Factor structure, internal consistency and distribution of Female Sexual Function Index among Mexican women with early diagnostic of breast cancer

 Background: Female Sexual Dysfunction (FSD) occurs frequently in women with breast cancer due to oncologic treatments. It is essential to have a validated instrument to diagnose and quantify FSD in this population accurately. Objective: To validate the Female Sexual Function Index (FSFI). Method: The FSFI was applied to 272 sexually active Mexican women with recent diagnosis of breast cancer who had not initiated systemic cancer treatment. Results: The FSFI six-factor model is valid by confirmatory factor analysis, and the inventory and its factors have adequate internal consistency reliability. Conclusions: This study provides enough evidence about the reliability and factor structure of the FSFI questionnaire in the context of breast cancer clinical practice in Mexico.


Female Sexual dysfunction and breast cancer
Female Sexual Dysfunction (FSD) has been reported in 34.7% to 92% of women with breast cancer, with the average prevalence estimated to be higher than 60% (1) . When comparing the sexual function between young and older women diagnosed with breast cancer, a higher proportion of young women report FSD (2) . In fact, FSD is one of the most frequently unaddressed problems in this age group (3) . The increased severity of symptoms of FSD in young women may be due to the induction of early menopause as a side effect of cancer treatment (4)(5)(6) .
It is important to note that during routine medical appointments, FSD is one the least-addressed consequences of oncologic treatment, despite its high prevalence and its negative impact on quality of life. In this sense, Reese et al. (7) found that only 28% of healthcare providers informed women with cancer about the possibility of FSD secondary to oncologic treatment, and only 21% identified sexual concerns in their patients. Furthermore, treatment for the sexual problems that were recognized using the National Comprehensive Cancer Network (NCCN) Sexual Function Guidelines was offered to only 17% of patients (7) . According to Bober et al. (8) a "conspiracy of silence" between healthcare providers and patients exists regarding sexuality and FSD. This was illustrated by Kedde et al. (4) who reported that 6 out of 10 young women with breast cancer and FSD, did not seek medical attention for this issue.

The Female Sexual Function Index (FSFI): an instrument to evaluate FSD
There are several instruments with good psychometric properties that reduce the communication barriers between doctors and patients and facilitate the detection of FSD (1) . One of the instruments that is recommended by the NCCN is the FSFI. It should be noted that the study by Baser et al. (9) prompted the NCCN to recommend the use of this instrument to assess sexual function among women diagnosed with cancer.
The FSFI is a 19-item, self-report questionnaire that measures female FSD in a multidimensional way. Its final version arises from the study by Rosen et al. (10) in which a questionnaire of 30 items was tested in two populations. The first group consisted of 128 women diagnosed with female sexual arousal disorder according to the criteria of the Diagnostic and Statistical Manual of mental disorders, 4th edition (11) . The second group consisted of 131 healthy women. The FSFI was designed to assess 6 domains of female sexual function which include desire, arousal, lubrication, orgasm, satisfaction, and pain. 11 of the 30 items that were initially included, were removed through expert judgment and content ambiguity analysis. The internal consistency reliability values of the 6 expected factors were good in both groups and in the pooled sample (Cronbach's α ≥ 0.82). Based on the Kaiser criterion both in the 2 groups of women and in the joint sample, the number of factors was 4 with the 19 selected items. In the group of 128 women with FSD, when 5 factors were extracted through a principal component analysis, the expected configuration was obtained in the orthogonally rotated factor matrix, except for the two items of sexual desire and the four items of sexual arousal. These 6 items were grouped in the same factor. Therefore, it was not separated according to the two expected factors. In the group of 131 healthy women, when 5 or 6 factors were extracted and the factor matrix was rotated, the expected structure was not reproduced. Based on reliability data and theoretical-practical advantages, Rosen et al. (10) suggested that it is better to separate the factors of sexual desire (2 items) and sexual arousal (4 items), and to maintain the 6-factor structure designed with the 19 selected items (10) .
Wiegel et al. (12) conducted a study that included 568 American women to establish a threshold to diagnose FSD using the FSFI questionnaire. They determined that a threshold score of 26.55 was optimal to recognize women with FSD. With this cut-off value, they were able to correctly classify 70.7% of women with hypoactive sexual desire problems, lack of sexual arousal, anorgasmia, and dyspareunia as having FSD, and exclude a sexual disorder in 88.1% of healthy women.

Properties of FSFI in women with cancer
The metric properties of the FSFI have been studied in women with cancer. In a group of 181 female American cancer survivors, Baser et al. (9) found out that the 5-factor structure explained 81.4% of the total variance, as assessed by a principal components' analysis. This 5-factor structure was equivalent to the original factor structure described in the original study by Rosen et al. (10) the internal consistency values were high (Cronbach's overall α = 0.94 and ranged from 0.85 to 0.94 for the 5 factors). The FSFI scores demonstrated convergent validity by correlating inversely to menopausal symptoms, reproductive problems, and depression; and correlating directly to quality of life.
On the other hand, Bartula & Sherman (13) studied the factor structure of the FSFI in a sample of 399 sexually active Australian women diagnosed with breast cancer. They used confirmatory factor analysis through the maximum likelihood method. They found that the correlated 6-factor model, excluding item 14 (emotional closeness to partner), showed the best fit to the data compared to the models of 1 factor, 5 correlated factors, and 5 or 6 lower-order factors hierarchized to 1 higherorder factor. The internal consistency reliability values for the 6-factor structure (without the item number 14 in the sexual satisfaction factor) ranged from good (Cronbach's α = 0.89 for Sexual Satisfaction) to excellent (Cronbach's α = 0.96 for Vaginal Lubrication) and those for 3-week temporal stability ranged from r t1t2 = 0.75 for dyspareunia to r t1t2 = 0.86 for sexual desire.

FSFI properties in Spanish-speaking populations
The FSFI is available in Spanish, however it has not been validated for patients with cancer. Blümel et al. (14) translated and validated this instrument in a Chilean sample. A total of 371 sexually active healthy women were evaluated and high internal consistency values (Cronbach's α = 0.71 to 0.88) for the 6 domains, proposed by Rosen et al. (10) were demonstrated. However, the 6-factor model was not tested.
In Colombia, Vallejo-Medina et al. (15) translated the FSFI for its validation in the general population. The 6-domain-model was reproduced using a principal component analysis and oblique rotation. The internal consistency of the factors was good (Cronbach's α = 0.84 to 0.89).
In Spain, Sánchez-Sánchez et al. (16) translated and validated the FSFI using two samples, the first one included women from the general population and the other one included women with pelvic floor disorders. They obtained excellent short-term temporal stability values (2-4 weeks) (intraclass correlation coefficient [ICC] > 0.90) and internal consistency values that ranged from acceptable (Cronbach's α ≥ 0.70) to good (Cronbach's α ≥ 0.80) for the total score and its factors. Using the principal component analysis, the 6-domain-model was reproduced and showed adequate discriminant validity (Pearson's r 2 or shared variance from 0.13 to 0.44).

Problem Statement
Female sexual dysfunction is a common adverse effect of breast cancer treatments, however there is few information in Latin-American patients. Another concern is the instrument to measure the FSD in this population. Even though the FSFI has been validated in Spanish, this instrument has not been validated in female cancer patients.
Regarding the FSFI, Baser et al. (9) , carried out a study in women with cancer that showed weaknesses in its factor analysis, because they used the principal component analysis to validate a theoretical model. Bartula & Sherman (17) , also overcame these weaknesses by using a confirmatory factor analysis and defining two hierarchical models that theoretically justify the syndrome construct and the calculation of a total score. However, no bifactor model was specified when this type of model justifies the syndrome concept, having more flexible assumptions than the hierarchical models and usually yields better fit values than this latter model (18) . In a systematic review of 83 studies on the metric properties of the 19-item FSFI, concluded that the evidence of internal consistency reliability is enough and of moderate quality, but that the evidence of its structural validity is inconsistent and of low quality, therefore requiring further research. Consequently, aspects of psychometric validation remain pending (19) .
The purpose of this study is to validate the FSFI in young Mexican women with breast cancer, using the Spanish translation made by Blümel et al. (14) . Our four specific objectives are: 1) to test the 6 and 5 factor models; 2) verify the internal consistency reliability of the 19 items (general factor) and the 5 or 6 content domains (specific factors); 3) describe the distributions of the total score and its 5 or 6 factors; and, 4) estimate the prevalence of FSD in our sample using the cut-off point of ≤ 26.55 for FSD.

Type of study and design
Based on our objectives, this study is a validation study of a measurement instrument in breast cancer Mexican women. The data analyzed in this validation study are part of the baseline phase of a multicenter longitudinal prospective study to evaluate the application in Mexico of the Young and Strong Program for Young Women with Breast Cancer developed originally by the Dana-Farber Cancer Institute. It should be noted that the data for this article was collected from June 2014 to December 2019 and corresponds to a cross section (measurements in a single time per participant).

Subjects and data collection
Females between 18 to 44 years old with a recent diagnosis of breast cancer. The exclusion criteria were: illiteracy or having an intellectual disability that impedes the patient from reading and understanding the questions on the self-report questionnaire, and not being sexually active (to not have had sexual intercourse in the last four weeks, which is the time-frame evaluated by the FSFI). Patients were also eliminated from the study if they didn't answer all the questions of the measurement instrument.
A total of 441 Mexican women diagnosed with breast cancer at the baseline stage of their treatment were screened for the eligibility criteria. Patients in their first oncology appointment were asked to participate in this study. They had to answer an online questionnaire within a maximum period of three months from the diagnosis made by an oncologist. Patients' healthcare institutions and types of health insurance are described in table 1. All patients signed a written informed consent and none of them refused to participate. Due to sexual inactivity in the last four weeks, 169 out of 441 screened women were excluded from the study. There were no cases of intellectual disabilities. The sample size was determined by having at least five participants per parameter to be estimated in the factor models. The ratio was five participants per parameter to be estimated in the two bifactor models and in the correlated 6-factor model, and six participants per parameter to be estimated in the two hierarchical models and in the correlated 5-factor model. The sociodemographic data to describe the sample was taken from the medical records and the missing data was excluded from the descriptive analysis.

Measures
The translated FSFI version used in this study consists of 19 Likert scale survey questions and uses five ordinal categories. People are asked whether they were sexually active four weeks prior to the evaluation and each item is scored from 1 to 5. Rosen et al. (10) evaluated two groups, the first one consisted of 128 women with sexual dysfunction and the other consisted of 131 healthy women that matched their age (Cronbach's α = 0.97). They found excellent internal consistency for the following domains: sexual desire (questions 1,2), sexual arousal (questions 3-6), vaginal lubrication (questions 7-10), orgasm (questions [11][12][13], and pain during sex (questions [17][18][19], with the following Cronbach's α = (0.92, 0.95, 0.96, 0.94, 0.94), respectively.
Higher scores on the FSFI total score and individual dimensions indicated a better sexual function. In order to obtain the FSFI factor scores, we added all the items corresponding to each domain and then multiplied them by a specific factor ratio: 0.6 for sexual desire; 0.4 for orgasm, 0.4 sexual satisfaction, 0.4 for pain; 0.3 for sexual arousal; and 0.3 vaginal lubrication. For the 5-factor model, the sexual desire and arousal factor, which is made up of 6-items (questions 1-6), is multiplied by 0.2. This transforms the range of scores for each factor to a continuous scale, ranging from 1.2 to 6. The total score of the FSFI is obtained by adding the scores of the 6 or 5 individual factors. Hence, the FSFI total score for sexually active women ranges from 7.2 to 36 both in the 5-factor model and 6-factor models.

Data analysis
Factor analysis was used for testing the three types of models proposed (5 or 6 domains). The discrepancy function was optimized through Free-Scale Least Squares (FSLS). A moment matrix (arithmetic mean, standard deviation and polychoric correlation) was used as input data. This method was chosen because it suits ordinal variables, such as items with Likert-type scales. Standard error estimation and significance testing were performed using the Bias-Corrected Percentile (BCP) method with the extraction of 2,000 bootstrap samples. The data was assessed using eight indices: relative chi-square (χ2/df), goodness-of-fit Index (GFI), adjusted goodness-of-fit Index (AGFI), normed fit index (NFI), comparative fit index (CFI), relative fit index (RFI), standardized root-mean-squared residual (SRMR), and root-mean-square error of approximation (RMSEA). It was set that values ≥ 0.95 of the following indices (χ2/ df < 2, GFI, NFI, CFI and RFI) reflected a close fit; as well as AGFI ≥ 0.90, SRMR and RMSEA ≤ 0.05. Values ≥ 0.90 for (χ2/df < 3, GFI, NFI, CFI and RFI reflected an acceptable fit, as well as, AGFI ≥ 0.85, SRMR < 0.08 and RMSEA < 0.10. The equivalence in goodness of fit between the models was tested by the quotient between chi-square statistic difference and the difference in degrees of freedom (Δχ2/Δdf), difference in akaike information criterion (ΔAIC), as well as by the difference in GFI (ΔGFI), NFI (ΔNFI), and CFI (ΔCFI), SRMR (ΔSRMR), and RMSEA (ΔRMSEA) statistics. Absolutes values of │χ2/Δdf│ ≤ 2, │ΔAIC│< 4, and │ΔGFI│, │ΔNFI│, │ΔCFI│, │ΔRFI│, │ΔSRMR│ and │ΔRMSEA│ ≤ 0.01 reflected an equivalence in goodness of fit. The parsimony of the model was assessed using the Jame-Mulaik-Brett's parsimony ratio (PR). A PR value of <¼ was considered as low parsimony, and if the value was ≥ ¾ it was considered as high parsimony. Three parsimonious indices were calculated: parsimonious normed fit index (PNFI), parsimonious comparative fit index (PCFI), and parsimonious goodness-of-fit index (PGFI). Values ≥ 0.80 for PNFI and PCFI reflected a good relationship between fit and parsimony, as well as PGFI ≥ 0.70. Values < 0.60 for PNFI and PCFI reflected a poor relationship between fit and parsimony, as well as PGFI < 0.50 In the two factor models, the convergent validity was assessed through three criteria: an omega coefficient (ω) ≥ 0.70, standardized measurement weights (λi) ≥ 0.50, and average variance extracted (AVE) ≥ 0.54 for two indicators, 0.44 for three indicators, 0.37 for four indicators, 0.28 for six indicators, and 0.25 for seven or more indicators. The discriminant validity between factors was assessed through the heterotrait-monotrait ratio of correlations (HTMT) or quotient between the arithmetic mean of the n * m non-redundant correlations of the items crossed between two factors and the geometric mean of the means of the [n*(n-1)]/2 or [m*(m-1)]/2 non-redundant correlations between the items of each factor. An HTMT value ≤ 0.85 was stipulated as a threshold for a good level of discriminant validity, and an HTMT value ≤ 0.90 as a threshold for an acceptable level of discriminant validity.
Within each one of the two hierarchical factor models, two sub-models were distinguished. There is a higher order sub-model that corresponds to the direct effect of the general factor on the 5 or 6 hierarchical factors. On the other hand, there are the 5 or 6 lower order sub-models that correspond to the indirect effect of the general factor and the direct effect of the hierarchical factor on the items of a content domain. The convergent validity in the higher order sub-model was assessed using three criteria: λFi, ω coefficient and AVE. The following values showed convergent validity: λFi ≥ 0.50, ω ≥ 0.70, and AVE for 5 factors ≥ 0.32 and 0.28 for 6 factors. In the 5 or 6 lower-order sub-models, hierarchical omega (ωh_), average extracted variance (AVE_) and the proportion of explained common variance (ECV_) attributable to the higher-order general factor (GF) and the hierarchical factor (HF) were calculated to assess the contribution of these two types of factors. Values of ωh_GF, ωh_HF, ECV_GF and ECV_HF less than 0.10 reflected a trivial relative contribution, values (0.10 -0.29) a poor contribution, values (0.30 -0.69) a substantive contribution, values (0.70 -0.89) an excessive contribution, and values ≥ 0.90 were considered as unitary. Taking into account a minimum value for AVE (≥ 0.54 for two indicators, 0.44 for three indicators, 0.37 for four indicators, 0.28 for six indicators, and 0.25 for seven or more indicators) and a contribution of at least 30%, the minimum value of the AVE for the general (AVE_GF) or hierarchical factor (AVE_HF) should be: 0.16 for two indicators, 0.13 for three indicators, 0.11 for four indicators, 0.09 for six indicators, and 0.08 for seven or more. The maximum value that could be reached was 0.70 for a maximum contribution of 70%. A pooled assessment of the 5 or 6 lower order models was also carried out.
In the two bifactor models, the contribution of specific factor (SF) and general factor (GF) in each one of the 5 or 6 content domains was assessed using 6 indices: hierarchical omega related to the specific factor (ωh_SF), the general factor (ωh_ GF), explained common variance in relation to the specific factor (ECV_SF) and general factor (ECV_GF), as well as average variance explained by the specific factor (AVE_SF) and the average variance explained by the general factor (AVE_ GF). Values (0.30 -0.60) for the ωh and ECV reflected a significant and balanced contribution; values < 0.30 indicate a poor contribution and values > 0.70 showed an excessive contribution. Taking into account a minimum value for AVE and a contribution of at least 30%, the minimum value of the AVE for the general (AVE_GF) or specific factor (AVE_SF) should be 0.16 for two indicators, 0.13 for three indicators, 0.11 for four indicators, 0.09 for six indicators, and 0.08 for seven or more. The maximum value that could be reached was 0.70 for a maximum contribution of 70%.
For describing the distributions, the null hypothesis of normal distribution was tested through the D'Agostino-Pearson's K2 test and Kolmogorov-Smirnov's test with the Lilliefors correction. Due to non-compliance with normal distribution, the median (Mdn) was used as the central tendency statistic. The equivalence in central tendency among the factors was tested with Friedman's test. The effect size was estimated by Kendall's coefficient of concordance (W). With six degrees of freedom, a value of W < 0.10, 0.10-0.24, ≥0.25 was interpreted to reflect a small, medium and large effect size, respectively. Subsequent pairwise comparisons were carried out using Dunn's test.
The equivalence between the expected value of prevalence of FSD and the proportion of cases in the sample was tested with the one-tailed binomial test.
When testing statistical hypotheses, the significance level was set at 0.05. The calculations were made with the programs SPSS 24, module R version 2.4 for SPSS 24, AMOS 16, and Excel 2013 with the real statistics complement.

Sample Description
When comparing the sample of sexually active women in the last four weeks with the sexually inactive women, the distribution of frequencies of the seven healthcare institutions was statistically equivalent between the two samples (Fisher's exact test = 5.06, two-tailed p-value = 0.539), as well as the type of health insurance they had (χ2 [2, N = 419] = 1.86, right tail p-value = 0.395) ( Table 1). Table 2  , there were more housewives (58.9%) and fewer part-time jobs (15.5%) among sexually active women than among women without sexual activity (45.9% and 23.3%, respectively). There was also a significant difference in the cancer stage (Mann-Whitney's U test: Z U = -1.99, 2-tailed p-value = 0.046) with a small effect of the cancer stage on being sexually active in the four weeks prior to the survey (Rosenthal's r 2 > 0.010). The mean rank (MR) of the stage of cancer development was lower in the patients with sexual activity in the last four weeks (MR = 196.77) than in the patients without sexual activity (MR = 220.33). Note. Sociodemographic data was taken from the patient's medical record. Therefore, the missing values are the consequence that this data was missing from the file. Cancer stage: 0 (T0 = noninvasive ductal carcinoma in situ, N0 = absence or cancer with a size < 0.  Table 3 shows the fit indices, parsimony ratio, and parsimonious fit indices (relationship between fit and parsimony) of these six models. Table 4 shows the goodness of fit between the two models with the best fit (BM-5 and CFM-6) is compared with the remaining models. Tables 5 and 6 show the internal consistency reliability, as well as convergent and discriminant validity of the two correlated-factor models (CFM-5 and CFM-6).   Note. Δχ 2 /│Δdf│ = quotient between the chi-square difference statistic of the 5 remaining models and BM-5 or CFM-6 and the difference in absolute value between the degrees of freedom of the 2 models being compared, ΔAIC= difference between the Akaike Information Criterion of the 5 remaining models and BM-5 or CFM-6, ΔGFI = difference between the Goodness of Fit Indices of BM-5 or CFM-6 and the 5 remaining models, ΔAGFI = difference between the Adjusted Fit indices of BM-5 or CFM-6 and the 5 remaining models, ΔNFI = difference between the Normed Fit indices of BM-5 or CFM-6 and the 5 remaining models, ΔCF│ = difference between the Comparative Fit indices of BM-5 or CFM-6 and the 5 remaining models, │ΔRFI│ = difference between the Relative Fit indices of BM-5 or CFM-6 and the 5 remaining models, ΔRMSEA = difference between the Root Mean Square Error of Approximation the 5 remaining models and BM-5 or CFM-6, and ΔSRMR = difference in absolute value between the Standardized Root Mean Square Residual the 5 remaining models and BM-5 or CFM-6.     Table 7 shows the indices of the two hierarchical models (HM-5 and HM-6). It reports the omega coefficient and AVE (convergent validity) of the higher-order sub-model or direct effect of general factor on 5 or 6 hierarchical factors. On the other hand, it shows the hierarchical omega (ωh), AVE and the explained common variance (ECV) of the lower-order sub-models. In these last three statistics, the indirect effect attributable to the general factor and the direct effect attributable to the hierarchical factor are described. The total effect (sum of both effects) and direct effect are included. The indirect and total effect is calculated for the union of the 5 or 6 hierarchical sub-models.  ) and a higher-order general factor (sexual function). Pooled = when putting together the 6 or 5 lower-order hierarchical factors. Higher-order model or direct effect of the general factor on hierarchical factors: ω = omega coefficient and AVE = extracted mean variance. Lower-order models or indirect effect of the general factor and direct effect of hierarchical factor on items: ωh = hierarchical omega, AVE = extracted mean variance and ECV = explained common variance attributable to the indirect effect of the general factor (GF) and attributable to the direct effect of the hierarchical factor (HF), as well as the sum of both effects or total effect (T). Values that show an excessive or poor contribution are highlighted in bold. Table 8 shows the indices corresponding to the two bifactor models (BM-5 and BM-6). The direct effect due to the specific factor and the direct effect due to the general factor on each domain of content are also detailed. The total effect or sum of both effects is included. Furthermore, these two effects are calculated for the entire 19 items.  Among the six models specified, the bifactor model with 5 specific factors and 1 general factor (BM-5) had the best fit indices. The fit values of seven out of the eight contemplated indices were close and the SRMR had an acceptable fit value. Its parsimony was high (PR = 0.78 > 0.75) and the relationship between fit and parsimony was acceptable (Table 3). Its goodness of fit was greater than the one from the other models based on Δχ 2 /│Δdf│ and ΔAIC. The greatest difference was the bifactor model with 6 specific factors (BM-6) and the smallest difference was with the 6-correlated factors (CFM-6) ( Table 4). All measurement weights were significantly non-null (Figure 1). In the analysis of the 19 items or union of the five content domains, the contribution of the general factor was greater (0.70 > ωh = 0.63 and ECV = 0.61 > 0.30, and 0.70 > AVE = 0.46 > 0.08) than the one of the 5 specific factors (0.70 > ωh = 0.35 and ECV = 0.39 > 0.30, and 0.70 > AVE = 0.29 > 0.08), although without being excessive. Nevertheless, the contribution of the general factor was excessive compared to the specific factor, which was poor in both the three items of vaginal lubrication and in the three items of orgasm. On the contrary, the contribution of the specific factor was excessive compared to that of the general factor, which was poor in the 3 items of pain during sex (Table 8).
In the 6-factor model (CFM-6), the fit values of 5 out of the 8 indices were close, and the remaining three indices were acceptable. This model showed greater Note. Method for the point estimation of parameters: Scale-free least square. Bootstrap method to estimate standard errors and the significance of parameters: Bias-corrected percentile method, using 2000 bootstrap samples. Twotailed significance: *** p-value ≤ 0.001, and ** p-value ≤ 0.01. Items: Over the past 4 weeks, i1) how often did you feel sexual desire or interest?, i2) how would you rate your level (degree) of sexual desire or interest?, i3) did you feel sexually aroused ("turned on") during sexual activity or intercourse?, i4) how would you rate your level of sexual arousal ("turn on") during sexual activity or intercourse?, i5) how confident were you about becoming sexually aroused during sexual activity or intercourse?, i6) how often have you been satisfied with your arousal (excitement) during sexual activity or intercourse?, i7) how often did you become lubricated ("wet") during sexual activity or intercourse?, i8) how difficult was it to become lubricated ("wet") during sexual activity or intercourse?, i9) how often did you maintain your lubrication ("wetness") until completion of sexual activity or intercourse?, i10) how difficult was it to maintain your lubrication ("wetness") until completion of sexual activity or intercourse?, i11) when you had sexual stimulation or intercourse, how often did you reach orgasm (climax)?, i12) when you had sexual stimulation or intercourse, how difficult was it for you to reach orgasm (climax)?, i13) how satisfied were you with your ability to reach orgasm (climax) during sexual activity or intercourse?, i14) how satisfied have you been with the amount of emotional closeness during sexual activity between you and your partner?, i15) how satisfied have you been with your sexual relationship with your partner?, i16) how satisfied have you been with your overall sexual life?, i17) how often did you experience discomfort or pain during vaginal penetration?, i18) how often did you experience discomfort or pain following vaginal penetration?, and i19) how would you rate your level (degree) of discomfort or pain during or following vaginal penetration?
parsimony than the bifactor model with 5 specific factors (BM-5), as well as a better relationship between fit and parsimony (Table 3). Its goodness of fit was better than the bifactor model with 6 specific factors (BM-6) and the two hierarchical models (HM-5 and HM-6) by at least 4 indices: Δχ2/│Δdf│, ΔAIC, ΔRMSEA, and ΔRMSEA. The goodness of fit between the two correlated-factor models (CFM-6 and CFM-5) was very similar, although the index │χ2/Δdf│ showed that the 6-factor model (CFM-6) had a better fit than the 5-factor model (CFM-5) ( Table 4). The 6 factors of CFM-6 presented all their measurement weights significantly non-null (Figure 2), as well as convergent (λ > 0.50, ω > 0.70, and AVE ≥ 0.54 for 2 indicators, 0.44 for 3 indicators, and 0.37 for 4 indicators) and discriminant validity (HTMR < 0.85) ( Table 5 and 6). The internal consistency reliability values of the vaginal lubrication, sexual satisfaction and sexual arousal factors were excellent (ordinal α ≥ 0.90), the ones of the sexual desire and orgasm factors were good (ordinal α ≥ 0.80), and those of the pain during sex factor was acceptable (ordinal α ≥ 0.70) ( Table 5).
The consistency of the 19 items was excellent (ordinal α = 0.94). These properties were also fulfilled in the correlated 5-factor model (Tables 5 and 6). Finally, the models with the worst fit were the two hierarchical models (HM-5 and HM-6) (Tables 3 and 4). The higher-order sub-model (direct effect of general factor on 5 or 6 hierarchical factors) in HM-5 and HM-6 had convergent validity. The lowerorder sub-model (indirect effect of general factor and direct effect of hierarchical factor on items) in HM-5 and HM-6 showed also convergent validity and an important contribution both the general factor and the hierarchical factors in the conjunct of 19 items. The three items of sexual satisfaction, as well as the two items of sexual desire (HM-5) and the six items of sexual desire and arousal (HM-6) had greater weight of the general factor than hierarchical factors. However, the general factor had excessive contribution to the detriment of the hierarchical factors in the four items of sexual arousal, in the three items of orgasm, and in the four items of vaginal lubrication. On the opposite side, the hierarchical factor had an excessive contribution to the detriment of the general factor in the three items of pain during sex ( Table 7).

Distributions of scores on the general factor and specific factors
Considering that the CFM-6 showed the best properties, it was decided to calculate the scores of the six factors and a total score. Only the distribution of the sexual desire factor showed symmetry and was adjusted to a normal distribution by the D'Agostino-Pearson K 2 test (K 2 = 3.70, right-tailed p = 0.157). The other distributions did not follow a normal distribution, because they presented negative asymmetry or bias towards high scores with long tails to the left (Table 9).  The mean ranges of these four factors were higher than the mean ranges of sexual desire (MR = 1.87) and sexual arousal (MR = 2.80). The MR of sexual desire was significantly the lowest (Table 9). A more intuitive way of scoring the FSFI total score and the six factors is through an average scoring rule. Items are added and then divided by the number of items. This rule allows an absolute interpretation of the scores. By dividing the continuous range into five intervals of constant amplitude ([maximum value (5)minimum value (1)]/number of values on the item response scale (5) = 4/5 = 0.8), the scores on the FSFI and the six factors can be interpreted as corresponding with the five response categories of the items. The scores (1-1.79) correspond to the first response "never or almost never", which show very low functionality. Scores from 1.80-2.59 correspond to the second response "less than half the time" and show low functionality. Scores from 2.6-3.39 correspond to the third response "half the time" and indicate medium functionality. Scores from 3.4-4.19 correspond to the fourth response "more than half the time" and show high functionality. Finally, scores from 4.2-5 correspond to the fifth response "almost always or always" and show very high functionality. To convert the scores obtained in the range from 1.2-6 to a range from 1-5, you must multiply them by 5/6. For the FSFI total score, you must first divide it by six and then multiply it by 5/6.
Using the median as the central tendency statistic, the middle values of the FSFI total score (Mdn = 3.95), as well as the factors of sexual arousal (Mdn = 3.75) and pain during sex (Mdn = 4) corresponded to a high functionality (from 3.4 to 4.19). The medians of the factors of vaginal lubrication (Mdn = 4.25), orgasm (Mdn = 4.33) and sexual satisfaction (Mdn = 4.33) corresponded to very high functionality (from 4.2 to 5). However, the middle value of sexual desire factor (Mdn = 3) was in the interval of medium functionality (2.6-3.39) ( Table 9. Of the 272 women, we found very low sexual functionality in 0.7%, low in 4.4%, medium in 20.6%, high in 37.5% and very high in the 36.8%. These percentages clearly show a profile with an increasing trend (higher percentage the higher the index value) and negative skewness (long tail to left).

Prevalence of FSD
Using the cutoff point of 26.55 for the FSFI total score (Wiegel et al., 2005), there were 103 cases of FSD, which represents a prevalence of 37.9% (95% CI: 32%, 43.8%). The value 3.69 (which is equivalent to the value of 26.55 ranging from 1 to 5) corresponds to the sample percentile 36 (95% CI: 30 -42). By the binomial test, the null hypothesis of a prevalence of at least 40% (one-tailed p-value = 0.257) was maintained. In the total sample of 441 patients, which included women without sexual activity in the last four weeks (FSFI total score range from 1.2 to 6 < 26.55), the prevalence was 61.7% (95% CI: 57%, 66.4%). Using the binomial test, the null hypothesis of a prevalence of at least 60% (one-tailed p-value = 0.252) was maintained.

Discussion
Our first objective was to check the hypothetical models of 5 and 6 factors proposed for the FSFI in the 19-item format. Besides the specification of a hierarchical model made by Bartula & Sherman (17) , only the correlated-factor models had been previously contrasted. In the present study, hierarchical models and bifactor models were specified, justifying the calculation of a total score and specific factor scores (18,20) . However, the contrast of the single-factor model was not presented since the multifactorial models did not suggest it, either due to the lack of discrimination between their content domains or due to the excessive weight of the general factor in all content domains. It should be noted that the fit indices of the single-factor model were poor, just like it has been shown in previous studies (17) .
The bifactor model of 5 specific factors and one general factor (BM-5) obtained the best fit, followed by the CFM-6, but it was outperformed by the last one in parsimony and its relationship between fit and parsimony. This is not an unusual result since the bifactor model is more saturated or less parsimonious than the correlated and hierarchical factor models, hence it is necessary to check the contribution of the different factors (21) . The indices (omega, AVE and ECV) showed that the general factor had an important influence in the items of orgasm and vaginal lubrication in detriment of the specific factor, and poor influence in the pain during sex items. In the 6-factor model, when separating the contents of sexual desire and sexual arousal, the general factor had an important impact on the sexual arousal items in detriment of the specific factor. This data was also reproduced by the hierarchical model, but these models (5 or 6 hierarchical factors) showed the worst fit indices. However, the correlated 6-factor model did not have problems of convergent validity and the items were better explained by the factor they configure than by other factors. Therefore, this model proved to be more adequate for the data and it showed a good fit.
Stating that the correlated 6-factor model is the one that best represents the interrelationship between the items, the calculation of a total score is not theoretically justified. In this setting, the calculation becomes merely practical, based on its usefulness, such as having a cut-off point to diagnose FSD, and on the positive interrelationship between the 6 factors.
Among all the factors, pain during sex had the lowest correlations. Consistent with these data found in the correlated-factor model, the specific or hierarchical factor of pain during sex showed an inverse behavior to the rest of the factors in the bifactor and hierarchical factor models. Its effect on the items was excessive to the detriment of the general factor, where the general factor had a greater effect than the specific or hierarchical factor in the other content domains. This indicates that among women with cancer, pain during sex is the factor least related to the other FSD symptoms. The same result was previously obtained in a study made in Spanish women with pelvic floor disorders in which they reproduced the correlated 6-factor model with good discriminant validity between the factors, using principal component analysis and showing that the pain during sex factor had the lowest correlation with the other factors (16) . Additionally, Witting et al. (22) and Vallejo-Medina et al. (15) , they obtained a good fit for the correlated 6-factor model using confirmatory analysis reporting that the pain during sex factor had the lowest correlation. On the other hand, Bartula & Sherman (17) obtained a good fit for the correlated 6-factor model without problems of convergent and discriminant validity compared to a worse fit of the hierarchical model. In this last study, orgasm was the least related factor, whereas the study made by Baser et al. (9) showed that it was the vaginal lubrication factor. Therefore, pain during sex is not always the least related factor in women with cancer. These variations between studies in women with cancer could be due to side effects of the applied treatment (vaginal dryness, inhibition of the response to orgasm or sensitivity to pain), to different subjective criteria (mediated by culture) to assess sexual functions or simply for idiosyncratic characteristics of each sample.
The second objective was to verify the internal consistency reliability of the FSFI total score and its factors. According to the results of previous research in women with cancer (9,12,13,17) , the FSFI had an excellent internal consistency and the factors had values that ranged from excellent to good, except for pain during sex which had an acceptable internal consistency. In this study, pain during sex did not only showed the least interrelation in the set of symptoms of FSD, but also the internally variants of its symptoms were less consistent compared to the rest of the factors. It should be emphasized that the factor with the lowest internal consistency varies between studies where the 6-factor model has been reproduced. This is the case of the study made by Bartula & Sherman (17) where vaginal lubrication had the lowest internal consistency, while in Sánchez-Sánchez et al. (16) study it was orgasm, in Vallejo-Medina et al. (15) study were sexual desire and sexual arousal, in Witting et al. (22) it was sexual desire.
The third objective was to describe the distribution of the FSFI and its factors. Except for the sexual desire factor scores, the rest of the scores did not follow a normal distribution and showed skewness with a long tail towards the left. With the FSFI, this type of bias appears in both the non-clinical and clinical setting (16,22) , hence the cut-off points for diagnosing FSD is close to the pole of sexual functionality (12) . The cutoff point of 26.55 in the range of 7.2 -36 corresponds to 3.69 in the range of 1 -5. This is a value close to the midpoint (3.8) of the fourth interval (3.4, 4.2) that corresponds to a high sexual functionality.
Patients reported high sexual functionality. The median shows that these women report high functionality in sexual arousal and a very high functionality in lubrication, orgasm and sexual satisfaction. Only the middle value (median) and the average value (arithmetic mean) in sexual desire factor, which match, showed a medium functionality. The mean FSFI score in the present study (M = 27.41, biascorrected and accelerated bootstrap 95% CI: 26.78, 27.99) was clearly higher than that reported in women treated for breast cancer (M = 19.58, 95% CI 17.64-21.53) (1) , and even higher than the average obtained from a sample of the Spanish general population (M = 25.7, 95% CI: 24.84, 26.56) (16) , but lower than the reported in the Colombian general population (M = 29.46, 95% CI: 29.11, 29.82) (15) . Therefore, the women that participated in this study report a sexual functionality value within a range of the general population parameter.
It should be noted that the analyzed sample consisted mostly of young women (85%) and middle-aged women (15%). Most of them had a low income (88%), public health insurance, and had a middle school level of schooling. All of them had been recently diagnosed with breast cancer (maximum of three months before the questionnaire), were about to start their cancer treatment and reported having sexual intercourse with their partners. Our sample is more similar to the general population than to the clinical population regarding sexual side effects of cancer treatments or natural history of the disease. Compared to the excluded patients, they had earlystage cancer and more of them lived with their sexual partner.
The fourth objective was to estimate the prevalence of FSD in the sample. The prevalence of FSD was 37.9%, which corresponds to the one found in the general population (22)(23)(24) and close to the one from previous studies of women with cancer (> 60%) (1) . This result is expected since the participants of this study had recent diagnosis of breast cancer. Hence, the prevalence of FSD in the general population of breast cancer patients cannot be calculated. Among the limitations of the study was the use of incidental non-probability sampling, so conclusions should be taken with caution. There is no paired short-term data (days or weeks) per patient to assess the temporal reliability of FSFI and the stability of the factor structure. The Spanish translation of FSFI was assumed to be appropriate for Mexican women given the properties of the questionnaire in Chile and other Spanish-speaking countries. Finally, the DSM-V, known as the gold standard for clinical diagnosis (25) , was not used to diagnose sexual dysfunction, hypoactive sexual desire disorder, sexual arousal disorder, orgasmic disorder, and dyspareunia, in order to determine a cut-off value that optimizes diagnostic sensitivity and specificity.
In conclusion, in this sample of young Mexican women with breast cancer in the basal phase of treatment who had sexual intercourse in the 4 weeks prior to the survey, the correlated 6-factor model for the 19-item FSFI presented the best properties when considering goodness of fit, parsimony, as well as the convergent and discriminant validity of the factors. Its internal consistency reliability is excellent, and its factor reliabilities vary from excellent to good, with the exception of pain during sex, which was acceptable. The FSFI total score and factor distributions did not follow the normal probability law. They presented bias towards the left tail with the concentration of the scores in the high values of sexual functionality. The only exception was the distribution of the sexual desire factor which was symmetric. The measures of central tendency reflect a report of high sexual functionality. With the cutoff value of 26.55, approximately 4 out of 10 women had FSD, which is similar to the prevalence in the general population.