5 Univariate distribution checks

This section reports a series of univariate summary checks of the bacteremia dataset.

5.1 U1: Categorical variables

Age group, sex and bacteremia status are described by frequencies and proportions in each category.

Category	Count	Proportion
Age group
[16, 50]	5365	0.37
(65, 101]	5076	0.35
(50, 65]	4250	0.29
Sex
male	8536	0.58
female	6155	0.42
Presence of bacteremia
no	13511	0.92
yes	1180	0.08

Also plot the categories as simple bar charts.

Summary of categorical variables including outcome

5.2 Continuous variables

5.2.1 U2: Univariate distributions of continuous variables

5.2.1.1 U2: Structural variables

The only structural continuous variable is AGE. This variable is also a key predictor and reported in the following section (see below).

5.2.1.2 U2: Key predictors

Distribution of key predictors. Lines indicate the 5-number summary including reported numerical values (where possible).

The remaining predictors are reported in the appendix Section E.1.1.

5.2.1.3 U2: Predictors of medium importance

5.2.2 Numerical summaries

5.2.2.1 Key predictors

key_predictors Descriptives

key_predictors

6 Variables 14691 Observations

PLT: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
14649	42	718	1	220	130.1	50	81	140	204	277	369	445

lowest : 0 1 2 3 4 , highest: 1068 1211 1321 1639 2092

CREA: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
14532	159	674	1	1.329	0.8518	0.620	0.690	0.810	1.000	1.350	2.160	3.144

lowest : 0.26 0.27 0.28 0.29 0.3 , highest: 15.24 15.4 15.67 16.64 20.75

BUN: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
14519	172	947	1	22.66	16.92	7.1	8.6	11.6	16.6	26.9	44.8	60.8

lowest : 2.5 2.7 2.8 2.9 3 , highest: 160.6 171.3 171.9 176 184.8

NEU: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
13963	728	374	1	8.367	5.776	1.60	2.70	4.60	7.30	10.80	15.08	18.40

lowest : 0 0.1 0.2 0.3 0.4 , highest: 54 56.4 63.7 71.6 83.8

WBC: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
14229	462	2710	1	11.23	7.602	2.66	4.26	6.63	9.60	13.53	18.22	22.27

lowest : 0 0.01 0.02 0.03 0.04 , highest: 365.3 383.74 387.73 433.83 604.47

AGE: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
14691	0	85	1	56.17	20.78	24	29	43	58	70	79	84

lowest : 16 17 18 19 20 , highest: 96 97 98 99 101

5.2.2.2 Predictors of medium importance

medium_predictors Descriptives

medium_predictors

6 Variables 14691 Observations

FIB: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
12124	2567	1084	1	547.4	231	247	301	397	529	674	816	892

lowest : 55 60 66 67 69 , highest: 1506 1508 1529 1537 1593

POTASS: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
12683	2008	408	1	4.003	0.6004	3.20	3.39	3.66	3.95	4.29	4.67	4.92

lowest : 1.92 2.07 2.11 2.12 2.21 , highest: 8.57 11.34 13.55 14.6 36.62

ASAT: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
13537	1154	650	1	86.9	115.6	15	17	22	31	56	121	218

lowest : 3 5 6 7 8 , highest: 10845 11928 12079 12380 13991

ALAT: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
13704	987	578	1	67.66	90.07	9	11	16	26	48	101	175

lowest : 0 1 2 3 4 , highest: 7109 9136 9314 12329 15059

GGT: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
13429	1262	858	1	115.1	141.3	13.0	16.0	25.0	49.0	117.0	262.2	429.0

lowest : 3 5 6 7 8 , highest: 2932 3303 3782 3919 5171

CRP: Parameter analysis value (Numeric)

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
14536	155	3328	1	10.92	10.39	0.29	0.77	2.87	8.57	16.45	24.49	29.61

lowest : 0 0.01 0.02 0.03 0.04 , highest: 58.4 61.81 63.96 73.04 76.32

5.2.3 Suggested transformations

Next we investigate whether a pseudolog transformation of continuous variables may substantially symmetrize the univariate distributions of the continuous variables, and may hence be useful for multivariate summaries. We employ a function ida_trans for this purpose, which optimises the parameter sigma of the pseudo-logarithm for that purpose. The optimization targets the best possible linear correlation of the transformed values with normal deviates. If no better transformation can be found, or if the improvement in correlation is less than 0.2 correlation units, no transformation is suggested.

Display the proposed variable transformations and the new parameter codes.

PARAMCD	n
ALAT_T	14691
AMY_T	14691
AP_T	14691
ASAT_T	14691
BASO_T	14691
CK_T	14691
CREA_T	14691
EOS_T	14691
GBIL_T	14691
GGT_T	14691
LDH_T	14691
LIP_T	14691
LYM_T	14691
PAMY_T	14691
WBC_T	14691

Register transformed variables in the data set. The updated data set with suggested log transformed data sets is saved at data/IDA/ADLB_02.rds.

The IDA analysis plan and specifications are updated with the proposed variable transformations. A new flag is derived to indicate the categorization of predictors now including transformations.

5.2.4 Comparison of univariate distributions with and without pseudo-log transformation

The comparison is only shown for variables where a transformation is suggested. Note, all observed values, and the distribution min, max and interquartile range as reference lines, are displayed.

# Univariate distribution checks This section reports a series of univariate summary checks of the bacteremia dataset. ```{r uni01, message =FALSE, warning =FALSE , echo=FALSE} library(here) library(dplyr) library(tidyr) library(ggplot2) library(tidyselect) library(gt) library(gtExtras) library(patchwork) library(Hmisc) library(sjlabelled) set.seed(1972) ## for any simulation or numerical approx calculations # Load the first iteration of the IDA ready data sets ADSL <- readRDS(here::here("data", "IDA", "ADSL_01.rds")) ADLB <- readRDS(here::here("data", "IDA", "ADLB_01.rds")) ``` ## U1: Categorical variables Age group, sex and bacteremia status are described by frequencies and proportions in each category. ```{r U1-catplot, message=FALSE, warning =FALSE , echo=FALSE, include = TRUE} source(here("R", "U1-categorical.R")) u1_ard <- u1_describe(ADSL = ADSL) # u1_ard |> glimpse() ## Run this for word report u1_display_table_word(u1_ard) ## Run this for online website ##u1_display_table_html(u1_ard) ``` Also plot the categories as simple bar charts. ```{r u1-catplot2, message=FALSE, warning=FALSE, echo=FALSE} #| fig-cap: "Summary of categorical variables including outcome" #| fig-width: 18 #| fig-height: 5 #| fig-align: center source(here("R", "U1-categorical.R")) u1_display_plot(u1_ard) ``` ## Continuous variables ### U2: Univariate distributions of continuous variables #### U2: Structural variables The only structural continuous variable is AGE. This variable is also a key predictor and reported in the following section (see below). #### U2: Key predictors Distribution of key predictors. Lines indicate the 5-number summary including reported numerical values (where possible). The remaining predictors are reported in the appendix @sec-u2-remaining. ```{r uni02, message=FALSE, warning =FALSE , echo=FALSE} #| layout-ncol: 3 #| fig-width: 4 #| fig-height: 2 source(here::here("R", "U2-cont-describe-plot.R")) key_plts <- ADLB |> filter(KEY_PRED_FL01 == "Y") |> group_by(PARAM) |> group_map(~ describe_plot(.x, num_bins = 300)) for (plts in key_plts) { print(plts) } ``` #### U2: Predictors of medium importance ```{r uni03, message=FALSE, warning=FALSE, echo=FALSE} #| layout-ncol: 3 #| fig-width: 4 #| fig-height: 2 med_plts <- ADLB |> filter(MED_PRED_FL01 == "Y") |> group_by(PARAM) |> group_map(~ describe_plot(.x, num_bins = 300)) for (plts in med_plts) { print(plts) } ``` ### Numerical summaries #### Key predictors ```{r sumtools, results='asis', message =FALSE, warning =FALSE , echo=FALSE} key_predictors <- ADLB |> filter(KEY_PRED_FL01 == "Y") |> select(USUBJID, PARAMCD, AVAL) |> pivot_wider(names_from = "PARAMCD", values_from = "AVAL") |> select(-USUBJID) html(describe(key_predictors, size = "tiny")) ``` #### Predictors of medium importance ```{r uni06, results='asis', message =FALSE, warning =FALSE , echo=FALSE} medium_predictors <- ADLB |> filter(MED_PRED_FL01 == "Y") |> select(USUBJID, PARAMCD, AVAL) |> pivot_wider(names_from = "PARAMCD", values_from = "AVAL") |> select(-USUBJID) html(describe(medium_predictors, size = "tiny")) ``` ### Suggested transformations Next we investigate whether a pseudolog transformation of continuous variables may substantially symmetrize the univariate distributions of the continuous variables, and may hence be useful for multivariate summaries. We employ a function `ida_trans` for this purpose, which optimises the parameter `sigma` of the pseudo-logarithm for that purpose. The optimization targets the best possible linear correlation of the transformed values with normal deviates. If no better transformation can be found, or if the improvement in correlation is less than 0.2 correlation units, no transformation is suggested. ```{r uni08, message =FALSE, warning =FALSE , echo=FALSE} source(here("R", "fun_ida_trans.R")) ## need to rethink the param and paramcd interaction suggested_transforms <- ADLB |> group_by(PARAMCD) |> group_map(~ ida_trans(.x, equ.marg=0.2), .keep = TRUE) ``` Display the proposed variable transformations and the new parameter codes. ```{r} new_vars <- NULL for (param in suggested_transforms) if(!is.na(param$const)) new_vars <- bind_rows(new_vars, param$dat) ## TODO: losing the label attributes with this bind ADLB_02 <- bind_rows(ADLB, new_vars) ADLB_02 <- sjlabelled::copy_labels(ADLB_02, ADLB) new_vars |> group_by(PARAMCD) |> tally() |> gt() |> gt_theme_538() ``` Register transformed variables in the data set. The updated data set with suggested log transformed data sets is saved at `data/IDA/ADLB_02.rds`. The IDA analysis plan and specifications are updated with the proposed variable transformations. A new flag is derived to indicate the categorization of predictors now including transformations. ```{r savedata, message=FALSE, warning=FALSE, echo=FALSE} ADLB_02 <- ADLB_02 |> mutate( KEY_PRED_FL02 = case_when( PARAMCD %in% c("AGE", "WBC_T", "BUN", "CREA_T", "PLT", "NEU") ~ "Y" ), MED_PRED_FL02 = case_when( PARAMCD %in% c("POTASS", "FIB", "CRP", "ASAT_T", "ALAT_T", "GGT_T") ~ "Y" ), REM_PRED_FL02 = case_when( PARAMCD %in% c("MCV", "HGB", "HCT", "MCH", "MCHC", "RDW", "MPV", "LYM_T", "MONO", "EOS_T", "BASO", "NT", "APTT", "SODIUM", "CA", "PHOS", "MG", "HS", "GBIL_T", "TP", "ALB", "AMY_T", "PAMY_T", "LIP_T", "CHE", "AP_T", "LDH_T", "CK_T", "GLU", "TRIG", "CHOL", "BASOR_T", "EOSR", "LYMR", "MONOR", "NEUR", "PDW", "RBC") ~ "Y" ) ) attr(ADLB_02$KEY_PRED_FL02, "label") <- "Key predictor flag - including scale transformations, Section 2.2.5 U2" attr(ADLB_02$MED_PRED_FL02, "label") <- "Predictors of medium importance flag - including scale transformations" attr(ADLB_02$REM_PRED_FL02, "label") <- "Remaining predictors flag - including scale transformations" attr(ADLB_02$PARCAT02, "label") <- "Pseudo log transformed categories" attr(ADLB_02$SIGMA, "label") <- "Constant variable for Pseudo log transformation" saveRDS(ADLB_02, file = here("data", "IDA", "ADLB_02.rds")) ``` ### Comparison of univariate distributions with and without pseudo-log transformation The comparison is only shown for variables where a transformation is suggested. Note, all observed values, and the distribution min, max and interquartile range as reference lines, are displayed. ```{r uni-plots, message=FALSE, warning=FALSE, echo=FALSE, fig.height=3} #| layout-ncol: 2 ## plot side by side source(here("R", "fun_compare_dist_plot.R")) ## Load in updated data set with transformations ADLB_02 <- readRDS(here::here("data", "IDA", "ADLB_02.rds")) res <- ADLB_02 |> filter(PARCAT02 == "Y") |> group_by(PARAMCD) |> group_map(~ compare_dist_plot(.x), .keep = TRUE) for (plts in res) { print(plts) } ```