Mastherteshis analysis

Model selection farward elimination

### Model selection
Vorlagestudie:
  * Variables with P < 0.20 from the univariate analyses were selected as candidates for inclusion in the multivariate model and were
retained in the final model if they were significant at P < 0.10 or if they altered any of the other estimates (i.e., odds ratio) by more than 10% 

  * Or from my proposal: Thereby, the predictors are selected based on previous research (Field, 2012). From there, a forward modeling strategy will be used to identify variables with a p-value of under 0,25 from the univariable t-test and included in the multivariable model. They will be included in the preliminary main effects model if they achieve the threshold (p < 0,05) in the partial likelihood ratio test of the nested model or if they change any variables coefficient (𝛥𝛽̂ > 20%) substantially (Behnke, 2014 pp. 105-111; Hosmer, 2013, pp. 90-94).

  * Workflow: Nur variablen mit p<0.25 inkludieren aus "columne K des unadjusted model/univariate model", anschliessend "(Rao-Scott+F) LRT" durchführen und schauen ob p<0.05 oder  Variablenkoeffizient sich um: 𝛥𝛽̂ > 20%, verändert. 
  * For Man:

```{r}
# man
# variable list of variables with p-value of under 0,25:
# 13: education, language, nationality, ADL, FL, depression, bmi_cut, age_cut, (age), diabetes, osteoarthritis, urinary_incontinence, osteoporosis

# Forward selection strategy: Keep variable if P < 0.05 in the partial likelihood ratio test of the nested model or if they change any variables coefficient 𝛥𝛽̂ > 20%

# education model
fit_fs_education_m <- svyglm(I(fall=="fall last 12 months") ~ education, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# education + language model
fit_fs_education_language_m <- svyglm(I(fall=="fall last 12 months") ~ education + language, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_m, fit_fs_education_language_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_m, fit_fs_education_language_m, exp =TRUE)
# jtools::plot_summs(fit_fs_education_m, fit_fs_education_language_m) # graphic

########### exclude due to 1 & 2 ############

# education + nationality model
fit_fs_education_nationality_m <- svyglm(I(fall=="fall last 12 months") ~ education + nationality, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_m, fit_fs_education_nationality_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_m, fit_fs_education_nationality_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_m, fit_fs_education_nationality_m) # graphic

########### include due to 1 not 2 ############

# education + nationality + ADL model
fit_fs_education_nationality_ADL_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_m, fit_fs_education_nationality_ADL_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_m, fit_fs_education_nationality_ADL_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_m, fit_fs_education_nationality_ADL_m) # graphic

########### include due to 1 not 2 ############

# education + nationality + ADL + FL model
fit_fs_education_nationality_ADL_FL_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_m, fit_fs_education_nationality_ADL_FL_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_m, fit_fs_education_nationality_ADL_FL_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_m, fit_fs_education_nationality_ADL_FL_m) # graphic

########### include due to 2 not 1 ############

# education + nationality + ADL + FL + depression model
fit_fs_education_nationality_ADL_FL_depression_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL + depression, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_FL_m, fit_fs_education_nationality_ADL_FL_depression_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_FL_m, fit_fs_education_nationality_ADL_FL_depression_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_FL_m, fit_fs_education_nationality_ADL_FL_depression_m) # graphic

########### include due to 1 & 2 ############

# education + nationality + ADL + FL + depression + bmi_cut model
fit_fs_education_nationality_ADL_FL_depression_bmi_cut_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL + depression + bmi_cut, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_FL_depression_m, fit_fs_education_nationality_ADL_FL_depression_bmi_cut_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_FL_depression_m, fit_fs_education_nationality_ADL_FL_depression_bmi_cut_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_FL_depression_m, fit_fs_education_nationality_ADL_FL_depression_bmi_cut_m) # graphic

########### exclude due to 1 & 2 ############

# education + nationality + ADL + FL + depression  + age_cut
fit_fs_education_nationality_ADL_FL_depression_age_cut_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL + depression + age_cut, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_FL_depression_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_FL_depression_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_FL_depression_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_m) # graphic

########### exclude due to 1 & 2 ############ 
# We retained age (age_cut) in the model regardless of statistical significance because it was deemed to be an important confounder

# education + nationality + ADL + FL + depression  + age_cut + diabetes
fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL + depression + age_cut + diabetes, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_FL_depression_age_cut_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m) # graphic

########### include due to 1 & 2 ############

# education + nationality + ADL + FL + depression  + age_cut + diabetes + osteoarthritis
fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL + depression + age_cut + diabetes + osteoarthritis, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m) # graphic

########### include due to 1 not 2 ############

# education + nationality + ADL + FL + depression  + age_cut + diabetes + osteoarthritis + urinary_incontinence
fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL + depression + age_cut + diabetes + osteoarthritis + urinary_incontinence, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m) # graphic

########### include due to 1 & 2 ############

# education + nationality + ADL + FL + depression  + age_cut + diabetes + osteoarthritis + urinary_incontinence + osteoporosis
fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_osteoporosis_m <- svyglm(I(fall=="fall last 12 months")~education + nationality + ADL + FL + depression + age_cut + diabetes + osteoarthritis + urinary_incontinence + osteoporosis, 
               design = wdat_17_m,
               family = quasibinomial(logit))

# 1) model comparison and LR-test p < 0.05
anova(fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_osteoporosis_m)

# 2) Coefficent comparison 𝛥𝛽̂ > 20%
export_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_osteoarthritis_urinary_incontinence_osteoporosis_m, exp = TRUE)
# jtools::plot_summs(fit_fs_education_nationality_ADL_FL_depression_age_cut_m, fit_fs_education_nationality_ADL_FL_depression_age_cut_diabetes_m) # graphic

########### include due to 1 & 2 ############

# final model man: 
final_model_m<- svyglm(I(fall=="fall last 12 months") ~ education + nationality + ADL + FL + depression + age_cut + diabetes + osteoarthritis + urinary_incontinence + osteoporosis, 
               design = wdat_17_m,
               family = quasibinomial(logit))
final_model_ma<- jtools::summ(final_model_m,exp = TRUE, vifs = TRUE, confint = TRUE, digits = 6)
final_model_ma


# woman
# variable list of variables with p-value of under 0,25:
# 13: language, smoke, ADL, FL, depression, bmi_cut, age_cut, SHS, diabetes, osteoarthritis, stroke, urinary_incontinence, activity

```

Results flowchart

## Results

  * flow chart Inclusion exclusion
  * 14:
  * 14 (a). Give characteristics of study participants (e.g.,
demographic, clinical, social) and information on
exposures and potential confounders.
  * Table. Characteristics
  * 14 (b). Indicate the number of participants with missing
data for each variable of interest.
  * Cross-sectional study: Report numbers of outcome events
or summary measures./ Table. Prevalence of Current Asthma and Diagnosed Hay Fever
by Average Alternaria alternata Antigen Level in the Household