VOWR

Vital Operational Waiting Risk for Healthcare Systems

Overview

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.

Why VOWR?

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?

Installation

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")

Required data structure

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

Quick start

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        16584

Provider profiling

vowr_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.

Risk classification

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                           36

Risk 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

Risk visualisation

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.

Survival analysis

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       640

The survival output includes:

provider start date;
provider end date;
first breach date;
breach status;
time until breach.

Kaplan-Meier comparison by risk group

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.

Cox proportional hazards model

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-16

The Cox model supports statistical inference about the association between provider characteristics and faster threshold breach.

One-command workflow

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

Main functions

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

Interpretation

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.

Example reporting statement

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.

Development status

Current development status:

package builds successfully;
package loads successfully;
tests pass;
no errors;
no warnings;
core workflow operational.

Citation

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.

Author

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

License

This package is released under the MIT License.

Disclaimer

VOWR is intended for statistical analysis, research, and operational monitoring. It should support, not replace, expert judgement in healthcare planning, management, or policy decisions.