Biostat R Reference Guide
Reference for biostatistics 1 and 2
Welcome
This is a markdown adapted version of the pdf also available in the repository. If there are typo’s, information I should add, or simply things I did wrong please let me know and I can update it. Additionally this markdown will contain additional depth since I can fit it in.
Currently this markdown lacks proper formating for the code and lacks the color coding present in the pdf copy. At some point I plan to add actual code with working examples.
This was a project completed for Biostatistics 6451 at the University of Minnesota. The documents are here to serve as a reference to anyone who would like them. I hope they are found useful
-Jonathan
What Is R
In the simplest terms, R is a calculator, often chosen by statisticians and data visualizers due to its vast package support and standards.
More complicatedly, R is a functional programming language with aspects of an object-oriented one written in C and Fortran, though less rigid. Computationally, R is slow and utilizes only a single computer core and RAM, which may not impact most tasks unless dealing with large datasets or complex algorithms. However, R compensates with its rich ecosystem of packages, oRering extensive functionality for statistical analysis, data manipulation, visualization, and more, making it a popular choice for both beginners and experienced data scientists alike. Additionally, its open-source (Publicly available) nature fosters a vibrant community where users can collaborate, contribute, and continually improve the language and its capabilities. Python is a common comparison; it oRers better computational optimization and better flexibility for tasks beyond statistics however it lacks package quality standards, many of the visualization tools, and statistics specific functions. The other comparison is SAS which falls on the opposite side of the spectrum; it is typically seen as less daunting and simpler but lacks many of the tool’s R and python have easily available. SAS does have extensive package support, testing before release, and isn’t open source making it the choice of government for stability, at a cost.
Steps of Analysis
- What is your question?
- Gather and Process Data
- Exploratory Data Analysis (EDA)
- Choose Analysis or Model Technique(s)
- Conduct Analysis
- Interpret Results
- Communicate Findings of Analysis
Writing Reports (Non-academic)
Introduction (1)
Data (2) – Who, What, Where, When, How many
Exploratory Data Analysis (3) – Chart Time!
Methods (4) – Try to explain your brain process
Results (5 & 6)– Get output, explain output
Conclusion (7) – explain output (Non-Statistically)
Basics of R
Functions – Similar to math, these take input and produce an output. All functions have inputs; these can Be populated or require input. If you are ever confused about what a Function does or its inputs ( params ), Simply type? function in the console And the documentation will appear.
Assign output to a variable Like this:
Out <- Function ( Input ) ; <- is assignAdditionally, get data like this:
Var <- Data$VarImportant Maybe Not So Basics
Conditionals
Conditional (Booleans) – “If” statements; For computer science TRUE/T = yes or 1; FALSE/F = no or 0. Conditionals are: If T then X, else (if not X) then Y
Besides the typical less then or greater then you can use! to indicate not.! is.na () would return False for NA values, when it normally would give True. Additionally you can use == to specify something to match. “Apple” == “Apple” ; TRUE
Similarly, when attempting to bunch conditionals use | to say or, and use & to say and. Ifelse ( Data, X > Y & X < Z ) is saying X larger then Y but smaller then Z.
Data Structures and Types
Data Storage and Types in R: At the base of computational statistics and programming is data and data structures. These not only have diRerent uses but using the wrong types can cause issues in functions.
Vectors – single dimension that can hold a single type of data; highly eRicient.
Matrices – Two-dimension storage of only numeric data; allows for matrix math and is more eRicient.
Data Frames – The most common. two-dimension storage that allows columns to have diRerent types of data; IneRicient and slow but allows for superior data manipulation of all types.
Lists – The holder, allows for storage of other data structures; slow and require careful syntax
Arrays – Matrices with additional dimension; eRicient, supports math, but is memory intensive.
Tibbles – essentially a data frame with extra features; can cause issues in functions.
Types of Data – Review
Numeric Continuous : Measure 79.2, Heart rate Discrete : Count 1,2,3…, I have one cat
Factors (Categorical) Ordinal : Groups with Order 1 - 5 scale, income group Nominal : A group without order Nationality or Ethnicity Binary or Indicator: 0 or 1; Yes or No
In R these often are considered only These unless you specify
Global R Options
Just some basics that can be incredibly useful.
Options(scipen = 999 )This will stop R from reporting large digits in scientific notation
Options(digits = 3 )This will set default rounding in R to 3 or what you please. This does not always work
Set.seed( n )This normally is not always important. However if you randomize or bootstrap this will make it reproducible by others.
Functionality
Packages
What is a package? Packages, or libraries (for our case they are the same), are collections of functions or tools which can be used to perform a task. In R many of the packages revolve around data and statistics making these packages essential to most of the work we do in R. Often they are significantly faster than we could write ourselves, not only because they already exist, but because they a written in a faster programming language and then use R as an interface. Simply, if a function exists in a package, use that one.
Packages Used
| Package | Description |
|---|---|
| Tidyverse | Collection of common packages essential for most people |
| Tidymodels | Collection of packages for model testing and training |
| Psych | Used for summary statistics functions |
| Ggstatsplot | Cool plots, not essential |
| Ggpubr | Used for themes, creating tables/charts for publication |
| Ggtexttable | Create tables from existing dataframes |
| Gtsummary | Used in creation of Table 1 (lifesaver) |
| Flextable | Same as above |
| RColorBrewer | Used to choose non-standard colors of plots |
| Ggfortify | Used for a couple of things, truthfully not sure how to explain |
| Jtools | Statistical test output |
| ResourceSelection | Statistical test output |
| Lmtest | Statistical test output |
| Car | Used for a couple things normally, for us statistical test output |
| Survival | Core package of survival analysis |
| Multcomp | Statistical test output |
| Survminer | Builds on survival, can be finicky |
| MASS | Statistical test output, model selection |
| VGAM | Ordinal regression |
| Ggcorrplot | Fun way to visualize correlation plots |
| AER | Testing Dispersion |
Installing and Loading Packages
Install.packages("Lib") Load installed packages:
library(Lib) To use a function from a specific package do:
package::Function()Data Loading
Readr : Common Package used for various types of data Readxl: Package to read excel files Haven: Package developed to read SAS file outputs Code Example
Data <- read_csv("File_Path")“csv” can be replaced with specific file of interest. Xlsx has some weird extra parameters so just don’t use them. Excel will make you sad.
Directories and File Paths
Directories are where the computer or software wants to choose files from.
An example path would be /Users/YourAccount/Folder where each instance after the / is a different directory; the Users directory contains the YourAccount directory and that contains your files.
You can change this by doing:
setwd("Path")When entering the path make sure to “/” for paths. I often find when you copy it will use “\”, particularly on windows
Once you are in a set directory to access a file or folder in current directory use “./” Additionally to access a file one directory back “../” ; so using the above if you’re in the Folder but need to access another folder in the YourAccount directory you would do “../Folder2”
Data Processing (Forcats, Dplyr)
The following can be combined with tidyverse pipes; you don’t need to specify data within the function permitted the variable exists in the input. For more information I suggest this book from the creator.
Data pipe example
NewData <- Data %>% Function()Processing Functions
As.XXX such as as.numeric(), as.factor() – Used to change how R sees variables. For example we may see 1 and 0 as binary but R may not and think it’s a number. Check this using the str() function.
You can change that by doing the following:
Var <- as.factor(Binary_Var)Mutate: Used to create new variables or change existing ones
Data %>% mutate(NewVar = Function(OldVar ))Ifelse: Base conditional; if x, then A, else, B – Useful for creating indicators
ifelse(Data, Conditional(Var), Then, else )Case_when() or Fct_recode() – Both are usedto change variables but is cleaner than doing multiple ifelse() functions
Data %>% case_when(conditional ~ "Category A", conditional ~ "Category B", TRUE ~ "Other")
Note: TRUE = Cases not captured by conditional
mutate(NewVar = fct_recode(Var, `Level1` = "1", `Level2` = "2"))Subset(), Select(), Filter() - All Similar function to get more specific data
subset(Data, conditional1 & conditional2) - Get rows match conditional
select(Data$Column1 , Data$Column2 ) -- select specific columns
filter() -- Nearly exact to subset but more eRicient with larger dataRelevel() – Set the group you want as Null, or want compared against.
relevel(Factor_Var, Ref ) ; Ref is the group you want compared tooSummary Statistics
Key Functions
Str(Data) – provides high level overview of data, its variables, and types
round(Data, round = n) – when numeric is inputted, it will round to n
describe(Data$Var) – provides summary statistics (mean, med, sd, iqr,…)
describeBy(Data$Var, group = Data$Group_Var) – Similar but by grouping variable
summary(Model) ; Summ(Model) – both of these exist to give output from models.
Summary is built into R although summ gives more information
tidy(Model) – creates a “tidy” data frame as output for models
Table() and prop.table() can be used to give information about two categorical variables.
Placing the output of table() into prop table will give the proportions of the groups.
table(Row_Var, Col_Var)T-test
t.test(Var, Group,
alternative = "two.sided")besides running a t-test, providing only a continuous variable will return the confidence interval ; for models use confint(Model)
Correlations normally will require you to filter NA’s using na.omit(Data)
cor(Data)
to specify two rows of data:
cor(Var1, Var2)Alternatively, if you don’t want to remove NA’s:
cor(Data, use = "pairwise.complete.obs") -- This will impute NA'sCreation of Visuals - Tables
Table 1
Table <- tbl_summary(data = Data, include = c(Var1, Var2,....),
by = Group_Var,
statistic = list(all_continuous() ~ "{mean} ({sd})", all_categorical() ~ "{n} ({p}%)"),
label = list(Var1 ~ "Full Name"),
missing = "no",
digits = all_continuous() ~ 2 ) %>%
add_n() %>%
add_overall() %>%
modify_header(label = "TableTitle") %>%
modify_spanning_header(c("stat_1", "stat_2") ~ "**Group_Var**") %\>%
add_stat_label() ; for each level in group add additional "stat_n"This is one of few functions which gives clear errors and help.
Ggtexttable – Allows to convert dataframe to table output easy
Table <- ggtexttable(Data, rows = c("Row1",...) ,
cols = c("col1",...) ,
theme = ttheme("theme")) %>%
tab_add_title(text = "title")Tip: use the tidy function to create a data frame you can input here
Creation of Visuals - Charts
What and What to Use (Briefly)
Single continuous – Histogram + density
Continuous and Categorical – Boxplot + violin
Two continuous – point (scatter) + Smooth (line)
Discrete and categorical – Column
Color
When using R you have the ability to set colors by using names such as “blue” or using hex code (#0000FF). In ggplot the default color palette is set up to be colorblind friendly and encourage thinking about that.
ggplot Core function
Ggplot(Data, aes(x = Var1, y = Var2, fill = "Color", alpha = opacity)) +
geom_XXXX() +
ggtitle("Title") +
xlab("X Axis") +
ylab("Y Axis")Geom’s are the code for types of plots; geom_hist () = histogram The aes() block can be specified in the initial function or if you want to plot diRerent variables, or even datasets you can put it inside of the geom.
Additional things
To add things to a ggplot simple just put a + and then function.
+ Facet_wrap(.~Group, scales = "free" )Used to produce multiple plots by group. If you specific scale = free, the x and y can use different mins and maxs
+ Coord_flip() Should you have too many categories this will flip x and y. This will produce a tall plot instead of a wide plot; useful for documents
+ Geom_point()This is your scatterplot geom; other geoms are normal
+ Theme()This is customization function. It allows you to alter every single aspect on a ggplot from subtle movements of elements, removing the legend, or changing the font. While not complicated, it is dense.
Other oddities
when trying to change the color, one would think it is the color option, that however often changes the outline. The fill option changes main color.
Often times ggplot will have packages built on top of it, meaning external functions will use ggplot to produce output. This can be seen with autoplot() , and the survminer package. Additionally, using the correlations, we can use the ggcorrplot package and the ggcorrplot () function to produce a heatmap. This makes it easy to visualize correlations
Ggcorrplot(Cor_Data)Statistical Models
General Format
The following pages are arranged to attempt to give a background of what these things are, when you’d want to use them, and why. Then the code will be given, followed by assumptions, and lastly some limitations.
General things in regression:
P Fishing: Adding more variables usually will make a model more significant; that doesn’t make it more useful. Additionally, having 30, participants is amazing; it also makes most things significant. Look beyond P.
Overfitting: due to us rarely having every possible data point, when designing models to be used outside of an analysis it is important to not include too many variables. This may result in the model being super predictive of your dataset, but not others.
Linear Regression
What, When Why
Used for understanding relationships between continuous variables.
How
lm_model <- lm(Y ~ X1 + X2,
data = YourData) ; can also use glm()Assumptions
- L: Linearity
- I: Independence
- N: Normality
- E: Equal Variance Can be checked using plots the autoplot() function from ggfortify
autoplot(lm_model)Produces: Residuals vs Fitted, Q-Q plot, Scale Vs Location, Cooks
Other ways to check assumptions
shapiro.test(residuals(lm_model)) -- Normal residuals (Normality)
bptest(lm_model) -- Homoscedasticity (Equal Variance)
car::vif(lm_model) -- No Multicollinearity (independence)Limitations
- Limited to Additive Relationships: Linear regression struggles with capturing interactions or non-linear relationships.
- Limited Extrapolation: Linear regression is not suitable for making predictions outside the range of observed data.
- Assumption of Linearity: Assumes linear relationships, may miss complex patterns which often exist in life.
Logistic Regression
What, When Why
Estimates the probability of binary outcomes, often used for classification. It’s valuable in predicting the likelihood of events or binary responses.
How
logit_model <- glm(Y ~ Predictor,
data = YourData,
family = "binomial")Assumptions
- Independence
- Linearity of Log Odds
- No Multicollinearity (see Linear Regression; vif()
fitted_values <- predict(logit_model, type = "link")
ggplot(data, aes(x = independent_var, y = fitted_values)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE)
GOF <- hoslem.test(Outcome_Var, fitted(logit_model) )Limitations
- Need Binary Outcome - Inflexible compared to advanced statistical methods.
Poisson Regression
What, When Why
Models count data, assuming events occur independently at a constant rate over time/Space. Suitable for analyzing rare events or incidence rates.
How
poisson_model <- glm(Y ~ Predictor, data = YourData,
family = "poisson")
If over dispersed: family = quasipoisson(link = "log")Variable Denominator
poisson_model <- glm(Outcome ~ Predictor, data = YourData,
offset = log(Offset_Variable),
family = poisson(link = "log"))Assumptions
- Count Data: Assumes the outcome variable is counts of events.
- Independence: Assumes observations are independent.
Linear Log Rates: predictors and log rates have linear relationship.
Homogeneity of Rates: Assumes variance equals the mean
dispersiontest(poisson_model)Limitations
- Assumes Equal Mean and Variance: assumes variance equals mean, often unrealistic.
Survival & Cox Regression
What, When Why
Analyzes time-to-event data, considering censoring and identifying factors affecting survival probabilities. Cox Proportional Hazards Model is particularly useful for estimating hazard ratios.
Censoring
Censoring in survival analysis is when some subjects’ outcomes aren’t observed within the study period, often due to loss to follow-up.
How
Cox_model <- coxph(Surv(Time, Event) ~ Predictor, data = YourData)Assumptions
Proportional Hazards: Hazard ratios are constant over time.
Independence of Censoring: Censoring is non-informative.
Cox_Sum <- Cox.zph(Cox_model)
Ggcoxzph(Cox_Sum)Limitations
Proportional Hazards: Violations can lead to biased estimates.
Independence of Censoring: Assumes that censoring is unrelated to the outcome.
Ordinal Regression
What, When Why
Models the relationship between predictors and ordered categorical outcomes. It’s beneficial for analyzing data with ordered response levels.
How
Ordinal_model <- polr(Ordinal ~ Predictor, data = YourData)Assumptions
Proportional Odds: Odds of higher outcome categories versus lower ones are constant across predictor levels.
Independence of Observations: Observations are independent.
testpoe(Ordinal_model) -- Test for Proportional OddsLimitations
- Proportional Odds: Violations indicate diRering relationships between predictors and categories. - Personally dislike this method because it seems odds for interpretation; multinomial regression can be accomplished by using family = multinomial() in glm, but doesn’t factor order
Log-Binomial Regression
What, When Why
Estimates relative risks directly for binary outcomes, providing straightforward interpretations of predictor effects
How
LB_model <- glm(Dependent ~ Predictor,
data = YourData ,
family = binomial(link = "log"))Assumptions - Binomial Distribution: Outcome variable follows a binomial distribution. - Log-linearity: Predictors have a log-linear relationship with the log- odds.
Limitations
- Convergence Issues: May not converge, especially with small sample sizes or high outcome prevalence.
Model Selection
What, When, Why
Use the computer to select model covariates to optimize the model. I believe this is most useful for predictive models although in data where little is known about covariates it can provide useful insight.
How
full_model <- lm(y ~ ., data = data)
stepwise_model <- stepAIC(full_model, direction = "both")Notes: Direction can be “both”, “forward”, “backward” Forward : Start at empty model and add important variables Backward : Start at full model and remove variable with minimal impact Both : Start at nothing and add, however allows computer to remove or go backwards to provide optimal output
Limitations
- Computational Demand: Realistically you always want to use both in prediction as it will always provide the best output (forward is good for discovery though). However, in cases where your model has extensive dimensions you may opt for forward or backward due to computational demand of using the “both” setting with lots of data.