Multiple regression and model building

Multiple logistic regressions were fitted based on the hierarchical backward

elimination (HBE) approach described by Kleinbaum (1994) and the minimal models were reported.

4.3.2.1 Model building strategies for predicting not having a family physician

As discussed in Chapter 3, Andersen (1968, 1973, 1995) grouped the factors that can influence health behaviour into three levels in a logic sequence. Therefore, multiple logistic regression models were built in a hierarchical manner to assess the association of the predictors in each block and not having a family doctor using all cases with complete data (Cohen & Cohen 1983). The three blocks of predictors were entered into the logistic regression models in a hierarchical manner (Cohen & Cohen 1983), with the predisposing factors entered first, followed by the enabling/impeding factors, and the need factors. This entry order was followed to examine the additional variance explained by each set of variables on the outcome when the predisposing variables were initially controlled, as well as the final contribution of need variables. The effects of enabling/impeding predictors were similarly examined after control for predisposing factors. The effects of need factors were similarly examined after

considering both predisposing and enabling/impeding factors. Comparing to solely by selection statistically significant explanatory variables through techniques such as stepwise logistic regression, the effects of predisposing variables can be examined

without improper adjustment by proximate or intermediate variables (Victora et al., 1997). Model goodness-of-fit was estimated using a likelihood-based pseudo R-square measure yielded by SAS version 9.2 (SAS institute, 2008). The pseudo R-squared in logistic regression is similar to the R-squared derived from least squares regression. It was considered to have the interpretation as the percentage of variability that is explained by the variables in the model. The model building strategies are detailed as follows:

i. Considering the exploratory nature of the study, 18 potential predictors were identified based on the Gelberg-Andersen Behavioural Model for Vulnerable Populations, prior research findings, and conceptual reasons. Independent variables were examined for multicollinearity using the tolerance value. Only the tolerance value between two conceptually similar and associated trans-specific variables, i.e. stage of medical transition and current hormone use, was found to be higher than the cut-off value of 0.1 (Belsley, 1980). One way to resolve multicollinearity is to drop the collinear variable from the model (Mahajan, Jain, & Bergier, 1977). Since trans-specific health needs at different transition stages (including current hormone use) were well represented by medical transition status, current hormone use was later removed in order to maintain adequate statistical power as recommended for multiple analysis. The minimum tolerance for the remaining 17 independent variables was 0.34, indicating no problem with multicollinearity.

ii. The events for this multivariable analysis were relatively low. In order to limit the number of predictors and obtain parsimonious models, hierarchical backward

elimination (HBE) approach described by Kleinbaum (1994) was used to select potential predictors and avoid over-fitting. One of the advantages of using backward elimination is that it is less sensitive to model specifications, as compared to forward and stepwise elimination (Harrell, 1996). Gender spectrum (i.e., FTM/MTF) was forced to remain during the selection procedures because we wish to examine its

possible interactions with other predictors. The three selection procedures were all performed in SAS version 9.2 (SAS institute, 2008). SAS-callable SUDAAN version 9.01 (Research Triangle Institute, Research Triangle Park, NC) was not used to select important predictive variables because the software does not directly handle

automated elimination procedures. However, to run a backward regression using SUDAAN, variables have to be sequentially eliminated and calculations have to be conducted manually. Due to the sequentially use of SAS version 9.2 (SAS institute, 2008) for HBE and SAS-callable SUDAAN version 9.01 (Research Triangle Institute, Research Triangle Park, NC) for multiple logistic analysis, the cut-off significant level for BWE was adjusted to a more conservative statistical significance level of 0.2 (Slevin, 2004).

A significant level of 0.2 was used in the SAS automated eliminations to allow for retention of potential important predictive factors and interaction effects. Only the variables significant at p<0.2 were passed to the multiple logistic regressions. The first BWE include all the predisposing factors (i.e., age, race, marital status, education, employment, living in felt gender, and gender spectrum) and the possible interaction between gender spectrum and race/ethnicity. In the second stage, all the variables or interaction term(s) retained in the first BWE were entered in the second backward selection along with all the enabling/impeding factors and the interaction term

between gender identity incongruence and gender spectrum. Similarly, the final BWE included need variables and the variables significant at 0.2 in the second BWE. Table 5.1a denoted at which stage the elimination of variables or interaction terms occurred using HBE in SAS 9.2 (SAS institute, 2008).

iii. The three groups of variables retained from BWE in SAS version 9.2 (SAS

institute, 2008) were respectively used to develop the hierarchical logistic regressions (Cohen & Cohen 1983). For the full model, regression analysis tests on the data were performed at the 0.05 level of significance. Since the analysis was exploratory in

nature, the variables with a significant level between 0.05 and 0.1 were reported for descriptive purposes, as indicating trends for further research. SAS-callable

SUDAAN version 9.01 (Research Triangle Institute, Research Triangle Park, NC) was used to account for weighting and the complex sample design. For the categorical independent variables, the means, standard errors, and p-values were calculated using its survey logistic regression fit with PROC RLOGIST (Research Triangle Institute, Research Triangle Park, NC).

4.3.2.2 Model building strategies for predicting uncomfortable physician-patient discussion about trans status and/or trans-related health needs

Based on the conceptual framework that describing the hierarchical relationships between the two levels of predictors (see figure 3), hierarchical logistic regression was performed to identify the significant independent determinants of "not

comfortable discussing about his/her trans status or trans specific health concerns with family physician". As noted by Victora et al. (1997), this approach allows for the effects of the distal sociodemographic factors to be assessed without improper adjustment by proximate predictors that may be mediators of the effects of distal variables.

Since we were interested in the differences in care seeking behaviours or health care access patterns between FTM and MTF, all analyses were stratified by gender

spectrum. The two models incorporating the distal and proximal predictors were built with p-values less than 0.05. Before entering independent variables into multiple logistic regression models, multicollinearity was examined using the tolerance value. The minimum tolerance for the 9 independent variables was 0.34, indicating no problem with multicollinearity. Firstly, the effect of sociodemographic predictors on the outcome variable was analyzed. Secondly, the proximate variables were entered in the first model, and the effects of the proximate variables were examined in the

presence of the distal level variables.