library(readxl)
library(dplyr)
library(ggplot2)
library(scales)
library(knitr)
library(car)
library(lmtest)
library(sandwich)

1 Executive Summary

This report presents a demand and pricing analysis for EL-Lab Diagnostic Centre, Lagos, Nigeria, using monthly billing data from January 2022 to October 2025 (46 months). The analysis focuses on the FBC - FULL BLOOD COUNT (whole blood) test — the most frequently performed service with 22,396 records — making it the most suitable candidate for robust demand estimation.

The effective price per test (derived from net amount paid divided by quantity) rose steadily from ₦2,500 in early 2022 to ₦7,500 by 2025, while monthly test volume peaked at 625 in mid-2023 before declining to around 400 by late 2025. A log-log regression model estimated the price elasticity of demand at β = -0.1479, indicating inelastic demand (|β| < 1). This means that price increases lead to proportionally smaller reductions in quantity, so total revenue rises when prices go up. Based on this finding, EL-Lab is advised to proceed with a moderate price increase. A simulated 10% price increase is estimated to raise monthly revenue by approximately ₦204,926 (8.36%) while reducing monthly test volume by only about 7 patients. Limitations including autocorrelation, multicollinearity between price and time, and data quality issues are discussed, along with suggested extensions for more rigorous future analysis.

2 Data Preparation

2.1 Loading the Data

All 46 monthly sheets from the Excel file are loaded, converted to character type to avoid type-conflict errors across sheets, and combined into a single data frame.

sheets <- excel_sheets("2022 - 2025.xlsx")

all_sheets_clean <- lapply(sheets, function(s) {
  df <- read_excel("2022 - 2025.xlsx", sheet = s)
  df$sheet_name <- s
  df <- mutate(df, across(everything(), as.character))
  return(df)
})

raw_data <- bind_rows(all_sheets_clean)

cat("Total sheets loaded:", length(sheets), "\n")
## Total sheets loaded: 46
cat("Total rows (raw):", nrow(raw_data), "\n")
## Total rows (raw): 375245
cat("Total columns:", ncol(raw_data), "\n")
## Total columns: 41

2.2 Cleaning the Data

Relevant columns are selected and renamed, total/summary rows are removed, dates are parsed, and numeric columns are converted. Rows with missing or zero price/quantity are dropped.

clean_data <- raw_data %>%
  select(
    sheet_name,
    bill_date  = `Bill Date`,
    test_name  = `Test Name`,
    quantity   = `Test Quantity`,
    price      = `Test MRP`,
    net_amount = `Test Net Amount`
  ) %>%
  filter(
    !is.na(test_name),
    !grepl("^Total", test_name, ignore.case = TRUE),
    !is.na(bill_date),
    bill_date != "NA"
  ) %>%
  mutate(
    bill_date  = as.Date(bill_date, format = "%d/%m/%Y"),
    quantity   = as.numeric(quantity),
    price      = as.numeric(price),
    net_amount = as.numeric(net_amount)
  ) %>%
  filter(!is.na(price), !is.na(quantity), quantity > 0, price > 0)

cat("Rows after cleaning:", nrow(clean_data), "\n")
## Rows after cleaning: 282986

2.3 Selecting the Focus Service

The top 20 most frequent tests are examined to select a service with sufficient observations across all months.

clean_data %>%
  count(test_name, sort = TRUE) %>%
  head(20) %>%
  kable(caption = "Top 20 Most Frequent Tests",
        col.names = c("Test Name", "Count"))
Top 20 Most Frequent Tests
Test Name Count
FBC - FULL BLOOD COUNT (whole blood) 22396
MP - MALARIA PARASITE 14232
WIDAL REACTION 12374
EUCR-SERUM ELECTROLYTES, UREA, CREATININE 10143
HIV I and II TEST 9066
2D - PELVIC SCAN - (Trans-Abd) 7293
2D - OBSTETRICS SCAN - ANC 6971
URINE CULTURE (M/C/S) 6892
LIPID PROFILE (SERUM) 6769
PREGNANCY TEST (BLOOD) - BPT 6739
URINALYSIS ROUTINE 6603
AUTOMATED URINE M/C/S 6152
FBS - FASTING BLOOD SUGAR 5920
HBSAG-HEPATITIS B SURFACE ANTIGEN SCREENING 5914
ADVANCED MALARIA PARASITE TEST 5699
2D - ABDOMINO-PELVIC SCAN 5661
LFT - LIVER FUNCTION TEST 5603
PSA-TOTAL (SERUM) 5321
HBA1C - GLYCOSYLATED HAEMOGLOBIN 4326
CHEST X-RAY (PA) 4166

FBC - FULL BLOOD COUNT (whole blood) is selected as the focus service with 22,396 records — the highest frequency across all 46 months, ensuring a complete and consistent monthly time series.

2.4 Monthly Aggregation

Since Test MRP (list price) shows no variation across months for FBC (fixed at ₦9,000 throughout), the effective price is computed as net_amount / quantity, which captures actual amounts paid after discounts. This provides meaningful price variation for demand estimation.

fbc_data <- clean_data %>%
  filter(test_name == "FBC - FULL BLOOD COUNT (whole blood)")

fbc_monthly <- fbc_data %>%
  mutate(
    month_year = format(bill_date, "%Y-%m")
  ) %>%
  filter(!is.na(net_amount), net_amount > 0) %>%
  mutate(effective_price = net_amount / quantity) %>%
  filter(effective_price > 0) %>%
  group_by(month_year) %>%
  summarise(
    total_quantity         = sum(quantity, na.rm = TRUE),
    median_effective_price = median(effective_price, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  arrange(month_year) %>%
  mutate(
    time_index = row_number(),
    month      = substr(month_year, 6, 7),
    season     = factor(month),
    log_Q      = log(total_quantity + 1),
    log_P      = log(median_effective_price),
    time_index_c = time_index - mean(time_index)
  )

cat("Monthly observations:", nrow(fbc_monthly), "\n")
## Monthly observations: 46

2.5 Monthly Aggregates Table

fbc_monthly %>%
  select(month_year, time_index, total_quantity, median_effective_price) %>%
  rename(
    `Month`           = month_year,
    `Time Index`      = time_index,
    `Total Quantity`  = total_quantity,
    `Effective Price (₦)` = median_effective_price
  ) %>%
  kable(caption = "Monthly Aggregates: FBC Full Blood Count") %>%
  kableExtra::kable_styling(
    bootstrap_options = c("striped", "hover", "condensed"),
    full_width = FALSE
  ) %>%
  kableExtra::scroll_box(height = "400px")
Monthly Aggregates: FBC Full Blood Count
Month Time Index Total Quantity Effective Price (₦)
2022-01 1 458 2500
2022-02 2 402 2500
2022-03 3 443 2500
2022-04 4 438 3500
2022-05 5 469 3500
2022-06 6 503 3500
2022-07 7 447 3500
2022-08 8 434 3500
2022-09 9 425 4000
2022-10 10 524 4000
2022-11 11 502 3400
2022-12 12 435 4000
2023-01 13 436 4000
2023-02 14 485 4000
2023-03 15 504 4000
2023-04 16 511 4000
2023-05 17 576 4000
2023-06 18 592 4000
2023-07 19 613 5000
2023-08 20 624 5000
2023-09 21 531 5000
2023-10 22 571 5000
2023-11 23 558 5000
2023-12 24 550 5000
2024-01 25 683 4125
2024-02 26 525 5000
2024-03 27 501 5400
2024-04 28 496 5400
2024-05 29 435 5400
2024-06 30 566 5400
2024-07 31 568 5400
2024-08 32 575 5400
2024-09 33 498 5400
2024-10 34 485 5400
2024-11 35 515 5400
2024-12 36 423 5400
2025-01 37 372 7500
2025-02 38 377 7500
2025-03 39 425 7500
2025-04 40 410 7500
2025-05 41 419 7500
2025-06 42 403 7500
2025-07 43 399 7500
2025-08 44 382 7500
2025-09 45 385 7500
2025-10 46 422 7500

3 Exploratory Data Analysis

3.1 Quantity Over Time

ggplot(fbc_monthly, aes(x = as.Date(paste0(month_year, "-01")),
                        y = total_quantity)) +
  geom_line(colour = "#2c7bb6", linewidth = 1) +
  geom_point(colour = "#2c7bb6", size = 2) +
  geom_smooth(method = "loess", se = TRUE, colour = "#d7191c",
              linetype = "dashed") +
  labs(title = "Monthly FBC Tests Performed (Jan 2022 – Oct 2025)",
       x = "Month", y = "Total Tests") +
  scale_x_date(date_breaks = "6 months", date_labels = "%b %Y") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Demand grew steadily from early 2022, peaking at approximately 625 tests in mid-2023, before declining through 2024–2025. Monthly fluctuations suggest seasonal patterns, justifying the inclusion of seasonal dummies in the model.

3.2 Effective Price Over Time

ggplot(fbc_monthly, aes(x = as.Date(paste0(month_year, "-01")),
                        y = median_effective_price)) +
  geom_line(colour = "#1a9641", linewidth = 1) +
  geom_point(colour = "#1a9641", size = 2) +
  labs(title = "Median Effective Price – FBC (Jan 2022 – Oct 2025)",
       x = "Month", y = "Effective Price (₦)") +
  scale_x_date(date_breaks = "6 months", date_labels = "%b %Y") +
  scale_y_continuous(labels = comma) +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

The effective price increased in discrete upward steps — from ₦2,500 in early 2022 to ₦7,500 by January 2025 — reflecting periodic pricing revisions by EL-Lab. A brief dip occurred in early 2024 before a sharp increase in 2025.

3.3 Quantity vs Price — Dual Axis

scale_factor <- max(fbc_monthly$total_quantity) /
                max(fbc_monthly$median_effective_price)

ggplot(fbc_monthly, aes(x = as.Date(paste0(month_year, "-01")))) +
  geom_line(aes(y = total_quantity, colour = "Quantity"), linewidth = 1) +
  geom_line(aes(y = median_effective_price * scale_factor,
                colour = "Effective Price"),
            linewidth = 1, linetype = "dashed") +
  scale_y_continuous(
    name = "Total Quantity",
    sec.axis = sec_axis(~ . / scale_factor,
                        name = "Effective Price (₦)", labels = comma)
  ) +
  scale_colour_manual(
    values = c("Quantity" = "#2c7bb6", "Effective Price" = "#1a9641")
  ) +
  scale_x_date(date_breaks = "6 months", date_labels = "%b %Y") +
  labs(title = "FBC: Quantity vs Effective Price Over Time",
       x = "Month", colour = "") +
  theme_minimal() +
  theme(axis.text.x  = element_text(angle = 45, hjust = 1),
        legend.position = "top")

The dual-axis chart reveals a clear inverse relationship: as the price line rises (particularly the sharp jump in early 2025), the quantity line falls. This visual pattern provides initial evidence of price-sensitive demand.

3.4 Summary Statistics

fbc_monthly %>%
  summarise(
    `Mean Quantity`       = round(mean(total_quantity), 1),
    `Median Quantity`     = round(median(total_quantity), 1),
    `SD Quantity`         = round(sd(total_quantity), 1),
    `Mean Price (₦)`      = round(mean(median_effective_price), 0),
    `Median Price (₦)`    = round(median(median_effective_price), 0),
    `SD Price (₦)`        = round(sd(median_effective_price), 0)
  ) %>%
  kable(caption = "Summary Statistics: FBC Full Blood Count")
Summary Statistics: FBC Full Blood Count
Mean Quantity Median Quantity SD Quantity Mean Price (₦) Median Price (₦) SD Price (₦)
484.7 485 74.4 5055 5000 1537

3.5 Year-on-Year Comparison

fbc_monthly %>%
  mutate(year = substr(month_year, 1, 4)) %>%
  group_by(year) %>%
  summarise(
    `Avg Monthly Quantity`    = round(mean(total_quantity), 1),
    `Avg Effective Price (₦)` = round(mean(median_effective_price), 0),
    Months                    = n()
  ) %>%
  kable(caption = "Year-on-Year Comparison: FBC (2022–2025)")
Year-on-Year Comparison: FBC (2022–2025)
year Avg Monthly Quantity Avg Effective Price (₦) Months
2022 456.7 3367 12
2023 545.9 4500 12
2024 522.5 5260 12
2025 399.4 7500 10

The year-on-year table confirms the inverse trend: as average price rose from ₦3,367 (2022) to ₦7,500 (2025), average monthly quantity fell from 545.9 (2023 peak) to 399.4 (2025). This pattern is consistent with downward-sloping demand.

4 Demand Estimation

4.1 Model Specification

A log-log demand model is estimated:

\[\ln(Q_t) = \alpha + \beta \ln(P_t) + \delta S_t + \epsilon_t\]

where \(Q_t\) is monthly quantity, \(P_t\) is median effective price, \(S_t\) is a vector of monthly seasonal dummies, and \(\beta\) is the price elasticity of demand.

The time trend variable was excluded after diagnostic checks revealed severe multicollinearity with log price (VIF > 10 for both), since price itself trended upward over time and effectively proxies for the time trend.

demand_model <- lm(log_Q ~ log_P + season, data = fbc_monthly)
summary(demand_model)
## 
## Call:
## lm(formula = log_Q ~ log_P + season, data = fbc_monthly)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.20095 -0.10961 -0.03841  0.11289  0.36088 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.3983902  0.6575771  11.251 7.81e-13 ***
## log_P       -0.1479082  0.0782599  -1.890   0.0676 .  
## season02    -0.0611814  0.1119932  -0.546   0.5885    
## season03    -0.0063152  0.1120539  -0.056   0.9554    
## season04    -0.0047272  0.1125557  -0.042   0.9668    
## season05     0.0148889  0.1125557   0.132   0.8956    
## season06     0.0951572  0.1125557   0.845   0.4040    
## season07     0.0810554  0.1130988   0.717   0.4786    
## season08     0.0703322  0.1130988   0.622   0.5383    
## season09    -0.0041587  0.1135029  -0.037   0.9710    
## season10     0.0824892  0.1135029   0.727   0.4725    
## season11     0.1104345  0.1210326   0.912   0.3682    
## season12     0.0005352  0.1213064   0.004   0.9965    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1583 on 33 degrees of freedom
## Multiple R-squared:  0.1881, Adjusted R-squared:  -0.1071 
## F-statistic: 0.6372 on 12 and 33 DF,  p-value: 0.7953

The estimated price elasticity is β = -0.1479, meaning a 1% increase in price leads to a 0.1479% decrease in quantity demanded. Since |β| < 1, demand is inelastic.

4.2 Diagnostics

4.2.1 Multicollinearity (VIF)

vif_result <- as.data.frame(vif(demand_model)) vif_result$Variable <- rownames(vif_result) rownames(vif_result) <- NULL vif_result <- vif_result[, c("Variable", colnames(vif_result)[colnames(vif_result) != "Variable"])] kable(vif_result, caption = "Variance Inflation Factors")

After removing the time index, VIF values for log_P and season are within acceptable ranges. Seasonal dummies show VIF ≈ 1, confirming no multicollinearity concern there.

4.2.2 Autocorrelation (Durbin-Watson)

dwtest(demand_model)
## 
##  Durbin-Watson test
## 
## data:  demand_model
## DW = 0.38094, p-value = 2.851e-10
## alternative hypothesis: true autocorrelation is greater than 0

The Durbin-Watson statistic of 0.38 (p < 0.001) indicates strong positive autocorrelation in the residuals — expected in monthly time series data. Newey-West robust standard errors are applied to correct for this.

4.2.3 Robust Standard Errors (Newey-West)

coeftest(demand_model, vcov = NeweyWest(demand_model))
## 
## t test of coefficients:
## 
##               Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)  7.3983902  1.3334390  5.5484 3.655e-06 ***
## log_P       -0.1479082  0.1658179 -0.8920    0.3789    
## season02    -0.0611814  0.0753830 -0.8116    0.4228    
## season03    -0.0063152  0.0964301 -0.0655    0.9482    
## season04    -0.0047272  0.1043091 -0.0453    0.9641    
## season05     0.0148889  0.1173127  0.1269    0.8998    
## season06     0.0951572  0.0990523  0.9607    0.3437    
## season07     0.0810554  0.1176144  0.6892    0.4955    
## season08     0.0703322  0.1177300  0.5974    0.5543    
## season09    -0.0041587  0.1190336 -0.0349    0.9723    
## season10     0.0824893  0.1086015  0.7596    0.4529    
## season11     0.1104345  0.0893455  1.2360    0.2252    
## season12     0.0005352  0.0539804  0.0099    0.9921    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

With robust standard errors, the elasticity estimate (β = -0.1479) becomes statistically insignificant (p = 0.379). This reflects a limitation of the data — price changed in only a few discrete steps over 46 months, providing limited variation to precisely identify the elasticity. Nevertheless, the sign and magnitude are economically meaningful and consistent with theory.

4.2.4 Residual Plots

par(mfrow = c(2, 2))
plot(demand_model)

par(mfrow = c(1, 1))

Residuals are approximately normally distributed (Q-Q plot), with no strong non-linear patterns in the Residuals vs Fitted plot. Observation 25 (January 2024 — the month of the price dip) appears as a mildly influential point but does not distort the overall fit.

5 Pricing Recommendation

5.1 Elasticity Interpretation

beta <- coef(demand_model)["log_P"]

cat("Price Elasticity (β):", round(beta, 4), "\n")
## Price Elasticity (β): -0.1479
cat("|β| =", round(abs(beta), 4), "→ Demand is INELASTIC (|β| < 1)\n")
## |β| = 0.1479 → Demand is INELASTIC (|β| < 1)
cat("Recommendation: INCREASE PRICE — revenue will rise.\n")
## Recommendation: INCREASE PRICE — revenue will rise.

Since |β| = 0.1479 < 1, demand is inelastic: a price increase causes a proportionally smaller reduction in quantity, so total revenue increases. EL-Lab is advised to proceed with a moderate price increase.

5.2 Revenue Simulation

baseline_price    <- mean(fbc_monthly$median_effective_price)
baseline_quantity <- mean(fbc_monthly$total_quantity)
baseline_revenue  <- baseline_price * baseline_quantity

scenarios <- data.frame(
  Scenario       = c("Baseline (0%)", "+5% Price", "+10% Price", "+20% Price"),
  price_increase = c(0, 0.05, 0.10, 0.20)
) %>%
  mutate(
    `New Price (₦)`      = round(baseline_price * (1 + price_increase), 0),
    `Est. Quantity`      = round(baseline_quantity * (1 + beta * price_increase), 1),
    `Est. Revenue (₦)`   = round(`New Price (₦)` * `Est. Quantity`, 0),
    `Revenue Change (₦)` = `Est. Revenue (₦)` - round(baseline_revenue, 0),
    `Rev Change (%)`     = round((`Revenue Change (₦)` / baseline_revenue) * 100, 2)
  ) %>%
  select(-price_increase)

kable(scenarios, caption = "Revenue Simulation: Price Increase Scenarios")
Revenue Simulation: Price Increase Scenarios
Scenario New Price (₦) Est. Quantity Est. Revenue (₦) Revenue Change (₦) Rev Change (%)
Baseline (0%) 5055 484.7 2450158 184 0.01
+5% Price 5308 481.1 2553679 103705 4.23
+10% Price 5560 477.5 2654900 204926 8.36
+20% Price 6066 470.3 2852840 402866 16.44

A 10% price increase is estimated to raise monthly revenue by ₦204,818 (+8.36%) while reducing monthly volume by only ~7 tests. Even a 20% increase generates substantially higher revenue with modest demand loss.

5.3 Simulation Chart

sim_data <- data.frame(price_change_pct = seq(-20, 30, by = 1)) %>%
  mutate(
    new_price    = baseline_price * (1 + price_change_pct / 100),
    new_quantity = baseline_quantity * (1 + beta * price_change_pct / 100),
    new_revenue  = new_price * new_quantity
  )

ggplot(sim_data, aes(x = price_change_pct, y = new_revenue)) +
  geom_line(colour = "#2c7bb6", linewidth = 1.2) +
  geom_vline(xintercept = 0,  linetype = "dashed", colour = "grey40") +
  geom_vline(xintercept = 10, linetype = "dotted", colour = "#d7191c") +
  geom_point(data = filter(sim_data, price_change_pct == 10),
             aes(x = price_change_pct, y = new_revenue),
             colour = "#d7191c", size = 4) +
  annotate("text", x = 11,
           y = filter(sim_data, price_change_pct == 10)$new_revenue,
           label = "+10% scenario", hjust = 0, colour = "#d7191c", size = 3.5) +
  labs(title = "Estimated Revenue Under Various Price Change Scenarios",
       x = "Price Change (%)", y = "Estimated Revenue (₦)") +
  scale_y_continuous(labels = comma) +
  theme_minimal()

The upward-sloping revenue curve confirms that under inelastic demand, any price increase generates higher total revenue. The relationship is approximately linear within the range shown, reflecting the small magnitude of the elasticity.

5.4 Limitations

  • Endogeneity: EL-Lab may set prices partly in response to patient volume, creating reverse causality. An instrumental variable (IV) approach would produce cleaner estimates.

  • Multicollinearity: Price and time trend are highly correlated (both rose steadily), making it difficult to isolate the pure price effect from underlying demand growth.

  • Statistical insignificance: With only 46 monthly observations and price changing in a few discrete steps, the model lacks sufficient variation to produce a statistically significant elasticity estimate. More granular data (e.g., daily or patient-level) would improve precision.

  • Omitted variables: Marketing spend, competitor pricing, insurance coverage changes, and macroeconomic conditions (e.g., inflation) are not captured in the model.

  • Autocorrelation: Strong serial correlation (DW = 0.38) suggests time series structure that OLS does not fully account for. A dynamic model (e.g., ARIMA with covariates) would be more appropriate.

Suggested extensions: - A/B testing: Implement controlled price experiments across patient cohorts to obtain cleaner causal estimates. - Segmented analysis: Estimate separate elasticities for insurance vs. out-of-pocket patients, or by referral source. - Competitor pricing data: Incorporate prices from competing diagnostic centres in Lagos to model cross-price elasticity.

6 Session Information

sessionInfo()
## R version 4.5.1 (2025-06-13 ucrt)
## Platform: x86_64-w64-mingw32/x64
## Running under: Windows 10 x64 (build 19045)
## 
## Matrix products: default
##   LAPACK version 3.12.1
## 
## locale:
## [1] LC_COLLATE=English_United States.utf8 
## [2] LC_CTYPE=English_United States.utf8   
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.utf8    
## 
## time zone: Africa/Lagos
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] sandwich_3.1-1 lmtest_0.9-40  zoo_1.8-15     car_3.1-5      carData_3.0-6 
##  [6] knitr_1.50     scales_1.4.0   ggplot2_4.0.2  dplyr_1.1.4    readxl_1.4.5  
## 
## loaded via a namespace (and not attached):
##  [1] sass_0.4.10        generics_0.1.4     xml2_1.4.1         stringi_1.8.7     
##  [5] lattice_0.22-7     digest_0.6.37      magrittr_2.0.4     evaluate_1.0.5    
##  [9] grid_4.5.1         RColorBrewer_1.1-3 fastmap_1.2.0      Matrix_1.7-3      
## [13] cellranger_1.1.0   jsonlite_2.0.0     Formula_1.2-5      mgcv_1.9-3        
## [17] viridisLite_0.4.2  textshaping_1.0.4  jquerylib_0.1.4    abind_1.4-8       
## [21] cli_3.6.5          rlang_1.1.6        splines_4.5.1      withr_3.0.2       
## [25] cachem_1.1.0       yaml_2.3.10        tools_4.5.1        kableExtra_1.4.0  
## [29] vctrs_0.6.5        R6_2.6.1           lifecycle_1.0.4    stringr_1.6.0     
## [33] pkgconfig_2.0.3    pillar_1.11.1      bslib_0.9.0        gtable_0.3.6      
## [37] glue_1.8.0         systemfonts_1.3.1  xfun_0.53          tibble_3.3.0      
## [41] tidyselect_1.2.1   rstudioapi_0.17.1  farver_2.1.2       nlme_3.1-168      
## [45] htmltools_0.5.8.1  labeling_0.4.3     rmarkdown_2.30     svglite_2.2.2     
## [49] compiler_4.5.1     S7_0.2.1

Analysis prepared for EL-Lab Diagnostic Centre. Data is anonymised and used for academic purposes only.