Clinical Dataset
set.seed(123)
n <- 150 # Number of patients
clinical_data <- tibble(
Country = sample(c("France", "Germany", "UK", "Italy", "Spain"), n, replace = TRUE),
Age = rnorm(n, mean = 60, sd = 10),
Sex = sample(c("Male", "Female"), n, replace = TRUE),
Cancer_Type = sample(c("Lung", "Breast", "Colorectal", "Healthy"), n, replace = TRUE),
Cancer_Stage = sample(1:4, n, replace = TRUE),
Weight = rnorm(n, mean = 75, sd = 15),
Height = rnorm(n, mean = 170, sd = 10),
Fatigue_Score = sample(0:10, n, replace = TRUE),
Physician_Score = sample(0:10, n, replace = TRUE),
CRP = rnorm(n, mean = 5, sd = 2),
IL6 = rnorm(n, mean = 10, sd = 5),
Leukocytes = rnorm(n, mean = 6.5, sd = 2),
Neutrophils = rnorm(n, mean = 55, sd = 10),
Lymphocytes = rnorm(n, mean = 35, sd = 8),
KRAS_Mutation = sample(c("Mutated", "Wild-type"), n, replace = TRUE),
Treatment_Response = sample(c("Complete", "Partial", "None"), n, replace = TRUE)
)
head(clinical_data)
#> # A tibble: 6 × 16
#> Country Age Sex Cancer_Type Cancer_Stage Weight Height Fatigue_Score
#> <chr> <dbl> <chr> <chr> <int> <dbl> <dbl> <int>
#> 1 UK 64.5 Female Lung 3 61.6 180. 8
#> 2 UK 60.4 Male Healthy 4 43.9 175. 5
#> 3 Germany 55.8 Female Lung 1 77.3 178. 3
#> 4 Germany 39.5 Female Healthy 1 73.8 171. 1
#> 5 UK 71.3 Female Healthy 1 73.5 179. 6
#> 6 Spain 45.4 Female Breast 4 78.2 184. 8
#> # ℹ 8 more variables: Physician_Score <int>, CRP <dbl>, IL6 <dbl>,
#> # Leukocytes <dbl>, Neutrophils <dbl>, Lymphocytes <dbl>,
#> # KRAS_Mutation <chr>, Treatment_Response <chr>Descriptive Statistics
We summarize categorical and multinomial variables using
print_multinomial.
print_multinomial(select(clinical_data, "Cancer_Type"))
#> # A tibble: 4 × 3
#> Variables Levels Statistics
#> <chr> <fct> <chr>
#> 1 Cancer_Type Breast 31 (20.7%)
#> 2 Cancer_Type Colorectal 36 (24%)
#> 3 Cancer_Type Healthy 39 (26%)
#> 4 Cancer_Type Lung 44 (29.3%)Here, we see if the distribution of cancer types and treatment responses is balanced across the dataset. If a category is underrepresented, statistical comparisons may lack power.
Binary variables can be summarized using
summary_binomial.
summary_binomial(select(clinical_data, c("KRAS_Mutation", "Sex")))
#> # A tibble: 2 × 2
#> Variables Statistics
#> <chr> <chr>
#> 1 KRAS_Mutation Mutated : 64 (42.7%)
#> 2 Sex Female : 78 (52%)Checking for imbalances in binary variables is crucial. If
KRAS_Mutation is highly imbalanced, conclusions regarding
its association with outcomes should be interpreted cautiously.
For continuous variables, summary_numeric provides a
robust summary.
print_numeric(select(clinical_data, c("Age", "Weight", "CRP")))
#> # A tibble: 3 × 10
#> Variables `Mean+/-SD` `Median+/-IQR` `Q1-Q3` Range Kurtosis Skewness Normality
#> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <chr>
#> 1 Age 59.9+/-9.9 58.8+/-12.8 53.5;6… 39.5… 0 0.5 *
#> 2 CRP 4.9+/-2.2 5+/-3.1 3.3;6.5 -0.2… -0.6 0 ns
#> 3 Weight 73.6+/-14.6 73.7+/-20.7 63.3;84 32.9… -0.2 -0.1 ns
#> # ℹ 2 more variables: Zeros <int>, NAs <int>
summary_numeric(clinical_data$Age)
#> # A tibble: 1 × 2
#> Variables `Median+/-IQR`
#> <chr> <chr>
#> 1 x 58.8+/-12.8We verify if the distributions are symmetric or skewed. A strong skew might indicate outliers or a non-normal distribution requiring transformation before parametric testing.
Identifying Outliers
Outliers in continuous variables can affect statistical analyses. We use different methods to detect them:
identify_outliers(clinical_data$CRP, method = "iqr")
#> 65 138
#> 10.39679 -0.15288
identify_outliers(clinical_data$CRP, method = "percentiles")
#> 1 3 5 6 8 9 10
#> 8.3134481 3.1290760 7.6413795 3.3149919 2.3978950 3.0335076 2.7260567
#> 11 13 14 15 17 18 20
#> 6.5718339 7.0840632 6.9596322 0.3681530 8.0072611 7.7231960 6.4619270
#> 22 24 26 29 32 34 37
#> 1.6904591 2.5296148 9.6856059 1.1423246 2.0109577 8.5924038 6.9686532
#> 41 42 45 47 49 51 53
#> 1.0635006 6.9962251 1.0653040 7.9710068 2.9247392 6.7639155 3.1759631
#> 54 55 58 59 61 63 65
#> 1.7084062 2.4285751 8.6285764 3.0199275 6.8558961 2.6936643 10.3967902
#> 66 70 71 72 75 78 79
#> 9.6581565 1.7176185 7.0088403 6.6258744 1.1835822 3.1078309 7.9568659
#> 80 82 84 89 90 94 95
#> 6.5516459 2.7315312 0.8203162 2.5309310 2.4729368 1.7363015 0.9751352
#> 97 98 102 104 105 106 108
#> 3.2022552 7.1503529 8.6788003 8.7396548 7.2354010 6.5513664 9.4546493
#> 112 113 114 115 116 119 120
#> 9.1914104 7.1803523 2.7092527 0.8903842 7.5161296 1.2543664 8.4874727
#> 122 123 125 126 128 131 132
#> 1.7135104 7.5253174 3.0938029 2.5521838 7.5803915 7.3143079 7.1365233
#> 133 135 138 140 146 150
#> 7.4986945 3.2458000 -0.1528800 6.8177517 2.1789440 2.0953922
identify_outliers(clinical_data$CRP, method = "hampel")
#> 1 5 8 15 17 18 22
#> 8.3134481 7.6413795 2.3978950 0.3681530 8.0072611 7.7231960 1.6904591
#> 24 26 29 32 34 41 45
#> 2.5296148 9.6856059 1.1423246 2.0109577 8.5924038 1.0635006 1.0653040
#> 47 54 55 58 65 66 70
#> 7.9710068 1.7084062 2.4285751 8.6285764 10.3967902 9.6581565 1.7176185
#> 75 79 84 89 90 94 95
#> 1.1835822 7.9568659 0.8203162 2.5309310 2.4729368 1.7363015 0.9751352
#> 102 104 108 112 115 116 119
#> 8.6788003 8.7396548 9.4546493 9.1914104 0.8903842 7.5161296 1.2543664
#> 120 122 123 126 128 133 138
#> 8.4874727 1.7135104 7.5253174 2.5521838 7.5803915 7.4986945 -0.1528800
#> 146 150
#> 2.1789440 2.0953922
identify_outliers(clinical_data$CRP, method = "mad")
#> 1 5 8 15 17 18 22
#> 8.3134481 7.6413795 2.3978950 0.3681530 8.0072611 7.7231960 1.6904591
#> 24 26 29 32 34 41 45
#> 2.5296148 9.6856059 1.1423246 2.0109577 8.5924038 1.0635006 1.0653040
#> 47 54 55 58 65 66 70
#> 7.9710068 1.7084062 2.4285751 8.6285764 10.3967902 9.6581565 1.7176185
#> 75 79 84 89 90 94 95
#> 1.1835822 7.9568659 0.8203162 2.5309310 2.4729368 1.7363015 0.9751352
#> 102 104 108 112 115 116 119
#> 8.6788003 8.7396548 9.4546493 9.1914104 0.8903842 7.5161296 1.2543664
#> 120 122 123 126 128 133 138
#> 8.4874727 1.7135104 7.5253174 2.5521838 7.5803915 7.4986945 -0.1528800
#> 146 150
#> 2.1789440 2.0953922
identify_outliers(select(clinical_data, CRP), method = "sd")
#> 15 26 29 34 41 45 58
#> 0.3681530 9.6856059 1.1423246 8.5924038 1.0635006 1.0653040 8.6285764
#> 65 66 75 84 95 102 104
#> 10.3967902 9.6581565 1.1835822 0.8203162 0.9751352 8.6788003 8.7396548
#> 108 112 115 119 120 138
#> 9.4546493 9.1914104 0.8903842 1.2543664 8.4874727 -0.1528800Different methods have different sensitivity levels. The
iqr method identifies extreme values based on quartiles,
while mad and hampel are robust to skewed
distributions. sd assumes normality and may not be ideal
for skewed data.
Correlation Analysis
mcor_test(clinical_data[, c("CRP", "IL6", "Leukocytes")], method = "pearson")
#> CRP IL6 Leukocytes
#> CRP 1.00000000 0.05415309 -0.04326444
#> IL6 0.05415309 1.00000000 0.07126276
#> Leukocytes -0.04326444 0.07126276 1.00000000
mcor_test(
clinical_data[, c("CRP", "IL6", "Leukocytes")],
clinical_data[, c("Physician_Score", "Fatigue_Score")],
method = "spearman",
p.value = TRUE,
method_adjust = "bonferroni"
)
#> $estimate
#> CRP IL6 Leukocytes
#> Physician_Score -0.003373907 -0.02593512 0.005017972
#> Fatigue_Score 0.125182200 0.00348041 0.109012944
#>
#> $p.value
#> CRP IL6 Leukocytes
#> Physician_Score 1.00000 1 1
#> Fatigue_Score 0.76154 1 1Pearson’s correlation assumes linear relationships, whereas Spearman’s is rank-based and better suited for skewed or non-linear associations. If Pearson’s r differs significantly from Spearman’s rho, the relationship might not be linear.
Group Comparisons
ANOVA (Parametric)
anova_res <- anova_test(data = clinical_data, Age ~ Country)
print_test(anova_res)
#> [1] "Anova, F(4, 145) = 2, p = 0.13"A significant ANOVA result suggests at least one group mean differs. If non-significant, we fail to reject the null hypothesis that all means are equal.
Kruskal-Wallis (Non-Parametric)
kruskal_res <- kruskal_test(data = clinical_data, CRP ~ Cancer_Type)
print_test(kruskal_res)
#> [1] "Kruskal-Wallis, K(3) = 0, p = 0.96"This test is an alternative to ANOVA when normality is violated. A significant result means at least one group median differs.
Wilcoxon Test (Two Groups)
wilcox_res <- wilcox_test(data = clinical_data, IL6 ~ KRAS_Mutation)
print_test(wilcox_res)
#> [1] "Wilcoxon, W = 2450, p = 0.25"A significant result suggests IL6 levels differ significantly
between KRAS_Mutation groups.
Chi-Square and Fisher’s Exact Test
chi2_res <- chisq_test(table(clinical_data$Cancer_Type, clinical_data$Treatment_Response))
print_chi2_test(chi2_res)
#> [1] "X2(6) = 6, P = 0.421, N = 150"Chi-square tests independence between categorical variables. A significant result suggests an association between cancer type and treatment response.
post_hoc_chi2(clinical_data$Cancer_Type, method = "chisq")
#> # A tibble: 6 × 9
#> group1 group2 n statistic df p p.signif FDR fdr.signif
#> <chr> <chr> <int> <dbl> <dbl> <dbl> <chr> <dbl> <chr>
#> 1 Breast Colorectal 67 0.373 1 0.541 ns 0.7 ns
#> 2 Breast Healthy 70 0.914 1 0.339 ns 0.7 ns
#> 3 Breast Lung 75 2.25 1 0.133 ns 0.7 ns
#> 4 Colorectal Healthy 75 0.12 1 0.729 ns 0.729 ns
#> 5 Colorectal Lung 80 0.8 1 0.371 ns 0.7 ns
#> 6 Healthy Lung 83 0.301 1 0.583 ns 0.7 nsPost-hoc tests determine which specific categories differ, useful when the chi-square test is significant.
Session Information
#> R version 4.5.2 (2025-10-31)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.3 LTS
#>
#> Matrix products: default
#> BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
#>
#> locale:
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#> [4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
#> [7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: UTC
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
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#> other attached packages:
#> [1] GimmeMyStats_1.0.0 magrittr_2.0.4 rstatix_0.7.3 lubridate_1.9.4
#> [5] forcats_1.0.1 stringr_1.6.0 dplyr_1.1.4 purrr_1.2.1
#> [9] readr_2.1.6 tidyr_1.3.2 tibble_3.3.1 ggplot2_4.0.1
#> [13] tidyverse_2.0.0
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#> loaded via a namespace (and not attached):
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#> [4] lattice_0.22-7 numDeriv_2016.8-1.1 tzdb_0.5.0
#> [7] vctrs_0.7.0 tools_4.5.2 Rdpack_2.6.4
#> [10] generics_0.1.4 proxy_0.4-29 pkgconfig_2.0.3
#> [13] Matrix_1.7-4 RColorBrewer_1.1-3 S7_0.2.1
#> [16] desc_1.4.3 lifecycle_1.0.5 compiler_4.5.2
#> [19] farver_2.1.2 textshaping_1.0.4 lmerTest_3.2-0
#> [22] carData_3.0-5 htmltools_0.5.9 class_7.3-23
#> [25] sass_0.4.10 yaml_2.3.12 Formula_1.2-5
#> [28] nloptr_2.2.1 pillar_1.11.1 pkgdown_2.2.0
#> [31] car_3.1-3 jquerylib_0.1.4 MASS_7.3-65
#> [34] cachem_1.1.0 reformulas_0.4.3.1 boot_1.3-32
#> [37] abind_1.4-8 nlme_3.1-168 tidyselect_1.2.1
#> [40] digest_0.6.39 stringi_1.8.7 splines_4.5.2
#> [43] fastmap_1.2.0 grid_4.5.2 cli_3.6.5
#> [46] utf8_1.2.6 broom_1.0.11 e1071_1.7-17
#> [49] withr_3.0.2 scales_1.4.0 backports_1.5.0
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#> [67] fs_1.6.6