CE(95)02
24 April 1995
To: All Persons Responsible
Dear Colleague
I know that some centres have expressed an interest in receiving more information on the model that is to be used to adjust the raw data to produce the results of IVF and DI treatments for individual centres. I, therefore, enclose a copy of the statistical details of the model.
If you wish to discuss any aspects of the document, please contact Bill Parslow. Please let us have any comments on the details by 10th May 1995.
Yours faithfully
Flora Goldhill
Chief Executive
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Statistical Details of the Model used to Adjust Live Birth Rates from IVF
1. Introduction
There are several factors that have been shown to affect the live birth rate of a women having IVF. For example the age of the woman, the type of treatment she has (for example using fresh or frozen embryos), whether she has had previous live births, whether she has had previous IVF pregnancies or whether she has had previous unsuccessful IVF treatment will all affect her chances of having a live birth. Also the presence of any male factors for infertility affect the success rates.
Therefore it is not reasonable to compare the live birth rates for each centre, without making some allowances for the fact that different centres will treat different types of women. For instance some centres will treat much older women than other centres. One method of comparing epidemiological measures across populations is to use indirect adjustment to control for confounding1. However, if there are 1 or more confounders that are continuous rather than categorical indirect adjustment becomes impractical as the strata in the whole population have few observations, and the stratum specific measures and their standard errors become very unstable. To overcome these problems a form of regression adjustmentlj was used. Note that if only categorical variables are being analysed and all the strata are large the two methods will give the same results.
2. The Statistical Model
A logistic regression model is fitted to predict the probability of a treatment cycle resulting in a live birth given the age of the women being treated, the type of treatment she is receiving and various other prognostic factors about her. The model is fitted to data from all the centres, except for the women that have been excluded from all the analysis (details are given in (4)). All models are fitted using PROC LOGIST in SAS. The fitted model is then used to calculate the probability of having a live birth for each women in a particular centre given their actual age and other covariates. The sum of these probabilities gives the expected proportion of these women having a live birth. The actual number of women having a live birth is also calculated for each centre. The ratio of expected number of births to total number of births that occurred gives a comparative measure of the centres "effectiveness"". ie those with values higher than 1 have a higher live birth rate than the average and those with values lower than 1 have a lower live birth rate than average.
The expected live birth rate in women under 38 is also calculated by using the fitted model to calculate the probability of having a live birth of all the women in all the centres who are under 38. The adjusted live birth rate for each centre is calculated by multiplying the "effectiveness" ratios by the expected live birth rate in women under 38. Therefore the adjusted live birth rate given for each centre is the live birth rate that the centre would be predicted to achieve if it treated only women under 38.
The standard errors of the adjusted live birth rates are calculated using the standard errors of a binomial proportion with the adjusted live birth rate being the proportion and the number of women treated in that centre being the sample size. This is a reasonable approximation.
3. Factors included in the Model
3.1) The age of the mother
The age of the mother at the time of the treatment cycle is calculated to the nearest month. The model fits it as a linear, quadratic and cubic term.
3.2) The type of treatment
Nine different categories for the type of treatment the women has are entered as dummy variables into the model. The categories are:
1. Partner's sperm ; fresh embryo transfer ; stimulated ; male factors
2. Partner's sperm ; fresh embryo transfer ; stimulated ; no male factors
3. Partner's sperm ; fresh embryo transfer ; unstimulated ; male factors
4. Partner's sperm ; fresh embryo transfer ; unstimulated ; no male factors
5. Partner's sperm ; frozen embryo transfer ; male factors
6. Partner's sperm ; frozen embryo transfer ; no male factors
7. Donated sperm ; fresh embryo transfer ; stimulated
8. Donated sperm ; fresh embryo transfer ; unstimulated
9. Donated sperm ; frozen embryo transfer
3.3) Previous Live Births
If a woman has had previous live birth or not is entered into the model as a binary variable.
3.4) Previous IVF Treatments
Five dummy variables are entered into the model as follows:
1. If a woman has had previous IVF treatment which resulted in a pregnancy
2. If a woman has had 1 previous IVF treatment which did not result in a pregnancy
3. If a woman has had 2 previous IVF treatments which did not result in a pregnancy
4. If a woman has had 3 previous IVF treatments which did not result in a pregnancy
5. If a woman has had 4 or more previous IVF treatments which did not result in a pregnancy
(The baseline category is a woman having IVF for the first time).
3.5) The number of embryos transferred
This is not in the model at present, but due to the consultation process it will be included in the revised model.
4. Exclusions from the Model
Women being treated with donated embryos or donated eggs are excluded from the analysis. Women using donated embryos were excluded, because the number of women is very small and the number of centres offering such treatment is restricted (17 centres). Similarly with women using donated eggs, although the numbers are much larger only 21 centres offered such treatment.
5. The Fitted Model
| Factor in the model | Odds ratio | 95% Confidence Interval |
| Intercept | 0.18 | 0.16 0.20 |
| Age - linear | 0.93 | 0.99 0.99 |
| Age - quadratic | 0.91 | 0.98 0.99 |
| Age - cubic | 0.95 | 0.99 1.00 |
| Treatment Group*: 1 | 0.84 | 0.76 0.92 |
| Treatment Group*: 2 | 1.00 | |
| Treatment Group*: 3 | 0.38 | 0.27 0.53 |
| Treatment Group*: 4 | 0.41 | 0.28 0.60 |
| Treatment Group*: 5 | 0.89 | 0.74 1.06 |
| Treatment Group*: 6 | 0.79 | 0.65 0.97 |
| Treatment Group*: 7 | 1.30 | 1.13 1.50 |
| Treatment Group*: 8 | 0.72 | 0.31 1.96 |
| Treatment Group*: 9 | 0.72 | 0.50 1.03 |
| Previous Live Birth | 1.24 | 1.12 1.37 |
| 1st time IVF | 1.00 | |
| Previous IVF Pregnancy | 1.18 | 1.03 1.35 |
| 1 previous IVF treatment - no pregnancy | 0.86 | 0.78 0.95 |
| 2 previous IVF treatments - no pregnancy | 0.84 | 0.74 0.96 |
| 3 previous IVF treatments - no pregnancy | 0.76 | 0.63 0.91 |
| 4 or more previous IVF treatments - no pregnancy | 0.62 | 0.50 0.75 |
*: see (3.2) for different treatment groups.
6. The Results
The adjusted live birth rates do not differ-greatly from the raw live birth rates, in all centres the difference is less than 2%.
References
1. Armitage P, Berry G (1987) Statistical methods in medical research. 2nd ed. Oxford: Blackwell.
2. Wilcosky TC, Chambless LE (1985) A comparison of direct adjustment and regression adjustment of epidemiologic measures. J Chron Dis 1985;38:849-56.
3. Lee J (1981) Covariance adjustment of rates based on the multiple logistic regression model. J Chron Dis 1981;34:415-26.
Statistical Details of the Model used to Adjust Live Birth Rates from DI
1. Introduction
There are several factors that have been shown to affect the live birth rate of a women having di. For example the age of the mother, the presence of any female factors for infertility, whether she has had previous live births, whether she has had previous DI pregnancies or whether she has had previous unsuccessful DI treatment will affect her chances of having a live birth.
Therefore the same method of regression adjustment will be used to adjust for the fact that different centres will treat different types of women.
2. The Statistical Model
As for IVF, a logistic regression model is fitted to predict the probability of a treatment cycle resulting in a live birth given the age of the women being treated, the type of treatment she is receiving and various other prognostic factors about her. All models are fitted using PROC LOGIST in SAS.
3. Factors included in the Model
3.1) The age of the mother
The age of the mother at the time of the treatment cycle is calculated to the nearest month. The model fits it as a linear, quadratic and cubic term.
3.2) The type of treatment
Whether the woman is stimulated or not is included as a binary variable. Whether any female factors for infertility are given or not is also included.
3.3) Previous Live Births
If a woman has had previous live birth or not is included in the model as a binary variable.
3.4) Previous DI Treatments
If a woman has had previous DI treatment which resulted in a pregnancy is entered as a binary variable
The number of previous DI treatments not resulting in a pregnancy is entered as a continuous variable. If the number of treatments is greater than 35 the number is assumed to be 35.
4) The fitted model
| Factor in the model | Odds ratio | 95% Confidence Interval |
| Intercept | 0.05 | 0.04 0.05 |
| Age - linear | 0.93 | 0.91 0.94 |
| Age - quadratic | 0.99 | 0.99 0.99 |
| Age - cubic | 0.99 | 0.99 1.00 |
| Female factors | 1.45 | 1.16 1.80 |
| Stimulated cycle | 1.04 | 0.95 1.15 |
| Previous Live Birth | 1.16 | 1.02 1.33 |
| 1st time DI | 1 | |
| Previous DI Pregnancy | 1.43 | 1.26 1.63 |
| Number previous DI treatments - no pregnancy | 0.97 | 0.95 0.98 |
5. The Results
The adjusted live birth rates differ from the raw live birth rates by less than 2% for all the centres.
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