Introduction

The aim of this study is to investigate whether an association exists between serum bilirubin with sex, age, treatment and standardised blood clotting time.

Methods

Statistical Analysis

We are going to used the pbc data set from the survival library.
Continuous variables are presented as mean and standard deviation while categorical variables as counts and percentages. Differences in serum bilirubin, age and standardised blood clotting time between males and females were analyzed by the unpaired Student’s t tests for continuous variables. To investigate the association between serum bilirubin with sex, age, treatment and standardised blood clotting time a linear regression was performed. A p-value <0.05 was considered statistically significant and no correction for multiple testing was performed.

library(lattice)
library(knitr)
library(survival)
library(effects)
library(arsenal)

R.Version()$version.string

[1] “R Under development (unstable) (2021-01-01 r79758)”

packageVersion("lattice")

[1] ‘0.20.41’

packageVersion("knitr")

[1] ‘1.30’

packageVersion("survival")

[1] ‘3.2.7’

packageVersion("effects")

[1] ‘4.2.0’

packageVersion("arsenal")

[1] ‘3.6.1’

Results

Table 1 presents descriptive statistics with the results of the t-test analysis.

Table 1: Descriptive statistics with test
	m (N=44)	f (N=374)	Total (N=418)	p value
bili				0.573
Mean (SD)	2.866 (2.319)	3.263 (4.591)	3.221 (4.408)
Range	0.600 - 9.500	0.300 - 28.000	0.300 - 28.000
age				< 0.001
Mean (SD)	55.711 (10.978)	50.157 (10.241)	50.742 (10.447)
Range	33.476 - 78.439	26.278 - 76.709	26.278 - 78.439
protime				0.151
N-Miss	0	2	2
Mean (SD)	10.941 (0.931)	10.707 (1.031)	10.732 (1.022)
Range	9.700 - 14.100	9.000 - 18.000	9.000 - 18.000

Figure 1 represents the desnity plots of serum bilirubin per gender.

Figure 1: Density plots of serum bilirubin per gender

Regression analysis

The results of the regression analysis are presented in Table 2. Since we expect that the effect of sex, treatment and standardised blood clotting time on serum bilirubin would be different per age range, we assumed two models. One model includes only main effects and the other model includes an interaction term of age with all the other variables.

Linear regression without interactions

Table 2: The coefficients, standard errors and p-values
	Estimate	Std. Error	Pr(>\|t\|)
(Intercept)	-15.2051	2.8636	0.0000
sexf	0.8703	0.7692	0.2587
age	-0.0056	0.0238	0.8134
trtplacebo	0.4856	0.4865	0.3189
protime	1.6533	0.2455	0.0000

Linear regression with interactions

Table 2: The coefficients, standard errors and p-values
	Estimate	Std. Error	Pr(>\|t\|)
(Intercept)	-48.0844	15.2169	0.0017
age	0.6078	0.2796	0.0305
sexf	2.6118	3.8551	0.4986
trtplacebo	1.4057	2.3571	0.5514
protime	4.5506	1.3375	0.0008
age:sexf	-0.0332	0.0684	0.6274
age:trtplacebo	-0.0188	0.0462	0.6843
age:protime	-0.0538	0.0245	0.0286

Effect plots

The effect plots are based on the model with interaction terms.

Serum bilirubin with age

plot(effect("age", fm2))

Serum bilirubin with treatment

plot(effect("trt", fm2))

Serum bilirubin with standardised blood clotting time

plot(effect("protime", fm2))

Serum bilirubin with standardised blood clotting time and sex

plot(effect(c("protime", "sex"), fm2))

Conclusions

We may conclude that:

A strong clinical association was found between serum cholesterol and standardised blood clotting time
A weak association was found between sex and serum bilirubin
- The same holds for age and treatment

Strengths and weaknesses of our study are:

Small sample size

Statistical Report

Eleni-Rosalina Andrinopoulou

15 February 2021