Chapter 12 Univariate distribution checks

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

12.1 Data set overview

Using the Hmisc describe function, we provide an overview of the data set. The descriptive report also provides histograms of continuous variables. For ease of scanning the information, we group the report by measurement type.

12.1.1 Demographic and lifestyle variables

Demographic and lifestyle variables

6 Variables   5972 Observations

---

age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	660	1	54.87	17.64	32.17	34.58	41.65	53.75	67.25	76.50	80.83

lowest : 30.00000 30.08333 30.16667 30.25000 30.33333 , highest: 84.58333 84.66667 84.75000 84.83333 84.91667

---

gender

n	missing	distinct
5972	0	2

 Value        Male Female
 Frequency    2935   3037
 Proportion  0.491  0.509
 

---

educationadult: education level

n	missing	distinct
5968	4	3

 Value      Less than high school           High school More than high school
 Frequency                   1683                  1448                  2837
 Proportion                 0.282                 0.243                 0.475
 

---

bmi: body mass index kg/m2

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5928	44	2161	1	29.07	6.804	20.78	22.12	24.73	28.08	32.23	37.07	40.80

lowest : 13.36 14.65 14.70 15.91 15.92 , highest: 62.50 62.77 63.42 63.87 130.21

---

smokecigs: smoking status

n	missing	distinct
5970	2	3

 Value        Never  Former Current
 Frequency     2911    1759    1300
 Proportion   0.488   0.295   0.218
 

---

alcohol: alcohol consumption

n	missing	distinct	Info	Mean	Gmd
5577	395	3	0.776	1.516	0.624

 Value          1     2     3
 Frequency   3090  2098   389
 Proportion 0.554 0.376 0.070
 

---

12.1.2 Physiological measurements

Lab measurements

3 Variables   5972 Observations

---

sys: Systolic blood pressure mg/dl

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5698	274	137	1	127.4	22.26	100.0	105.0	113.0	124.0	138.0	154.0	166.1

lowest : 73 80 81 83 85 , highest: 226 230 238 256 270

---

lbxtc: Total cholesterol mg/dl

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5742	230	264	1	204.1	46.4	143	155	175	201	228	258	277

lowest : 82 83 85 92 94 , highest: 431 440 458 539 650

---

lbdhdd: HDL cholesterol mg/dl

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5742	230	109	1	54.64	17.91	33	37	43	52	64	76	85

lowest : 17 22 23 24 25 , highest: 146 151 152 154 188

---

12.1.3 Comorbidities

Comorbidities

4 Variables   5972 Observations

---

diabetes

n	missing	distinct
5972	0	2

 Value         No   Yes
 Frequency   5214   758
 Proportion 0.873 0.127
 

---

chf: congestive heart failure

n	missing	distinct
5972	0	2

 Value         No   Yes
 Frequency   5739   233
 Proportion 0.961 0.039
 

---

cancer

n	missing	distinct
5972	0	2

 Value         No   Yes
 Frequency   5359   613
 Proportion 0.897 0.103
 

---

stroke

n	missing	distinct
5972	0	2

 Value        No  Yes
 Frequency  5734  238
 Proportion 0.96 0.04
 

---

12.1.4 Physical activity variables

Physical activity

16 Variables   5972 Observations

---

tac: total activity counts per day

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5965	1	244811	143738	69233	94872	150571	223572	314224	417410	486450

lowest :	8263.000	8931.833	12123.000	14642.000	15656.000
highest:	981517.167	986261.000	986593.800	1097823.500	1122542.600

---

tlac: total log activity count (log(1+activity))

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5969	1	2900	873.5	1613	1900	2385	2911	3431	3877	4164

lowest :	313.0835	364.4561	400.8157	429.9288	466.0362
highest:	5436.1548	5492.5395	5588.3401	5655.4680	6122.6779

---

mvpa: Moderate or vigorous physical activity minutes

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	1163	1	19.19	20.9	0.800	1.429	4.000	12.000	26.762	46.000	59.921

lowest :	0.0000000	0.1428571	0.1666667	0.2000000	0.2500000
highest:	180.8333333	186.2000000	194.8000000	208.5000000	249.0000000

---

wt: total accelerometer wear time minutes

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	3613	1	866.1	139.8	684.3	721.0	782.9	852.1	922.0	1000.6	1111.5

lowest : 600.000 601.500 602.000 603.000 604.000 , highest: 1425.286 1426.250 1426.286 1426.857 1440.000

---

tlac.1: total log actvity count 12:00AM-2:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	2656	0.829	30.92	51.83	0.00	0.00	0.00	0.00	24.38	94.43	169.25

lowest :	0.0000000	0.1569446	0.1831020	0.2299197	0.2559656
highest:	597.3808309	620.0469233	674.1677375	709.3300116	719.0239316

---

tlac.2: total log actvity count 2:00AM-4:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	1770	0.653	19.09	34.47	0.00	0.00	0.00	0.00	2.91	51.83	110.64

lowest :	0.00000000	0.09902103	0.11552453	0.15694461	0.23104906
highest:	586.34967162	611.00545824	617.44773130	737.25383394	775.42871350

---

tlac.3: total log actvity count 4:00AM-6:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	2834	0.855	43.29	70.78	0.00	0.00	0.00	0.00	38.74	147.59	248.43

lowest :	0.0000000	0.1155245	0.1386294	0.2299197	0.2682397
highest:	679.1484297	697.1093552	704.5766819	719.3198459	769.6014301

---

tlac.4: total log actvity count 6:00AM-8:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5285	0.998	177	178.6	0.00	0.00	36.94	137.34	282.09	416.35	496.25

lowest :	0.0000000	0.2299197	0.3465736	0.6148132	0.6839274
highest:	774.8811640	792.6938042	822.1482092	832.9933042	857.9018816

---

tlac.5: total log actvity count 8:00AM-10:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5834	1	339.3	191.7	39.52	102.56	221.28	346.74	460.18	552.17	610.19

lowest :	0.0000000	0.2310491	0.7250248	0.8652549	1.0357837
highest:	812.0225306	812.8675420	813.2942210	824.5800445	888.1759271

---

tlac.6: total log actvity count 10:00AM-12:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5931	1	407.7	163.6	150.4	218.6	316.2	415.0	506.7	589.9	634.9

lowest :	0.0000000	0.6986213	2.6001909	4.5903937	5.7234361
highest:	807.7712473	808.7247458	811.5701740	884.1169241	892.0314653

---

tlac.7: total log actvity count 12:00PM-2:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5947	1	418	146.9	192.1	250.4	337.6	423.5	507.2	581.3	623.7

lowest :	0.000000	1.734669	2.704424	5.605670	6.387910
highest:	788.370472	796.082067	813.380498	821.733575	885.445891

---

tlac.8: total log actvity count 2:00PM-4:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5954	1	411.7	147.8	192.1	243.1	323.6	414.3	501.7	577.5	619.9

lowest :	0.000000	1.974752	3.096473	4.094345	5.772020
highest:	792.683985	837.042353	846.553847	877.212734	904.872351

---

tlac.9: total log actvity count 4:00PM-6:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5955	1	397	140.3	185.4	234.8	316.4	401.8	483.5	553.6	591.4

lowest :	0.000000	2.957040	3.401197	4.148165	5.084134
highest:	771.497952	783.128869	801.039991	809.429425	822.294800

---

tlac.10: total log actvity count 6:00PM-8:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5932	1	337.6	151.3	114.1	165.5	246.6	339.5	433.1	504.4	548.9

lowest :	0.000000	1.311822	1.353699	1.753975	3.459493
highest:	778.168243	778.774433	802.020060	851.421446	860.123328

---

tlac.11: total log actvity count 8:00PM-10:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5786	1	223.2	158.2	10.22	42.32	116.77	212.72	315.90	411.75	471.84

lowest :	0.0000000	0.6229449	0.6708919	1.0233141	1.0525597
highest:	724.9040071	753.8848070	821.4989318	826.3463412	839.8942777

---

tlac.12: total log actvity count 10:00PM-12:00AM

        n  missing distinct     Info     Mean      Gmd      .05      .10      .25 
     5972        0     4943    0.995    95.37    114.3    0.000    0.000    6.693 
      .50      .75      .90      .95 
   55.438  141.863  251.308  328.945 
 

lowest :	0.00000000	0.09902103	0.17328680	0.27798716	0.41291025
highest:	683.58618305	698.46723961	702.66304648	707.15487443	733.61717206

---

12.2 Categorical variables

We now provide a closer visual examination of the categorical predictors.

12.3 Continuous variables

A closer visual examination of continuous predictors and the outcome variable.

There is evidence of influential points in some of the distributions. This is explored further with targeted summaries. A more detailed univariate summaries for the variables of interest are also provided below.

12.3.1 Age

Figure 12.1: Distribution of age

12.3.2 Blood pressure

Figure 7.1: Distribution of SBP

12.3.3 Body mass index

Figure 7.2: Distribution of respiratory rate

There is a participant with an unusual high value (130.2). It is possible that this is an entry error (bmi=30.2).

12.3.4 Outcome= Time of moderate or vigrous physical activity and related variables

Figure 7.3: Distribution of time of moderate/vigorous activity [minutes]

After transforming MVPA with \(\log_{10}(x+1)\):

Figure 7.4: Distribution of log10 (1+MVPA)

Figure 7.5: Distribution of wear time [minutes]

Figure 7.6: Distribution of log total activity count

12.4 Section session info

## R version 4.1.3 (2022-03-10)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17763)
## 
## Matrix products: default
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## [3] LC_MONETARY=English_Austria.1252 LC_NUMERIC=C                    
## [5] LC_TIME=English_Austria.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] Hmisc_4.6-0     Formula_1.2-4   survival_3.2-13 lattice_0.20-45
##  [5] forcats_0.5.1   stringr_1.4.0   dplyr_1.0.8     purrr_0.3.4    
##  [9] readr_2.1.2     tidyr_1.2.0     tibble_3.1.6    ggplot2_3.3.5  
## [13] tidyverse_1.3.1 here_1.0.1     
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## loaded via a namespace (and not attached):
##  [1] fs_1.5.2            lubridate_1.8.0     RColorBrewer_1.1-2 
##  [4] httr_1.4.2          rprojroot_2.0.2     tools_4.1.3        
##  [7] backports_1.4.1     bslib_0.3.1         utf8_1.2.2         
## [10] R6_2.5.1            rpart_4.1.16        DBI_1.1.2          
## [13] colorspace_2.0-3    nnet_7.3-17         withr_2.5.0        
## [16] tidyselect_1.1.2    gridExtra_2.3       compiler_4.1.3     
## [19] cli_3.2.0           rvest_1.0.2         htmlTable_2.4.0    
## [22] xml2_1.3.3          labeling_0.4.2      bookdown_0.25      
## [25] sass_0.4.1          scales_1.1.1        checkmate_2.0.0    
## [28] digest_0.6.29       foreign_0.8-82      rmarkdown_2.13     
## [31] base64enc_0.1-3     jpeg_0.1-9          pkgconfig_2.0.3    
## [34] htmltools_0.5.2     highr_0.9           dbplyr_2.1.1       
## [37] fastmap_1.1.0       htmlwidgets_1.5.4   rlang_1.0.2        
## [40] readxl_1.3.1        rstudioapi_0.13     jquerylib_0.1.4    
## [43] generics_0.1.2      farver_2.1.0        jsonlite_1.8.0     
## [46] magrittr_2.0.2      patchwork_1.1.1     Matrix_1.4-0       
## [49] Rcpp_1.0.8.3        munsell_0.5.0       fansi_1.0.3        
## [52] lifecycle_1.0.1     stringi_1.7.6       yaml_2.3.5         
## [55] grid_4.1.3          crayon_1.5.1        haven_2.4.3        
## [58] splines_4.1.3       hms_1.1.1           knitr_1.38         
## [61] pillar_1.7.0        reprex_2.0.1        glue_1.6.2         
## [64] evaluate_0.15       latticeExtra_0.6-29 data.table_1.14.2  
## [67] modelr_0.1.8        png_0.1-7           vctrs_0.3.8        
## [70] tzdb_0.2.0          cellranger_1.1.0    gtable_0.3.0       
## [73] assertthat_0.2.1    xfun_0.30           broom_0.7.12       
## [76] cluster_2.1.2       ellipsis_0.3.2