Use of Twins as Mutual Proxy Respondents in a Case-Control Study of Breast Cancer: Effect of Item Nonresponse and Misclassification

Ann S. Hamilton and Thomas M. Mack

From the Department of Preventive Medicine, Keck School of Medicine at the University of Southern California, Los Angeles, CA.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
A case-control study of breast cancer in twins diagnosed before 1988 was used to characterize the effects on odds ratios when proxy responses from co-twins are used. North American disease-discordant pairs were ascertained through advertisements, and mailed questionnaires were returned from both members of 671 pairs and from one member of 391 pairs. Biases from the proxy response were attributed to nonresponse or misclassification. Nonresponse varied according to type of exposure variable, depth of detail requested, joint exposure status of the pair, respondent's case-control status, zygosity, and social closeness of the pair. Misclassification was minimal, generally nondifferential, and a high degree of reliability between the proxy and self-report was indicated by the kappa statistic and the intraclass correlation coefficient. By using double-respondent pairs, a method was developed to adjust proxy responses for both sources of bias. These adjustments resulted in minor changes to the odds ratios for the variables studied (age at menarche, reproductive factors, and hormone use). A larger difference was observed between the odds ratios based on all pairs and those based on double-respondent pairs only. These findings demonstrate that, for these variables in this population, twins are reliable proxies for each other and that results from single-respondent pairs should be included.

breast neoplasms; case-control studies; proxy; reproducibility of results; twins

Abbreviations: ERT, estrogen replacement therapy; FFTP, first full-term pregnancy; ICC, intraclass correlation coefficient; ORall pairs, odds ratio for all twin pairs; ORproxy(0), odds ratio based on self-report from the case versus her proxy report about her co-twin; ORproxy(1), odds ratio based on self-report from the control versus her proxy report about her co-twin; ORself, odds ratio based on self-report from the case versus self-report from the control; ORself(0), odds ratio based on self-report from the subset of pairs in which the case provided proxy information about the control; ORself(1), odds ratio based on self-report from the subset of pairs in which the control provided proxy information about the case.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
In case-control studies that use twin pairs as matched sets, each twin can provide information about himself or herself as well as the co-twin. When both twins participate, these dual sources of information can be used to determine reliability of the exposure data; even in the absence of an independent verification method, high reliability may be seen as an indication of high validity. Moreover, the quality of the proxy responses can be assessed in reference to self-reported information to judge the value of those proxy responses from pairs in which only one twin is able or willing to participate. Including these pairs not only increases the sample size, which is especially helpful when subgroup analyses are required, but also permits study of a more representative group of cases (1Go).

While twins may be well informed about each other and highly motivated to participate, there is still a potential for misclassification of personal exposure status. Both twins in a pair (i.e., the affected twin and the unaffected co-twin) are aware of the affected twin's disease and exposure history, and each may provide answers subject to recall bias. Further, proxy information from twins is also subject to a liability that is generally present in case-control studies but has not been emphasized: The respondent's own exposure experience (as well as that of the co-twin) may influence the proxy response.

A comparison of proxy responses to self-reports in case-control studies usually is not possible or is limited to a small subset of case-control pairs. This study of female-female twin pairs discordant for breast cancer provided the opportunity to compare self-reported and proxy responses from the members of a large number of matched sets. We examined the ability of twins to answer for each other, assessed the impact of nonresponse and inaccurate response on resulting odds ratios for which proxy information is used, and determined the importance of including in the analysis pairs in which only one twin responds.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Development of the twin registry
From 1980 to 1991, advertisements seeking "twins with cancer" (or other chronic disease) were placed periodically in North American magazines and newspapers. Readers were requested to respond by telephone or mail; 12,134 twin pairs affected with cancer (including 16,119 cancers in 14,631 persons) were reported directly by the twins themselves or by their relatives (including parents, other siblings, cousins, and others). Each reported pair was contacted by telephone and was asked to provide information about the case's birth date, sex, perceived zygosity, and the time and place of diagnosis and, if appropriate, of death. The development and representativeness of this twin registry has been described previously (2Go).

After signed permission was received, validating medical records were routinely sought (successfully for 71.4 percent of the respondents) and were coded by using the second edition of the International Classification of Diseases for Oncology (3Go). Tumor specimens were requested for review of the histologic cancer diagnosis on a site-specific priority basis, as resources permitted. Few errors were found in the initial diagnoses of the common solid epithelial malignancies (breast, lung, colon, etc.). These specimens included a sample of discordant and concordant breast cancers (678, or 65 percent of those requested, were reviewed initially; 127 breast cancer specimens were also reviewed subsequently). No major discrepancies were found between the original and the validation diagnosis of breast cancer or between the histologic classification assigned by the original pathologist and the one assigned by the morphologic reviewer. Roughly 94 percent of the breast cancer diagnoses were of invasive disease.

Ordinary perceptions of zygosity by adult twins are usually unambiguous and consistent; when both members of a pair agree, their perceptions are accurate in over 90 percent of pairs (4Go). We previously used molecular methods to evaluate the accuracy of self-assessed zygosity among more than 50 pairs of adult twins affected by chronic disease (5Go, 6Go); all laboratory findings to date have agreed with self-assessments of zygosity, and the latter were accepted in our study.

Both disease-discordant and -concordant female breast cancer pairs were mailed questionnaires, which obtained information on risk factors for breast cancer. Among the pairs ascertained before 1988, there were 1,532 female breast cancer pairs. For 1,098 of these pairs, the questionnaire was mailed to both members; for 434 pairs, the questionnaire was mailed to only one twin because of the death of the co-twin or other reasons. Thus, questionnaires were mailed to 2,630 women. A total of 2,040 questionnaires were returned, for a response rate of 77.6 percent among twins as individuals. By pair, both twins responded for 779 pairs and one twin responded for 482 pairs, which provided responses from 1,261 pairs or 82.3 percent of the total number of pairs contacted. Of these responding pairs, 1,062 were disease discordant, and they constituted the subset of pairs used in the current analyses.

In addition to including a large number of direct queries, the questionnaire elicited proxy information about reproductive factors, use of exogenous hormones, and smoking behavior. To assure that responses would be obtained independently from each twin, both a red and a black pen accompanied the questionnaire. Each respondent was instructed to first complete the questionnaire by using the black pen and then, after consultation with the twin, to make any changes with the red pen. In this study, the original, unmodified answers (written in black pen) were used to assure that the responses were the ones derived independently.

Those pairs in which both twins returned the questionnaire were referred to as "double-respondent pairs" (n = 671) and those in which only one twin returned the questionnaire as "single-respondent pairs" (n = 391). When the single-respondent pairs were added to the double-respondent pairs, the total group was referred to as "all pairs" (n = 1,062). Inclusion of all pairs provided a sample size 59 percent larger than the sample limited to double-respondent pairs. Among the 391 single-respondent pairs, 295 respondents were controls and 96 were cases. Among the twin pairs in which the control was the sole respondent, the major reason for non-response by the case was mortality (75 percent); this reason was true less often for controls (34.5 percent) when the corresponding case was the sole respondent.

Statistical methods
In this study, we described and characterized proxy response errors, determined the effect of using proxy responses to calculate odds ratios, described methods for adjusting these odds ratios for misclassification and nonresponse, and determined the effect of including the single-respondent pairs in the overall analysis. Two potential sources of proxy response error were examined: 1) failure to respond to a proxy question (item nonresponse) and 2) inaccurate proxy response, as judged in comparison to the response provided by the subject (misclassification). If the subject's self-report is considered to reflect "truth," then the sensitivity and specificity of the proxy responses in relation to this standard provide one method of measuring misclassification. Misclassification can also be inferred to some degree by measuring the reliability of the responses using various measures of agreement between the proxy response and the subject's self-report, namely, the percentage of responses that agree, the kappa statistic for a dichotomous variable, and the intraclass correlation coefficient (ICC) for a continuous variable (7Go).

Since cases and controls may systematically recall selected variables differently, all analyses were conducted in parallel for the case as respondent, who provided proxy responses for her co-twin (the control), and for the control as respondent, who provided proxy responses for her co-twin (the case). Each analysis was repeated for two strata of zygosity (monozygotic twins and dizygotic twins). The matched odds ratios presented were based on the ratios of exposure-discordant pairs, and 95 percent confidence intervals were calculated. In addition, ratios of selected odds ratios were determined that quantified the amount of bias due to misclassification alone and that due to the combination of misclassification and nonresponse (referred to as "bias ratios").

To quantify the separate and combined effects of misclassification and nonresponse on odds ratios when proxy information is used, adjustment parameters were first developed from the double-respondent pairs. The following five different comparisons from these pairs were used:

  1. Comparison of the case's self-reported information to the proxy response about the case given by the co-twin (the control).
  2. Comparison of the control's self-reported information to the proxy response about the control given by the co-twin (the case).
  3. The odds ratio based on self-report from the case versus self-report from the control (ORself), which was considered the unbiased "gold standard." Two other odds ratios based on self-reported data were also used: ORself(0), based on the subset of pairs in which the case provided proxy information about the control; and ORself(1), based on the subset of pairs in which the control provided proxy information about the case.
  4. The odds ratio based on self-report from the case versus her proxy report about her co-twin (the control) (ORproxy(0)), for which only the questionnaires returned by cases were used.
  5. The odds ratio based on self-report from the control versus her proxy report about her co-twin (the case) (ORproxy(1)), for which only the questionnaires returned by controls were used.

Comparisons 1 and 2 were used to assess reliability of the proxy response (i.e., the kappa statistic and the ICC) and to measure sensitivity and specificity of the proxy response (when the self-report was considered "truth"). In addition, the number of missing proxy responses in these comparisons was used to measure item nonresponse and to provide (selection) percentages of response within each group. The sensitivity, specificity, and selection percentages were developed separately for the respondent's exposure status (i.e., exposed and nonexposed); in this unique circumstance in which co-twins were used as proxy respondents, the proxy respondent was also a member of the case-control pair. These parameters were then applied to the proxy responses from the single-respondent pairs (in the appropriate zygosity, case-control status, and exposure status categories) to produce adjustments based on the experience of the double-respondent pairs. (The Appendix illustrates this method in detail for dizygotic twins, when the control is the respondent, for the variable age at menarche.)

The overall effect of the use of unadjusted proxy responses on odds ratio estimates can also be derived from the double-respondent pairs by comparing the three types of odds ratios listed above (comparisons 3–5). To determine the effect of misclassification, we used the subset of pairs in which both a self-report and a proxy response were available. The ratio of the proxy-derived odds ratio (i.e., ORproxy(0) and ORproxy(1)) to the self-reported odds ratio (i.e., ORself(0) and ORself(1)) from the same subset of pairs constitutes a measure of bias due to misclassification. (In ordinary case-control studies (8Go), this measure has been obtained by calculating the ratio of such odds ratios derived from different respondent strata.) Similarly, the ratio of the proxy-derived odds ratios (i.e., ORproxy(0) and ORproxy(1)) to the self-reported odds ratio based on all pairs with self-reports from both twins (ORself) demonstrates the combined effects of both misclassification and nonresponse.

The final goal was to combine the adjusted responses from the single-respondent pairs and the self-reports from the double-respondent pairs to create an adjusted OR(all pairs) and to determine the degree of bias in this odds ratio that would be due to the proxy data if they remained unadjusted. In addition, we sought to examine the effect of incorporating the single-respondent pairs into the analysis (as opposed to basing the analysis solely on the double-respondent pairs). Bias ratios were computed that separately compared the ORself from the double-respondent pairs and the unadjusted odds ratio based on all pairs (unadjusted ORall pairs) with the adjusted odds ratio for all pairs (adjusted ORall pairs).


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Description of twin pairs by participation status
The double-respondent pairs of twins were more likely to be monozygotic in comparison with the single-respondent pairs (59.3 percent of double-respondent pairs vs. 49.8 percent of single-respondent pairs in which only the control participated and 38.5 percent of those in which only the case participated (table 1)). The average age at diagnosis differed slightly according to the participation status of the pair. For the cases in double-respondent pairs, the average age was 50.1 years and was slightly higher (52.2 years) when only the case responded and slightly lower (47.4 years) when only the control did (table 1). The latter group also had the highest percentage of those diagnosed at less than age 50 years (59.0 percent), reflecting the higher mortality rate among cases diagnosed at a younger age.


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TABLE 1. Selected characteristics of North American female-female twin pairs discordant for breast cancer, by zygosity and participation status, diagnosed before 1988

 
Because of their greater genetic and environmental similarity, monozygotic twins would be expected to be closer and more knowledgeable about each other than dizygotic twins are. However, in each zygosity group, we expected the completeness and accuracy of proxy information to be related to the frequency of regular communication. To assess this hypothesis, we developed a variable termed social "closeness." Each twin pair that met two or more of the following criteria was considered relatively "close": 1) visitation at least once a month, 2) telephone contact at least once a month, and 3) feeling "like being part of the same person." Among monozygotic pairs (n = 553), 70.3 percent were classified as "close," as were 41.0 percent of dizygotic pairs (n = 456). This discrepancy by zygosity was unrelated to the participation status of the pairs.

Item nonresponse
Variables for which proxy information was obtained included age at menarche, parity, age at first full-term pregnancy (FFTP), use of oral contraceptives, use of estrogen replacement therapy (ERT), menopausal status, menopausal age, smoking status, and number of cigarettes smoked per day. Item nonresponse was examined for these variables according to the participation status of the pair (figure 1). For ease of presentation, the percentages shown in this figure are based on the responses of the control (reporting about the case). The availability of proxy responses from cases (reporting about controls) was similar; when there were differences, the nonresponse rate for the cases was usually lower and less variable. The frequency of item nonresponse varied substantially, with nonresponse uniformly less than 5 percent for smoking status and more than 40 percent for number of cigarettes smoked per day. In general, monozygotic twins provided proxy information (from both cases and controls) more often than dizygotic twins did.



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FIGURE 1. Percentages of controls who failed to respond to a proxy item about cases, by participation status of the pair for selected variables and by zygosity: North American female-female twin pairs discordant for breast cancer diagnosed before 1988. FFTP, first full-term pregnancy; OC, oral contraceptive; ERT, estrogen replacement therapy; Cigs, cigarettes; MZ, monozygotic; DZ, dizygotic.

 
Proxy information was slightly less available from single-respondent pairs than from double-respondent pairs for age at menarche, parity, age at FFTP, oral contraceptive use, and number of cigarettes smoked per day. Information on menopausal status and ERT use was less available from the single-respondent pairs in both zygosity groups, presumably because the less obvious characteristics of late adulthood were not as likely to have been discussed before the twins were separated by the death of one of them.

Modification of item nonresponse by other twin characteristics was examined in more detail by using age at menarche as an example (figure 2). The prevalence of response was slightly lower among the pairs considered "not close" versus those who were "close," especially for dizygotic cases. The response rate for pairs in which the case was diagnosed at age 50 years or more was slightly lower than the rate for those pairs in which the case was diagnosed at a younger age. For both zygosity groups, a response was more likely if the subject had an earlier age at menarche (i.e., <12 vs. >=12 years). For the pairs discordant for age at menarche, there was a slight trend toward a higher response rate when the case's versus the control's menarche occurred earlier.



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FIGURE 2. Percentages of twins in selected subgroups that failed to respond to proxy queries used to determine age at menarche (years), by case-control status of the respondent and by zygosity: North American female-female twin pairs discordant for breast cancer diagnosed before 1988. *, based on double-respondent (Resp.) pairs; Age of Dx, age of diagnosis (years); Cont, control; MZ, monozygotic; DZ, dizygotic; refer to the text for the definition of "close."

 
Despite this variability, availability of proxy information was not associated with variation in self-reported mean age at menarche (table 2). When similar comparisons were made according to availability of a proxy response for the other variables, no differences were found for mean age at FFTP or mean age at menopause between those with a proxy response and those without. Among the groups being compared, none of the differences in the percentage who were postmenopausal was significant between those with and without proxy responses. However, both cases and controls with proxy responses had a significantly lower average number of livebirths than those for whom no proxy information was given, and the mean age at first use of oral contraceptives tended to be lower for those with versus without proxy information. In addition, those with a proxy response were more likely than those without one to be oral contraceptive users. Although some variation was evident in mean age at first ERT use and the percentage who used ERT, no consistent or statistically significant differences were found. In summary, the differences were generally consistent between case and control respondents and between both zygosity groups. Parity for those with a proxy response was lower than for those without proxy information; for oral conceptive use, those with a proxy response were more likely to be users and to be younger at first use than those for whom a proxy response was not provided.


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TABLE 2. Self-reported characteristics of subjects, by availability of proxy response for selected variables{dagger} and by case-control status of respondent and zygosity: North American female-female twin pairs discordant for breast cancer diagnosed before 1988

 
Validity
Both sensitivity and specificity of the proxy response (for age at menarche) were found to be related to the exposure status of the respondent, especially among monozygotic twins (table 3). When the respondent was exposed (i.e., had an early menarche herself), the sensitivity of the proxy response was higher than otherwise. Likewise, when the respondent was unexposed (i.e., had a later menarche), the specificity of the proxy response was higher. For example, among monozygotic twin cases, sensitivity was 1.00 for respondents with an early menarche and 0.37 otherwise. Specificity for this same group was 0.43 when the respondent had an early menarche and 0.96 otherwise.


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TABLE 3. Sensitivity and specificity of proxy responses for age at menarche* based on double-respondent pairs, by exposure status of respondent: North American female-female twin pairs discordant for breast cancer diagnosed before 1988

 
We assumed the self-reports to be accurate, and proxy errors that did occur were examined for direction and magnitude. In general, those proxy responses that differed from the self-reports were as likely to overestimate as to underestimate age at menarche and therefore seemed to represent nondifferential misclassification. The mean absolute difference between the proxy response and the self-report was approximately 0.5 years for the monozygotic twins and 0.7 years for the dizygotic twins. Just as for age at menarche, the majority of disagreements between the self- and proxy responses regarding age at FFTP were within 1 year of each other and appeared to be nonsystematic. The proxy errors that occurred for parity were more likely to underestimate than to overestimate number of births. The errors were larger for number of cigarettes smoked per day but were generally nonsystematic, although dizygotic control respondents tended to underestimate the daily number of cigarettes smoked.

Reliability
In general, a kappa statistic or an ICC greater than 0.75 is considered a mark of excellent reliability, whereas values from 0.40 to 0.75 represent fair to good agreement and lower values only poor agreement (9Go). Proxy estimates from both cases and controls for the co-twin's age at menarche showed fair to good agreement with self-reports, irrespective of zygosity (kappa = 0.60 for monozygotic twins, kappa = 0.63–0.64 for dizygotic twins) (table 4). When age at menarche was considered a continuous variable, the ICC was 0.75 or higher for all subgroups except dizygotic control respondents (0.70). The ICC values were slightly higher than the kappa values because the former measure takes into account magnitude as well as the fact of disagreement. If the perceived difference is small relative to the overall variation, the ICC is relatively high; in the present study, errors were generally quite small.


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TABLE 4. Measures of reliability* between proxy responses and self-reported data for selected variables, by zygosity and respondent status, based on double-respondent pairs: North American female-female twin pairs discordant for breast cancer diagnosed before 1988

 
For almost all other variables, and within each zygosity and case-control respondent group, the kappa value was higher than 0.8; for some, it was higher than 0.9. Agreement was highest for parity, age at FFTP, and menopausal status and was only slightly lower for oral contraceptive use and ERT use. For two variables (age at first ERT use and number of cigarettes smoked per day) among the dizygotic twins, the kappa values measuring the agreement between the case self-report and the proxy response from the control were lower than those measuring the agreement between the control self-report and the proxy response from the case. This type of result also occurred for monozygotic twins for the variables related to smoking. In these instances, the controls' proxy responses were found to be less consistent with the cases' self-reports than for the other variables; this finding may imply that, in some circumstances, the control is not as reliable a proxy respondent as the case.

Odds ratio adjustments
ORproxy(0), ORproxy(1), ORself(0), ORself (1), and ORself were calculated for each variable from the double-respondent pairs. Two odds-ratio bias ratios were calculated reflecting the degree of bias due to misclassification and nonresponse; small differences were found between the various odds ratio estimates for age at menarche as a dichotomous variable (i.e., <12 vs. >=12 years). The bias ratio reflecting misclassification alone among case respondents (i.e., ORproxy(0)/ORself(0)) was 0.96 for dizygotic twins (1.44/1.50) and 0.58 for monozygotic twins (0.43/0.74), indicating some underestimation of the odds ratios for which proxy data were used in this group. The bias ratio for control respondents (i.e., ORproxy(1)/ORself(1)) was 0.82 for dizygotic twins (1.40/1.71) and 1.10 for monozygotic twins (0.77/0.70). By comparing ORproxy(0) and ORproxy(1) with ORself, based on all self-reports (regardless of availability of proxy responses), we could quantify the combined effect of misclassification and nonresponse. In this example, this bias ratio for case respondents was 0.96 (1.44/1.50) for dizygotic twins and 0.63 (0.43/0.68) for monozygotic twins. For control respondents, the respective ratios were 0.93 (1.40/1.50) and 1.13 (0.77/0.68). None of these ratios was statistically significant.

Adjustment parameters based on sensitivity and specificity, by respondent exposure status and selection percentages derived from the double-respondent pairs, were applied (as demonstrated in the Appendix) to adjust the responses from the single-respondent pairs and to obtain the adjusted ORall pairs for age at menarche, age at FFTP, parity, and oral contraceptive use (table 5). Two bias ratios were calculated that showed the effect of 1) use of ORself versus adjusted ORall pairs, which was used to demonstrate bias in not including the single-respondent pairs in the analysis; and 2) inclusion and adjustment of the single-pair proxy data (unadjusted ORall pairs vs. adjusted ORall pairs). For age at menarche, the first bias ratio between ORself and adjusted ORall pairs was 0.75 (0.68/0.91) for monozygotic twins and 1.16 (1.50/1.29) for dizygotic twins. The bias ratios reflecting comparison of the unadjusted and adjusted ORall pairs were closer to 1 for both zygosity groups (0.85 (0.77/0.91) for monozygotic twins and 1.04 (1.34/1.29) for dizygotic twins).


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TABLE 5. Comparison of odds ratio estimates for selected variables, by zygosity: North American female-female twin pairs discordant for breast cancer diagnosed before 1988

 
For age at FFTP, ORself for monozygotic twins was almost identical to both unadjusted and adjusted ORall pairs (1.29 vs. 1.28 and 1.24); for dizygotic twins, ORself was 24 percent lower than adjusted ORall pairs (0.91 vs. 1.19), but unadjusted ORall pairs was only 8 percent lower (1.10 vs. 1.19). Unadjusted ORall pairs also more closely approximated the comparably adjusted odds ratio for parity than did ORself for both zygosity groups. ORself was 25 percent (for monozygotic twins) to 33 percent (for dizygotic twins) higher than adjusted ORall pairs, whereas unadjusted ORall pairs was only 2 percent higher (for monozygotic twins) and 3 percent lower (for dizygotic twins) than the adjusted odds ratio. For oral contraceptive use, little effect of adjustment or inclusion of all pairs was shown for monozygotic twins; for dizygotic twins, ORself was 20 percent higher than adjusted ORall pairs, and unadjusted ORall pairs was 14 percent higher.

In summary, when the absolute values of the percentage differences were averaged for these four variables, ORself varied from adjusted ORall pairs by 16 percent for monozygotic twins and 21 percent for dizygotic twins. In both zygosity groups, unadjusted ORall pairs varied by about 7 percent.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
In previous studies, odds ratios from different respondent strata could be assessed for heterogeneity only under assumptions made about the probability of proxy response, given different exposure and disease status (8Go). By using both self- and proxy responses for the majority of the cases and controls, we directly assessed proxy reports in terms of both misclassification (in relation to the self-report) and nonresponse. Moreover, because we used twin pairs, the proxy respondents themselves were included in the study as controls or cases; thus, joint exposure between the subject and the proxy respondent could be evaluated for its effect on both availability and misclassification of proxy responses.

Misclassification in general was found to be minimal, as evidenced by small mean absolute differences between self-reported and proxy responses. Errors that did occur seemed to be nonsystematic. High reliability between self- and proxy reports was shown by high kappa and ICC values. Thus, when twins provide proxy information about their twin partners, they appear to do so knowledgeably, at least with respect to the variables assessed in our study.

Larger effects could be attributed to nonresponse. Evidence of some bias due to differential nonresponse was found for certain variables and in certain subgroups. The provision of proxy data for some variables (e.g., parity, oral contraceptive use) was sometimes related to the respondent's exposure level. Even in these instances, however, the actual effect of bias on the odds ratios produced by inclusion of proxy information was minimal.

Overall, there were larger differences between the odds ratios from the double-respondent pairs (ORself) and the adjusted ORall pairs (in which the single-respondent pairs were included) than between the latter and the unadjusted ORall pairs. This finding suggests that the determinants for nonparticipation (e.g., death or refusal) may be more important sources of bias than that introduced by use of proxy information. This finding is based on the assumption that the nature of errors and nonresponse introduced by the proxy respondents from single-respondent pairs is comparable to that introduced by the members of double-respondent pairs. The importance of including the single respondents, and the relatively small amount of bias introduced by using twins as proxy respondents found in our study, may not necessarily apply to other studies. The twin registry from which these pairs were obtained was assembled by ascertainment of prevalent cases and included pairs with deceased cases who were represented by the living co-twin. Thus, the single respondents most likely represent a nonrandom subgroup of the cases who survived for a shorter period of time. Twins may also be better proxy respondents for each other than other relatives are, who may not be as close to the case; thus, the amount of bias in the proxy responses may be lower. In addition, these results were developed from a subgroup of female twins, who may be better proxy respondents for each other than male twins would be.

Our descriptions provide confidence that, for variables such as these, use of unadjusted results from all twin pairs in this data set may be appropriate; however, the analysis should be repeated by using separate subsets of the study group (e.g., stratified by age at diagnosis and degree of social closeness) to determine whether there are some subgroups in which the biases introduced by proxy response are larger. The adjustment methods discussed in this paper can be applied to stratified and univariate analyses but not to logistic regression methods.

While the results of this rather unique study cannot necessarily be applied directly to other studies in which proxy data are used, our study demonstrated that twins are generally knowledgeable about their co-twins' reproductive histories, although this knowledge diminished as more detail was requested. An important finding likely to pertain to case-control studies with singleton subjects was that the respondent's own exposure level determines the sensitivity and specificity of the proxy response. Specifically, sensitivity of the proxy response was higher when the respondent herself was exposed and lower when she was unexposed. In contrast, specificity was higher when the proxy respondent was herself unexposed and lower when she was exposed. Other studies that use proxy data should consider including questions, when relevant, about the proxy respondent's own exposure levels for the study variables in question.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Adjustment of Proxy Responses from Single-Respondent Pairs
This Appendix describes in detail how adjustment parameters were developed from the double-respondent pairs and were then applied to the responses from the single-respondent pairs to adjust proxy responses for misclassification and nonresponse. The first step, adjustment for misclassification (adj1), is a variation on a method used previously to correct for misclassification in a matched-pair study (10Go). As in that circumstance, the pair counts expected under conditions of misclassification (T', U', V', W') are related to the correctly classified counts (T, U, V, W in Appendix table 1) by the four equations that follow.


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APPENDIX TABLE 1. Correctly classified counts of pairs in a matched-pair study, based on exposure levels of both members of the pairs*

 




where:








In this example, considering the self-report to be classified correctly and the control to be the respondent, it is assumed that Tp0 = 1 and Tn0 = 1; thus, Fn0 = 0 and Fp0 = 0. (Similarly, when the case is the respondent, it is assumed that Tp1 = 1 and Tn1 = 1 and that Fn1 = 0 and Fp1 = 0.) The estimates of Tp1 (sensitivity) and of Tn1 (specificity) require the proxy report about the case to be compared with the case's self-report as the standard. Since (in this unique circumstance, in which the proxy respondent is also a member of the case-control pair) the respondent's personal exposure status is matched to the subject's exposure status, it is necessary to use two measurements of sensitivity and specificity, depending on the exposure status of the respondent (from text table 3). When the control has been exposed and is the respondent, the values for Tp1 and Tn1 are represented by Tp1resp.exp and Tn1resp.exp and, when the unexposed control is the respondent, by Tp1resp.unexp and Tn1resp.unexp. Tp1resp.exp and Tn1resp.exp are used in the equations for T' and V' (since these cells contain pairs in which the control is exposed), and Tp1resp.unexp and Tn1resp.unexp are used in the equations for U' and W' (cells in which the control is unexposed). (Analogously, when the case is the respondent, Tp0resp.exp and Tn0resp.exp are used in the equations for T' and U' (case exposed), while Tp0resp.unexp and Tn0resp.unexp are used in the equations for V' and W' (case unexposed).)

To obtain the correctly classified counts (T, U, V, W), the unadjusted counts derived from the control's questionnaire (representing T', U', V', W') and the appropriate values for Tp1, Tn1, Fp1, and Fn1 are used in four equations that are solved simultaneously:




In this example, the solutions are T = 10, U = 29, V = 17, and W = 90.

Since these computations are based on double-respondent pairs, these estimates can be compared with the actual correctly classified counts available from self-reports. Solving these equations produces results identical to those obtained by using the self-reports from the subgroup of double-respondent pairs in which proxy responses are available from the control. The odds ratios adjusted for misclassification (adj1) are based on the ratio of the numbers of misclassification-adjusted discordant pairs (U/V).

The second step is to further adjust these estimates for item nonresponse (adj2). Selection percentages (or the percentage for which proxy responses are available) for each cell were determined on the basis of the counts obtained when the total number of double-respondent pairs with self-reports was used as the denominator in each cell of the matched-pair table and the number based on the misclassification-adjusted counts as the numerator: ST = 10/13 = 0.77, SU = 29/39 = 0.74, SV = 17/26 = 0.6=, and SW = 90/167 = 0.54. These selection percentages were then used to derive secondarily adjusted counts (T2, U2, V2, W2) referred to as follows: T2 = T/ST = 10/0.77 = 13 and so on for U2, V2, and W2.

The adjustment parameters derived from the double-respondent pairs (i.e., Tp, Tn, Fn, Fp, ST, SU, SV, and SW) were then applied to the comparable subset of single-respondent pairs. Continuing with the example of pairs in which dizygotic twin controls responded, the unadjusted counts, misclassification-adjusted counts, and nonresponse-adjusted counts for the single-respondent pairs are shown in Appendix table 2. A final adjustment was made to assure that the correction for item nonresponse reflected the actual number of missing proxy responses. Here, the adjustment procedure added 59.8 pairs to the table, whereas there were actually 50 pairs with missing data. Thus, the increased number of pairs in each cell was multiplied by 50/59.8 to proportionately reduce the number in each cell to ensure that the total number of pairs in the adjusted figures reflected the actual number missing in the study.


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APPENDIX TABLE 2. Steps in the adjustment for misclassification and nonresponse of cell counts based on proxy data from single-respondent pairs for the variable age at menarche (years) using the subset of dizygotic twins, control responding: North American female-female twin pairs discordant for breast cancer diagnosed before 1988

 
The ultimate effect on the odds ratio for a younger age at menarche in this single-respondent subset of 136 pairs (dizygotic twins, control responding) was to decrease the estimate by 2 percent from 1.00 (10/10) to 0.98 (16.1/16.4). For dizygotic twins, case responding, there were 53 total pairs; although the adjustment increased the number of discordant pairs from 6/5 to 11.3/9.1, the odds ratio was unchanged (1.2). As these figures indicate, the increase in the number of discordant pairs is substantial. However, because of the potential variability introduced in the steps involved in these adjustments, the increased precision in these adjusted estimates would not be as great as these numbers would indicate.


    ACKNOWLEDGMENTS
 
Supported in part by Public Health Service grants CA32262 and CA42581 and US Department of Defense award DAMD17-94-J-4290.

The authors acknowledge the important contributions of Dr. Dennis Deapen, Janice Schaefer, Data Management, and Registrars Kathy Heller, Melanie Santa Maria, and Beverly Wingert.


    NOTES
 
Correspondence to Dr. Ann S. Hamilton, Keck School of Medicine at the University of Southern California, Norris Comprehensive Cancer Center, 1441 Eastlake Avenue, MC 9175, Los Angeles, CA 90089-9175 (e-mail: ahamilt{at}hsc.usc.edu).


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

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Received for publication September 17, 1999. Accepted for publication January 27, 2000.