Statistical analysis
Handling missing responses. Missing data is a common problem in survey research. Until recently, the only methods widely available for analyzing incomplete data focused on “removing” the missing values by ignoring subjects with incomplete information or by substituting plausible values (eg, means or regression predictions) for the missing items. These ad hoc methods, although simple to implement, have serious drawbacks,9 including the potential introduction of bias. In the past 2 decades, substantial progress has been made in developing statistical procedures for missing data. In an incomplete data set, the observed values provide indirect evidence about the likely values of the unobserved data and one can use the available data to make estimates of the values of the missing data. Because any one estimate is uncertain, one may repeat the process a number of times and then average over these estimates for the missing values in the statistical analysis. Rubin developed the paradigm of multiple imputation, which carries out the averaging via simulation; each missing value is replaced by plausible values drawn from their predictive distribution.10 The variation among the number of imputations reflects the uncertainty with which the missing values can be predicted from the observed ones. After performing identical analyses on each data set, the results are combined according to simple rules to produce overall estimates and standard errors that reflect missing-data uncertainty. We used the publicly available software program, Amelia,11 to generate 5 data sets containing imputed values for those subjects with missing values for I-QOL. Variables in the imputation model included age, education, type of incontinence, number of incontinent episodes, I-QOL, and scores on the physical and mental components of the SF-12.
Regression analysis. Logistic regression was used to investigate factors associated with incomplete responses to the I-QOL instrument. The relations between the I-QOL scores and predictor variables were modeled with multiple linear regression. Before the regression, we used generalized additive models,12 a method that uses data smoothers to graphically display the pattern of relationships, to explore the shape of nonlinear relations, and suggest linearizing transformations. Model checking included an analysis of residuals.13
An important measure of the impact of incontinence is whether or not subjects consider their incontinence to be a “problem.” To compare the performance of the I-QOL and generic quality of life measures in discriminating between women who found and did not find their incontinence to be a problem, we computed the area under receiver operating characteristic curves.14 Computations were done with the Stata statistical package.15
RESULTS
Prevalence of incontinence
Of the 605 respondents, 310 (51%) reported urinary incontinence in the month before the survey. Table 1 shows the distribution of the respondents by age and incontinence status. Among our respondents, the prevalence of incontinence decreased slightly with age, a trend of borderline statistical significance (P = .08). Most surveys have reported that the prevalence of incontinence increases with age. We have no explanation for why this was not the case in our survey.
Incomplete responses to the I-QOL
The I-QOL is a questionnaire instrument with 22 items and the score is computed from all items. In such a situation, missing responses might be an important problem, leading to the reduction of sample size and study power. In our survey, 11 subjects (3.5%) replied to none of the I-QOL items; however, at least 1 item was missing for 49 other subjects. Thirty subjects missed 1 item, 4 missed 2 items, 3 missed 3 items, and 12 each missed 4 to 20 items. The number of missing responses for the 22 questions ranged from 5% to 7%, with the exception of the statement, “I worry about having sex,” for which the missing rate was 13%. Even though the missing rate for individual items was no higher than 13%, only 250 (80.7%) of I-QOL scores were complete.
Table 2 shows those variables significantly associated with incomplete response in a logistic regression model. Older women and women who had not graduated from high school were less likely to return a completed instrument, as were women who reported only urge incontinence. In addition, women who reported that incontinence was a problem were less likely to complete all the questions. These associations suggested that omitting women with incomplete responses from the analyses of I-QOL might introduce selection bias. We managed this problem by making use of the methods of multiple imputation.
Associations of I-QOL with incontinence factors
The I-QOL is scored in the range of 0 to 100, with lower scores indicating lower quality of life. The mean value of I-QOL among respondents was 83 (range, 15-100). We anticipated that the I-QOL scores would vary systematically with incontinence-related factors and planned to investigate these relationships with a linear regression model. We suspected, however, that the relationships between I-QOL and the number of daytime and nighttime episodes of incontinence might be nonlinear. We thus explored these relations with nonparametric regression methods, and Figure 1 shows the relations as estimated with a generalized additive model.12 The method of generalized additive models is a computer-intensive one that makes no prior assumptions about the shape of the relations between the outcome and the explanatory variables. It fits smooth, arbitrarily shaped functions to the data by a method that is a generalization of the “moving average.” Figure 1 shows that the I-QOL decreased as the number of incontinence episodes increased, but then reached a plateau when the frequency of occurrence was about 1 episode per day. In other words, quality of life worsened as the number of incontinence episodes increased from less than once per week to once per day. However, once incontinence was occurring daily, there was no further decrease in the perceived quality of life as incontinence episodes became more frequent than once per day. We found that these plateau relations could be satisfactorily modeled with logarithmic transformations of the number of incontinence episodes; ie, log (number of incontinence episodes per week + 1), where the 1 has been added to avoid log(0), which is undefined mathematically.