llr_score: Compute the log-likelihood ratio score

In vlad: Variable Life Adjusted Display and Other Risk-Adjusted Quality Control Charts

Description

Compute the log-likelihood ratio score.

Usage

llr_score(df, coeff, R0 = 1, RA = 2, yemp = TRUE)

Arguments

df	Data Frame. First column are Parsonnet Score values within a range of 0 to 100 representing the preoperative patient risk. The second column are binary (0/1) outcome values of each operation.
coeff	Numeric Vector. Estimated coefficients alpha and beta from the binary logistic regression model.
R0	Double. Odds ratio of death under the null hypotheses.
RA	Double. Odds ratio of death under the alternative hypotheses. Detecting deterioration in performance with increased mortality risk by doubling the odds Ratio RA = 2. Detecting improvement in performance with decreased mortality risk by halving the odds ratio of death RA = 1/2.
yemp	Logical. If TRUE use observed outcome value, if FALSE use estimated binary logistc regression model.

Value

Returns a single value which is the log-likelihood ratio score.

Author(s)

Philipp Wittenberg

References

Steiner SH, Cook RJ, Farewell VT and Treasure T (2000). Monitoring surgical performance using risk-adjusted cumulative sum charts. Biostatistics, 1(4), pp. 441–452.

Steiner S (2014). Risk-Adjusted Monitoring of Outcomes in Health Care. In Lawless JF (ed.), Statistics in Action, pp. 225–242. Informa UK Limited.

Rigdon SE and Fricker RD (2015). Health Surveillance. In Chen DG and Wilson J (eds) Innovative Statistical Methods for Public Health Data, pp. 203–249. Springer, Cham.

Examples

## Not run: 
library(vlad)
## see Steiner et al. (2000) p. 446 or Steiner (2014) p. 234
coeff <- c("(Intercept)" = -3.68, "Parsonnet" = 0.077)
## Log-likelihood ratio scores for detecting an increase in the failure rate:
## low risk patients with a Parsonnet score of zero

llr_score(df = data.frame(as.integer(0), 0), coeff = coeff, RA = 2)
llr_score(df = data.frame(as.integer(0), 1), coeff = coeff, RA = 2)

## higher risk patients with a Parsonnet score of 50
llr_score(df = data.frame(as.integer(50), 0), coeff = coeff, RA = 2)
llr_score(df = data.frame(as.integer(50), 1), coeff = coeff, RA = 2)

## see Steiner (2014) p. 234
## Log-likelihood ratio scores for detecting an decrease in the failure rate:
## low risk patients with a Parsonnet score of zero
llr_score(df = data.frame(as.integer(0), 0), coeff = coeff, RA = 1/2)
llr_score(df = data.frame(as.integer(0), 1), coeff = coeff, RA = 1/2)

## higher risk patients with a Parsonnet score of 50
llr_score(df = data.frame(as.integer(50), 0), coeff = coeff, RA = 1/2)
llr_score(df = data.frame(as.integer(50), 1), coeff = coeff, RA = 1/2)

## see Rigdon and Fricker p. 225 and 226
## detecting an increase in the failure rate:
coeff <- c("(Intercept)" = -3.67, "Parsonnet" = 0.077)
df <- data.frame(Parsonnet = c(19L, 19L, 0L, 0L), status = c(0, 1, 0, 1))
lapply(seq_along(df$Parsonnet), function(i) round(llr_score(df = df[i, ], coeff = coeff,
 RA = 2), 4))

## detecting an decrease in the failure rate:
round(llr_score(df = data.frame(19L, 0), coeff = coeff, RA = 1/2), 5)

## End(Not run)

Example output

[1] -0.02430466
[1] 0.6688425
[1] -0.4333383
[1] 0.2598089
[1] 0.0123775
[1] -0.6807697
[1] 0.3163545
[1] -0.3767927
[[1]]
[1] -0.0945

[[2]]
[1] 0.5986

[[3]]
[1] -0.0245

[[4]]
[1] 0.6686

[1] 0.05083

vlad documentation built on Feb. 15, 2021, 5:12 p.m.