
  38–39 0.85 0.56 1.29 0.83 0.53 1.32 0.87 0.48 1.59 
  40–42 0.48 0.24 0.98 0.44 0.21 0.95 0.55 0.19 1.65 
  ≥43 0.14 0.02 0.77 0.12 0.02 0.72 0.13 0.01 1.46 
 Embryo 
  1 0.60 0.37 0.97 0.56 0.33 0.96 0.55 0.32 0.96 
  2 0.75 0.58 0.98 0.73 0.54 0.98 0.74 0.54 1.02 
  3 0.82 0.64 1.04 0.80 0.61 1.04 0.81 0.61 1.08 
  4 0.89 0.70 1.11 0.87 0.68 1.13 0.87 0.66 1.15 
  5 1.00 0.79 1.26 1.00 0.77 1.29 1.01 0.76 1.34 
  6       
  7–8 1.13 0.92 1.40 1.15 0.90 1.45 1.16 0.89 1.50 
  9–12 1.21 0.98 1.49 1.23 0.97 1.56 1.25 0.97 1.63 
  ≥13 1.31 1.01 1.70 1.35 1.00 1.80 1.38 0.99 1.91 
 Years infertile 
  0–2 1.25 1.03 1.52 1.31 1.05 1.63 1.34 1.05 1.72 
  3 1.05 0.86 1.29 1.06 0.85 1.33 1.08 0.84 1.38 
  4 11       
  5 0.91 0.74 1.12 0.91 0.72 1.14 0.91 0.71 1.16 
  6 0.91 0.73 1.14 0.90 0.71 1.16 0.90 0.69 1.17 
  7–8 0.84 0.68 1.04 0.83 0.65 1.05 0.82 0.64 1.06 
  ≥9 0.85 0.69 1.05 0.84 0.66 1.05 0.82 0.64 1.06 
 Year 1.05 1.00 1.11 1.05 0.99 1.12 1.05 0.97 1.14 
 Tubal diagnosis 0.75 0.66 0.86 0.73 0.63 0.85 0.73 0.62 0.85 
 Endometriosis 1.28 1.06 1.55 1.32 1.06 1.65 1.35 1.05 1.75 
 Attempt 
  1st       
  2nd 0.82 0.71 0.94 0.84 0.72 0.98 0.84 0.71 0.99 
  3rd 0.83 0.69 1.00 0.87 0.70 1.08 0.89 0.70 1.13 
  4 or more attempts 0.71 0.59 0.87 0.77 0.61 0.97 0.77 0.60 1.00 
 Previous birth 1.36 1.17 1.58 1.37 1.15 1.62 1.44 1.18 1.77 
E sub-model 
 Age 
  ≤26 1.65 1.12 2.44 1.63 1.10 2.41 1.79 1.08 2.97 
  27–29 1.57 1.16 2.14 1.55 1.14 2.11 1.68 1.13 2.48 
  30–31 1.39 1.05 1.84 1.38 1.04 1.83 1.46 1.02 2.07 
  32–33 1.12 0.85 1.47 1.11 0.84 1.47 1.14 0.81 1.62 
  34–35       
  36–37 0.99 0.73 1.34 0.99 0.73 1.33 0.95 0.65 1.39 
  38–39 0.74 0.51 1.08 0.74 0.51 1.07 0.70 0.44 1.10 
  40–42 0.56 0.28 1.14 0.56 0.28 1.13 0.43 0.17 1.07 
  ≥43 0.62 0.07 5.29 0.62 0.07 5.28 0.49 0.03 8.97 
 Male diagnosis 1.10 0.98 1.23 1.10 0.98 1.23 1.13 1.00 1.28 
 Year 1.01 0.95 1.06 1.01 0.95 1.06 1.00 0.94 1.08 
 Growth rate 
  <0.7 0.38 0.31 0.47 0.38 0.31 0.47 0.35 0.27 0.44 
  0.7–1.0 0.54 0.44 0.67 0.54 0.44 0.67 0.51 0.41 0.64 
  1.0–1.3       
  >1.3 0.40 0.27 0.58 0.39 0.27 0.58 0.37 0.25 0.57 
 Grade 
  1 0.19 0.13 0.27 0.19 0.13 0.27 0.17 0.11 0.25 
  2 0.57 0.45 0.73 0.57 0.45 0.72 0.54 0.42 0.69 
  3 0.86 0.75 1.00 0.86 0.75 1.00 0.84 0.72 0.98 
  4       
 Embryo transfer 
  1 1.10 0.75 1.60 1.09 0.75 1.59 1.11 0.75 1.63 
  2ET       
  3 0.83 0.66 1.04 0.83 0.66 1.05 0.87 0.68 1.13 
 Correlation parameters 
  σU    0.71 0.25 1.16    
  σE       0.85 0.60 1.10 
MOR    1.96 1.27 3.03 2.25 1.77 2.86 

σU and σE are the fitted standard deviations on a log-odds scale and MOR expresses these as a the median odds ratio between any two randomly chosen couples. An OR of 1 indicates the reference categories.

The correlations themselves are however not small, with estimates in terms of the inter-patient heterogeneity giving median odds ratios of around 2. That is, after taking into account all the measured prognostic factors (age, history, embryo grade, etc.), any two randomly chosen otherwise identical couples have a factor of 2 difference in their odds of conceiving.

Formal comparison of the fits (Table III) indicates that the model with embryo sub-model correlations is the best fit to the data and a statistically significant improvement on the uncorrelated model. However, in terms of prediction, the three models have virtually identical AUC measures, these reflecting the very similar model predictions in a single cycle. In Fig. 1, we show the predicted live birth (singleton or multiple) and multiple birth probabilities for the two correlated models compared with the standard uncorrelated model. We see that the correlated models give almost identical predictions for individual outcomes, but that adding correlation to the E sub-model does show greater differences in individual predictions and a slight tendency to predict higher twin rates. As shown in Table II the effect of treatment attempt is somewhat diminished if we allow for embryo-level correlations. This effect is examined more closely in Table IV where we note that the effect of attempt which was highly significant if we ignore correlations loses statistical significance in the presence of inter-cycle correlations. These conclusions are not sensitive to the choice of sub-model chosen for the attempt number covariate (data not shown). However, we note from Table II that the effect estimates themselves are not greatly diminished. Within the correlated EU model, it is possible to obtain estimates of the outcomes in couples given that they have had one or more previous failures (this is analogous to the estimates produced by Dias et al. (2008)). These so-called empirical Bayes estimates are shown, for a typical couple in Fig. 2, alongside the estimates from the uncorrelated model. Here we see that (upper panels) if we ignore correlations we would see only a modest loss in success as the number of treatment failures increases, and this loss is smaller in single embryo transfer (SET) compared with double embryo transfer (DET) cycles. In contrast if we allow for correlations, previous failures do suggest a more substantial drop in live birth rate. When considering live birth outcomes, the two correlated models yield similar predictions. Interestingly, this is not so for twin rates (Fig. 2, lower panels) where the presence of E-level correlations leads to a prediction that for any individual couple having a number of previous failures implies their expected twin rate will be modestly lowered in subsequent cycles. When there is appreciable inter-patient variability in embryo viability, couples with failures will have, on average, poorer quality embryos and the probability of twins given pregnancy is dependent on the viability of the second embryo. In contrast U sub-model correlations imply that the couples with failures have an overall reduced probability of success due to non-embryo factors, and therefore if there is a live birth then the proportion that produces twins is not changed.

Table III

Comparison of the models with correlations in U, E or neither sub-model along with validation statistics.

 No correlation Correlation in U sub-model Correlation in E sub-model 
AIC 15574.6 15573.1 15564.9 
P v no correlation  0.061 0.0006 
AUC (no LB; singleton; twins) 0.67; 0.63; 0.69 0.67; 0.63; 0.69 0.67;0.63; 0.69 
 No correlation Correlation in U sub-model Correlation in E sub-model 
AIC 15574.6 15573.1 15564.9 
P v no correlation  0.061 0.0006 
AUC (no LB; singleton; twins) 0.67; 0.63; 0.69 0.67; 0.63; 0.69 0.67;0.63; 0.69 

Rows give the AIC, the significance level of a likelihood ratio test for no correlation and the area under the ROC curve measure of the predictive ability for no live birth, singleton and twin outcomes.

Table IV

Comparison of models with and without attempt number.

 No correlation Correlation in U sub-model Correlation in E sub-model 
AIC (with attempt) 15574.6 15573.1 15564.9 
AIC (no attempt) 15585.3 15573.9 15565.1 
P v attempt 0.0008 0.079 0.10 
 No correlation Correlation in U sub-model Correlation in E sub-model 
AIC (with attempt) 15574.6 15573.1 15564.9 
AIC (no attempt) 15585.3 15573.9 15565.1 
P v attempt 0.0008 0.079 0.10 

AIC with and without attempt in the model along with a likelihood ratio test for the inclusion of attempt.

Figure 1

Predicted (population-averaged) live birth (panels a and b) and twin rates (c and d) per transfer cycle comparing models with inter-cycle correlations (a and c) in the U sub-model and (b and d) in the E sub-model with the model ignoring such correlations. For clarity outcomes are shown for 500 randomly selected patients

Figure 1

Predicted (population-averaged) live birth (panels a and b) and twin rates (c and d) per transfer cycle comparing models with inter-cycle correlations (a and c) in the U sub-model and (b and d) in the E sub-model with the model ignoring such correlations. For clarity outcomes are shown for 500 randomly selected patients

Figure 2

Predicted outcomes (a and b, live birth and c and d, twin rates per transfer cycle) for a typical patient as the number of previous treatment failures increases. In each panel three estimates are shown: an uncorrelated model where repeat cycles are independent and model explicitly inter-cycle correlation with and without an explicit term for attempt number. For the upper panels predictions are shown for single (SET) and double (DET) embryo transfers. In panels a and c the inter-cycle correlation is included in the U sub-model and in b and d the correlation is in the E sub-model.

Figure 2

Predicted outcomes (a and b, live birth and c and d, twin rates per transfer cycle) for a typical patient as the number of previous treatment failures increases. In each panel three estimates are shown: an uncorrelated model where repeat cycles are independent and model explicitly inter-cycle correlation with and without an explicit term for attempt number. For the upper panels predictions are shown for single (SET) and double (DET) embryo transfers. In panels a and c the inter-cycle correlation is included in the U sub-model and in b and d the correlation is in the E sub-model.

Discussion

Previous work has only considered inter-cycle correlations in IVF outcomes in a limited way, here we have exploited the EU model approach to look at such correlations between both embryo viability and the couples receptivity between repeat cycles from the same couple. The data here suggest strongly that there are such correlations and that they act predominantly through the embryo component. Thus, this suggests that there are factors which vary from patient to patient which substantially affect embryo viability and which are not measured with the covariates considered here. Such factors may include a propensity towards chromosomal aneuploidy or other genetic factors beyond those simply associated with increasing chronological age or identified as differences in morphological grade.

The estimates of the magnitude of the inter-cycle correlation are surprisingly large, with median odds ratios of around 2 between any two randomly selected, otherwise identical, couples. This suggests that there is still considerable scope for determining factors which predict outcome, particularly those affecting embryo viability. These may include improved grading (Cutting et al., 2008; Alpha Scientists in Reproductive Medicine and ESHRE Special Interest Group of Embryology, 2011) or novel biomarkers (e.g. Brison et al., 2004; Seli et al., 2007; Katz-Jaffe et al., 2009). Culture to blastocyst stage resolves some of the embryo uncertainty during cell culture and it might be informative to compare these estimates with those from repeat blastocyst transfers. Similar magnitude effects have been seen in a cruder analysis of the same data set (Roberts et al., 2010a), in a simpler analysis of the UK national data (Hirst et al., 2011) and in an analysis of the latter data using an EU approach (Roberts, unpublished). These estimates compare with a larger MOR of 3.3 (95% CI: 2.9–4.0) if no covariates are included in the model.

The presence of such correlations does suggest that previous treatment failure is indeed prognostic. Estimates of the effect of such failures from cross-sectional data show a decreased live birth rate with increasing attempt number, but these estimates are inevitably biased as patient choice and treatment policy means that the patient groups having different numbers of cycles are composed of patients with different characteristics and prognosis. Estimates such as those of Fig. 2 give direct estimates of the losses expected for individual patients following treatment failure. Although greater than would be estimated from cross-sectional data, these losses are actually quite modest and suggest that in excess of 10 treatment failures are required to reduce the chances of subsequent success by half (and even more in SET cycles). This has implications for the counselling of couples as it implies that a treatment failure should be considered more a matter of bad luck and only slightly lowers their chances for subsequent treatments. It also has implications for policy-makers as it suggests that rationing patients to only a small number of treatments has little clinical justification.

We confirm previous results using an EU approach (Roberts et al., 2010a) that correlations between patient receptivities have negligible effect on the parameter estimates or predictive accuracy of the models. In contrast correlations between embryo viabilities do have an, albeit small, effect on the parameter estimates, and do have a small effect on the model predictions. Given the inherent biases and uncertainties in observational data sets, this is likely to be a minor problem for the practical application of such models.

Although the data set here is large, the proportion of repeat cycles is relatively small. The limitations of the data set have been discussed previously (Roberts et al., 2010b), and it is possible that the intra-patient effects seen here as correlations might be associated with unmeasured or poorly measured covariates. The data here relate to fresh, cleavage stage, transfers and it would be informative to investigate the correlations between fresh and frozen embryos and whether blastocyst transfer provides further information which reduces the effects.

In conclusion we have shown that it is possible to identify and estimate substantial correlations between embryo-transfer cycles from the same couples. These correlations have been shown to be predominately associated with inter-patient differences in embryo viability rather than with patient factors, although some influence of both cannot be ruled out. Whilst the bias induced in predictive models is small, the magnitude of the effects suggests that there are still important factors relating to embryo viability to be identified. These effects do need to be incorporated in any modelling or prediction concerning multi-cycle outcomes. The magnitude of the correlations suggests that for any individual couple previous cycle failures do not imply a greatly reduced prognosis for future cycles.

Authors' roles

S.A.R. conceived and led the project, designed the study and performed the analyses presented and wrote the paper. C.S. developed the methodology and software and contributed to the manuscript.

Funding

S.A.R. is supported by the NIHR Manchester Biomedical Research Centre. C.S. was supported by a Medical Research Council studentship.

Conflict of interest

None declared.

Acknowledgements

The data reanalysed here were collated as part of the towardSET project funded by the NIHR Health Technology Assessment programme (project number 05/43/01) and that work has been published in full in the Health Technology Assessment journal (Roberts et al., 2010b). The views and opinions expressed are those of the authors and do not necessarily reflect those of the Department of Health or our advisors. We acknowledge helpful discussions with Andy Vail and Daniel Brison and the support of the towardSET collaboration in providing the data.

References

Alpha Scientists in Reproductive Medicine and ESHRE Special Interest Group of Embryology
The Istanbul consensus workshop on embryo assessment: proceedings of an expert meeting
Hum Reprod
 , 
2011
, vol. 
26
 (pg. 
1270
-
1283
)
Baker
VL
Luke
B
Brown
MB
Alvero
R
Frattarelli
JL
Usadi
R
Grainger
DA
Armstrong
AY
Multivariate analysis of factors affecting probability of pregnancy and live birth with in vitro fertilization: an analysis of the Society for Assisted Reproductive Technology Clinic Outcomes Reporting System
Fertil Steril
 , 
2010
, vol. 
94
 (pg. 
1410
-
1416
)
Brison
DR
Houghton
FD
Falconer
D
Roberts
SA
Hawkhead
J
Humpherson
PG
Lieberman
BA
Leese
HJ
Identification of viable embryos in IVF by non-invasive measurement of amino acid turnover
Hum Reprod
 , 
2004
, vol. 
19
 (pg. 
2319
-
2324
)
Cutting
R
Morroll
D
Roberts
SA
Pickering
S
Rutherford
A
Elective single embryo transfer: guidelines for practice British Fertility Society and Association of Clinical Embryologists
Hum Fertil (Camb)
 , 
2008
, vol. 
11
 (pg. 
131
-
146
)
Dias
S
McNamee
R
Vail
A
Bias in frequently reported analyses of subfertility trials
Stat Med
 , 
2008
, vol. 
27
 (pg. 
5605
-
5619
)
Hirst
WM
Vail
A
Brison
DR
Roberts
SA
Prognostic factors influencing fresh and frozen IVF outcomes: an analysis of the UK national database
Reprod BioMed Online
 , 
2011
, vol. 
22
 (pg. 
437
-
448
)
Jonsdottir
I
Lundin
K
Bergh
C
Double embryo transfer gives good pregnancy and live birth rates in poor responders with a modest increase in multiple birth rates: results from an observational study
Acta Obstet Gynecol Scand
 , 
2011
, vol. 
90
 (pg. 
761
-
766
)
Katz-Jaffe
MG
McReynolds
S
Gardner
DK
Schoolcraft
WB
The role of proteomics in defining the human embryonic secretome
Mol Hum Reprod
 , 
2009
, vol. 
15
 (pg. 
271
-
277
)
Larsen
K
Merlo
J
Appropriate assessment of neighborhood effects on individual health: integrating random and fixed effects in multilevel logistic regression
Am J Epidemiol
 , 
2005
, vol. 
161
 (pg. 
81
-
88
)
Makubate
B
Senn
S
Planning and analysis of cross-over trials in infertility
Stat Med
 , 
2010
, vol. 
29
 (pg. 
3203
-
3210
)
Nelson
SM
Lawlor
DA
Predicting live birth, preterm delivery, and low birth weight in infants born from in vitro fertilisation: a prospective study of 144,018 treatment cycles
PLoS Med
 , 
2011
, vol. 
8
 pg. 
e1000386
 
Roberts
SA
Models for assisted conception data with embryo-specific covariates
Stat Med
 , 
2007
, vol. 
26
 (pg. 
156
-
170
)
Roberts
SA
Hirst
WM
Brison
DR
Vail
A
Embryo and uterine influences on IVF outcomes: an analysis of a UK multi-centre cohort
Hum Reprod
 , 
2010a
, vol. 
25
 (pg. 
2792
-
2802
)
Roberts
SA
McGowan
L
Hirst
W
Brison
D
Vail
A
Lieberman
B
Towards single embryo transfer? Modelling clinical outcomes of potential treatment choices using multiple data sources: predictive models and patient perspectives
Health Technol Assess
 , 
2010b
, vol. 
14
 (pg. 
1
-
237
)
Roberts
SA
McGowan
L
Mark
HW
Vail
A
Rutherford
A
Lieberman
BA
Brison
DR
Reducing the incidence of twins from IVF treatments: predictive modelling from a retrospective cohort
Hum Reprod
 , 
2011
, vol. 
26
 (pg. 
569
-
575
)
Seli
E
Sakkas
D
Scott
R
Kwok
SC
Rosendahl
SM
Burns
DH
Noninvasive metabolomic profiling of embryo culture media using Raman and near-infrared spectroscopy correlates with reproductive potential of embryos in women undergoing in vitro fertilization
Fertil Steril
 , 
2007
, vol. 
88
 (pg. 
1350
-
1357
)
Speirs
AL
Lopata
A
Gronow
MJ
Kellow
GN
Johnston
WIH
Analysis of the benefits and risks of multiple embryo transfer
Fertil Steril
 , 
1983
, vol. 
39
 (pg. 
468
-
471
)
Steer
CV
Mills
CL
Tan
SL
Campbell
S
Edwards
RG
The cumulative embryo score: a predictive embryo scoring technique to select the optimal number of embryos to transfer in an in-vitro fertilization and embryo transfer programme
Hum Reprod
 , 
1992
, vol. 
7
 (pg. 
117
-
119
)
Stylianou
C
Predictive modelling of assisted conception data with embryo-level covariates. Statistical issues and application
2011
UK
University of Manchester
 
Ph.D. Thesis
Templeton
A
Morris
JK
Parslow
W
Factors that affect outcome of in-vitro fertilisation treatment
Lancet
 , 
1996
, vol. 
348
 (pg. 
1402
-
1406
)
Vail
A
Gardener
E
Common statistical errors in the design and analysis of subfertility trials
Hum Reprod
 , 
2003
, vol. 
18
 (pg. 
1000
-
1004
)
Zhou
H
Weinberg
CR
Evaluating effects of exposures on embryo viability and uterine receptivity in in vitro fertilization
Stat Med
 , 
1998
, vol. 
17
 (pg. 
1601
-
1612
)