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Volume 59 2004/3-4
Attrition in the COCON Cohort Between 2000 and 2002
Nicolas Razafindratsima [*] Nicolas Razafindratsima, Institut National d’Études Démographiques, 133 bd Davout, 75980 Paris Cedex 20, Tel: 33 (0)1 56 06 20 76, Fax: 33 (0)1 56 06 21 99 Ngoy Kishimba [*] COCON Group
The COCON (COhort CONtraception) survey on contraception, unplanned pregnancy and induced abortion in France, was set up to interview by telephone a representative sample of women aged 18-44, and to follow them up annually over five years. Between 2000 and 2002, the survey sample fell in size by one third, from 2,863 to 1,912 women. This article describes this attrition process and evaluates the biases that it causes in the analyses.
The attrition is due, in roughly equal proportions, to two factors: first, an inability to re-contact the women; second, refusals to be re-interviewed. It is highly selective, concerning primarily foreign women, of low educational level, young and living alone, and was responsible for modifying the structure of the sample followed up and the means for several survey variables of interest. However, the attrition has little impact on the multivariate analyses. Finally, the implications of attrition in COCON are limited as regards the biases caused, and are seen mainly as the loss of precision in the estimates due to the reduction in sample size. L’enquête Cohorte Contraception (Cocon), consacrée à la contraception, aux grossesses non prévues et à l’interruption volontaire de grossesse en France, a visé à interroger par téléphone un échantillon représentatif de femmes de 18 à 44 ans, puis à les suivre annuellement pendant cinq ans. Entre 2000 et 2002, l’échantillon de l’enquête s’est réduit d’un tiers, passant de 2 863 à 1 912 femmes. L’article décrit cette déperdition et évalue les biais qu’elle engendre sur les analyses.
La déperdition découle de deux facteurs, qui y contribuent chacun pour près de moitié : d’une part, de l’impossibilité de recontacter les femmes et, d’autre part, des refus de réinterrogation. Très sélective, elle a surtout concerné les femmes étrangères, peu diplômées, jeunes et non en couple, ce qui a modifié la structure de l’échantillon suivi et les moyennes de plusieurs variables d’intérêt de l’enquête. Toutefois, la déperdition n’a guère d’impact sur les analyses multivariées. Finalement, les conséquences de la déperdition dans Cocon sont limitées quant aux biais engendrés, et se situent essentiellement au niveau de la baisse de la précision des estimations due à la diminution de la taille de l’échantillon. La encuesta Cohorte Anticoncepción (Cocon), consagrada a la anticoncepción, a los embarazos no planificados y a la interrupción voluntaria del embarazo en Francia, tenía como objetivo interrogar por teléfono a una muestra representativa de mujeres de 18 a 44 años y de seguirlas anualmente durante cinco años. Entre el 2000 y el 2002, la muestra de la encuesta se redujo en un tercio, pasando de 2,863 a 1,912 mujeres. Este artículo describe tal pérdida de efectivos y evalúa el sesgo que supone para los análisis.
La pérdida de efectivos se debe a dos factores de importancia similar: la imposibilidad de volver a ponerse en contacto con las mujeres y el rechazo de éstas a ser interrogadas de nuevo. Puesto que tal pérdida ha sido altamente selectiva y ha afectado principalmente a las mujeres extranjeras, con bajo nivel educativo, jóvenes y sin pareja, la estructura de la muestra y por consiguiente los valores medios de diferentes variables de interés se han modificado. Sin embargo, los sesgos derivados de la pérdida de efectivos no son importantes y afectan esencialmente el nivel de precisión de las estimaciones debido a la disminución del tamaño de la muestra.
The attrition is due, in roughly equal proportions, to two factors: first, an inability to re-contact the women; second, refusals to be re-interviewed. It is highly selective, concerning primarily foreign women, of low educational level, young and living alone, and was responsible for modifying the structure of the sample followed up and the means for several survey variables of interest. However, the attrition has little impact on the multivariate analyses. Finally, the implications of attrition in COCON are limited as regards the biases caused, and are seen mainly as the loss of precision in the estimates due to the reduction in sample size. L’enquête Cohorte Contraception (Cocon), consacrée à la contraception, aux grossesses non prévues et à l’interruption volontaire de grossesse en France, a visé à interroger par téléphone un échantillon représentatif de femmes de 18 à 44 ans, puis à les suivre annuellement pendant cinq ans. Entre 2000 et 2002, l’échantillon de l’enquête s’est réduit d’un tiers, passant de 2 863 à 1 912 femmes. L’article décrit cette déperdition et évalue les biais qu’elle engendre sur les analyses.
La déperdition découle de deux facteurs, qui y contribuent chacun pour près de moitié : d’une part, de l’impossibilité de recontacter les femmes et, d’autre part, des refus de réinterrogation. Très sélective, elle a surtout concerné les femmes étrangères, peu diplômées, jeunes et non en couple, ce qui a modifié la structure de l’échantillon suivi et les moyennes de plusieurs variables d’intérêt de l’enquête. Toutefois, la déperdition n’a guère d’impact sur les analyses multivariées. Finalement, les conséquences de la déperdition dans Cocon sont limitées quant aux biais engendrés, et se situent essentiellement au niveau de la baisse de la précision des estimations due à la diminution de la taille de l’échantillon. La encuesta Cohorte Anticoncepción (Cocon), consagrada a la anticoncepción, a los embarazos no planificados y a la interrupción voluntaria del embarazo en Francia, tenía como objetivo interrogar por teléfono a una muestra representativa de mujeres de 18 a 44 años y de seguirlas anualmente durante cinco años. Entre el 2000 y el 2002, la muestra de la encuesta se redujo en un tercio, pasando de 2,863 a 1,912 mujeres. Este artículo describe tal pérdida de efectivos y evalúa el sesgo que supone para los análisis.
La pérdida de efectivos se debe a dos factores de importancia similar: la imposibilidad de volver a ponerse en contacto con las mujeres y el rechazo de éstas a ser interrogadas de nuevo. Puesto que tal pérdida ha sido altamente selectiva y ha afectado principalmente a las mujeres extranjeras, con bajo nivel educativo, jóvenes y sin pareja, la estructura de la muestra y por consiguiente los valores medios de diferentes variables de interés se han modificado. Sin embargo, los sesgos derivados de la pérdida de efectivos no son importantes y afectan esencialmente el nivel de precisión de las estimaciones debido a la disminución del tamaño de la muestra.
The COCON survey was set up to observe women’s contraceptive practices over five years. While memory errors are a problem in retrospective approaches, a prospective approach has to contend with the difficulties of follow-up. How does selective attrition occur from the initial representative sample, and what effect does it have over time on the results obtained ? To open this set of articles from the survey, Nicolas Razafindratsima, Ngoy Kishimbaand the COCON Group address the issue of the bias caused by selection from the sample, which after two years of follow-up had lost one-third of its members. A very detailed analysis allows the authors to evaluate the nature of the selection and its impact on measurement of the variables under investigation, and in so doing legitimize the results that follow.
To improve knowledge of contraceptive use and induced abortion in France, a team composed of researchers from INSERM, INED and CNRS initiated a cohort study — the COhort CONtraception or “cocon” survey — in 2000. The main aims were to analyse social factors linked to the occurrence of unplanned pregnancies and requests for abortion, and to study the responses of the health system and the effects of the different contraceptive methods on women’s health. The survey methods used (described in detail in the introductory article) were organized around two major decisions: first, to re-interview the participating women each year over five years (between 2000 and 2004); second, to conduct the interviews by telephone.
All longitudinal studies are confronted with the problem of sample attrition or loss to follow-up, i.e. the loss of part of the sample between successive interview waves. Geographic mobility and refusals to answer second or subsequent interviews mean that it is practically impossible to contact all of the subjects present at one wave in the next wave. Yet unequal probabilities of re-interview according to individual characteristics can bias analyses made at the cohort level. Furthermore, attrition raises the question of loss of precision in the estimates obtained, since this loss increases as sample size falls.
The COCON cohort did not escape the phenomenon of attrition. During the first round of interviews (2000), 2,863 women were questioned, but those re-interviewed in 2001 and 2002 numbered only 2,218 and 1,912 respectively, corresponding to a one-third reduction between the first and third waves. It is thus important to understand the reasons for this loss to follow-up and to evaluate its implications for the analyses. In particular, we want to test whether attrition causes bias in the variables of interest to the survey. In the course of this evaluation, we consider whether telephone interviews at regular intervals are an appropriate instrument for follow-up surveys on such a sensitive topic.
After describing the data and techniques used, we present the results of the analysis: first, the magnitude of the attrition and its determinants, second, the analysis of the biases.
I. Method of analysis
This section presents the data used to characterize the attrition and sets out our method of analysis. Unless otherwise stated, all the variables included in the analysis relate to characteristics reported by the women during the first wave of interviews (2000).
Unless otherwise stated, the analyses use unweighted data. We considered the sample for the first wave as a complete population subject to attrition, which meant that we attributed the same weight to each of its units, independently of how it had been selected. The results of the analysis justified this choice a posteriori because the main variable determining the weighting (the stratum to which sample members belong, based on experience of unplanned pregnancy or induced abortion) was virtually unrelated to attrition.
1. Descriptive analysis
The descriptive analysis of attrition is based primarily on the “contact files”, which record details of all calls made to the women. The data provide information about the outcome of each call: refusal, person unknown, absent, appointment arranged, etc.
We used these “contact files” to define the following criteria for each woman that we wanted to re-interview:
- non-contact: when the interviewers never managed to speak with the woman during the data collection period (whether or not contact was made with another member of the household);
- refusal, which took two forms: 1) refusal expressed at the end of the previous year’s interview (explicitly or because the woman did not want to leave a number where she could be contacted); 2) refusal to participate when contacted the following year, including explicit refusals but also women who made appointments for interviews that never actually took place within the collection period, which can be treated as a disguised form of refusal.
In part III, we give the distribution of attrition according to these different categories and according to the characteristics of the women.
2. Analysis of bias
The statistical methods for analysing bias in longitudinal surveys are described in detail in the box in the next page. Our aim here is to determine whether the biases caused by attrition in the COCON cohort are “ignorable” or “non-ignorable”, in the meaning given to those terms by Fitzgerald et al. (1998). Selection is “ignorable” if the modelling of the variables of interest to the study, performed on the sample of re-interviewed women, gives unbiased coefficients. On the other hand, “non-ignorable” selection means that the modelling produces biased coefficients that must be corrected by weighting the units with a corrective factor.
Our working hypothesis was that we are dealing with “selection on observable variables”, i.e. that the variables present in the different waves of the COCON study are sufficient to model correctly both attrition and the variables of interest to the study. This hypothesis is obviously open to question and may even be overturned. For example, if changing contraception from one year to the next (unobserved for women who are not re-interviewed) is related to attrition, the hypothesis is not supported. However, by making use of all the information available in the survey it is possible to minimize the bias due to unobservable factors.
As Alderman et al. (2001) point out, the fact that the tests used do not detect biases does not necessarily mean that such biases do not exist, but simply that they are too small to be detected by the methods employed. This limitation is inherent to statistical tests in general, and not specifically to those used for studying attrition in longitudinal surveys.
Two groups of variables can be identified: first, variables of specific interest for the survey; second, the individual characteristics that are used to model these variables of interest.
Types of attrition and the tests for bias that can be performed
We apply here the concepts described by Fitzgerald, Gottschalk and Moffitt (1998), as used by Alderman et al. (2001), and adopt their notation. This approach differs from that usually used in the literature on sampling (Little and Rubin, 1987). We simply summarize the results and refer the reader to the article by Fitzgerald et al. (1998) for the mathematical proofs and additional details. For developments and applications of this method, see the special issue of the Journal of Human Resources (1998).
Types of attrition
The main problem caused by attrition from a panel is bias, i.e. the estimations are distorted because the distribution of the probability that individuals will attrite between successive survey waves is not uniform but depends on individual characteristics.
Assume that we observe a sample on dates 1,…,T. The dependent variable Y (variable of interest) is assumed to be explained by a series of independent variables X. We are interested in the density of Y for a known X, i.e. f(yt/xt). We represent attrition at each date 1,….T by an indicator variable At, which has the value 0 if the unit (subject) could be interviewed and 1 if not. Yt is thus observed if At=0.
Thus, we obtain:
Yt observed if At=0.
Assume that Xt is known for all units (re-interviewed subjects and those lost to follow-up), if for example we are considering time-invariant characteristics or previous values of Y.
Equation [1] can be estimated only for re-interviewed units. Hence we know f(yt/xt,At = 0). To determine f(yt/xt) for the whole sample, it is necessary to use information on the probability of not being re-interviewed. We assume that this is induced by a latent variable A*:
where Zt is a series of variables observable for all units, but distinct from Xt. For example, Zt includes previous values, fixed characteristics of the respondent or information requiring no interview, such as the sex of the interviewer.
This gives the following classifications:
- there is “selection on unobservables” when
This means that the attrition function Pr(At=0/yt,xt,zt) cannot be reduced, or that vt is not independent of εt/xt. This means that non-observable variables (not included in X or in Z) act both on variable Y and on the probability of not being re-interviewed.
- attrition exhibits “selection on observables” when:
This means that, conditional on xt and zt, the attrition function is independent of the dependent variable (or variable of interest) yt, and thus that attrition is independent of unobservable factors that affect the error term εt of relation [1].
We can next distinguish three types of attrition with “selection on observables” :
- attrition is “completely at random” if Pr(At=0/yt,xt,zt) can be reduced to Pr(At=0): the probability of being lost to follow-up is the same for all units and does not depend on yt, or zt, or xt. This is unrealistic in practice because the probability of exiting a sample is usually associated with individual characteristics;
- selection on observables is “ignorable” if one of the two following conditions is met:
- yt and zt are independent conditional on xt and At=0, meaning that zt and vt are independent of εt/xt.
- the probability of attrition Pr(At=0/yt,xt,zt) = Pr(At=0/ xt,zt) can be reduced to Pr(At=0/ xt), i.e. the probability of attrition is independent of the variable zt, or
in equation [2]. - selection on observables is “non-ignorable” when neither condition (a) nor condition (b) is satisfied. This means that yt and zt are both endogenous (explained by the same process).
When attrition is “ignorable”, estimation of equation [1] Yt =β0+ β1 Xt+εt on only the units not subject to attrition gives unbiased estimates of coefficients β0 and β1. It is then pointless to allow for attrition. Conversely, when attrition is “non-ignorable”, a corrective factor must be applied to allow for it. Fitzgerald et al. (1998) show that an unbiased estimate of coefficients β0 and β1 can be obtained by weighting each unit not subject to attrition by the following weight (weights must be normalized before application):
Tests that can be performed
“Selection on unobservables” is extremely hard to detect because of the difficulty in finding pertinent Z variables (called instruments). Fitzgerald, Gottschalk and Moffitt carried out indirect tests for this in the case of the American “Panel Study of Income Dynamics” (PSID), by comparing the results from the PSID with those obtained using data from other panels in which attrition was non-existent or smaller. But the authors noted the limitations of their method, notably because it is applicable only to the cross-sectional data from the PSID, and is thus not a general solution for this type of problem.
Bias is easier to detect in the case of “selection on observables”. As seen in the previous section, one of the following two conditions must be satisfied for selection to be considered “ignorable”: either zt has no effect on At, or zt is independent of yt conditional on xt and At=0. A possible way of testing for bias is to see if the candidate Z variables (e.g. previous values of Y) significantly affect A. Another possibility is to use a test proposed by Becketti, Gould, Lillard and Welch (1988), called the BGLW test. Here the value of y in the first wave (y1) is regressed on x1 and on A, which is an indicator showing whether the unit is subject to attrition at any time t between 2 and T. A coefficient significantly different from zero for A means that loss to follow-up is “non-ignorable”.
The BGLW test is closely related to the test based on the regression of A on x1 and y1. Fitzgerald et al. (1998) show that the BGLW test is actually the inverse of the direct estimation of the attrition probability function.
The PSID is a survey from the University of Michigan, specifically on employment and income. The survey was conducted for the first time in 1968 and is still running.
Variables of interest
The variables of interest are of two kinds:
- first, the main method of contraception used at the time of the first interview. Women were classified by their main contraceptive method, or by the most effective method when several were used simultaneously. Women not using contraception were distributed between the following categories: sterilized, sterile, pregnant, trying to conceive, no sexual partner [1]. By convention, the women in these categories were considered to be “not concerned by contraception” and the others were considered to be “concerned by contraception”, i.e. at risk of an unwanted pregnancy;
- second, a series of three indicators related to reproductive history:
- previous unwanted pregnancy (answer to the following question, which was put to all women: “Have you ever become pregnant accidentally ?”);
- previous induced abortion;
- wanting a(nother) child in the future (put to women who had had sexual intercourse at least once and who were not pregnant).
Other individual characteristics
The explanatory variables used in the models were: age (18-24 years old, then in five-year age groups); number of children (0 to 4 or more); educational level (none, primary or lower secondary school certificate; lower secondary vocational qualification; upper secondary qualification (baccalauréat) or two years of higher education; more than two years of higher education); marital status (married, cohabiting, not in couple); nationality (French or foreign).
In some of the models estimated, we also included the importance of religion in the woman’s life
[2], and her socio-occupational category (SOC). For the latter variable, a number of infrequent categories for which the variables of interest showed only small variations were combined. Because of their relative proximity on the earnings scale (Cases et al., 1996), farmers were grouped with manual workers, while self-employed trade and business people were grouped with managers and higher intellectual professions. The other SOC were intermediate professions, sales and clerical workers, and the economically inactive.
Tests carried out
Our approach is based on that of Alderman et al. (2001). Three series of tests were carried out:
- Comparison of the means for the variables: to form an idea of the extent of attrition depending on whether or not the initial sampling plan is taken into account, we calculated both the unweighted and weighted means (with the final survey weighting described in the introductory article) for different variables according to their status with respect to attrition. The size of the differences between the means was assessed using Student’s t test;
- Modelling the probability of not being re-interviewed in 2002: this examines the relationship between attrition and three outcome variables of the COCON study (main contraceptive method, previous unplanned pregnancy and previous induced abortion). For each variable, we estimated two logit models: in the first, we introduced, as explanatory variables, only the variable of interest and the constant [3]; in the second we included the other characteristics of the woman with the explanatory variables. This, therefore, is an evaluation of the impact of the variable of interest on attrition, other things being equal. Attrition that is weakly related to the variable of interest should result in a low significance for this variable in these logit models;
- BGLW tests (Becketti et al., 1988, see box), which involve specifying an explanatory model for the variable of interest in the first wave (2000) and then comparing the regression coefficients estimated for the women still in the sample in the last wave (2002) and for those lost to follow-up. The equality of all the coefficients in the model is tested using the likelihood ratio method. We tested the equality of the coefficients first without and then with the constant [4]. Testing the equality of the coefficients without the constant amounts to judging whether the differences between the categories introduced and the reference category are modified across the samples, without regard to the differences of mean level between the samples. Including the constant in the test, on the other hand, requires taking into account any differences of mean level.
A first series of BGLW tests was performed initially on the following variables of interest, introduced in dichotomous form: “sterilized”, “want a(nother) child”, “previous abortion” and “previous unplanned pregnancy”. We next looked more specifically at the main method of contraception used, this time restricting the analysis to women who were “concerned by contraception”. We modelled use of the pill, the IUD, a contraceptive method other than the pill, IUD or condom, and finally the fact of not using any contraception. The estimated models are logit models, in which each method is introduced as a dichotomous variable. In addition to the characteristics usually included in contraception studies (age, number of children, educational level, nationality), socio-occupational category and the importance of religion were also introduced among the explanatory variables.
Table 1 summarizes the different elements of our procedure.
Table 1
Summary of tests performed
II. Level of attrition and explanatory factors
The COCON first-wave sample (2000) comprised 2,863 women. Of these, 2,218 were re-interviewed in 2001 and 1,912 in 2002. By the end of the third interview, therefore, the COCON sample had decreased in size by one-third. Table 2 summarizes the data collection in the two follow-up surveys.
Table 2
Data collection in the follow-up surveys
1. Attrition is high in the first year of follow-up, but appreciably lower the next year
Between 2000 and 2001, 22.5% of women were lost to follow-up (Table 3). This rate is lower than that observed in the COCON pilot survey carried out between 1998 and 1999 (33.8%)
[5], but is high compared with that observed in other longitudinal surveys. A recent French survey of the general population (the European Community Household Panel survey) achieved an attrition rate of 9.4% between the first and second waves (carried out in 1994 and 1995) (Chambaz and Legendre, 1999). The methods and objectives of these two studies were however very different
[6], making comparison difficult.
Table 3
Attrition from the cocon cohort between 2000 and 2002
Between 2001 and 2002, the attrition rate in the COCON cohort fell to 13.8%, which is a large reduction on the previous year. A trend to lower attrition after the first follow-up interview has often been observed in longitudinal surveys. This was also the case for the French European Panel survey, in which the attrition rate was only 3.5% between waves 2 and 3 (Chambaz and Legendre, 1999); in the United States, in the Panel Study of Income Dynamics (PSID), attrition was nearly 11% in the first year, but only 4% in the following years (Fitzgerald et al., 1998). It would seem that the most mobile subjects and those most reluctant to participate are “lost” mainly in the first year but that thereafter the sample tends to stabilize.
2. Two main reasons for attrition: non-contact and refusals
The research group decided to exclude from follow-up women who had had a hysterectomy and were thus no longer concerned by contraception
[7]. Excepting these exclusions from the target population, three factors were responsible for some women not being re-interviewed:
- The woman expressed a refusal to be re-interviewed at the end of the previous year’s interview ;
- It was impossible to contact the woman in the follow-up year ;
- The woman refused to be re-interviewed when contacted the following year.
The relative importance of these different factors, by period, is shown in Table 4.
Table 4
Relative importance of the reasons for loss to follow-up (%)
In total, between 2000 and 2002, 44% of losses to follow-up were due to inability to contact the women; refusal expressed at the end of the previous interview or during the current interview explained 56% of losses. The proportion of attrition due to non-contact is thus high, despite the measures taken to keep the women’s contact details up to date and to contact them even when their telephone number had changed.
The failure rates (non-contact and refusal) decreased between the two waves, as the comparison of the data collection operations shows (Table 2). The rate of non-contact halved between 2001 and 2002, dropping from 9.5% to 4.6%. This results partly from there being more telephone numbers with which to contact the woman (the woman’s own phone number plus those of her close friends or relatives, which by the end of the 2002 interviews could be as many as seven numbers)
[8]. However, it may also have been due to the smaller proportion of women changing telephone number in the sample re-interviewed in 2001. Refusal rates also declined between 2001 and 2002. At the end of the 2001 interview, 5.8% of women refused to participate in the 2002 survey; in 2002, only 3.2% of women said they did not want to be interviewed in 2003. The refusal rate at the time of contact fell from 7.3% in 2001 to 5.1% in 2002
[9].
3. Strong selection on socio-demographic characteristics
The relative importance of the different reasons for attrition varied according to the women’s socio-demographic characteristics (Table 5). Inability to contact the women by telephone was more common among young subjects (under age 29) and those not living in a couple. This difficulty in contacting young people by telephone is a classic phenomenon that has been observed in other studies (Firdion, 1996). In the 2001 wave, contact was also harder to establish with less educated women (< secondary school vocational qualification) and foreign women. For all categories of women, however, the non-contact rate fell between 2001 and 2002. The decline was particularly large for the categories that were hardest to contact in 2001: for example, 20.4% of the foreign women could not be contacted in 2001, compared with 6.5% in 2002. Similarly, 12% of women aged 18-24 could not be contacted in 2001, compared with 7% in 2002.
Table 5
Frequency of the reasons for loss to follow-up according to characteristics of the women (unweighted results)
The reasons for refusal are to be sought not only in the socio-demographic characteristics of the individuals but in the sensitive nature of the topic, the length of the questionnaire and the characteristics of the interviewer (age, sex, experience with telephone surveys etc.). The interaction between interviewer and respondent, the sensitive nature of the topic, or the interview duration (if this is felt to be too long), are all factors that can cause women to refuse to be re-interviewed.
A weak association was found between refusal rates and interviewer characteristics. For example, in 2000, 5.8% of the women interviewed by men refused to participate the following year, compared with 5.7% of those interviewed by women. In 2001, the percentages were 2.9% and 3.5% respectively. Similarly, the fact that the woman had been asked to reply to sensitive questions
[10] did not seem to increase the refusal rate. Interview duration equally seemed to have no effect on refusal rates. Indeed, refusal rates tended to be lower for the longest interviews: in 2000, 28.5%
[11] of women whose interview lasted less than 20 minutes refused to be re-interviewed in 2001, compared with only 2.3% of those whose interview lasted over 50 minutes (Table 5).
Refusal seemed to be linked more to the socio-demographic characteristics of the women than to the characteristics of the interviews. The consequences of these differences in attrition rates for the structure of the final sample can be captured by the comparisons of means presented in the next section.
III. Results from the models for analysing bias
In this section, we evaluate in detail the biases generated by the selective nature of attrition. We look at the overall loss at the end of the second follow-up survey: subjects “lost to follow-up” are defined as women who were not in the 2002 sample, regardless of the reason (excluded from the sample, refusal to participate or non-contact)
[12]. We do not therefore attempt to distinguish the point at which individual women exited the sample, but consider simply the total loss at the end of the third wave.
1. Comparison of means
For the variables linked to reproductive history, little difference was observed between the re-interviewed sample and that lost to follow-up (Table 6). The proportions of women with experience of unplanned pregnancy or induced abortion did not differ significantly between the two samples. The only appreciable variation was in the proportion of women wanting a child in 2000 (35.1% in the re-interviewed sample and 30.3% among those lost to follow-up). But this difference is not significant when the weighted data are used.
Table 6
Means for variables according to sample
By contrast, the distribution of women according to the main method of contraception used in 2000 differed greatly between the samples. For all women, the percentage using the pill or the IUD was higher in the re-interviewed sample than in the lost to follow-up sample, whereas the proportion of sterilized women was significantly smaller in the re-interviewed sample. Similarly, women using no contraception accounted for 2% of re-interviewed women and 4.5% of women lost to follow-up. These differences persist if only women “concerned by contraception” in 2000 are considered.
We also found a significant variation in the structure by age, with women aged 40-44 (in 2000) occupying a smaller place in the sample re-interviewed in 2002. The proportion of women aged 18-24 in 2000 is also smaller, though the difference is not significant. This lower proportion of women in the two extreme age groups is compensated by an increase in the proportion of women aged 30-39 among those successfully followed up. The percentage of foreign women was also considerably lower in the re-interviewed sample: 9.8% of women lost to follow-up were foreign compared with only 4% of women followed up. Finally, the distribution by educational attainment was significantly modified. Women with the lowest qualifications were least likely to be re-interviewed, with the result that the sample of followed-up women included a higher proportion of women with an upper secondary school qualification (baccalauréat) or higher education.
The size of the woman’s household was also a discriminating variable. Women who lived alone in 2000 were more likely than the others to be missing from the 2002 sample. As a corollary, the proportion of women not living in a couple also decreased between the two waves. The distribution by size of place of residence did not change substantially. Follow-up seems to have been lower among women living in the Paris region, but the fall in their proportion is weakly significant and even not significant after weighting. However, this result should be interpreted with caution due to missing values for place of residence.
These findings need to be confirmed by models that take account of structural effects. This is the aim of the logit models on the probability of leaving the sample, the results from which are presented in the next section.
2. Results from logit models of attrition
The first variable of interest that we used to model sample loss between 2000 and 2002 is the main method of contraception used in 2000. On its own (model [1]), this variable revealed significant differences between the groups: sterilized women and women using a reversible method other than the pill, IUD or condom were more likely to leave the sample, compared with pill users (Table 7). The same is true for women not using any contraception. IUD users, on the other hand, were more likely to be re-interviewed.
Table 7
Factors influencing the probability of not being re-interviewed in 2002 (coefficients from logit models)
Even when we controlled for other characteristics of the women (age, number of children, wants a(nother) child, qualification level, marital status, nationality), we still found differences according to the main method of contraception used. The differences were in the same direction as in the previous model, but their absolute values were lower. Furthermore, the coefficient corresponding to IUD users became non-significant at the 10% level.
Concerning individual characteristics, we found that age and number of children did not have significant effects on loss to follow-up. Nationality and marital status, on the other hand, did have a significant effect: foreign women and women not living in a couple in 2000 were more likely to be lost. We also found that the probability of being re-interviewed increased with the level of education, and was higher in women who wanted a(nother) child.
The logit model that included experience of unplanned pregnancy as the only explanatory variable was at the limit of significance (the chi-2 of the test for nullity of all the coefficients is low, and its significance is rejected at the 5% level). The coefficient of the variable, which was significant at the 10% level, indicated that the women who had had an unplanned pregnancy were more likely to be re-interviewed.
The model linking loss to follow-up only with experience of induced abortion was not significant at the 10% level compared with that including only the constant. The model became significant (the chi2 test for the model’s goodness of fit was significant at 1%) only when other explanatory variables were introduced. However, the coefficient of the “previous induced abortion” variable was no longer significant. This can be taken to show the lack of a link between loss to follow-up and previous abortion.
3. Results of the BGLW tests
The test proposed by Becketti, Gould, Lilliard and Welch (1988), the “BGLW test”, involves comparing the equality of the regression coefficients estimated over the followed-up sample and over the lost to follow-up sample. In this section we perform these tests, each time preceding them with the results of regressions on the initial sample (2000) and then on the sample of followed-up women. These are the samples most frequently used in the analyses based on the COCON cohort.
Modelling the variables linked to reproductive history
We began by modelling the following four dependent variables: sterilization, wants a child, previous abortion or previous unplanned pregnancy (Table 8). The explanatory variables tested were age, number of children, educational level, marital status and nationality. When modelling sterilization, we excluded the “nationality” variable because none of the foreign women re-interviewed had been sterilized. Also, for the age variable, women under 30 were placed in the reference group, because no woman under 25 had been sterilized. When modelling the “wants a child” variable, the sample analysed contained all the women who had had sexual intercourse and who were not pregnant in 2000, i.e. 2,671 women, of whom 1,788 were still present in 2002.
Table 8
Factors influencing variables linked to reproductive history according to the sample (coefficients of logit models)
The goodness-of-fit tests on the models all led to rejection of the null hypothesis for all of the coefficients at the 1% level. This indicates that the explanatory variables included were pertinent.
The signs of the coefficients obtained were generally consistent with our expectations. Sterilization, previous abortion or previous unwanted pregnancy tended to become more frequent with age and number of children
[13]. Conversely, wanting a child was less frequent among older women and those who already had several children. Educational level had only a small effect on abortion and unwanted pregnancy. However, it was strongly linked to being sterilized: this characteristic was more common in women with low educational qualifications.
The coefficients for women in the 2000 sample and for those in the 2002 sample generally followed the same pattern. However, in the initial sample, French women were less likely than foreign women to have had an induced abortion, whereas the opposite was observed in the re-interviewed samples. This difference, however, was not significant.
The tests of equality of the coefficients not including the constant all led to rejection of the hypothesis of a difference between the regression coefficients for the re-interviewed sample and for the lost to follow-up sample. The tests of equality of the coefficients including the constant also led to rejection of the hypothesis of modification for the dependent variables “wants a(nother) child” and “previous abortion”. Conversely, the equality of all the coefficients was rejected at the 5% level for “sterilized” and “previous unplanned pregnancy”.
Overall, the BGLW tests performed for the four variables of interest showed that there was no attrition bias for wanting a child and previous abortion. In contrast, for sterilization and experience of unwanted pregnancy, the tests showed a significant variation in the level of the variables between the two samples. This difference, however, did not modify the effects specific to each variable (represented by the coefficients), i.e. the differences between the estimates according to the modalities of the explanatory variables from one sample to another.
Modelling of the main contraceptive method used
We next tested for bias when studying contraception. Four dependent variables were modelled: use of the pill, use of the IUD, use of a reversible method other than the pill, IUD or condom
[14] and finally, contraceptive non-use (Table 9). The pill and IUD are the two most common methods of contraception in France. In 2000, they were used by 46% and 16% respectively of women aged 18-44 in France (Table 3 in the introductory article and Bajos et al., 2003).
Table 9
Factors influencing the main contraceptive method according to sample (coefficients of logit models)
In this section we restrict our analysis to women “concerned by contraception” (not sterilized or sterile, with a sexual partner, and not trying to conceive). The explanatory variables were those usually used to study contraceptive behaviour: age, number of and desire for children, educational level, marital status (Toulemon and Leridon, 1992a and 1992b). Two other characteristics of the woman that may be linked to contraception were also included: the importance attached to religion and the socio-occupational category. Such models have recently been fitted for data from the COCON 2000 survey (Leridon et al., 2002). We also included nationality, as this characteristic is strongly linked to loss to follow-up.
The goodness-of-fit tests (chi2) on the regressions performed on the initial sample were all significant at the 1% level. The same was true of the model for use of the pill and IUD for the re-interviewed sample. Conversely, the significance of the model for use of contraceptive methods other than the pill, IUD or condom for the sample re-interviewed in 2002 was rejected at the 1% level and was accepted only at the 5% level. In the case of non-use of contraception, the chi2 test led to rejecting the model’s validity for the 2002 sample even at the 10% level. The same model estimated over the initial sample, however, seemed of good quality: this shows that attrition causes a loss of power in the model for non-use of contraception. This result is partly due to the low frequency of the phenomenon.
The models showed strong differences in the contraceptive methods chosen by women according to their characteristics. Use of the pill decreased with age, whereas that of the IUD increased. Having more children was associated with a reduction in use of the pill in favour of the IUD. Being religious was positively associated with use of the pill, and negatively with use of the IUD; and it had no effect on the use of other reversible methods. Nationality had an effect on the use of methods other than the pill, IUD or condom: other things being equal, the latter was more widely used by foreign women. Non-use concerned predominantly women with a lower educational level and foreign women. Overall, these differences in the use of different contraceptive methods according to individual characteristics are independent of the sample used for the regression analysis (all women or only re-interviewed women).
Comparison of regression coefficients between the followed-up and lost to follow-up samples in 2002 leads to rejecting the hypothesis of dissimilarity for “reversible method other than pill, IUD or condom” and “no method”. For these variables, therefore, attrition does not create bias. For IUD use, the hypothesis of equality of the coefficients is accepted if the constant is not taken into account, and rejected at the 10% level when it is taken into account. Finally, for the pill, the hypothesis of equality is rejected at the 10% level whether or not the constant is included. The difference of log-likelihoods is however weakly significant: at the 5% level, the hypothesis of equality of the regression coefficients is still accepted in both cases.
In total, for the four contraceptive methods studied, the loss of sample subjects between 2000 and 2002 did not cause any major bias. It is thus not essential to make allowance for attrition when analysing the variables of interest.
Conclusion
The aim of this study was to describe and analyse attrition in the COCON survey, one-third of whose sample members were lost to follow-up between 2000 and 2002. The attrition rate was high in the first year (22.5%) and considerably lower in the second year (13.8%). For 44% of the women not re-interviewed, this was because they could not be contacted by telephone. Change of telephone numbers between two waves of the survey was thus an important cause of sample attrition, in spite of the measures taken to keep the women’s contact details up to date. Most of the remaining losses were due to refusal to be re-interviewed. However, refusal seemed not to be linked to the sensitive nature of the survey subject, the length of the telephone interview or the characteristics of the interviewer.
Attrition was very selective, affecting primarily women with low qualifications, the youngest and oldest women, foreign women and those living alone or not in a couple. Despite this strong selection on individual characteristics, the loss to follow-up did not produce major bias when modelling the variables of interest (for either reproductive history or contraceptive method used). Excepting the differences of level for being sterilized and previous unplanned pregnancy, all the tests carried out concluded that the coefficients from the multivariate models were stable regardless of whether estimation was on the re-interviewed women or on those lost to follow-up. These conclusions are consistent with those of Fitzgerald et al. (1998), Alderman et al. (2001) and Breuil-Genier and Valdelièvre (2001), and support the use of longitudinal surveys despite the problems of attrition. In particular, use of the telephone survey mode does not seem unsuitable for conducting successive waves of interviews, providing adequate measures are taken to limit the losses caused by changes of telephone number between interviews.
Finally, the only real problem associated with attrition in the case of the COCON survey is the loss of precision due to the fall in the number of participants. On the assumption that the rate of loss to follow-up observed between the second and third rounds of interviews applies equally in subsequent rounds, the final COCON sample will contain roughly 1,400 women, which is half of the initial sample. A sample of this size, however, may be inadequate for estimating some indicators of interest to the study with the required precision.
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NOTES
[*]
Institut National d’Études Démographiques.Translated by Alex Edelman and Associates.
Institut National d’Études Démographiques.Translated by Alex Edelman and Associates.
[1]The distribution of women between the categories for this variable is given in the introductory article.
The distribution of women between the categories for this variable is given in the introductory article.
[2]A dichotomous variable, derived from answers to the question “Is religion important in your life ?”
A dichotomous variable, derived from answers to the question “Is religion important in your life ?”
[3]This procedure amounts to comparing the percentages of attrition according to the category of the explanatory variables.
This procedure amounts to comparing the percentages of attrition according to the category of the explanatory variables.
[4]The multivariate estimations were performed by means of the “logit” procedure in the STATA software. Various tests can then be conducted on the estimated coefficients. Gould (2002) describes the practical use of tests for comparing the coefficients derived from two samples with this software.
The multivariate estimations were performed by means of the “logit” procedure in the STATA software. Various tests can then be conducted on the estimated coefficients. Gould (2002) describes the practical use of tests for comparing the coefficients derived from two samples with this software.
[5]Though it should be noted that the interval between the two waves was 16 months in the pilot survey.
Though it should be noted that the interval between the two waves was 16 months in the pilot survey.
[6]The French “European Panel” survey, carried out by INSEE, uses a methodology common to 14 EU member states. This is a longitudinal survey, specifically focused on employment and income, in which the primary sampling unit is the household. Once a household is selected, all individuals aged 17 or over are interviewed (and followed up). The data are collected in face-to-face interviews (Breuil-Genier and Valdelièvre, 2001).
The French “European Panel” survey, carried out by INSEE, uses a methodology common to 14 EU member states. This is a longitudinal survey, specifically focused on employment and income, in which the primary sampling unit is the household. Once a household is selected, all individuals aged 17 or over are interviewed (and followed up). The data are collected in face-to-face interviews (Breuil-Genier and Valdelièvre, 2001).
[7]They numbered 29 in 2001 and 18 in 2002.
They numbered 29 in 2001 and 18 in 2002.
[8]The contact number used in 2000, the number given at the end of the 2000 interview, the number of a relative or close friend, a number obtained from this person and sometimes a number supplied by the woman via a reply card or a free phone service. The updating of the telephone numbers in 2002 made it possible to add the number of another close friend or relative plus a number found in the telephone directory.
The contact number used in 2000, the number given at the end of the 2000 interview, the number of a relative or close friend, a number obtained from this person and sometimes a number supplied by the woman via a reply card or a free phone service. The updating of the telephone numbers in 2002 made it possible to add the number of another close friend or relative plus a number found in the telephone directory.
[9]45 women from the 2000 sample refused to be re-interviewed in 2001 but accepted for 2002. In 2002, only about 10 of these women completed interviews. In our calculations these “momentary” refusals have been grouped with the “definitive” refusals.
45 women from the 2000 sample refused to be re-interviewed in 2001 but accepted for 2002. In 2002, only about 10 of these women completed interviews. In our calculations these “momentary” refusals have been grouped with the “definitive” refusals.
[10]The sensitive questions tested included “Have you already had sexual intercourse with a man ?”, “Does contraception have a positive or negative effect on the desire to have sexual inter course ?” and “Does contraception have a positive or negative effect on pleasure during sexual intercourse ?”
The sensitive questions tested included “Have you already had sexual intercourse with a man ?”, “Does contraception have a positive or negative effect on the desire to have sexual inter course ?” and “Does contraception have a positive or negative effect on pleasure during sexual intercourse ?”
[11]This percentage includes 120 women who stopped the interview before being asked if they would accept to be re-interviewed in 2001. If we exclude these women, 4.6% of woman whose interviews lasted less than 20 minutes in 2000 refused to be re-interviewed.
This percentage includes 120 women who stopped the interview before being asked if they would accept to be re-interviewed in 2001. If we exclude these women, 4.6% of woman whose interviews lasted less than 20 minutes in 2000 refused to be re-interviewed.
[12]The excluded women could have been omitted from the calculations. Their small number should not, however, substantially modify the results.
The excluded women could have been omitted from the calculations. Their small number should not, however, substantially modify the results.
[13]For abortion, similar results have been obtained in other countries (Powell-Griner and Trent, 1987; Wilder, 2000).
For abortion, similar results have been obtained in other countries (Powell-Griner and Trent, 1987; Wilder, 2000).
[14]These other methods were mostly periodic abstinence, withdrawal, and to a lesser extent local methods such as spermicides.
These other methods were mostly periodic abstinence, withdrawal, and to a lesser extent local methods such as spermicides.
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