Description

The acc_margins function examines the impact of so-called process variables on the measurement variables. This implementation combines a descriptive and model-based approach.

acc_margins is an implementation of the Unexpected location and Unexpected proportion indicators, as well as a descriptor for Unexpected shape and Unexpected scale. These belongs to the Unexpected distributions domain in the Accuracy dimension.

For more details, see the user’s manual and source code.

Descriptive approach

For each level of the group_vars the marginal distribution is shown in addition to an overall distribution. The R-package ggplot2 is used to illustrate these distributions in a combination of plot types. For:

  1. continuous data

and for

  1. discrete data

are used. The user is not obliged to specify whether measurements are continuous or discrete. This is done by the acc_margins function. Optional is the specification of the distribution in the metadata.

Model-based approach

For the calculation of adjusted marginal means the R-package emmeans is used which computes equally weighted marginal effects of factor-variables. Details on the difference between crude calculation of means and marginal effects is given in the very good example provided by the emmeans package: Run vignette("basics", package = "emmeans") to see the corresponding vignette. emmeans can process a broad number of different models Lenth et al., 2016,, e.g. regression models with several independent variables such as from multiple linear models or generalized linear models. For each level of a process variable marginal means are calculated including confidence intervals. The following models are supported by this quality indicator function:

  • linear models
  • generalized linear models (binomial, 2 categories)
  • generalized linear models (Poisson, \(\gt\) 2 categories but \(\le\) 15 categories)

Usage and arguments

acc_margins(
  resp_vars = NULL,
  group_vars = NULL,
  co_vars = NULL,
  label_col = "LABEL",
  threshold_value = 0.5,
  study_data = NULL,
  meta_data = NULL
)

The function has the following arguments:

  • resp_vars: mandatory, a character specifying the measurement variable of interest. The variable must be of float or integer type.
  • group_vars: the variable used for grouping (e.g., observer, device, reader). Defaults to NULL for output without grouping.
  • co_vars: optional, a vector of covariables, e.g. age or sex.
  • threshold_type: optional, either empirical or user. In case empirical is chosen a multiplier of the scale measure is used, in case of user a value of the mean or probability (binary data) has to be defined see Implementation and use of thresholds
  • threshold_value: a multiplier or absolute value. See also Implementation and use of thresholds.
  • study_data: mandatory, the data frame containing the measurements.
  • meta_data: mandatory, the data frame containing the item-level metadata.
  • label_col: optional, the column in the metadata data frame containing the labels of all the variables in the study data.

We recommend specifying HARD_LIMITS for the measurement variable (and for the covariables, if applicable) to restrict the analysis to admissible numerical values. Similarly, VALUE_LABELS for grouping variables ensure that only valid groups are considered here.

Implementation and use of thresholds

The acc_margins function allows two different specifications of thresholds using the same arguments of the function.

Threshold: empirical

The specification of threshold_value is optional, since the default of threshold_value is set to 1. threshold_value serves as a multiplier of the following measures:

  • continuous data: standard deviation (SD)
  • binary data: variance (\(p*(1-p)\))
  • count data: variance (\(\lambda\))

Count data with more than 15 categories are treated as continuous data.

Threshold: user

If user is used instead, a threshold_value is a mandatory argument. The meaning of threshold_value is different to the threshold_type empirical. The user may define a value on the measurement scale of the measurement variable. For example, in case of SBP one may set threshold_value to 120. Each level of the aux_variable is highlighted if the confidence interval of marginal means does not contain the predefined threshold_value of 120. In case of a binomial distribution the user must define the probability \(\in [0; 1]\).

This option should only be chosen if the distribution is known to the user.

Example output

To illustrate the output, we use the example synthetic data and metadata that are bundled with the dataquieR package. See the introductory tutorial for instructions on importing these files into R, as well as details on their structure and contents.

For the acc_margins function, the metadata columns DATA_TYPE and MISSING_LIST are relevant:

VAR_NAMES LABEL MISSING_LIST DATA_TYPE
1 v00000 CENTER_0 NA integer
3 v00002 SEX_0 NA integer
4 v00003 AGE_0 NA integer
6 v01003 AGE_1 NA integer
7 v01002 SEX_1 NA integer
8 v10000 PART_STUDY NA integer
9 v00004 SBP_0 99980 | 99981 | 99982 | 99983 | 99984 | 99985 | 99986 | 99987 | 99988 | 99989 | 99990 | 99991 | 99992 | 99993 | 99994 | 99995 float
10 v00005 DBP_0 99980 | 99981 | 99982 | 99983 | 99984 | 99985 | 99986 | 99987 | 99988 | 99989 | 99990 | 99991 | 99992 | 99993 | 99994 | 99995 float
11 v00006 GLOBAL_HEALTH_VAS_0 99980 | 99983 | 99987 | 99988 | 99989 | 99990 | 99991 | 99992 | 99993 | 99994 | 99995 float
12 v00007 ASTHMA_0 99980 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
14 v00009 ARM_CIRC_0 99980 | 99981 | 99982 | 99983 | 99984 | 99985 | 99986 | 99987 | 99988 | 99989 | 99990 | 99991 | 99992 | 99993 | 99994 | 99995 float
15 v00109 ARM_CIRC_DISC_0 99980 | 99981 | 99982 | 99983 | 99984 | 99985 | 99986 | 99987 | 99988 | 99989 | 99990 | 99991 | 99992 | 99993 | 99994 | 99995 integer
16 v00010 ARM_CUFF_0 99980 | 99987 integer
20 v20000 PART_PHYS_EXAM NA integer
21 v00014 CRP_0 99980 | 99981 | 99982 | 99983 | 99984 | 99985 | 99986 | 99988 | 99989 | 99990 | 99991 | 99992 | 99994 | 99995 float
22 v00015 BSG_0 99980 | 99981 | 99982 | 99983 | 99984 | 99985 | 99986 | 99988 | 99989 | 99990 | 99991 | 99992 | 99994 | 99995 float
23 v00016 DEV_NO_0 NA integer
25 v30000 PART_LAB NA integer
26 v00018 EDUCATION_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
27 v01018 EDUCATION_1 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
28 v00019 FAM_STAT_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
29 v00020 MARRIED_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
30 v00021 N_CHILD_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
31 v00022 EATING_PREFS_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
32 v00023 MEAT_CONS_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
33 v00024 SMOKING_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
34 v00025 SMOKE_SHOP_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
35 v00026 N_INJURIES_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
36 v00027 N_BIRTH_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
37 v00028 INCOME_GROUP_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
38 v00029 PREGNANT_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
39 v00030 MEDICATION_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
40 v00031 N_ATC_CODES_0 99980 | 99983 | 99988 | 99989 | 99990 | 99991 | 99993 | 99994 | 99995 integer
43 v40000 PART_INTERVIEW NA integer
44 v00034 ITEM_1_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
45 v00035 ITEM_2_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
46 v00036 ITEM_3_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
47 v00037 ITEM_4_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
48 v00038 ITEM_5_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
49 v00039 ITEM_6_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
50 v00040 ITEM_7_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
51 v00041 ITEM_8_0 99980 | 99983 | 99988 | 99989 | 99991 | 99993 | 99994 | 99995 integer
53 v50000 PART_QUESTIONNAIRE NA integer


We show two examples including different distributions of study data and assume that one examiner may not adhere to the SOP (Standard Operating Procedure). The following distributions are selected:

  1. continuous data
  2. count data with \(\le\) 15 categories
v00000 v00001 v00002 v00003 v00004 v00005 v01003 v01002 v00103 v00006
3 LEIIX715 0 49 127 77 49 0 40-49 3.8
1 QHNKM456 0 47 114 76 47 0 40-49 1.9
1 HTAOB589 0 50 114 71 50 0 50-59 0.8
5 HNHFV585 0 48 120 65 48 0 40-49 3.8
1 UTDLS949 0 56 119 78 56 0 50-59 4.1
5 YQFGE692 1 47 133 81 47 1 40-49 9.5
1 AVAEH932 0 53 114 78 53 0 50-59 5.0
3 QDOPT378 1 48 116 86 48 1 40-49 9.6
3 BMOAK786 0 44 115 71 44 0 40-49 2.0
5 ZDKNF462 0 50 116 74 50 0 50-59 2.4 


margins_1 <- acc_margins(
  resp_vars = "SBP_0",
  group_vars = "USR_BP_0",
  co_vars = c("AGE_0", "SEX_0"),
  label_col = "LABEL",
  threshold_value = 0.5,
  study_data = sd1,
  meta_data = md1
)

The function generates two outputs: 1) A data frame (output 1) summarizing the descriptive analysis results of emmeans including a summary variable GRADING with 2 possible values of 0 or 1, indicating whether data quality issues were found. In the latter case (i.e, value = 1), one or more levels of the group_variable deviates more than eligible from the overall distribution (i.e., they are outside the threshold limits); 2) A summary plot (output 3) containing the marginal means including confidence intervals. In case of oddities the marginal mean is displayed in red.

Example 1: normally distributed data

Output 1: Summary data frame for the different classes:

The summary data frame is called using mp1$SummaryData:

USR_BP_0 margins SE n CL
USR_121 125.5941 0.5526398 160 [124.5104; 126.6778]
USR_123 124.8324 0.5267178 176 [123.7995; 125.8653]
USR_165 125.0142 0.5236881 178 [123.9873; 126.0412]
USR_201 132.1729 0.6283335 124 [130.9407; 133.4050]
USR_243 132.0782 0.3980998 308 [131.2975; 132.8588]
USR_275 132.9775 0.9420737 55 [131.1301; 134.8248]
USR_301 124.3595 0.3437771 413 [123.6853; 125.0336]
USR_303 126.4420 0.9256808 57 [124.6269; 128.2572]
USR_352 126.6869 0.9435185 55 [124.8367; 128.5370]
USR_482 125.5566 0.5805627 145 [124.4181; 126.6950]
USR_483 125.5491 0.5685333 151 [124.4343; 126.6640]
USR_484 125.0051 0.5489800 162 [123.9286; 126.0816]
USR_537 125.4129 0.4110002 289 [124.6069; 126.2188]
USR_542 124.9735 0.5137529 185 [123.9661; 125.9809]
USR_559 123.5100 1.2977372 29 [120.9652; 126.0547]


Output 2: Summary Table

A table of summary data is generated for the respective variable. This table provides the values of the calculated data quality indicators, and it is necessary for the generic function dataquieR::dq_report() to summarize all information for examined variables.

Variables FLG_acc_ud_loc PCT_acc_ud_loc
SBP_0 1 20

Output 3: Summary plot

The Summary plot is made of box plots and violin plots combined per level (e.g., per each examiner), and a density plot (flipped and aligned with the y-axis) on the right based on the overall data. The plots include lines of the overall mean and the deviation from the mean defined by the user via thresholds.

The summary plot frame is called using mp1$SummaryPlot:

Example 2: count data

NOTE: If the number of categories exceeds 20 unique values the function will switch to a continuous distribution for the purpose of better illustration.

Output 3: Summary plot

The example regarding count data is restricted to the SummaryPlot which can be called using margins_2$SummaryPlot:

Interpretation

Marginal means

Marginal means rests on model based results, i.e. a significantly different marginal mean depends on sample size. Particularly in large studies, small and irrelevant differences may become significant. The contrary holds if sample size is low.

Algorithm of the implementation

  1. The implementation can be applied on a single variable only.
  2. Missing codes are removed from resp_vars (if defined in the metadata)
  3. Deviations from limits, as defined in the metadata, are removed
  4. The distribution of resp_vars is determined
  5. The model-class fitting the distribution is selected (5a) The use of co_vars for adjustment is optional
  6. An output data frame is generated for each level of group_vars.
  7. A summary plot is generated.

Limitations

Selecting the appropriate distribution is complex. Dozens of continuous, discrete or mixed distributions are conceivable in the context of epidemiological data. Their exact exploration is beyond the scope of this data quality approach. The function discriminates four cases:

  1. continuous data
  2. count data with \(\le\) 15 categories
  3. count data with \(\gt\) 15 categories

Nonetheless, only two different plot types are generated. The third case is treated as continuous data. This is in fact a coarsening of the original data but for the purpose of clarity this approach is chosen.

Concept relations

Lenth, R.V. et al. (2016). Least-squares means: The r package lsmeans. Journal of Statistical Software 69, 1–33.