Example ANCOVA

a <- (describe(HIVdata))
html(a)

## Warning in png(file, width = 1 + k * w, height = h): 'width=10, height=13' are
## unlikely values in pixels

## Warning in png(file, width = 1 + k * w, height = h): 'width=13, height=13' are
## unlikely values in pixels

## Warning in png(file, width = 1 + k * w, height = h): 'width=13, height=13' are
## unlikely values in pixels

HIVdata

29 Variables 131 Observations

subject_id

n	missing	distinct
131	0	131

lowest : Hs60020 Hs60021 Hs60030 Hs60046 Hs60064 , highest: Hs90151 Hs90158 Hs90171 Hs90190 Hs90224

visit_

n	missing	distinct	value
126	5	1	Visit 1

 Value      Visit 1
 Frequency      126
 Proportion       1

visit_age_fc_sample

n	missing	distinct
126	5	31

lowest : 50 51 52 53 54 , highest: 83 84 85 90 94

sex

n	missing	distinct	Info	Mean	Gmd
126	5	1	0	1	0

 Value        1
 Frequency  126
 Proportion   1

ethnicity

n	missing	distinct	Info	Sum	Mean	Gmd
126	5	2	0.532	97	0.7698	0.3572

hiv

n	missing	distinct
126	5	2

 Value      hiv_1 hiv_2
 Frequency     66    60
 Proportion 0.524 0.476

frailty_results

n	missing	distinct	Info	Mean	Gmd
89	42	3	0.786	2.461	0.666

 Value          1     2     3
 Frequency      8    32    49
 Proportion 0.090 0.360 0.551

demographics_complete

n	missing	distinct	Info	Mean	Gmd
131	0	1	0	0	0

 Value        0
 Frequency  131
 Proportion   1

cmv_screen

n	missing	distinct	Info	Mean	Gmd
126	5	1	0	1	0

 Value        1
 Frequency  126
 Proportion   1

cmv_screen_expt_id

n	missing	distinct
126	5	8

lowest :	10/30/2017	10/4/2016	11/7/2018	5/1/2007	5/1/2017
highest:	5/1/2007	5/1/2017	5/24/2017	6/20/2016	7/10/2018

 Value      10/30/2017  10/4/2016  11/7/2018   5/1/2007   5/1/2017  5/24/2017
 Frequency          12         10         65          1          6         10
 Proportion      0.095      0.079      0.516      0.008      0.048      0.079
                                 
 Value       6/20/2016  7/10/2018
 Frequency          10         12
 Proportion      0.079      0.095

microgen_cmv_titer

        n  missing distinct     Info     Mean      Gmd      .05      .10      .25 
      126        5      116        1    550.9    609.1    22.25    75.50   174.25 
      .50      .75      .90      .95 
   326.00   568.00  1384.50  2058.25

lowest : 0 11 22 23 31 , highest: 2220 2688 2852 3482 3607

cmv_nt80_expt_id

n	missing	distinct
15	116	2

 Value      CPC20180323    JU170707
 Frequency           14           1
 Proportion       0.933       0.067

cmv_nt80_titer_value

n	missing	distinct	Info	Mean	Gmd
15	116	4	0.927	13.33	14.86

 Value          0    10    20    40
 Frequency      5     4     4     2
 Proportion 0.333 0.267 0.267 0.133

cmv_analyses_complete

n	missing	distinct	Info	Mean	Gmd
131	0	1	0	0	0

 Value        0
 Frequency  131
 Proportion   1

cd8_temra

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
76	55	72	1	58.25	28.66	13.73	23.25	39.40	58.75	79.33	89.20	94.12

lowest : 1.88 9.90 11.20 13.20 13.90 , highest: 94.10 94.20 94.30 94.70 97.30

cd4_temra

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
76	55	75	1	20.62	22.8	0.940	1.370	4.713	10.400	32.750	57.500	67.350

lowest : 0.12 0.32 0.79 0.88 0.96 , highest: 67.00 68.40 72.60 74.40 90.20

t_phenotype_complete

n	missing	distinct	Info	Mean	Gmd
131	0	2	0.731	1.16	0.9818

 Value         0    2
 Frequency    55   76
 Proportion 0.42 0.58

il6_il8_tnfa_exp

n	missing	distinct
126	5	4

 Value      LD20190507 LD20190508 LD20190509 LD20190510
 Frequency          37         38         38         13
 Proportion      0.294      0.302      0.302      0.103

il6

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
125	6	45	0.738	7.423	9.266	0.690	1.014	3.200	3.200	3.200	13.984	34.140

lowest : 0.06 0.13 0.19 0.24 0.26 , highest: 65.19 69.66 72.97 75.20 86.17

il8

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
124	7	107	0.999	15.77	22.5	1.000	1.145	2.428	4.405	12.758	31.455	59.571

lowest : 0.07 0.15 0.45 0.73 0.80 , highest: 70.82 76.39 83.86 190.54 370.98

 Value          0     5    10    15    20    25    30    35    45    55    60    70
 Frequency     33    43    16     9     3     5     3     1     1     2     2     2
 Proportion 0.266 0.347 0.129 0.073 0.024 0.040 0.024 0.008 0.008 0.016 0.016 0.016
                                   
 Value         75    85   190   370
 Frequency      1     1     1     1
 Proportion 0.008 0.008 0.008 0.008

For the frequency table, variable is rounded to the nearest 5

tnf_alpha

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
126	5	126	1	19.2	13.33	6.40	8.11	10.40	15.65	22.15	31.50	48.47

lowest :	4.491577	4.808064	5.514630	5.919339	6.044060
highest:	55.701246	61.758789	65.352217	80.931237	97.885357

tnfr_exp

n	missing	distinct	value
36	95	1	LD20190514

 Value      LD20190514
 Frequency          36
 Proportion          1

tnf_r1

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
36	95	36	1	1258	715.4	531.9	603.7	882.4	1073.4	1260.7	1514.2	2029.6

lowest :	462.7777	514.1947	537.8335	577.8936	629.5173
highest:	1444.0389	1584.3421	2026.4912	2038.8579	7260.0319

tnf_r2

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
36	95	36	1	5440	3428	2046	2418	3374	4876	6065	7203	9734

lowest :	1449.436	1754.086	2143.818	2225.529	2610.625
highest:	6907.902	7498.126	9671.871	9918.845	28465.864

age_cat

n	missing	distinct
131	0	2

 Value      <= 60 years  > 60 years
 Frequency           79          52
 Proportion       0.603       0.397

Variables with all observations missing:

age, hiv_diagnosis_method, hiv_test_id, hiv.factor

\[y = \beta_o + \beta_1 (il6) + \beta_2({age}) + \beta_3(il6*age) + \epsilon \]

HO: Is there a difference in slopes HO: no difference in slopes

test.slopes <- lm(il8 ~ il6 + age_cat + il6*age_cat , data=p, na.action=na.exclude)
anova(test.slopes)

## Analysis of Variance Table
## 
## Response: il8
##              Df Sum Sq Mean Sq F value  Pr(>F)  
## il6           1  10375 10374.5  6.7850 0.01037 *
## age_cat       1    640   640.4  0.4188 0.51877  
## il6:age_cat   1    164   163.8  0.1071 0.74405  
## Residuals   119 181956  1529.0                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

qplot(x=il6, y=il8, data=p, color=age_cat) + geom_smooth(method="lm")

## `geom_smooth()` using formula 'y ~ x'

## Warning: Removed 8 rows containing non-finite values (stat_smooth).

## Warning: Removed 8 rows containing missing values (geom_point).

\[y = \beta_o + \beta_1 (il6) + \beta_2({age}) + \epsilon \] Ho: Parallel Slopes Ho: not parallel

test.parallel <- lm(il8 ~ il6 + age_cat , data=p, na.action=na.exclude)
anova(test.parallel)

## Analysis of Variance Table
## 
## Response: il8
##            Df Sum Sq Mean Sq F value  Pr(>F)  
## il6         1  10375 10374.5  6.8358 0.01008 *
## age_cat     1    640   640.4  0.4220 0.51720  
## Residuals 120 182120  1517.7                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

\[y = \beta_o + \beta_1 (il6) + \epsilon \]

test.common <- lm(il8 ~ il6 , data=p, na.action=na.exclude)
anova(test.common)

## Analysis of Variance Table
## 
## Response: il8
##            Df Sum Sq Mean Sq F value   Pr(>F)   
## il6         1  10375 10374.5  6.8686 0.009897 **
## Residuals 121 182760  1510.4                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Example ANCOVA

Bonnie LaFleur

7/2/2021