Parameter Sourcing, Reference Cost Lists and Utility Catalogues When Local Data Are Sparse

อ่านฉบับภาษาไทย (Thai version)

Abstract

A district hospital committee is weighing a new preventive treatment, C, against the current option, A. Its model says C costs 150,000 THB more per patient for 1.00 extra QALY, a year of life weighted by its quality, under a limit of 160,000 THB per QALY. No local study supplied the inputs, so the analyst borrowed them. A reference cost list prices a follow-up visit at 1,200 THB in an older year: 1,380 THB at this year's prices, and 4,140 THB for three visits. Published weights for the sick state that C prevents disagree: 0.75 when the trial patients' answers are scored with Thai public preferences, 0.80 in a published collection of weights from another country, which pushes C to 187,500 THB per QALY. The trial supplies the effect but not the local risk. An evidence ledger records every choice, and a simple test shows which input range could change the decision: the weight, not the visit count.

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Three numbers the model had to borrow

A district hospital committee is deciding whether to offer a new preventive treatment, C, instead of the current option, A. The analyst's model says C costs 150,000 THB more per patient and adds the equivalent of one extra year in full health.

Each year lived is weighted by its quality, from 1 for full health to 0 for death, and the weight is called a utility. So 10 years in a state weighted 0.70 count as 7.0 healthy years, and restoring full health gains 3.0. Such a weighted year is a QALY, a quality-adjusted life year, so C adds 1.00 QALY.

The full lesson is in QALY, DALY and the Utilities Behind Them: What Is Actually Being Measured. It also covers the DALY, a year of healthy life lost instead of gained, which this article does not use. Living 10 years with a condition weighted 0.20 adds 2.0 years lived with disability.

Is that good value? The incremental cost-effectiveness ratio (ICER) is the extra cost divided by the extra health gained against the next best option: here 150,000 THB ÷ 1.00 = 150,000 THB per QALY. The committee compares it with a threshold of 160,000 THB, the most the health system is willing to pay for one QALY, so C looks like good value.

The post that teaches the ICER in full also teaches dominance, the rule that removes an option when another costs less and gives at least as much health. An option D costing 20,000 THB more than C for 0.10 QALY less is dominated by C. This article does not need the rule; both lessons are in ICER, Dominance and the Cost-Effectiveness Plane: Reading the Thai Threshold of 160,000 Baht per QALY.

None of the numbers inside that model came from a study in this district. The analyst borrowed them: a price from a national list of service costs, a weight for the sick state from a published collection of weights, and the effect of C from a trial run elsewhere. Each borrowed number answers someone else's question, so it cannot be dropped into the model just because its source is respectable. This article checks three of them: the cost of a follow-up visit, the weight of the sick state and the risk of the event without C.

All prices, indices, weights and visit counts here are illustrative, not values from a real list.

Write down what the number must mean

Read first on this site. These posts teach in full how to write the question a model input must answer, and how to keep one traceable row for each input. This section keeps only the three inputs that C's model borrowed.

• Finding Model Inputs in the Literature: Match the Estimate to the Question
• Auditable Model Inputs: Build a Parameter Table You Can Trace

Every input of the model is a parameter: a quantity that controls the calculation, such as the price of a visit or the weight of the sick state. A precise number for a different quantity is still the wrong input, so the analyst writes down what each one must mean before searching [1]. For the visit, that is the extra follow-up visits a patient on C makes at a district clinic, priced as the health system pays for them, in this year's money.

That definition rules candidates out quickly. A list price for a specialist visit at a teaching hospital is a different service. An incidence of 2 new cases per 1,000 person-years in the whole district is a rate, events per person-time among everyone (see Incidence, Prevalence and the Right Denominator: The Epidemiology Beneath Cost-of-Illness and Markov Models), not the risk among the patients offered C. A weight needs four things named: the health state, the questionnaire that described it, who answered it and whose preferences scored it.

A cost list gives a price, not a visit count

Read first on this site. This post teaches in full how a cost is restated from one price year to another with a price index, and the checks an entry in a national cost list needs before use. It also teaches discounting, which converts a future cost into its value today. At 3% a cost of 1,834 THB due in year 3 is worth 1,678 THB today, a step this section does not need, so it keeps only the visit that C adds.

• Whose cost, in which year: the foundation article on costing and price years

A district hospital rarely knows what one of its visits costs: the staff time, the room, the tests and a share of the running costs. So the analyst looks the price up in a national list of standard prices for health services, built from costing studies in many hospitals. The list gives 1,200 THB for a follow-up visit at a district hospital. A list like this is called a reference cost list [2].

The list's price was set in an earlier year. The consumer price index (CPI) stood at 100 in that year and stands at 115 now, on the same base, so the price is multiplied by 115/100 to restate it.

How many visits a patient makes is a separate input. Local clinic records show 3 extra visits per patient on C on average, and the clinics' own averages run from 2 to 4. So the range says how unsure the district's average is, not how much single patients differ. The cost of these visits is part of C's 150,000 THB extra.

Three checks before the price enters the model

The fit check in the last step asks three questions: the same setting, the same service unit, the same cost content. This list passes all three, but a teaching-hospital price would fail the first, and a list without buildings and equipment the third. The answers decide where a price goes.

When all three match, the price enters the base case, the main analysis that the committee reads first. When one check fails, the price can still be used, but only in a named scenario: a side analysis that states the assumption it makes. When several fail, the list answers a different question, so the input is marked as research needed. It is not adjusted until it looks right.

# One follow-up visit from the reference cost list, restated to this year's prices, then counted.
source_cost <- 1200    # THB per visit, in the list's price year
source_cpi <- 100      # price index in the list's year
target_cpi <- 115      # price index this year, on the same base
visits <- 3            # extra visits per patient on C, from local clinic records
ratio <- target_cpi / source_cpi
restated <- source_cost * ratio
cat("Price index ratio:", formatC(ratio, format = "f", digits = 2), "\n")
cat("Restated THB per visit:", restated, "| short by", restated - source_cost, "as listed\n")
cat("Base-case visit total THB:", restated * visits, "| as listed:", source_cost * visits, "\n")
cat("Two-visit scenario THB:", restated * 2, "\n")
cat("Four-visit scenario THB:", restated * 4, "\n")
cat("Ten more index points at 3 visits add THB:", source_cost / source_cpi * 10 * visits, "\n")

Price index ratio: 1.15
Restated THB per visit: 1380 | short by 180 as listed
Base-case visit total THB: 4140 | as listed: 3600
Two-visit scenario THB: 2760
Four-visit scenario THB: 5520
Ten more index points at 3 visits add THB: 360

# Recap numbers for three ideas the linked posts teach in full; this article does not use them.
years <- 10       # years lived with a condition
weight <- 0.20    # its disability weight
cat("Years lived with disability:", formatC(years * weight, format = "f", digits = 1), "\n")
d_more_cost <- 20000   # THB option D costs more than C
d_less_qaly <- 0.10    # QALY option D gives less than C
cat("C dominates D:", d_more_cost > 0 && d_less_qaly > 0, "\n")
cost <- 1834      # THB due in year 3
rate <- 0.03      # discount rate per year
cat("Worth today THB:", round(cost / (1 + rate)^3), "\n")

Years lived with disability: 2.0
C dominates D: TRUE
Worth today THB: 1678

A utility catalogue gives a weight, and someone's preferences with it

Read first on this site. This post teaches in full how a questionnaire and a country's scoring table turn a patient's answers into a weight, and what to write beside the weight. This section keeps only the weight of the sick state that C prevents.

• QALY, DALY and the Utilities Behind Them: What Is Actually Being Measured

C's extra QALY comes from the sick state it prevents. In the model, a patient on C spends 4.0 fewer years in that state than a patient on A, a figure the model builds from the trial's effect and the district's own risk (the third input, below). Each of those years counts as only a fraction of a healthy year, equal to the state's weight, so the gain is 4.0 × (1 − weight). The whole result therefore rests mainly on the weight of the sick state.

No Thai study has measured this state, so the analyst looked for published weights and found three candidates. The trial's patients described their state on the EQ-5D-5L, a standard five-question form, and the Thai value set, the scoring table built from the Thai public's preferences [3], turns their answers into 0.75. A published collection from another country, which gathers weights for many conditions from many studies, lists 0.80 for the same diagnosis, scored with that country's preferences; a small study abroad reports 0.70.

A published collection like the second source is called a utility catalogue. With the Thai 0.75, each year in the sick state lacks 0.25 of a healthy year. So C gains 4.0 × 0.25 = 1.00 QALY and costs 150,000 ÷ 1.00 = 150,000 THB per QALY. With the other country's 0.80, each year lacks only 0.20: C gains 4.0 × 0.20 = 0.80 QALY, and 150,000 ÷ 0.80 = 187,500 THB per QALY, above the 160,000 THB threshold.

The same model with a different catalogue entry gives the committee a different answer. So a catalogue is where the search for a weight starts, not a certificate that its number fits this model.

A weight is checked like a price. Which questionnaire described the state, and which version of it? Does the catalogue's health state match the model's, or only its diagnosis? Whose preferences scored it: value sets for the same questionnaire differ from country to country, so a weight from another country's public brings that country's preferences along with its arithmetic [4].

# Where C's 1.00 extra QALY comes from: years spared in the sick state times the health each year lacks.
years_spared <- 4.0      # fewer years in the sick state on C than on A, per patient (the model)
extra_cost <- 150000     # THB more for C than for A, per patient
# The same rule as the QALY recap: 10 years at 0.70 count as 7.0 healthy years, so full health adds 3.0.
cat("10 years at 0.70:", formatC(10 * 0.70, format = "f", digits = 1), "QALYs | gain",
    formatC(10 * (1 - 0.70), format = "f", digits = 1), "\n")
for (w in c(0.75, 0.80, 0.70)) {   # Thai value set; another country's catalogue; a third source
  lost <- 1 - w
  gain <- years_spared * lost
  cat("Weight", formatC(w, format = "f", digits = 2),
      "| lost per year", formatC(lost, format = "f", digits = 2),
      "| QALYs gained", formatC(gain, format = "f", digits = 2),
      "| THB per QALY", format(extra_cost / gain, big.mark = ","), "\n")
}

10 years at 0.70: 7.0 QALYs | gain 3.0
Weight 0.75 | lost per year 0.25 | QALYs gained 1.00 | THB per QALY 150,000
Weight 0.80 | lost per year 0.20 | QALYs gained 0.80 | THB per QALY 187,500
Weight 0.70 | lost per year 0.30 | QALYs gained 1.20 | THB per QALY 125,000

The effect can travel; the local risk usually cannot

Read first on this site. These posts teach in full how to pair a trial's ratio with a local risk, and how to judge how far an effect can be trusted across all the trials found. This section keeps only what the trial of C supplies.

• Finding Model Inputs in the Literature: Match the Estimate to the Question
• Beyond the Evidence Pyramid: GRADE Certainty and Choosing Effectiveness Inputs for Economic Models

The trial of C supplies the effect, not the third input, the risk of the event without C. In the trial, 8 of 66 treated patients and 13 of 60 controls had the event, 12.12% against 21.67%. The risk on C divided by the risk on the controls is the risk ratio, 0.56, with a 95% confidence interval from 0.25 to 1.26 that shows how unsure the trial still is. In C's model, this effect applied to the district's own risk produces the 4.0 years a patient on C avoids in the sick state.

Each kind of input has its own best source, so no single ranking of study designs serves them all. The effect needs comparative evidence like this trial, ideally every trial a systematic search can find, with how far each outcome's evidence can be trusted (its certainty) judged outcome by outcome. The risk without C needs representative local records, a price needs costing studies or a cost list, and a weight needs preferences valued with a recognised method. Local billing records, however many, cannot show what C does.

The 21.67% is a different kind of number. It describes 60 trial patients, chosen by the trial's entry rules and followed for the trial's length of time, not the patients this district would treat. So a model usually takes the relative effect, a ratio such as this risk ratio, from the trials and the risk without treatment from local records [1]. Those records need the right people, the right denominator and the same follow-up; the analyst found such records at the district hospital and kept the trial's 21.67% only as a check.

Whether a number can travel from the setting where it was measured to the decision at hand is called transportability. Relative effects often travel reasonably well; local risks, prices and preferences often do not, which is why the 1,200 THB and the 0.80 needed checking at all.

# What the trial of C can supply: its two risks and the risk ratio with its 95% confidence interval.
events <- c(C = 8, A = 13)
patients <- c(C = 66, A = 60)
risk <- events / patients
rr <- risk[["C"]] / risk[["A"]]
se <- sqrt(sum(1 / events) - sum(1 / patients))
ci <- exp(log(rr) + c(-1, 1) * qnorm(0.975) * se)
cat("Risk on C %:", formatC(100 * risk[["C"]], format = "f", digits = 2),
    "| risk on A %:", formatC(100 * risk[["A"]], format = "f", digits = 2), "\n")
cat("Risk ratio:", formatC(rr, format = "f", digits = 2), "\n")
cat("95% CI:", formatC(ci, format = "f", digits = 2), "\n")
rate <- 2 / 1000     # the district's new cases per person-year: a rate, not this risk
cat("District rate per person-year:", rate, "\n")

Risk on C %: 12.12 | risk on A %: 21.67
Risk ratio: 0.56
95% CI: 0.25 1.26
District rate per person-year: 0.002

Missing, misfit or too uncertain

Not every gap is the same, and the response depends on which one it is. Evidence is unavailable when a documented search finds nothing, as for local patients' own answers about the sick state. It is inapplicable when it answers a different question, as the other country's 0.80 does. It is imprecise when it answers the right question with a wide range, as the clinic averages of 2 to 4 visits do.

Each calls for its own response. A missing number needs another kind of source or structured expert judgement, a misfit one belongs in a named scenario, and an imprecise one has its whole range carried through the model [5]. More decimal places fix none of them.

When nothing has been measured, the analyst can ask experts in a planned way. Several clinicians answer the same written question with a lowest, a most likely and a highest value, and a rule fixed in advance combines their answers; this is called structured expert elicitation. Its result is the experts' judgement with its spread, not a newly observed fact, and the ledger records it that way.

Which gap could change the committee's answer?

Read first on this site. This post teaches sensitivity analysis for health economic evaluation in full, one input at a time and all inputs together. This section keeps only the two inputs of C's model given a range here.

• Uncertainty and Sensitivity Analysis in Health Economic Evaluation: Principles, Tools, and Application

Every input is uncertain and research money is limited, so the useful question is which uncertainty could change the decision. C sits at 150,000 THB per QALY against a threshold of 160,000 THB. With 1.00 QALY gained, that leaves 160,000 × 1.00 − 150,000 = 10,000 THB of room before the answer flips.

Take the visit count first. With 2 visits instead of 3, C's extra cost falls by one visit's 1,380 THB to 148,620 THB, and with 4 it rises to 151,380 THB. With 1.00 QALY gained, those are also its costs per QALY, both under the threshold. To use up the 10,000 THB of room, each patient would need 10,000 ÷ 1,380 = 7.25 more visits, far outside the records.

Now the weight. C stays under the threshold only while it gains at least 150,000 ÷ 160,000 = 0.938 QALY. That needs a weight of at most 1 − 0.938 ÷ 4.0 = 0.766 for the sick state. The Thai 0.75 sits just under that line and the other country's 0.80 above it, while the small study's 0.70 gives 1.20 QALYs and 125,000 THB per QALY.

The value of an input at which the decision flips is called its switch value: 7.25 extra visits for the count, a weight of 0.766 for the sick state.

Where the research money goes

So new evidence is worth buying for the weight, not the visits. A small survey of local patients in the sick state, scored with the Thai value set, would show which side of 0.766 they fall on. A survey costs money and time, so it is worth buying only because its answer could flip the decision. The visit count stays in the base case as a range, and the other country's 0.80 is reported as a named scenario.

This test covers the two inputs given ranges here. The trial's own range, 0.25 to 1.26, reaches past 1, the point where C would spare no years at all. So the effect is the next input to test. Probabilistic Sensitivity Analysis: From Parameter Distributions to CEAC shows how a model carries several such ranges at once.

# Which input could change the committee's answer? Threshold 160,000 THB per QALY.
extra_cost <- 150000; gain <- 1.00; threshold <- 160000
visit_price <- 1380     # THB per visit; the base case has 3 visits
for (v in c(2, 4)) cat("Visits", v, "| extra cost THB", extra_cost + (v - 3) * visit_price, "\n")
room <- threshold * gain - extra_cost
cat("Room under the threshold THB:", room, "| extra visits it takes:",
    formatC(room / visit_price, format = "f", digits = 2), "\n")
need <- extra_cost / threshold
cat("QALYs gained needed:", formatC(need, format = "f", digits = 3), "\n")
cat("Highest sick-state weight that keeps C under the threshold:",
    formatC(1 - need / 4.0, format = "f", digits = 3), "\n")

Visits 2 | extra cost THB 148620
Visits 4 | extra cost THB 151380
Room under the threshold THB: 10000 | extra visits it takes: 7.25
QALYs gained needed: 0.938
Highest sick-state weight that keeps C under the threshold: 0.766

Write each choice where the next analyst can find it

Read first on this site. This post teaches in full how to build a table with one traceable row for each input. This section keeps only the rows of C's model and where each one goes.

• Auditable Model Inputs: Build a Parameter Table You Can Trace

A year from now someone will ask why the model used the Thai 0.75 and not the other country's weight. The answer has to be on record, not in the analyst's memory. So for every input the analyst keeps one row: what the parameter means, where the search looked and when, the source and its version, the estimate and its range, every change made to it and where it went. That record is called an evidence ledger, and keeping it is what [1] recommends.

Here is the ledger for C, one row per input, filled in from the sections above. The table shows the five columns the committee needs first. The full ledger also keeps each search, its date and each source's version.

Before a source earns its row, two judgements are kept apart: bias asks whether it measured its own question well, applicability asks whether that question is ours. A careful study from another country can score well on the first and badly on the second, which is exactly the story of the 0.80.

The next article, Early Health Technology Assessment, Headroom Pricing and Benefit-Package Decisions, works with even fewer local numbers: a technology that has no trial of its own yet.

The series, in learning order

1. Health Economics Series Guide: Read the Evidence Before the Costs
2. Incidence, Prevalence and the Right Denominator: The Epidemiology Beneath Cost-of-Illness and Markov Models
3. Design, Model and Estimand: What Each Study Design Can Actually Estimate
4. Risk Ratio, Odds Ratio, Risk Difference and NNT: One 2×2 Table, Four Answers
5. The Hazard Ratio Is Not a Risk Ratio: Proportional Hazards, Restricted Mean Survival Time and Model Inputs
6. Chance, Bias and Confounding: Why an Association Is Not Yet a Treatment Effect
7. Beyond the Evidence Pyramid: GRADE Certainty and Choosing Effectiveness Inputs for Economic Models
8. From Sensitivity to Cost per Case Detected: Predictive Values, Prevalence and the Economics of Screening
9. Whose Cost, in Which Year? Perspective, Opportunity Cost, Inflation and Discounting
10. QALY, DALY and the Utilities Behind Them: What Is Actually Being Measured
11. ICER, Dominance and the Cost-Effectiveness Plane: Reading the Thai Threshold of 160,000 Baht per QALY
12. Decision Trees, Markov Cohorts and Probabilistic Sensitivity Analysis: How a Model Turns Evidence into a Decision
13. Cost-Effective Is Not Affordable, and Efficient Is Not Fair: Budget Impact and Equity
14. Parameter Sourcing, Reference Cost Lists and Utility Catalogues When Local Data Are Sparse (this article)
15. Early Health Technology Assessment, Headroom Pricing and Benefit-Package Decisions
16. Communicating Health Economic Evidence: From Model Outputs to Policy Briefs

Related in the wiki: Incidence, Prevalence and the Right Denominator: The Epidemiology Beneath Cost-of-Illness and Markov Models · Beyond the Evidence Pyramid: GRADE Certainty and Choosing Effectiveness Inputs for Economic Models · Whose Cost, in Which Year? Perspective, Opportunity Cost, Inflation and Discounting · QALY, DALY and the Utilities Behind Them: What Is Actually Being Measured · Decision Trees, Markov Cohorts and Probabilistic Sensitivity Analysis: How a Model Turns Evidence into a Decision