In HealthEconomicsHackathon/inflatably: Inflating Costs to Present Value (PV) Using Different Source Rates

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This document covers the basic use of the package inflatably.

Background

When using costs in a cost analysis (e.g. cost-effectiveness calculation) there are several necessary considerations.

• Currency
• Time
• Context

Often the specific cost with respect to time (and currency) is not available and so we need to inflate the observed cost to the desired target value for a given context.

• Currency A $\rightarrow$ currency B
• Time A $\rightarrow$ time B

We fill focus on context-dependent inflation. For further discussion and a focus on multiple currency inflation see [@Turner2019].

For original cost $C_0$, target cost $C_T$ and fraction yearly inflationary factor $i$ for $n$ years, the general inflation formula is as follows.

$$ C_T = (1 + i_{1})(1 + i_{2}) \cdots (1 + i_{n}) \times C_0 $$

Clearly, for the same $i$ each year this simplifies to

$$ C_T = C_0(1 + i)^n $$

The values of $i$ are context dependent, e.g. different for salaries or resources. So, to be more precise, we can explicitly denote the inflation factor as $i^s_{y_j}$ where $s$ indicates the source (corresponding to the context) and $y_j$ is the year from which a inflation factor is taken.

$$ C_T = (1 + i^s_{y_1})(1 + i^s_{y_2}) \cdots (1 + i^s_{y_n}) \times C_0 $$

Example

In this example we inflate the original cost £1 observed in 2014 to 2016 prices using the Hospital and Community Health Services (HCHS) inflation rates.

library(inflatably)

inflation_adjust_cost_data(from_year = 2014,
                           to_year = 2016,
                           from_cost = 1,
                           inflation_df_nm = "HCHS")
1*1.004*1.01

The function returns the inflated cost and also records the inflation source, original year and cost and target year for reproducability.

References

HealthEconomicsHackathon/inflatably documentation built on Dec. 15, 2019, 2:24 a.m.