Interpreting difference in logistic regression coefficients after data handling

Question

I am building a multiple logistic regression model in which 10 variables (1 variable of interest and 9 covariates) are included. In total, I have 286 rows of data.

12 rows of data are unfortunately, missing values for 3 of the covariates. I therefore decided to exclude these rows prior to using the glm model to make things neater.

To my surprise, I realised that the coefficients were different from if I had not done any exclusion, and let glm deal with the 'missingness'. Here, the R gives me a prompt that '12 observations deleted due to missingness' at the end of running the code.

Is there an explanation for this difference? More importantly, should I be manually excluding the incomplete rows or leave it to glm to remove those?

I have attached the code that I used below, along with the two differing outputs.

####Loading data, make subset of data with relevant parameters and col names###
data<-read.csv("CAP_diet_micronutrients.csv", nrows=530)
colnames(data)[1]='CAP'
analyse<-data[,c(1,10,7, 303, 308, 806, 65,682,49,827:841,2)]

library(dplyr)
library(data.table)
library(ggplot2)
library(sjPlot)
library(sjmisc)
library(sjlabelled)
library(stats)
library(tidyr)
library(lmtest)
library(chest)

###giving relevant column names and labelling data### 
colnames(analyse)<-c( "Case","Age", "Eyecolour","Skincolour","Sunburn","Education", "Familyhx1", "BMI","all_trans_retinol","lutein","zeaxanthin","a-cryptoxanthin","b-cryptoxanthin", "a_carotene","b_carotene","lycopene","ubiquinone","d_tocopherol","g_tocopherol","a_tocopherol","d_tocotrienol","g_tocotrienol","a_tocotrienol")
analyse$'Case' <- factor(analyse$Case, levels=c(0,1))
analyse$'Education' <-  factor(analyse$Education, levels=c(0,1,2,3),labels=c("Never","1-6 years", "7-10 years",">10 years"))
analyse$'Eyecolour' <- factor(analyse$'Eyecolour', levels=c(0,1),labels=c("Light brown","Black/dark brown"))
analyse$'Skincolour' <-  factor(analyse$'Skincolour', levels=c(1,3,4),labels=c("Very white/white","Light tan","Tan/dark brown/black"))
analyse$'Sunburn' <-factor(analyse$'Sunburn', levels=c(4,3,2,1),labels=c("Never","Seldom", "Occasionally","Frequently"))
analyse$Familyhx1<- analyse$Familyhx1 %>%  #family history in particular, required further manipulations due to categorizing
  # option 4 represented "unknown" cancer history and had to be omitted.
  na_if(4) %>% 
  # option 3 and option 2 both represented past history of cancer in 1o relatives and had to be combined.
  replace(.==3, 2) %>% 
  #putting correct labels on 
  factor(levels=c(1,2),labels=c("No","Yes")) 

#subsetting only participants with completed covariates and micronutrient levels##  
##This is the one line of code that results in different coefficients, even though the logistic regression model automatically subset the 274 rows of data for which all covariates are adjusted for##
dt<-analyse %>% drop_na(Age, Education, 'BMI','Familyhx1','all_trans_retinol') 

#logistic regression for retinol
#1 all_trans_retinol (median analysis)
w<-quantile(subset(dt, Case==0, select='all_trans_retinol'),0:2/2, na.rm=TRUE)
dt$retinolmedian<-ifelse(dt$all_trans_retinol <= w[2], "<= Median", 
                         ifelse(dt$all_trans_retinol >w[2], "> Median", NA)) 
retinolmedian<-dt$retinolmedian
dt$retinolmedian<-as.factor(dt$retinolmedian)
dt$retinolmedian<-relevel(dt$retinolmedian, ref="<= Median")
crudeoddsretinolmedian<-glm(prostaterisk ~ retinolmedian, family = binomial(link = "logit"))
adjustedoddsretinolmedian<-glm(prostaterisk ~ retinolmedian + age + education + familyhx +bmi + Eyecolour + Skincolour + Sunburn, family = binomial(link = "logit"))

With the above codes I get the output:

adjustedoddsretinolmedian  ##THIS IS OUTPUT ONE WITH SUBSETTING ##

all:  glm(formula = prostaterisk ~ retinolmedian + age + education + 
    familyhx + bmi + Eyecolour + Skincolour + Sunburn, family = binomial(link = "logit"))

Coefficients:
                   (Intercept)           retinolmedian> Median                             age              education1-6 years  
                       -9.2211                          1.8047                          0.1004                          0.5553  
           education7-10 years              education>10 years                     familyhxYes                             bmi  
                        0.4106                          1.6839                          1.4142                         -0.0905  
     EyecolourBlack/dark brown             SkincolourLight tan  SkincolourTan/dark brown/black                   SunburnSeldom  
                        1.9385                          0.9632                          0.8592                          0.1913  
           SunburnOccasionally               SunburnFrequently  
                        0.8926                          2.2314  

Degrees of Freedom: 273 Total (i.e. Null);  260 Residual
Null Deviance:      374.6 
Residual Deviance: 232.3    AIC: 260.3

However, after I remove 'Sunburn', 'Skincolour' and 'Eyecolour' during subsetting and let glm remove the rows with missingness instead, I get a different output.

adjustedoddsretinolmedian ## THIS IS OUTPUT TWO, WITHOUT SUBSETTING FOR EYE COLOUR, SKINCOLOUR AND SUNBURN ##

Call:  glm(formula = prostaterisk ~ retinolmedian + age + education + 
    familyhx + bmi + Eyecolour + Skincolour + Sunburn, family = binomial(link = "logit"))

Coefficients:
                   (Intercept)           retinolmedian> Median                             age              education1-6 years  
                      -9.48321                         1.93527                         0.10300                         0.55615  
           education7-10 years              education>10 years                     familyhxYes                             bmi  
                       0.39554                         1.58786                         1.45186                        -0.08927  
     EyecolourBlack/dark brown             SkincolourLight tan  SkincolourTan/dark brown/black                   SunburnSeldom  
                       1.98861                         0.89964                         0.77817                         0.17177  
           SunburnOccasionally               SunburnFrequently  
                       0.73251                         2.26092  

Degrees of Freedom: 273 Total (i.e. Null);  260 Residual
  (12 observations deleted due to missingness)
Null Deviance:      374.6 
Residual Deviance: 230.8    AIC: 258.8

I note that both the AIC and coefficients are also different, even though the degree of freedom is the same.

I am struggling to understand why the two outputs should be any different.

Thank you for any insight you could share on this.

Answer 1

You define one of the predictor variables after dropping NAs, so that would be the first place to look. It's likely that the median value of all_trans_retinol is different depending on whether you include cases with missing values on the other variables or not, which means retinolmedian is defined differently in the two models. If you had defined all your variables prior to dropping cases with missing values, you would have got the same results.