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The characteristics of sexual partnerships are of interest in the context of fertility and the epidemiology of sexually transmitted infections. Our interest here is in whether condom use in Britain is linked to characteristics of the participants alone, or also to characteristics of the partnership. Association with partnership factors such as type or duration has been shown elsewhere,^{1–4} which suggests that people have strategies regarding condom use that may vary by partner. A greater understanding of the factors associated with condom use could help direct condom promotion toward the most appropriate individuals, and also toward the partnership contexts where condom use is low.

In this paper we analyze condom use at first and last sexual encounter in recent heterosexual partnerships as reported in the British National Survey of Sexual Attitudes and Lifestyles, 2000.^{5} Incomplete data present a particular challenge. Although interest lies in all partnerships in the last year, participants are asked to provide detailed information only for their most recent 3 partnerships due to constraints of recall and interview time. This design is similar to other studies.^{6,7} Thus we may know that a participant has had 5 partnerships, but have details of only 3. A second challenge arises because some partnerships (but not all) are eligible to be reported twice (ie, by both partners). A third challenge arises because condom use is more common among people who have more partnerships, an example of informative cluster size.^{8–10}

We present a methodology based on devising suitable weights for analysis to deal with each of those challenges. Our primary analyses are based on data concerning partnerships reported by participants who report 2 or more partners, and focus on the association between condom use and partnership factors after adjusting for participant factors in a weighted logistic regression model.

#### METHODS

##### The Survey Data

British National Survey of Sexual Attitudes and Lifestyles 2000 is a stratified probability sample survey of British residents aged 16 to 44 years (4762 men and 6399 women). Interviews were conducted between May 1999 and February 2001. Methodologic details have been published elsewhere.^{5} Briefly, a sample of 40,523 addresses was selected in geographic clusters, with oversampling in London. One randomly selected resident from every household was invited to participate. The response rate was 65%. Trained interviewers conducted face-to-face interviews in respondents’ homes, followed by computer-assisted self-interview for more sensitive questions. Ethical approval was obtained from University College Hospital, North Thames Multicenter, and all local research ethics committees in Britain. Weights were developed for analysis based on inverse-selection probabilities, poststratified to the mid-1999 population estimates for Britain by age group, sex, and region.

Participants reported the total number of heterosexual and homosexual partners in the last 3 months, the last year, the last 5 years, and ever. Participants were asked later to provide detailed information concerning their most recent 3 partnerships in the last 5 years, as defined by the occasion of last sex. For those who reported partners of both sexes but whose most recent 3 were all of 1 sex, information was also requested for the most recent partnership of the other sex. Partnerships are treated as not reported if the year, relationship status, and condom use are all not reported. Where the date of last sex was incomplete we used the total number of partners to deduce whether the partnership was in the time period. We treat the number reported in detail as the total if (1) this is greater than the total number given or (2) the total number was not provided. For each participant we can thus calculate the number of partnerships not reported in detail, which we also consider to be missing.

We focus on heterosexual partnerships in the last year. Of the 11,161 survey participants, 9598 reported 1 or more partners. Of these, 9374 participants reported in detail on a total of 12,128 partnerships—79% of the 15,488 reported. Among all partnerships, 16% are “missing by design” in that participants were not asked to report them, and 6% are missing due to nonresponse.

The rate of reporting in detail varies by the total number of partners, being highest for participants with only 1 partner in the period (eTable 1, available with the online version of this article). Detailed reporting does not vary by the sex of the respondent, given the total number of partners.

Some explanatory factors are partnership specific, such as duration of the partnership and status at interview. Age is recorded for both participant and partner, but other factors such as marital status are recorded only for participants.

Figure 1 presents examples of possible patterns of recent partnerships. Participant 1 reports a most recent partnership of 5-month duration, although with a short concurrent partnership, and a third most recent partnership of 2-month duration. Participant 2 has a pattern of monogamous relationships, and participant 3 has 1 primary relationship and brief concurrent relationships.

Having had a larger number of partners in the last year is associated with greater condom use at last sex and shorter partnership duration (eTable 2). A longer duration of partnership and lower condom use at last sex are reported for the most recent partnerships compared with the second and third most recent partnerships.

##### Weighting for Missing Partnerships

We propose weighting through a 2-stage process, first for missing partnerships (ie, those not reported in detail) and second for the population of interest. Our description assumes that all participants report their most recent 3 partnerships in detail, or the number in the time period if less; however, our strategy can easily be generalized. For participant 1 (Fig. 1) as an example, assuming a total of 5 partnerships, the aim is to weight the 3 partnerships reported in detail to represent themselves and the 2 missing partnerships within the last year.

The weighting for missing partnerships can be seen as an example of inverse probability of selection weighting, a standard method to deal with possible bias from selection (or nonresponse) in surveys. Such weighting is also recommended in many epidemiologic contexts (such as those with repeated measurements) to reduce bias from either time-varying confounding or dropout.^{11,12}

The calculation of full selection probabilities, representing the chance of being among the 3 most recent partnerships at a varying interview date, is complex and not possible from the available data. Hence in this section we present 4 methods to calculate weights—all of which can be seen as the inverse of simplified approximate selection probabilities based on increasing quantities of information.

The weights are scaled to the total numbers of partners, either within participants or within strata of participants. Because the total number of partners is informative, we define the strata by participant sex and the total number of partners (grouped by 1, 2, 3, and 4 or more). The advantage of scaling within participant is protection against unknown heterogeneity between participants. The disadvantage is that the weights will often be more variable (eg, participants with a large total number of partners must have high weights) that typically leads to inefficiency. The partnerships reported by participants with 3 or fewer partners are assigned a weight of 1 in every scheme. In our example, there are relatively few participants with partnerships for which none is reported in detail (eTable 1). For simplicity, such participants and their missing partnerships are dropped from analysis.

##### Weighting Schemes

The simplest possible analysis is an unweighted analysis of all partnerships reported in detail. The missing partnerships are assumed similar to the partnerships reported by all participants. We proposed 3 additional weighting schemes, which we call the basic, the primary, and the alternative.

##### Basic Weighting Scheme

Our basic weighting scheme assumes for participant 1 that the missing 2 partnerships have the same characteristics as the 3 reported, which are therefore weighted equally by 5/3 to represent all partnerships. For participant *i*, define *Ti* to represent the total number of partners in the time period of interest, and *Ci* the stratum to which the participant belongs, and *TC* to represent the set of data concerning *T* for all members of each stratum. Define for participant *i* and partnership *j* = 1, 2, 3, an indicator of selection for reporting in detail *Sij* taking value 1 if reported and 0 otherwise. Then the basic participant probability of selection is Pr [*Sij* = 1|*Ti*] and its inverse, the weight, is defined by

if the participant has 4 or more partners, and is 1 otherwise. The basic stratum probability of selection is Pr[*Sij* = 1|*Ci, TC*] and its inverse, the weight, is

where *Ni* is the total number of participants in stratum *Ci*.

##### Primary Weighting Scheme

Our primary weighting scheme assumes for participant 1 that the 2 missing partnerships have ended and are therefore similar to the 2 reported partnerships that have ended (the second and third most recent), which are therefore each weighted by 2. The ongoing partnership (most recent) is weighted by 1 to represent only itself. In our example, partnerships are assumed to be ongoing when the participant is married/cohabiting and the partnership status is married/cohabiting. Where the participant is not cohabiting, a partnership is deduced to be ongoing when sex occurred in the last month and has occurred on more than 1 occasion.

Let *Vij* be an indicator taking value 1 when partnership *j* reported by participant *i* is ended at interview and 0 if ongoing. Define *Vi* to be the set of indicators for participant *i* and define *VC* to be the data concerning *V* for all participants in each stratum. Then the primary participant probability of selection Pr[*Sij* = 1|*Ti, Vi*] is defined to be 1 if *Vij* = 0 or *Ti* ≤3 and otherwise (∑_{j = 1}^{3} *Vij*)/(*Ti* − 3 + ∑_{j = 1}^{3} *Vij*). The inverse defines weights to be

except for any participant *i* where ∑_{j = 1}^{3} *Vij* = 0 (ie, all reported partnerships ongoing) in which case we take *wijPP* = *wijBP*, or *Ti* ≤3 in which case *wijPP* = 1. The primary stratum probability of selection Pr[*Sij* = 1|*Ci, TC, VC*] is inverted to define weights

##### Alternative Weighting Scheme

The sampling of partnerships for detailed reporting is length biased, in that both longer partnerships and those followed by long periods without sex are more likely to be reported, as they have a higher chance of being ongoing or most recent on the date of interview. Such length-biased sampling is common in current-duration designs.^{13} Consequently we propose an alternative weighting scheme. We assign different weights to the ended partnerships so as to represent the missing partnerships, in inverse proportion to the duration of the partnership (within the last year) plus the period after the partnerships ends until the next partnership begins. The rationale for this scheme can be seen as defining proxy selection probabilities for the reported partnerships proportional to the time when the partnership is current or most recent. For example, for the second and third most recent partnerships of participant 1, these combined periods are 1 and 3 months, respectively. The period until next partnership is considered 0 for the concurrent second partnership. By inverting the combined periods as a proportion of a year we obtain initial weights of 12 and 4, respectively corresponding to 11 and 3 missing partnerships. The weights are then scaled to represent the 2 missing partnerships in the ratio of 11:3.

A multiple regression analysis of condom use at last sex in partnerships reported by participants with 4 or more partners in the last year (eTable 3) shows that both duration and whether the partnership is ongoing at interview are linked to condom use, but the ordering of the partnership by last sex is not. This supports our decision to weight according to the first of these 2 factors and not also the latter.

Let the sum of the partnership length and gap in whole months be denoted by *Lij*, and the set of these indicators for participant *i* by *Li* and for all participants in each stratum by *LC*. If the time period of interest is *M* months then initial selection probabilities for ended partnerships can be defined as Pr[*Sij* = 1|*Ti, Lij*] = *LijM−1* and so inverse weights can be defined by *MLij*^{−1}. If the most recent partnership is ended, then the gap until the next partnership is unobserved but treated here as the gap until study interview. The number of missing partnerships represented by each ended partnership is *MLij*^{−1} − 1. These initial weights can then be scaled within each participant to sum to *Ti*. Thus the alternative participant probability of selection Pr[*Sij* = 1|*Ti, Li, Vi*] can be inverted to form weights,

except for any participant *i*, where all reported partnerships are ongoing, in which case *wijAP = wijBP*. For participant 1, the second and third most recent partnerships are then weighted by 20/14 and 36/14, respectively. The alternative stratum probability of selection Pr[*Sij* = 1|*Ci, TC, LC, VC*] is inverted to define weights.

##### Weighting for Different Populations and Model Fitting

Because the total number of partners is informative for condom use, we propose additional weighting for the population of interest, first for the population of partnerships in which interest is in behavior within a partnership. Partnerships that involve 2 people aged 16 to 44 have roughly twice the chance of being reported, compared with a partnership in which only 1 partner is aged 16 to 44; the exact chances depend also on whether a partnership is recent for both partners. We propose to double the weight attached to the latter partnerships, as an approximate solution to this problem.

Second, inference could be made for a typical partnership from the population of eligible individuals, where interest is in individual behavior that may be common across partnerships. This requires that the partnerships from each participant are weighted in sum by 1. For participant 1, this is achieved by multiplying the weight for missing partnerships, developed in the previous section, by the inverse of the total number of partners, ie, by 1/5.

The merits of each choice of population are briefly discussed later. In regression analysis where explanatory factors are partner specific but known only for the survey participant (eg, marital status), then a sex-specific analysis is often appropriate. Factors are then more readily interpretable (eg, as male marital status).

The final weighting for a partnership is the product of the participant’s original survey weight (see earlier), the weight for missing partnerships, and the weight for the population of interest. The logistic regression models of condom use are fitted by incorporating the final weights through weighted independence estimating equations, using the survey analysis functions of STATA (version 8; StataCorp, College Station, TX). This approach leads to unbiased estimation where the total number of partners is informative.^{9} Through specifying the geographic interview clusters as the primary sampling unit, the standard errors are robust to dependence in the data arising from the clustering of partnerships within participant and participants within clusters. We compute odds ratios (ORs) and 95% confidence intervals (CIs).

#### RESULTS

Table 1 presents the effect of our various weighting schemes on the estimated overall prevalence of condom use at last sex among heterosexual partnerships. For typical partnerships from the population of individuals, the effect of varying the scheme (ie, the assumptions made about the unreported partnerships) is minimal. For the population of partnerships, the range under the different assumptions is more substantial but still modest.

Across weighting schemes, the estimated prevalence of condom use is markedly higher for the population of partnerships than for individuals. This results from greater reporting of condom use among participants with higher numbers of partners.

Figure 2, based on primary weighting for the population of partnerships, shows the rate of condom use at first and last sex by the duration of the partnership, and whether the partnership is ongoing at interview. Condom use at last sex is highest for single-episode partnerships, and lowest for the longest ongoing partnerships; for each, duration is lower for ongoing than for terminated partnerships. For every partnership type, condom use is lower at last sex than first sex. Condom use at first sex is relatively high for single-episode partnerships and low for the longest partnerships, but the relationship between subsequent duration and condom use at first sex seems complex.

Our interest lies in whether this pattern reflects partnership factors or only participant factors. Table 2 presents for key factors the results of regression analyses for the population of participants that focus on partnership predictors of condom use at last sex that is restricted to participants reporting in detail, 2 or more partnerships. We focus on the adjusted ORs, because inherent confounding between some participant and partnership factors means some unadjusted ORs cannot be interpreted. For example, the within-participant partnership duration is difficult to interpret without adjustment for the participant’s average partnership duration. This is because a partnership cannot be shorter than average if the average is 1 occasion. Greater condom use is linked strongly to younger age and shorter average partnership duration. Of the partnership factors, condom use is greatest where that partnership had ended and was shorter than average (for men, adjusted OR = 2.0 [95% CI = 1.4–2.8] relative to longer and ongoing; for women, 2.4 [1.5–3.8]). Naive unweighted adjusted ORs are included for illustration (final column). The ORs are comparatively insensitive to the weighting scheme.

The age difference in the partnership was not linked to condom use. Before adjustment for other factors, lower condom use was seen (1) when men were more than 5 years older than their partners, (2) when the participant reported at least 1 ongoing partnership, (3) with fewer partners in the last year, and (4) with casual partnership. However, these associations (which were broadly similar for men and women) were reduced after adjustment for other factors (data not shown).

We see in Table 3 that, for men, condom use at first sex is greatest where the partnership is subsequently relatively long and ongoing at interview, in direct contrast to our findings for last sex.

#### DISCUSSION

We have presented an approach to the analysis of partnership data that allows both a sensitivity analysis to possible selection bias and inference for well-defined populations of interest. This approach can be implemented using standard survey analysis software.

In our analysis of condom use, the choice of weighting scheme for unreported partnerships had a minimal effect on prevalence estimates for a typical partnership from the population of people, and a greater but modest effect for the population of partnerships. This is first due to the low proportion of partnerships unreported. Second, within participants with 4 or more partnerships, the strength of association between factors linked to partnership selection and condom use was appreciable but not extreme. For measures of association with condom use, there was also little sensitivity to the weighting scheme; indeed a simple unweighted analysis led to similar inference. This indicates little interaction between the factors defining the weights and the explanatory factors considered in their association with condom use. Clearly interactions could occur in general, and the sensitivity of measures of association to missing partnerships and population for inference should be examined in each case.

To demonstrate that weighting can have a greater effect on estimates we modified our data in 2 ways. First we doubled the number of partners for those reporting 3 or more to increase the degree of missing data. Second we increased the strength of association between the factors linked to partnership selection and condom use by changing the shortest ended partnership reported as “no condom use” to “condom use,” in participants reporting 3 or more partnerships. Either change made a substantial impact. When made together, with scaling of weights by participant, the prevalence estimates for condom use in the population of partnerships without weighting, with basic weighting, and with alternative weighting were 36%, 49%, and 54%, respectively. This demonstrates that in other populations the choice of weighting scheme may be important, and a simple unweighted analysis alone could be strongly misleading.

The prevalence of condom use is much higher for the population of partnerships than individuals, as greater condom use is linked to a greater number of partners. The population of partnerships may be more appropriate for measuring risk in the general population, whereas the population of individuals is more appropriate when investigating the consequences of individual attitudes or practices. However, in many cases summary statistics, or even regression analysis, for both populations will be of interest. Measures of association with the outcome will differ for the 2 populations only when there is an interaction between the explanatory factor and the number of partners for a participant.

The analysis of partnership data is particularly prone to confounding. Even though key predictive factors can be obtained for the participant, these will often be unobtainable for the partner. With a participation rate of only 65% (in line with other major surveys in Britain^{14}), participation bias could be appreciable.^{15} The weighting approaches we propose are expected to reduce the possible selection bias, but these are all based on simplified selection probabilities. Residual bias may remain. However, bias may increase if there is systematic misreporting (eg, recall bias) or deviation from the intended sampling scheme for partnerships, and the weights introduced are linked to these errors. This might arise if, for example, misreporting of condom use is linked to partnership duration. The validity of self-reported condom use has been questioned.^{16}

There are other possible approaches to weighting for those partnerships that had not been reported in detail. We could define weights based on the timing information among those partnerships reported in detail. For example, we weighted partnerships of less than 6 months duration to represent missing partnerships when the latter must be concurrent with the reported partnerships, scaled by participant; we found a prevalence of condom use for the population of partnerships of 33%, similar to that seen with other approaches.

We have presented a methodology to fit marginal models; an alternative would be to fit random-effects models. However, weighting is not straightforward in random-effects regression,^{17} nor is the methodology to deal with informative cluster size.^{18}

We suggest that some participants could be invited to report all partnerships in detail, sampled perhaps on the basis of the total number of partners. This might require the provision of incentives to compensate for the time required, and also further aids to assist recall. This would inform the assumptions made concerning the missing partnerships. A direct question to determine whether a partnership is ongoing would help in construction of weights. Interviews from both partners within a number of partnerships would help the inference. Questions concerning conception intention would also help to interpret the findings regarding condom use, but these were not included in this study.

Our analysis suggests that people in Britain may have heterosexual condom use strategies, influenced by partnership duration and type, as has been suggested in other countries.^{1–4} This provides additional insight beyond previous analyses based on data from only the most recent partner.^{19} First, at least among men, we see condom use is lower among relatively short partnerships on the occasion of first sex but higher at later times. This may be because more casual partnerships begin more chaotically, but after the first occasion condom use is high as there is less inclination to switch to other methods of contraception or to conceive. Second, we found that condom use seems lower at last sex for ongoing partnerships than for terminated partnerships of the same duration. This may reflect that condom use at the same duration is lower among less casual partnerships. It is important for health promotion to know that, although people with higher numbers of partners have greater condom use in general, usage may be lower on the first occasion of more casual partnerships. A prospective study could confirm our findings, avoiding recall bias, and qualitative research could elucidate whether variation is due to deliberate strategies or an unplanned response to circumstances.