Vectors, Missing Values, and Conditions

1. A vector is a column-shaped collection

Imagine measuring five patients’ pulse rates. Five separate named objects are inconvenient. The function c() (“combine”) places values together.

pulse <- c(70, 82, 90, 68, 77)
pulse

[1] 70 82 90 68 77

length(pulse)

[1] 5

mean(pulse)

[1] 77.4

median(pulse)

[1] 77

min(pulse)

[1] 68

max(pulse)

[1] 90

The vector has 5 values. The mean is 77.4, the median is 77, and the smallest and largest readings are 68 and 90.

All values in an ordinary atomic vector share a basic type. Combining numbers and text usually converts the numbers into text. That is why we use tables with differently typed columns in the next chapter.

2. Build vectors in other ways

c() is fine for a few typed values, but there are shortcuts for patterns. : makes a run of whole numbers, seq() makes a sequence with a step (by) or a chosen number of points (length.out), and rep() repeats values. c() also joins vectors you already have.

1:5

[1] 1 2 3 4 5

10:6

[1] 10  9  8  7  6

seq(0, 100, by = 25)

[1]   0  25  50  75 100

seq(0, 1, length.out = 5)

[1] 0.00 0.25 0.50 0.75 1.00

rep("North", times = 3)

[1] "North" "North" "North"

rep(c("North", "South"), times = 2)

[1] "North" "South" "North" "South"

rep(c("North", "South"), each = 2)

[1] "North" "North" "South" "South"

more_pulse <- c(pulse, 85, 64)    # join an old vector and new values
more_pulse

[1] 70 82 90 68 77 85 64

times = 2 repeats the whole vector (North, South, North, South), while each = 2 repeats each element in turn (North, North, South, South). Use rep() to build a column of labels, and seq() to make axis breaks or a grid of ages.

3. Find a particular element

R counts positions beginning at 1, not 0. Square brackets select positions.

pulse[1]             # First pulse

[1] 70

pulse[3]             # Third pulse

[1] 90

pulse[c(1, 5)]       # First and fifth

[1] 70 77

pulse[-2]            # All except the second

[1] 70 90 68 77

These print 70, then 90, then 70 and 77, then the four values 70, 90, 68, 77 with the second one (82) left out. A negative position means “leave this one out”.

Brackets mean take part of something. Parentheses after a function name mean run the function.

4. Vectorized calculations

Most R calculations operate on every value in the vector.

pulse + 5

[1] 75 87 95 73 82

pulse >= 80

[1] FALSE  TRUE  TRUE FALSE FALSE

pulse[pulse >= 80]     # Only measurements >= 80

[1] 82 90

sum(pulse >= 80)       # TRUE counts as one; FALSE as zero

[1] 2

pulse + 5 adds 5 to each reading (75, 87, 95, 73, 82). pulse >= 80 gives FALSE TRUE TRUE FALSE FALSE. Putting that logical vector inside the brackets keeps 82 and 90, and sum() of the same logical vector is 2.

The final line counts how many readings meet a condition. It does not count unique patients unless each element belongs to a different patient.

Two vectors can also be combined element by element. When one is shorter, R recycles it, starting over from its first value. That is intended when the shorter vector has length 1 (as in pulse + 5). When the lengths do not divide evenly, R still gives a result but prints a warning, which usually signals a mistake.

pulse - c(60, 70, 80, 60, 70)       # same length: matched position by position

[1] 10 12 10  8  7

c(10, 20, 30, 40) + c(1, 2)         # recycled: 1, 2, 1, 2

[1] 11 22 31 42

c(10, 20, 30, 40) + c(1, 2, 3)      # lengths do not divide: warning

Warning in c(10, 20, 30, 40) + c(1, 2, 3): longer object length is not a
multiple of shorter object length

[1] 11 22 33 41

The second line returns 11, 22, 31, 42. The third still returns four numbers, but R warns that the longer length is not a multiple of the shorter one. Treat that warning as a bug to fix, not noise.

Two more summaries describe spread: var() is the variance (the square of the standard deviation, sd()) and range() returns the smallest and largest values.

var(pulse)

[1] 80.8

sd(pulse)

[1] 8.988882

range(pulse)

[1] 68 90

pulse[2] picks the second reading, 82, and pulse[pulse >= 80] keeps the readings 82 and 90.

5. Find, sort, and test values

which() returns the positions where a condition is TRUE; which.max() and which.min() return the position of the largest and smallest value. Use them when you need to know which patient, not just the value.

which(pulse >= 80)

[1] 2 3

which.max(pulse)

[1] 3

which.min(pulse)

[1] 4

The readings at or above 80 are in positions 2 and 3, the highest is in position 3, and the lowest is in position 4.

Three functions deal with order, and beginners often mix them up:

• sort() returns the values in order (decreasing = TRUE for largest first).
• order() returns the positions that would put the values in order. It is what you use to reorder a table later.
• rank() returns each value’s rank: 1 for the smallest.

sort(pulse)

[1] 68 70 77 82 90

sort(pulse, decreasing = TRUE)

[1] 90 82 77 70 68

order(pulse)

[1] 4 1 5 2 3

rank(pulse)

[1] 2 4 5 1 3

pulse[order(pulse)]      # same as sort(pulse)

[1] 68 70 77 82 90

order(pulse) starts with 4 because the smallest pulse is the fourth value. rank(pulse) starts with 2 because the first reading, 70, is the second smallest. Tied values get the average of their ranks.

For yes/no questions about a whole vector, any() asks whether at least one value is TRUE and all() asks whether every value is. ifelse() chooses between two results for each element; the tidyverse version, if_else(), appears in chapter 6.

any(pulse > 100)

[1] FALSE

all(pulse > 60)

[1] TRUE

ifelse(pulse >= 80, "high", "ok")

[1] "ok"   "high" "high" "ok"   "ok"  

No reading exceeds 100, so any() is FALSE; all are above 60, so all() is TRUE; and ifelse() returns one label per reading.

6. Missing means “not known”

In an EHR, a blank field may mean not measured, unavailable, or entered elsewhere. NA is R’s marker for missing; it is not zero.

bmi <- c(24.5, NA, 28.1, 31.0, NA)
is.na(bmi)

[1] FALSE  TRUE FALSE FALSE  TRUE

sum(is.na(bmi))

[1] 2

mean(bmi)                  # Returns NA

[1] NA

mean(bmi, na.rm = TRUE)    # Average of observed values only

[1] 27.86667

The option na.rm = TRUE removes missing observations from this calculation; it does not fill missing records in the dataset. Deleting patients with missing information can bias an analysis. Later, we learn to impute using training data only.

na.omit() returns the vector without its missing values (it also attaches a note of which positions were dropped). is.nan() checks for NaN, the “not a number” result of calculations like 0 / 0; it is FALSE for an ordinary NA.

na.omit(bmi)

[1] 24.5 28.1 31.0
attr(,"na.action")
[1] 2 5
attr(,"class")
[1] "omit"

is.nan(c(1, NA, 0 / 0))

[1] FALSE FALSE  TRUE

The kept values are 24.5, 28.1, and 31, followed by the attribute note. is.nan() flags only the third value.

7. Text vectors

Names, IDs, and clinic sites are text, and a few functions cover most cleaning work. Here are some made-up patient IDs and site names.

ids <- c("S0001", "S0012", "N0045", "S0100")
sites <- c("North clinic", "south clinic", "Mobile unit")

paste("Patient", ids)          # join with a space

[1] "Patient S0001" "Patient S0012" "Patient N0045" "Patient S0100"

paste0(ids, "_v1")             # join with no separator

[1] "S0001_v1" "S0012_v1" "N0045_v1" "S0100_v1"

nchar(ids)                     # number of characters

[1] 5 5 5 5

toupper(sites)

[1] "NORTH CLINIC" "SOUTH CLINIC" "MOBILE UNIT" 

tolower(sites)

[1] "north clinic" "south clinic" "mobile unit" 

substr(ids, 2, 5)              # characters 2 to 5: the number part

[1] "0001" "0012" "0045" "0100"

paste0() is paste() with no separator. substr() keeps the positions you ask for, so substr(ids, 2, 5) drops the leading letter.

strsplit() cuts text at a separator and returns a list, with one element per input string. sub() replaces the first match in each string and gsub() replaces every match.

strsplit("North;Mobile;South", split = ";")

[[1]]
[1] "North"  "Mobile" "South" 

sub("clinic", "site", sites)

[1] "North site"  "south site"  "Mobile unit"

gsub("0", "", ids)             # remove every zero

[1] "S1"  "S12" "N45" "S1" 

gsub("0", "", ids) removes every zero, so "S0100" becomes "S1", while sub() would remove only the first one.

grepl() asks whether each string matches a pattern and returns TRUE/FALSE; grep() returns the positions (or the matching strings, with value = TRUE). A leading ^ means “at the start”.

grepl("^S", ids)                    # IDs that start with S

[1]  TRUE  TRUE FALSE  TRUE

ids[grepl("^S", ids)]

[1] "S0001" "S0012" "S0100"

grep("clinic", sites)

[1] 1 2

grep("clinic", sites, value = TRUE)

[1] "North clinic" "south clinic"

Matching is case-sensitive, so a search for "South" would miss the lower-case "south clinic". Use tolower() first when capitalization is inconsistent. The stringr package offers friendlier versions of these functions with names such as str_detect().

8. Types, categories, and conversion

clinic_site <- c("North", "Mobile", "North", "South")
unique(clinic_site)

[1] "North"  "Mobile" "South" 

table(clinic_site)

clinic_site
Mobile  North  South 
     1      2      1 

sex <- factor(c("F", "M", "F", "F"), levels = c("F", "M"))
levels(sex)

[1] "F" "M"

unique() lists the sites once each (North, Mobile, South), table() counts them (Mobile 1, North 2, South 1), and levels(sex) prints "F" and "M".

A factor means a categorical variable whose allowable values are represented as levels. A factor is useful when a model needs to treat a code as a category rather than quantity.

Some categories have a natural order, such as severity. Add ordered = TRUE and list the levels from lowest to highest, and R can compare them. For an unordered factor, relevel() chooses which level comes first, which matters later because models treat the first level as the reference group.

severity <- factor(c("mild", "severe", "moderate", "mild"),
                   levels = c("mild", "moderate", "severe"),
                   ordered = TRUE)
severity

[1] mild     severe   moderate mild    
Levels: mild < moderate < severe

severity < "severe"

[1]  TRUE FALSE  TRUE  TRUE

site <- factor(c("North", "Mobile", "South", "North"))
levels(site)

[1] "Mobile" "North"  "South" 

levels(relevel(site, ref = "South"))

[1] "South"  "Mobile" "North" 

The printout shows mild < moderate < severe, and severity < "severe" is TRUE for every value except the severe one. Without relevel(), the levels are in alphabetical order; with it, "South" comes first.

Converting between types uses as.numeric(), as.integer(), and as.character(). When text cannot be read as a number, R returns NA and warns.

as.numeric(c("12", "7.5", "high"))

Warning: NAs introduced by coercion

[1] 12.0  7.5   NA

as.integer(7.9)                # drops the decimals

[1] 7

as.character(c(10, 20))

[1] "10" "20"

"high" becomes NA with the warning “NAs introduced by coercion”, and as.integer(7.9) is 7, not 8. When you see that warning in real data, look for entries such as "unknown" or ">200" typed into a numeric column.

9. Common vector traps

• mean("high") returns NA with a warning: the data are text rather than numeric.
• NA == NA is NA, not TRUE: use is.na() to check missingness.
• A numeric code is not automatically a meaningful number; site 1 + site 2 is not site 3.
• c(1, "two") becomes a character vector; inspect class() when unsure.

Example: run each trap and read what R says.

mean("high")

Warning in mean.default("high"): argument is not numeric or logical: returning
NA

[1] NA

NA == NA

[1] NA

is.na(NA)

[1] TRUE

class(c(1, "two"))

[1] "character"

mean("high") returns NA and warns that the argument is not numeric or logical. NA == NA prints NA, while is.na(NA) prints TRUE, which is the correct test. class(c(1, "two")) is "character", so the 1 became the text "1".

sbp <- c(115, 143, NA, 136, 151, 127)
mean(sbp)

[1] NA

mean(sbp, na.rm = TRUE)

[1] 134.4

sbp <- c(115, 143, NA, 136, 151, 127)
sum(!is.na(sbp) & sbp >= 140)

[1] 2

sbp <- c(115, 143, NA, 136, 151, 127)
sbp[c(length(sbp) - 1, length(sbp))]

[1] 151 127

tail(sbp, 2)

[1] 151 127

sbp <- c(115, 143, NA, 136, 151, 127)
sbp_zero <- sbp
sbp_zero[is.na(sbp_zero)] <- 0
mean(sbp_zero)

[1] 112

mean(sbp, na.rm = TRUE)

[1] 134.4

seq(20, 60, by = 10)

[1] 20 30 40 50 60

rep(c("North", "South"), each = 3)

[1] "North" "North" "North" "South" "South" "South"

c(1, 2, 3, 4, 5, 6) + c(1, 2, 3)

[1] 2 4 6 5 7 9

c(1, 2, 3, 4, 5) + c(1, 2, 3)

Warning in c(1, 2, 3, 4, 5) + c(1, 2, 3): longer object length is not a
multiple of shorter object length

[1] 2 4 6 5 7

v <- c(120, 135, 128, 150, 118)
which(v > 130)

[1] 2 4

which.max(v)

[1] 4

var(v)

[1] 168.2

range(v)

[1] 118 150

order(v)

[1] 5 1 3 2 4

rank(v)

[1] 2 4 3 5 1

v <- c(120, 135, 128, 150, 118)
any(v > 140)

[1] TRUE

all(v > 100)

[1] TRUE

ifelse(v >= 130, "high", "normal")

[1] "normal" "high"   "normal" "high"   "normal"

ids <- c("S0001", "N0045", "S0100")
nchar(ids)

[1] 5 5 5

substr(ids, 2, 5)

[1] "0001" "0045" "0100"

grepl("^S", ids)

[1]  TRUE FALSE  TRUE

sub("S", "Site", ids)

[1] "Site0001" "N0045"    "Site0100"

as.numeric(c("5", "8", "n/a"))

Warning: NAs introduced by coercion

[1]  5  8 NA

urgency <- factor(c("low", "high", "medium"),
                  levels = c("low", "medium", "high"), ordered = TRUE)
urgency

[1] low    high   medium
Levels: low < medium < high

site <- factor(c("North", "Mobile", "South"))
levels(site)

[1] "Mobile" "North"  "South" 

levels(relevel(site, ref = "South"))

[1] "South"  "Mobile" "North"