| Title: | Projecting Customer Retention Based on Fader and Hardie Probability Models |
|---|---|
| Description: | Project Customer Retention based on Beta Geometric, Beta Discrete Weibull and Latent Class Discrete Weibull Models.This package is based on Fader and Hardie (2007) <doi:10.1002/dir.20074> and Fader and Hardie et al. (2018) <doi:10.1016/j.intmar.2018.01.002>. |
| Authors: | Srihari Jaganathan |
| Maintainer: | Srihari Jaganathan <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2.0 |
| Built: | 2024-11-05 02:55:53 UTC |
| Source: | https://github.com/sriharitn/foretell |
BdW is a beta discrete weibull model implemented based on Fader and Hardie probability based projection methedology. The survivor function for BdW is
BdW(surv_value, h, lower = c(0.001, 0.001, 0.001), upper = c(10000, 10000, 10000))BdW(surv_value, h, lower = c(0.001, 0.001, 0.001), upper = c(10000, 10000, 10000))
surv_value |
a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100 |
h |
forecasting horizon |
lower |
lower limit used in |
upper |
upper limit used in |
fitted: |
Fitted values based on historical data |
projected: |
Projected |
max.likelihood: |
Maximum Likelihood of Beta discrete Weibull |
params - a, b and c:
|
Returns a and b paramters from maximum likelihood estimation for beta distribution and c |
Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.
Fader P, Hardie B, Liu Y, Davin J, Steenburgh T. "How to Project Customer Retention" Revisited: The Role of Duration Dependence. Journal of Interactive Marketing. 2018;43:1-16.
surv_value <- c(100,86.9,74.3,65.3,59.3) h <- 6 BdW(surv_value,h)surv_value <- c(100,86.9,74.3,65.3,59.3) h <- 6 BdW(surv_value,h)
BG is a beta geometric model implemented based on Fader and Hardie probability based projection methedology. The survivor function for BG is
BG(surv_value, h, lower = c(0.001, 0.001))BG(surv_value, h, lower = c(0.001, 0.001))
surv_value |
a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100 |
h |
forecasting horizon |
lower |
lower limit used in |
fitted: |
Fitted values based on historical data |
projected: |
Projected |
max.likelihood: |
Maximum Likelihood of Beta Geometric |
params - a, b:
|
Returns a and b paramters from maximum likelihood estimation for beta distribution |
Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.
surv_value <- c(100,86.9,74.3,65.3,59.3) h <- 6 BG(surv_value,h)surv_value <- c(100,86.9,74.3,65.3,59.3) h <- 6 BG(surv_value,h)
A dataset containing customer retention.
data(customer_retention)data(customer_retention)
A data frame 13 observations and 3 variables.
Time in years
% of regular customers surviving
% of high_end customers surviving
Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.
exltrend generates Microsoft(r) Excel(r) based linear, logarthmic, exponential, polynomial of order 2, power trends.
exltrend(surv_value, h)exltrend(surv_value, h)
surv_value |
a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100 |
h |
forecasting horizon |
fitted: |
A data frame of fitted Values based on historical data for linear (lin.p), exponential (exp.p), logarthmic (log.p), polynomial (poly.p) of order 2 and power (pow.p) trends. |
projected: |
A data frame of projected |
surv_value <- c(100,86.9,74.3,65.3,59.3) h <- 6 exltrend(surv_value,h)surv_value <- c(100,86.9,74.3,65.3,59.3) h <- 6 exltrend(surv_value,h)
LCW is a latent class weibull model implementation based on Fader and Hardie probability based projection methedology. The survivor function for LCW is
LCW(surv_value, h, lower = c(0.001, 0.001, 0.001, 0.001, 0.001), upper = c(0.99999, 10000, 0.999999, 10000, 0.99999))LCW(surv_value, h, lower = c(0.001, 0.001, 0.001, 0.001, 0.001), upper = c(0.99999, 10000, 0.999999, 10000, 0.99999))
surv_value |
a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100 |
h |
forecasting horizon |
lower |
lower limit used in |
upper |
upper limit used in |
fitted: |
Fitted Values based on historical data |
projected: |
Projected |
max.likelihood: |
Maximum Likelihood of LCW |
params - t1, t2, c1, c2, w:
|
Returns t1,c1,t2,c2,w paramters from maximum likelihood estimation |
Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.
Fader P, Hardie B, Liu Y, Davin J, Steenburgh T. "How to Project Customer Retention" Revisited: The Role of Duration Dependence. Journal of Interactive Marketing. 2018;43:1-16.
surv_value <- c(100,86.9,74.3,65.3,59.3,55.1,51.7,49.1,46.8,44.5,42.7,40.9,39.4) h <- 6 LCW(surv_value,h)surv_value <- c(100,86.9,74.3,65.3,59.3,55.1,51.7,49.1,46.8,44.5,42.7,40.9,39.4) h <- 6 LCW(surv_value,h)
A dataset containing drug persistency of patients in different therapeutic classes.
data(persistency_data)data(persistency_data)
A data frame 334 observatios and 3 variables:
Type of therapy. Unique values include: "Hypertension" "Occular Hypertension"
"Statin" "Insulin" "Epilepsy" "RA" "Osteoporosis" "Alzheimer""ADHD"
"Atrial Fibrillation". See references below.
Data was extracted using https://automeris.io/WebPlotDigitizer/
and discretized using akima package.
Time Period
% Patients retained
Hypertension: Solomon M, Goldman D, Joyce G, Escarce J. Cost Sharing and the Initiation of Drug Therapy for the Chronically Ill.Archives of Internal Medicine. 2009;169(8):740-748.
Occular Hypertension: Campbell J, Schwartz G, LaBounty B, Kowalski J, Patel. Patient adherence and persistence with topical ocular hypotensive therapy in real-world practice: a comparison of bimatoprost 0.01% and travoprost Z 0.004% ophthalmic solutions. Clinical Ophthalmology. 2014;8:927-935.
Statin: Kiss Z, Nagy L, Reiber I, Paragh G, Molnar M, Rokszin G et al. Persistence with statin therapy in Hungary. Archives of Medical Science. 2013;9(3):409-417.
Insulin: Roussel R, Charbonnel B, Behar M, Gourmelen J, Emery C, Detournay B. Persistence with Insulin Therapy in Patients with Type 2 Diabetes in France: An Insurance Claims Study. Diabetes Therapy. 2016;7(3):537-549.
Epilepsy: Lai E, Hsieh C, Su C, Yang Y, Huang C, Lin S et al. Comparative persistence of antiepileptic drugs in patients with epilepsy: A STROBE-compliant retrospective cohort study. Medicine. 2016;95(35):e4481.
RA: Neovius M, Arkema E, Olsson H, Eriksson J, Kristensen L, Simard J et al. Drug survival on TNF inhibitors in patients with rheumatoid arthritis comparison of adalimumab, etanercept and infliximab. Annals of the Rheumatic Diseases. 2013;74(2):354-360.
Osteoporosis: Kishimoto H, Maehara M. Compliance and persistence with daily, weekly, and monthly bisphosphonates for osteoporosis in Japan: analysis of data from the CISA. Archives of Osteoporosis. 2015;10(27):1-6.
Alzheimer: Suh D, Thomas S, Valiyeva E, Arcona S, Vo L. Drug persistency of two cholinesterase inhibitors: rivastigmine versus donepezil in elderly patients with Alzheimer's disease. Drugs & Aging. 2005;22(8):695-707.
ADHD: Beau-Lejdstrom R, Douglas I, Evans S, Smeeth L. Latest trends in ADHD drug prescribing patterns in children in the UK: prevalence, incidence and persistence. BMJ Open. 2016;6(6):1-8.
Atrial Fibrillation: Gomes T, Mamdani M, Holbrook A, Paterson J, Juurlink D. Persistence With Therapy Among Patients Treated With Warfarin for Atrial Fibrillation. Archives of Internal Medicine. 2012;172(21):1687-1689.