Objective 3 Long term projections of RRT population and payments of the RRT

error structure, a log link function and an offset of log (person risk‐time) which was suggested by Carstensen (2007). This was done by adding a drift term (a combined slope for period and cohort effects) with a selected number of

parameters (or knots) to either period or cohort effect. Placement of the drift on period or cohort depended on the subject of interest.

In this study, the main focus was on the effect of period, therefore the drift was allocated to the period variable. In the analysis, a point of period was fixed, and cohort fitted values were constrained to have zero slope. Age effect was then interpreted as age specific rate regarding the reference period.

As a result, the age‐period model was written as the first derivative functions of age, f(a) and period, g(p)as:

ln[(a,p)] = f(a) + g(p)

When a non‐linear regression model is estimated, the multiplicative age‐period model can be fitted by choosing a reference period p0 and a constraint g(p0)=0.

The model can be expressed as the function of rate as:

ln [(a,p)] = fp0 (a) +  (p-p0) + g(p);

where fp0 (a) is the function for age, denoting age‐specific rates in the reference period, p0;  is the slope of the log‐linear trend in period (the drift); and g( p) is the period function, which can be interpreted as a log relative risk of any period compared to the reference period, p0.

All tabulations of cohorts and population, descriptive analysis, and age‐period‐

cohort modelling were conducted using Stata version 12. Only goodness‐of‐fit in age‐period‐cohort analyses was assessed using R studio. All confidence

intervals are 95% confidence intervals.

4.4.3 Objective 3 Long term projections of RRT population and payments of the RRT programme

Method of objective 3: cost modelling and time-series projection of RRT population

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The method of this study involved three main steps. First, the study modelled yearly numbers of patients in the three RRT modalities into the future. Next, it estimated the annual costs of the RRT programme from the public payer’s perspective using the NHSO claims data. Finally, an estimated figure of the future budget needs was forecast.

4.4.3.1 Forecasting numbers of RRT population

This section looks at the method to forecast future numbers of RRT patients.

The auto‐regressive integrated moving average (ARIMA) technique was taken to develop a set of models to predict numbers of patients enrolling in the RRT programme by each modality: PD, HD, and KT.

i. Data source

Information on patients who registered in the RRT programme (including peritoneal dialysis, hemodialysis, and functioning kidney transplant) in the period of fiscal year 2008 to 2013 (1 October 2007‐30 September 2013) were obtained from the Disease Management System of the NHSO. The data

contained claims data of individuals, for example encrypted identification number, modality (PD, HD, or KT), registration date, exit from the programme date with the reason, and dispensed medications.

ii. Study population

Patients of all ages who were registered and retained in the RRT programme between the fiscal years 2008 and 2013 were included. This study also

identified anyone who had modality changes including kidney transplant during the study period. It excluded patients who had a history of temporary treatment with hemodialysis in a period shorter than 30 days and self‐pay HD patients. KT patients who had transplantation before the RRT programme started in 2008, although they received free erythropoietin from the NHSO, were excluded. Since the RRT programme is designed to cover patients with chronic kidney disease, those who are diagnosed with acute renal failure are not included in the database.

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iii. Data analysis

This study employed ARIMA modelling to forecast numbers of the RRT population by RRT modality consisting of 1) peritoneal dialysis, 2) hemodialysis, and 3) kidney transplant. In order to construct time series datasets, patient‐level data were collapsed into a monthly basis for each RRT modality.

Time‐series is a technique that can be used to predict future behaviour of a variable of interest by taking previous observations as the basis. The analysis of a time‐series model does not count on various independent variables that may influence the variable of interest (Linden, Adams et al. 2003). In this study, forecasting models are used to predict numbers of renal replacement therapy users in the next ten‐year period.

In healthcare, the time‐series modelling technique has been widely used in many areas such as medicine, epidemiology, and health services. Generally, time‐series analysis is used to discover the historical pattern in data series and forecast that pattern into the future (Makridakis, Wheelwright et al. 1998;

Linden, Adams et al. 2003). There are many categories of time‐series technique, of which the auto‐regressive integrated moving average (ARIMA, so called Box‐

Jenkins) is shown to be useful when the series exhibit any trend or seasonal variation (Makridakis, Wheelwright et al. 1998; You, Hoy et al. 2002; Linden, Adams et al. 2003).

A stationary series is the key feature that needs to be accomplished before fitting an ARIMA model. This can be done by taking first differences, that is, making a new series of the present value less the past value (Xt ‐ Xt‐1). After a time series has been stationarised by differencing, the next step is to determine whether AR (autoregressive) or MA (moving average) terms are needed to correct any autocorrelation that remains in the differenced series (Nau 2014).

Numbers of AR and MA terms can be identified by looking at the

autocorrelation function (ACF) and partial autocorrelation (PACF) plots of the original and differenced series. An ARIMA model is always represented by ARIMA(p,d,q), where p is the number of autoregressive(AR) parameter, d is the

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order of differencing (or integration, I) needed to remove the non‐stationary from the series, and q is the number of moving average(MA) parameter (Linden, Adams et al. 2003).

Makridakis, Wheelwright et al. (1998) suggested an approach which was applied to Box‐Jenkins’ time series modelling. They propose three phases of ARIMA modelling; Phase 1: Identification, Phase 2: Estimation and testing, and Phase 3: Forecasting. First, the identification, the data are plotted against time and determined if a transformation of the data is needed to stabilise the variance. If the data seem non‐stationary, the first differences of the data are taken until the data are stationary. Next, the estimation and testing, when the stationarity has been achieved, examine the autocorrelation function (ACF) and partial autocorrelation (PACF) plots to determine numbers of appropriate AR(p) or MA(q) terms for the appropriate model. After that, the chosen model(s) is fitted, and the Akaike Information Criterion (AIC) is used to determine a better model. Then the residuals from the chosen model are checked by plotting the ACF of the residuals, and a portmanteau test of residuals conducted. If they do not look like white noise (residuals are

uncorrelated or independently distributed), a modified model is tried until the white noise is achieved. Finally, the selected model can be used to calculate forecasts.

4.4.3.2 Estimating annual costs of the RRT programme

The cost of the RRT programme was conducted from the NHSO’s perspective.

Cost objects are PD, HD, and KT for the one‐year period. Only direct costs accounting for RRT services were included. Indirect costs such as travel costs and other costs impacting on patients’ families were excluded. The RRT programme’s claims and reimbursements in 2014 were acquired from the NHSO. Data were summarised into payments by each reimbursed item on a monthly basis by the NHSO. Material costs, labour costs, and investment costs, although were not separately identified in the NHSO’s payments, were

estimated here using proportions from selected past studies in order to provide

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each element of the cost from the public payer’s perspective. Costs were measured and reported in Thai Baht (50 Baht  ₤1, year 2014 price).

Table 4‐3 shows proportions of the material cost, labour cost, and capitation cost used in estimating their amounts in the total payment of each RRT modality.

Table 4‐3  Proportions (%) of three types of costs by RRT modality 

PD^1/ HD^2/ KT^3/

Material costs 74 43 79

Labour costs 25 40 18

Capital costs 1 13 3

PD=peritoneal dialysis, HD= hemodialysis, KT =kidney transplant

1/ Laonapaporn, Punthunane et al. (2014)

2/ Tisayaticom, Patcharanarumol et al. (2003)

3/ Suksamran, Kongsin et al. (2012)

The researcher used these figures to calculate the unit cost per patient‐year composed of the three main cost objects: material, labour, and capital.

4.4.3.3 Future budget needs

Results from the previous sections (costs and numbers of patients by each RRT modality) were drawn on to estimate future budget needs 2014‐2023. The estimated future costs for the RRT modalities were further used to assess effects of four cost drivers: number of patients, labour costs, material costs, and capital costs. This is to explain effects of these drivers: how they influence the unit cost of each RRT modality, and how to control programme costs during the ten‐year period. In this study, forecast budget needs are presented and

discussed in terms of 2014‐constant Baht.

After obtaining the predicted numbers of renal replacement therapy users, the total cost of each modality over the next 10 years (to the end of 2023) was estimated by multiplying the number of users by unit costs. Since there might be policy changes in the future, total costs of the programme were calculated under different scenarios.

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Selected scenarios

Three scenarios that were most likely to occur were obtained from interviews

 Scenario 1 assumed material costs would remain unchanged.

 Scenario 2 assumed material costs would increase.

 Scenario 3 assumed material costs would decrease.

4.5 Summary of objectives and methodology used in the study