27 Appendix – Intradepartmental Consultation Analysis

27.1 Supplementary Tables

27.1.1 Complete Pathologist Consultation Matrix

Complete Consultation Matrix (Asker vs Responder)
Asker	P10	P11	P15	P16	P17	P18	P2	P21	P23	P24	P3	P33	P4	P5	P6	P8	P9	P1	P13	P19	P20	P25	P27	P28	P32	P22	P14	P7	P26	P29	P30	P12
P1	14	3	1	1	24	1	17	3	25	1	1	4	1	15	1	14	32	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
P10	0	10	0	0	56	1	26	197	3	0	0	6	1	13	3	14	12	5	6	60	1	1	14	4	1	0	0	0	0	0	0	0
P11	2	0	0	3	3	4	12	2	13	0	0	5	3	21	27	16	48	0	5	3	0	1	2	1	0	0	0	0	0	0	0	0
P12	0	0	0	0	2	0	1	0	0	0	0	0	0	1	1	1	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0
P13	18	154	0	2	23	1	74	21	34	54	0	5	1	87	19	73	48	0	0	49	0	0	2	16	1	2	0	0	0	0	0	0
P14	0	1	0	9	9	2	22	0	0	0	1	11	0	35	3	0	35	2	0	9	0	0	0	0	0	0	0	0	0	0	0	0
P15	0	0	0	1	2	1	3	0	0	0	0	9	0	3	2	2	8	0	0	4	0	0	0	0	0	0	1	1	0	0	0	0
P16	0	7	0	0	0	5	9	14	7	0	0	0	6	19	1	1	30	0	2	4	0	1	3	2	0	0	0	0	0	0	0	0
P17	2	2	0	1	0	3	62	12	11	1	0	22	0	50	2	14	2	0	3	18	0	0	0	0	0	0	0	0	2	0	0	0
P18	11	35	0	2	6	0	14	16	37	0	2	7	28	35	17	10	58	2	1	1	0	3	9	21	1	0	0	1	0	1	1	0
P19	16	1	0	0	10	6	10	4	0	4	0	4	2	34	1	4	8	0	10	0	0	0	16	0	0	0	0	1	0	0	0	0
P2	13	2	0	4	45	4	0	17	16	11	0	9	1	44	56	12	7	7	12	9	0	0	1	2	0	0	0	0	3	0	0	0
P20	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
P21	74	6	0	19	16	1	27	0	8	1	0	1	0	16	0	10	2	0	8	2	0	0	1	4	0	0	0	0	0	0	1	0
P22	0	94	0	0	0	0	0	0	3	0	0	0	0	9	0	73	4	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0
P23	2	5	0	0	8	2	18	2	0	4	0	0	1	26	0	32	5	0	0	1	0	2	3	4	0	0	0	0	0	0	1	0
P24	0	0	0	0	6	0	52	4	5	0	0	0	0	20	0	13	30	0	0	6	0	0	4	0	0	0	0	0	0	0	0	0
P25	1	6	0	0	23	0	9	2	2	0	0	0	1	6	0	1	2	0	0	0	0	0	0	2	0	0	0	0	1	0	0	0
P26	0	4	0	1	1	0	22	1	2	0	0	0	1	6	0	0	12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
P27	4	16	0	2	0	7	2	1	19	3	0	0	17	8	0	3	13	0	1	11	0	2	0	14	2	0	0	0	0	0	8	0
P28	10	25	0	1	2	4	5	24	25	1	0	0	4	104	0	6	20	0	2	0	0	2	2	0	2	0	0	0	0	0	2	0
P29	16	18	0	0	0	0	2	19	4	2	0	0	1	19	0	2	7	0	0	0	0	2	0	7	0	0	0	0	0	0	0	0
P3	0	0	0	9	5	3	21	0	0	0	0	104	0	14	9	6	38	7	0	9	0	0	0	0	0	0	2	0	0	0	0	1
P30	0	3	0	0	0	1	0	1	1	0	0	0	0	1	0	1	1	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0
P31	1	0	0	0	0	0	0	0	3	10	0	0	0	1	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0
P32	0	1	0	0	0	1	0	1	3	0	0	0	2	0	0	0	0	0	0	0	0	0	1	3	0	0	0	0	0	0	0	0
P4	12	46	0	1	4	18	6	24	24	3	2	14	0	21	44	13	51	3	3	12	1	1	28	8	1	0	1	0	0	0	4	0
P5	4	2	0	12	7	2	36	18	4	15	4	9	0	0	7	4	19	2	0	4	0	0	3	22	0	0	2	0	0	0	0	0
P6	1	2	0	1	0	1	53	0	0	0	1	2	1	23	0	10	36	0	1	4	0	0	0	0	0	0	0	0	0	0	0	0
P7	0	3	0	2	1	7	52	0	2	0	0	4	2	3	5	7	12	0	0	10	0	0	0	0	0	0	1	0	0	0	0	0
P8	9	41	0	0	105	1	106	10	142	3	0	41	3	87	36	0	155	0	3	5	0	0	1	6	0	0	0	0	0	0	0	0
P9	6	34	0	4	4	6	23	6	14	7	3	4	3	30	20	4	0	0	11	3	0	2	2	6	0	0	1	0	0	0	1	0
NA	0	1	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0

27.1.2 Detailed Monthly Statistics

Detailed Monthly Consultation Statistics
Month	Total_Consultations	Unique_Cases	Unique_Askers	Unique_Responders	Min_TAT	Q1_TAT	Median_TAT	Mean_TAT	Q3_TAT	Max_TAT	SD_TAT	Within_24h	Pct_24h
2022-08-01	27	18	9	10	0.0	2.6	13.9	11.2	17.5	23.0	7.8	27	100.0
2022-09-01	59	49	14	11	0.4	3.4	14.2	13.0	17.5	103.1	14.6	57	96.6
2022-10-01	124	84	16	14	0.0	2.1	5.1	9.5	14.2	58.4	9.9	118	95.2
2022-11-01	192	107	16	14	0.1	3.2	14.2	13.0	17.5	96.9	13.4	177	92.2
2022-12-01	197	117	18	14	0.0	2.1	5.1	8.5	14.2	67.3	9.4	191	97.0
2023-01-01	208	128	18	15	0.0	2.1	5.1	10.3	17.5	96.1	14.7	193	92.8
2023-02-01	96	73	16	13	0.0	0.6	4.0	13.8	17.5	97.1	21.2	80	83.3
2023-03-01	119	84	14	13	0.0	0.9	4.7	16.4	20.1	99.3	23.5	91	76.5
2023-04-01	77	58	14	14	0.0	1.1	5.1	17.0	25.3	97.1	23.4	57	74.0
2023-05-01	96	75	17	12	0.0	1.0	5.3	14.4	19.3	97.5	21.3	82	85.4
2023-06-01	77	65	14	10	0.0	0.9	4.7	15.8	17.3	99.3	23.4	63	81.8
2023-07-01	87	65	16	13	0.0	1.2	3.7	12.8	12.0	92.5	20.7	72	82.8
2023-08-01	119	89	15	12	0.0	1.2	5.1	14.8	21.0	93.3	19.6	96	80.7
2023-09-01	90	69	17	14	0.0	0.9	5.1	16.4	21.9	97.9	24.0	69	76.7
2023-10-01	66	59	15	10	0.0	0.8	2.9	14.8	20.9	93.5	22.7	52	78.8
2023-11-01	85	68	17	13	0.0	0.7	3.5	17.1	23.5	103.5	24.4	65	76.5
2023-12-01	86	75	15	13	0.0	1.1	4.8	13.1	20.7	88.1	18.3	68	79.1
2024-01-01	90	83	14	12	0.2	1.4	3.9	11.2	17.7	69.1	15.6	76	84.4
2024-02-01	123	101	17	15	0.0	1.4	3.9	14.8	18.1	97.1	21.7	105	85.4
2024-03-01	124	104	15	14	0.0	0.6	3.4	8.2	11.3	73.9	12.6	116	93.5
2024-04-01	79	69	15	13	0.0	1.0	3.4	13.4	18.7	94.1	21.2	66	83.5
2024-05-01	159	134	19	15	0.0	0.7	2.7	9.5	11.3	73.9	15.2	141	88.7
2024-06-01	124	101	18	15	0.0	1.1	2.9	11.0	16.0	81.2	16.1	106	85.5
2024-07-01	142	121	18	15	0.0	0.4	1.9	8.1	7.6	101.8	14.5	129	90.8
2024-08-01	118	110	18	14	0.0	0.9	4.3	12.5	18.1	74.4	16.6	99	83.9
2024-09-01	112	105	18	14	0.0	1.2	3.0	9.7	14.7	96.6	15.5	104	92.9
2024-10-01	169	146	18	16	0.0	0.8	2.3	9.6	11.1	68.7	15.4	147	87.0
2024-11-01	117	97	19	14	0.1	0.9	3.0	10.2	15.5	87.0	14.8	103	88.0
2024-12-01	161	140	19	14	0.0	0.8	2.7	10.2	16.1	96.3	16.0	143	88.8
2025-01-01	241	210	20	17	0.0	0.6	2.0	8.1	11.3	90.2	13.9	220	91.3
2025-02-01	203	170	21	18	0.0	0.7	2.4	7.4	8.5	83.9	11.6	184	90.6
2025-03-01	261	180	20	18	0.0	0.8	2.9	9.9	14.1	77.3	15.3	230	88.1
2025-04-01	199	144	20	18	0.0	0.7	1.8	7.8	8.3	85.2	13.3	183	92.0
2025-05-01	240	177	20	17	0.0	0.6	1.9	6.0	5.0	72.9	10.9	227	94.6
2025-06-01	195	141	19	18	0.0	0.6	2.4	7.4	7.9	101.9	12.8	181	92.8
2025-07-01	228	188	20	18	0.0	0.9	2.4	8.4	11.3	96.2	15.3	212	93.0
2025-08-01	192	151	20	17	0.0	0.9	2.7	7.9	9.0	69.4	12.6	177	92.2
2025-09-01	231	166	22	19	0.0	1.0	2.5	10.0	13.7	102.4	16.8	205	88.7
2025-10-01	234	175	23	19	0.0	0.9	2.6	9.0	12.5	95.2	14.2	209	89.3
2025-11-01	288	217	23	22	0.0	1.0	3.0	8.4	11.6	94.9	13.1	263	91.3
2025-12-01	47	30	14	17	0.1	0.6	1.8	5.3	4.4	40.2	8.5	43	91.5

27.1.3 Pathologist-Level Performance Details

Detailed Performance Statistics by Responder
Responder	N	Min	Q1	Median	Mean	Q3	Max	SD	Within_24h	Pct_24h	Within_48h	Pct_48h
P5	751	0.0	0.7	2.0	7.6	6.7	103.1	14.0	692	92.1	729	97.1
P9	696	0.0	2.0	5.1	10.1	11.5	96.3	14.2	623	89.5	668	96.0
P2	684	0.0	0.9	2.1	6.5	5.0	97.5	12.6	642	93.9	668	97.7
P11	522	0.0	0.7	1.7	5.4	4.2	70.5	9.7	501	96.0	516	98.9
P23	407	0.0	1.2	3.0	7.1	9.9	69.2	10.3	383	94.1	400	98.3
P21	399	0.0	1.3	3.7	12.3	19.8	90.2	16.6	340	85.2	382	95.7
P17	362	0.0	4.0	20.3	24.5	32.5	101.9	23.9	233	64.4	304	84.0
P8	348	0.0	1.1	3.4	11.7	15.1	102.4	19.6	298	85.6	323	92.8
P33	261	0.0	17.5	17.5	19.2	17.5	97.9	18.0	224	85.8	241	92.3
P6	254	0.0	1.4	14.2	17.9	17.4	103.5	21.5	203	79.9	226	89.0
P19	227	0.0	1.2	2.6	7.9	5.3	73.9	13.0	206	90.7	221	97.4
P10	216	0.0	0.6	1.4	6.8	4.8	81.2	12.9	202	93.5	211	97.7
P28	124	0.0	1.0	3.0	9.8	12.7	95.2	16.0	112	90.3	120	96.8
P24	120	0.0	0.1	1.3	5.1	3.8	87.0	11.7	114	95.0	118	98.3
P27	94	0.0	0.3	1.1	4.7	2.9	48.6	9.5	88	93.6	93	98.9
P18	83	0.0	0.7	4.0	8.5	11.3	83.9	13.3	75	90.4	81	97.6
P4	79	0.1	2.4	8.9	12.1	16.1	92.0	14.5	72	91.1	76	96.2
P16	75	0.0	3.2	18.1	18.5	23.6	85.2	18.4	56	74.7	68	90.7
P13	68	0.0	0.6	1.8	7.3	3.7	72.3	13.5	63	92.6	65	95.6
P1	29	0.0	2.7	13.9	15.0	13.9	95.8	18.3	27	93.1	28	96.6
P30	18	0.1	1.5	3.4	6.9	10.4	25.4	8.1	17	94.4	18	100.0
P25	17	0.3	0.6	6.1	11.2	20.3	40.0	12.5	15	88.2	17	100.0
P3	15	0.9	5.0	5.5	13.2	12.8	61.6	17.8	12	80.0	14	93.3
P14	8	0.4	0.5	0.5	0.5	0.5	0.5	0.0	8	100.0	8	100.0
P32	8	0.3	0.7	1.4	14.1	16.8	71.6	24.6	7	87.5	7	87.5
P26	6	0.0	3.2	9.8	22.9	40.2	66.5	27.9	4	66.7	4	66.7
P22	3	0.4	0.4	0.5	0.5	0.5	0.6	0.1	3	100.0	3	100.0
P7	3	1.0	4.1	7.2	7.2	10.3	13.4	6.2	3	100.0	3	100.0
P20	2	1.1	6.9	12.7	12.7	18.5	24.3	16.4	1	50.0	2	100.0
P12	1	1.6	1.6	1.6	1.6	1.6	1.6	NA	1	100.0	1	100.0
P15	1	1.6	1.6	1.6	1.6	1.6	1.6	NA	1	100.0	1	100.0
P29	1	0.1	0.1	0.1	0.1	0.1	0.1	NA	1	100.0	1	100.0

27.2 Statistical Test Details

27.2.1 Normality Tests

Normality Tests for Turnaround Time (sample of 5000)
Test	Statistic	P_Value	Interpretation
Shapiro-Wilk	0.6496	<2e-16	Data significantly non-normal
Skewness	2.6880	—	Highly skewed
Kurtosis	11.2800	—	Heavy tails (leptokurtic)

27.2.2 Complete Statistical Test Results

Summary of Statistical Tests and Rationale
Research Question	Test Used	Reason for Test Choice	Key Assumption
Volume vs TAT correlation	Spearman correlation	Non-normal data, monotonic relationship	Monotonic relationship
Day of week effect on TAT	Kruskal-Wallis H test	Non-normal data, >2 groups	Independent groups
Time of day effect on TAT	Kruskal-Wallis H test	Non-normal data, >2 groups	Independent groups
Responder differences in TAT	Kruskal-Wallis H test	Non-normal data, >2 groups	Independent groups
Number of consultants vs TAT	Spearman correlation	Non-normal data, monotonic relationship	Monotonic relationship
Weekend vs weekday TAT	Mann-Whitney U test	Non-normal data, 2 groups	Independent groups
Temporal trend in volume	Adjusted Mann-Kendall trend test	Time series trend detection	Serial correlation/seasonality adjusted as needed

27.3 R Code for Key Analyses

27.3.1 Data Processing Code

Code

# Data processing example (from process_data.R)
library(readxl)
library(dplyr)
library(lubridate)
library(stringr)

# Read consultation data
# Read Primary Sources
df_paylasilan <- read_excel("data/Paylasilan Vakalar 2024.xlsx", skip=2)
df_vaka <- read_excel("data/2024_vaka_paylasildi.xlsx")
df_internal <- read_excel("data/2024_internal_consultation.xlsx")

# Prioritize Asker (Paylasilan > Internal > Vaka)
df_merged <- df_internal %>%
  left_join(df_paylasilan, by = "Case_ID") %>%
  left_join(df_vaka, by = "Case_ID") %>%
  mutate(
    Asker = coalesce(Asker_Paylasilan, Asker_Internal, Asker_Vaka),
    Start_Time = coalesce(Start_Time_Vaka, Start_Time_Internal),
    Responder = Responder_Internal,
    Completion_Time = Completion_Time_Internal
  )

# Join and calculate TAT
df_consultations <- df_vaka %>%
  inner_join(df_kalite, by = "Case_ID") %>%
  filter(Initiator != Responder) %>%
  filter(Completion_Time > Start_Time) %>%
  mutate(
    Turnaround_Time_Hours = as.numeric(
      difftime(Completion_Time, Start_Time, units = "hours")
    ),
    Turnaround_Time_Days = as.numeric(
      difftime(Completion_Time, Start_Time, units = "days")
    )
  )

27.3.2 Network Analysis Code

Code

library(igraph)

# Create network from consultation data
edges <- df %>%
  group_by(Asker, Responder) %>%
  summarise(Weight = n(), .groups = "drop")

# Create graph
network <- graph_from_data_frame(edges,
                                 directed = TRUE,
                                 vertices = unique(c(edges$Asker, edges$Responder)))

# Calculate centrality metrics
degree_in <- degree(network, mode = "in")
degree_out <- degree(network, mode = "out")
betweenness <- betweenness(network, directed = TRUE, weights = E(network)$Weight)
closeness <- closeness(network, mode = "all")
pagerank <- page_rank(network, weights = E(network)$Weight)$vector

# Community detection
communities <- cluster_louvain(network, weights = E(network)$Weight)

27.3.3 Predictive Modeling Code

Code

library(broom)

# Prepare features
df_model <- df %>%
  mutate(
    Hour = hour(Start_Time),
    DayOfWeek = wday(Start_Time, week_start = 1),
    IsWeekend = ifelse(DayOfWeek %in% c(6, 7), 1, 0),
    Month = month(Start_Time),
    Log_TAT = log(Turnaround_Time_Hours + 1)
  ) %>%
  group_by(Case_ID) %>%
  mutate(Case_Complexity = n()) %>%
  ungroup()

# Linear regression
model_lm <- lm(Log_TAT ~ IsWeekend + Hour + Month + Case_Complexity,
              data = df_model)

summary(model_lm)

# Logistic regression for fast response
df_model$Fast_Response <- ifelse(df_model$Turnaround_Time_Hours <= 24, 1, 0)

model_logistic <- glm(Fast_Response ~ IsWeekend + Hour + Month + Case_Complexity,
                     data = df_model,
                     family = binomial())

summary(model_logistic)

27.4 Glossary of Terms

Glossary of Technical Terms
Term	Definition
Asker	Pathologist who initiates a consultation request
Responder	Pathologist who provides consultation response
Turnaround Time (TAT)	Time between consultation request and completion
In-Degree	Number of consultations received (incoming edges)
Out-Degree	Number of consultations initiated (outgoing edges)
Betweenness Centrality	Measure of how often a node lies on shortest paths between other nodes
PageRank	Algorithm measuring importance based on link structure
Gini Coefficient	Measure of inequality in distribution (0=perfect equality, 1=perfect inequality)
Community Detection	Algorithmic identification of groups within a network
Network Density	Proportion of actual connections to possible connections
Reciprocity	Proportion of bidirectional relationships in network
Control Chart	Statistical process control tool showing mean and control limits
Outlier	Data point significantly different from others (typically >99th percentile)
KPI	Key Performance Indicator - metric used to evaluate success
SLA	Service Level Agreement - formal commitment to service standards
Triage	Process of categorizing by urgency or priority

27.5 Software and Package Versions

Key R Package Versions Used
Package	Version
dplyr	1.1.4
ggplot2	4.0.1
igraph	2.2.1
lubridate	1.9.4
knitr	1.51
kableExtra	1.4.0
broom	1.0.11
tidyr	1.3.2

R Version: R version 4.5.1 (2025-06-13)

Platform: aarch64-apple-darwin20

System: macOS Tahoe 26.2

27.6 Data Dictionary

Data Dictionary for Processed Dataset
Variable	Type	Description	Valid Range / Values
Case_ID	Character	Unique identifier for pathology case (format: XXXXX-YY)	Format varies by institution
Asker	Character (Code)	Anonymized code for pathologist requesting consultation (P1, P2, ...)	P1 through P[N] where N = number of pathologists
Responder	Character (Code)	Anonymized code for pathologist providing consultation (P1, P2, ...)	P1 through P[N] where N = number of pathologists
Start_Time	POSIXct	Timestamp when consultation was initiated (UTC)	Within study period
Completion_Time	POSIXct	Timestamp when consultation was completed (UTC)	After Start_Time, within study period
Turnaround_Time_Hours	Numeric	Duration of consultation in hours	> 0
Turnaround_Time_Days	Numeric	Duration of consultation in days	> 0

27.7 Additional Visualizations

27.7.1 Turnaround Time Distribution by Percentile

27.7.2 Heat Map: Consultations by Hour and Day of Week

27.8 Recommendations for Future Data Collection

To enhance future analyses, consider collecting:

Case Characteristics:
- Organ system
- Diagnosis category
- Case difficulty rating
- Specimen type
Consultation Context:
- Reason for consultation (second opinion, expertise, educational)
- Urgency level
- Subspecialty area
- Related clinical information needs
Pathologist Information:
- Years of experience
- Subspecialty training
- Full-time equivalent status
- Primary responsibilities
Outcome Measures:
- Diagnostic concordance
- Clinical utility rating
- Follow-up consultations needed
- Patient outcome data (if feasible)
Process Metrics:
- Time to first view (vs. completion)
- Number of views/accesses
- Communication events
- Escalations or re-assignments
Satisfaction Metrics:
- Requester satisfaction
- Consultant satisfaction
- Perceived value

27.9 Contact Information

For questions about this analysis, data requests, or to obtain additional information, please contact the Department of Pathology administration or the corresponding author listed in the manuscript.