VOWR is an R package for analysing monthly Referral-to-Treatment (RTT) waiting-time data in healthcare systems.
It provides an end-to-end statistical workflow for:
- provider-level performance profiling;
- waiting-time risk classification;
- operational risk visualisation;
- survival analysis of time-to-threshold breach;
- Kaplan-Meier comparison across provider risk groups;
- Cox proportional hazards modelling.
The package is designed for healthcare analysts, applied statisticians, operational researchers, NHS performance teams, and health-services researchers.
Healthcare waiting-time monitoring often relies on static averages. VOWR extends this by combining risk profiling, volatility detection, and survival-based breach modelling.
It helps answer questions such as:
- Which providers are stable?
- Which providers are unstable or deteriorating?
- Which providers breach waiting-time thresholds earliest?
- Are risk groups statistically different over time?
During local development, load the package with:
devtools::load_all()After GitHub release, users will be able to install using:
# install.packages("devtools")
# devtools::install_github("zerish12/VOWR")VOWR expects provider-month RTT data with the following columns:
| Column | Description |
|---|---|
provider_org_code |
Provider organisation code |
provider_org_name |
Provider organisation name |
period |
Month/date of observation |
mean_wait_weeks |
Mean waiting time in weeks |
backlog_total |
Total backlog |
bucket_total |
Total waiting-time bucket count |
library(VOWR)
data <- vowr_import()
head(data)
#> provider_org_code provider_org_name
#> 1 A0C5S SPAMEDICA GLOUCESTER
#> 2 RC9 BEDFORDSHIRE HOSPITALS NHS FOUNDATION TRUST
#> 3 RBV THE CHRISTIE NHS FOUNDATION TRUST
#> 4 RBT MID CHESHIRE HOSPITALS NHS FOUNDATION TRUST
#> 5 RBS ALDER HEY CHILDREN'S NHS FOUNDATION TRUST
#> 6 RBQ LIVERPOOL HEART AND CHEST HOSPITAL NHS FOUNDATION TRUST
#> period mean_wait_weeks backlog_total bucket_total
#> 1 01/10/2023 4.871831 950 710
#> 2 01/10/2023 20.628635 276210 239142
#> 3 01/10/2023 6.421240 11966 9294
#> 4 01/10/2023 21.395905 125128 107844
#> 5 01/10/2023 21.765385 71426 64480
#> 6 01/10/2023 15.741076 19338 16584vowr_profile() summarises provider-level waiting-time performance.
profile <- vowr_profile(data)
head(profile)
#> # A tibble: 6 × 7
#> provider_org_code provider_org_name n_months mean_wait median_wait volatility
#> <chr> <chr> <int> <dbl> <dbl> <dbl>
#> 1 8KL73 ENDOCARE DIAGNOST… 3 1.47 1.48 0.106
#> 2 A0C5S SPAMEDICA GLOUCES… 24 4.77 4.79 0.979
#> 3 A1D1B SPAMEDICA WEMBLEY 9 4.31 4.86 1.17
#> 4 A1U4J SPAMEDICA PORTSMO… 17 4.83 5.10 1.72
#> 5 A4M8P BUCKSHAW HOSPITAL 24 15.5 15.4 1.40
#> 6 A4Q9X NEWMEDICA LEICEST… 22 3.99 3.16 2.23
#> # ℹ 1 more variable: total_backlog <int>The output includes:
- number of observed months;
- mean waiting time;
- median waiting time;
- waiting-time volatility;
- total backlog.
vowr_flag() classifies providers into operational risk groups.
flagged <- vowr_flag(profile)
table(flagged$risk_flag)
#>
#> Critical (Breach & Unstable) High (Breach)
#> 21 114
#> Stable Warning (Unstable)
#> 398 36Risk groups are defined as:
| Risk group | Meaning |
|---|---|
Stable |
Provider is below threshold and not highly volatile |
Warning (Unstable) |
Provider is volatile but not currently above threshold |
High (Breach) |
Provider is above the waiting-time threshold |
Critical (Breach & Unstable) |
Provider is both above threshold and highly volatile |
vowr_plot() produces a provider risk map showing mean waiting time
against volatility.
risk_plot <- vowr_plot(flagged)
print(risk_plot)
This plot helps identify providers with high waiting times, high volatility, or both.
vowr_survival() estimates time until a provider first breaches the
waiting-time threshold.
surv <- vowr_survival(data)
surv$fit
#> Call: survfit(formula = surv_obj ~ 1)
#>
#> n events median 0.95LCL 0.95UCL
#> [1,] 551 216 NA NA NA
head(surv$surv_data)
#> # A tibble: 6 × 6
#> provider_org_code start_date end_date first_breach status time_days
#> <chr> <date> <date> <date> <dbl> <dbl>
#> 1 8KL73 2024-06-01 2024-08-01 NA 0 61
#> 2 A0C5S 2023-10-01 2025-12-01 NA 0 792
#> 3 A1D1B 2025-04-01 2025-12-01 NA 0 244
#> 4 A1U4J 2024-08-01 2025-12-01 NA 0 487
#> 5 A4M8P 2023-10-01 2025-12-01 2023-11-01 1 31
#> 6 A4Q9X 2024-03-01 2025-12-01 NA 0 640The survival output includes:
- provider start date;
- provider end date;
- first breach date;
- breach status;
- time until breach.
vowr_survival_merge() combines survival output with provider profiles
and risk groups.
surv_profile <- vowr_survival_merge(
surv_result = surv,
profile = profile,
flagged = flagged
)
head(surv_profile)
#> # A tibble: 6 × 13
#> provider_org_code start_date end_date first_breach status time_days
#> <chr> <date> <date> <date> <dbl> <dbl>
#> 1 8KL73 2024-06-01 2024-08-01 NA 0 61
#> 2 A0C5S 2023-10-01 2025-12-01 NA 0 792
#> 3 A1D1B 2025-04-01 2025-12-01 NA 0 244
#> 4 A1U4J 2024-08-01 2025-12-01 NA 0 487
#> 5 A4M8P 2023-10-01 2025-12-01 2023-11-01 1 31
#> 6 A4Q9X 2024-03-01 2025-12-01 NA 0 640
#> # ℹ 7 more variables: provider_org_name <chr>, n_months <int>, mean_wait <dbl>,
#> # median_wait <dbl>, volatility <dbl>, total_backlog <int>, risk_flag <chr>vowr_km_by_risk() then produces Kaplan-Meier curves comparing
time-to-breach across risk groups.
km_plot <- vowr_km_by_risk(surv_profile)
print(km_plot)
This figure assesses whether providers classified into different risk groups show different breach trajectories.
vowr_cox_model() estimates a Cox proportional hazards model using
provider-level risk indicators.
cox_fit <- vowr_cox_model(surv_profile)
summary(cox_fit)
#> Call:
#> survival::coxph(formula = survival::Surv(time_days, status) ~
#> mean_wait + volatility + total_backlog, data = model_data)
#>
#> n= 607, number of events= 234
#>
#> coef exp(coef) se(coef) z Pr(>|z|)
#> mean_wait 2.327e-01 1.262e+00 1.533e-02 15.180 < 2e-16 ***
#> volatility -3.745e-02 9.632e-01 3.924e-02 -0.954 0.34
#> total_backlog 1.166e-07 1.000e+00 2.569e-08 4.537 5.71e-06 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> exp(coef) exp(-coef) lower .95 upper .95
#> mean_wait 1.2620 0.7924 1.2246 1.30
#> volatility 0.9632 1.0382 0.8919 1.04
#> total_backlog 1.0000 1.0000 1.0000 1.00
#>
#> Concordance= 0.92 (se = 0.01 )
#> Likelihood ratio test= 437.8 on 3 df, p=<2e-16
#> Wald test = 399 on 3 df, p=<2e-16
#> Score (logrank) test = 512.8 on 3 df, p=<2e-16The Cox model supports statistical inference about the association between provider characteristics and faster threshold breach.
The full pipeline can also be run with vowr_workflow().
result <- vowr_workflow(data)
names(result)
#> [1] "profile" "flagged" "risk_plot" "survival"
#> [5] "survival_profile" "cox_model" "km_risk_plot"The workflow returns:
| Object | Description |
|---|---|
profile |
Provider-level summary table |
flagged |
Provider profile with risk groups |
risk_plot |
Risk classification plot |
survival |
Survival model output |
survival_profile |
Merged survival-profile-risk dataset |
cox_model |
Cox proportional hazards model |
km_risk_plot |
Kaplan-Meier plot by risk group |
Example:
print(result$km_risk_plot)
summary(result$cox_model)
#> Call:
#> survival::coxph(formula = survival::Surv(time_days, status) ~
#> mean_wait + volatility + total_backlog, data = model_data)
#>
#> n= 607, number of events= 234
#>
#> coef exp(coef) se(coef) z Pr(>|z|)
#> mean_wait 2.327e-01 1.262e+00 1.533e-02 15.180 < 2e-16 ***
#> volatility -3.745e-02 9.632e-01 3.924e-02 -0.954 0.34
#> total_backlog 1.166e-07 1.000e+00 2.569e-08 4.537 5.71e-06 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> exp(coef) exp(-coef) lower .95 upper .95
#> mean_wait 1.2620 0.7924 1.2246 1.30
#> volatility 0.9632 1.0382 0.8919 1.04
#> total_backlog 1.0000 1.0000 1.0000 1.00
#>
#> Concordance= 0.92 (se = 0.01 )
#> Likelihood ratio test= 437.8 on 3 df, p=<2e-16
#> Wald test = 399 on 3 df, p=<2e-16
#> Score (logrank) test = 512.8 on 3 df, p=<2e-16| Function | Purpose | Output |
|---|---|---|
vowr_import() |
Import RTT data | Data frame |
vowr_profile() |
Profile provider waiting-time performance | Summary table |
vowr_flag() |
Classify providers into risk groups | Risk-labelled table |
vowr_plot() |
Visualise provider risk | ggplot object |
vowr_survival() |
Estimate threshold-breach survival model | Survival fit and data |
vowr_survival_merge() |
Merge survival output with profile and risk flags | Analysis dataset |
vowr_km_by_risk() |
Plot Kaplan-Meier curves by risk group | Survival plot |
vowr_cox_model() |
Estimate Cox proportional hazards model | Cox model object |
vowr_workflow() |
Run the full VOWR pipeline | List of outputs |
A typical VOWR analysis may show that:
- stable providers remain below waiting-time thresholds for longer;
- high-risk providers breach earlier;
- critical providers combine high waiting times with high volatility;
- risk groups show different time-to-breach patterns.
This makes VOWR useful for:
- early-warning monitoring;
- provider risk stratification;
- healthcare performance dashboards;
- operational planning;
- reproducible health-services research.
A VOWR analysis can be summarised as:
Provider-level waiting-time profiles were constructed from monthly RTT panel data. Providers were classified into operational risk groups using mean waiting time and volatility. Time-to-threshold breach was examined using Kaplan-Meier survival curves and Cox proportional hazards models.
Current development status:
- package builds successfully;
- package loads successfully;
- tests pass;
- no errors;
- no warnings;
- core workflow operational.
If you use VOWR in research or applied analysis, please cite:
Khan MZ. VOWR: Vital Operational Waiting Risk for Healthcare Systems.
R package version 0.1.0.
Dr Muhammad Zahir Khan
Independent Researcher, United Kingdom
PhD in Applied Statistics
Member, Royal Statistical Society
Email: zahirstat007@gmail.com
ORCID: https://orcid.org/0009-0005-7645-8960
This package is released under the MIT License.
VOWR is intended for statistical analysis, research, and operational monitoring. It should support, not replace, expert judgement in healthcare planning, management, or policy decisions.