Data Requirements for autospc Analysis

library(autospc)
library(dplyr)

For each type of Statistical Process Control (SPC) chart supported by autospc, certain data columns must be specified, and those columns must meet certain requirements. This article sets out these requirements for each chart type.

There are two factors influencing the nature of these requirements. First, the statistical theory behind SPC charts places restrictions on the type of data each chart supports. For instance, the theory behind C-charts draws on the Poisson distribution, which is a discrete distribution defined on the non-negative integers. Therefore the variable of interest for a C-chart must be a non-negative integer ( \(0, 1, 2, \dots\)). Second, the types of objects used to represent data in R. For instance, a non-negative integer is most naturally represented as an object of type integer, but there may also be situations in which it is appropriate to use an object of type double.

The type requirements of autospc are intended to be a flexible as possible, whilst reflecting the natural usage of the R’s object types. For example, whilst technically an object of type integer can be coerced to type logical, autospc does not allow integer data to be used in place of logical in observation-level data for a P-chart, since the risk of confusion with aggregated data is too great.

Below is an example call to autospc(). Note that as is often the case, the first argument (data) is passed by position, and the rest are passed as named arguments.

autospc(
  ed_attendances_monthly, 
  chart_type = "C'", 
  x = month_start, 
  y = att_all
)

In what follows, we shall refer to the columns of the passed data (in this example, the data ed_attendances_monthly) by the names of the arguments they are passed to. So in this example, in the sentence “The y column must be either an integer or double”, what is really meant is “The att_all column must be either an integer or double”.

1 The subgrouping variable, `x`

The column specified as x will be used both in aggregating data into subgroups for plotting (where this is relevant), and as the variable plotted on the horizontal axis (i.e. ordering the data) on the chart. Object classes that are currently supported for x are: Date, POSIXct, numeric, and integer.

2 XMR charts

The data columns required for the XMR chart are as follows:

The subgrouping variable, to be plotted on the horizontal axis, x
The variable of interest, to be plotted on the vertical axis, y. This must be of type integer or double.

Unlike C/C’ charts (see Section 3), XMR charts place no further restriction on y: non-whole-number doubles are accepted without modification or warning, since XMR charts are suitable for continuous measurements as well as counts.

3 C and C’ charts

The data columns required for C and C’ charts are as follows:

The subgrouping variable, to be plotted on the horizontal axis, x
The count of events, to be plotted on the vertical axis, y. This must be of type integer or double.

Since C and C’ charts are for count data, y must consist of whole numbers only. autospc handles two R types that can represent whole numbers differently:

integer: accepted without modification or warning.
double: autospc checks whether all values of y are whole numbers (up to machine precision). If they are, the column is accepted without modification or warning. If at least one value has a non-zero fractional part, the values are rounded to the nearest whole number and a warning is issued:

At least one element of y has non-zero fractional part. Rounding to the nearest whole number. C and C’ charts are for count data, i.e. whole numbers only.

Any other type for y, including logical, will cause an error:

For a C or C’ chart, y must be of type integer or double.

4 P and P’ charts

P and P’ charts are for proportions. They require a numerator (the count meeting some criterion) and a denominator (the total count). autospc supports two ways of supplying this information, depending on the form in which the data are available: observation-level data using a logical y column, or aggregated data using numeric y and n columns. In both cases the x column is required as for the above chart types.

4.1 Observation-level data (no `n` specified)

If n is not specified, autospc expects y to be a column of type logical, where each row represents an individual observation and the value of y indicates whether that observation meets the criterion of interest (e.g. TRUE if a patient attending an emergency department was discharged, admitted or transferred within 4 hours, FALSE otherwise). In this case, autospc internally computes the numerator and denominator by aggregating over subgroups defined by x.

Any type for y other than logical when n is absent will cause an error:

n is not specified and y is not of type logical. For P and P’ charts, if n is not specified, y must be of type logical.

4.2 Aggregated data (`n` specified)

If n is specified, autospc expects both y (the numerator) and n (the denominator) to be counts, i.e. whole numbers. Both columns must be of type integer or double, and the same whole-number checking logic described for C/C’ charts in Section 3 applies independently to each:

integer: accepted without modification or warning.
double with all whole-number values: accepted without modification or warning.
double with at least one non-whole-number value: values are rounded to the nearest whole number and a warning is issued. For y the warning reads:

At least one element of y has non-zero fractional part. Rounding to the nearest whole number. P and P’ charts with n specified require y to be a count, i.e. whole numbers only.

For n the analogous warning reads:

At least one element of n has non-zero fractional part. Rounding to the nearest whole number. P and P’ charts with n specified require n to be a count, i.e. whole numbers only.

Any other type for y when n is present, including logical, will cause an error:

For a P or P’ chart with n specified, y must be of type integer or double.

Similarly, any type for n other than integer or double will cause an error:

For a P or P’ chart with n specified, n must be of type integer or double.

5 Summary

Table 5.1 summarises the column requirements for each chart type.

Table 5.1: Summary of data column requirements by chart type.
Chart type	y type(s) accepted	n type(s) accepted
XMR / MR	`integer`, `double`	not used
C / C’	`integer`, `double` (whole numbers only; non-integer doubles are rounded with a warning)	not used
P / P’ (observation level)	`logical`	not used
P / P’ (aggregated)	`integer`, `double` (whole numbers only; non-integer doubles are rounded with a warning)	`integer`, `double` (whole numbers only; non-integer doubles are rounded with a warning)

1 The subgrouping variable, x