Actuarial Notes

CAS Exam MAS-II Fall 2018, Question 1

Study guide: Exam MAS-II

In the supplemental material, you have been given a case study, "Systolic Blood Pressure Case Study", showing the results of different treatment options and the description of how that study was set up. There are different ways of setting up models to examine the benefits of the different treatment options. You have been asked which of two model structures will give a better fit to the experience.

The relevant output from the case study is reproduced below. Change in systolic blood pressure is modelled for 1,680 observations under eight treatment options, with random intercepts for 21 hospitals and for 210 doctors nested within them; Var_F_G_1 is Variance Group #1, which places the treatments in two variance strata.

Model 1 — all eight treatments as fixed effects, doctors nested within hospitals, constant variance, fitted by REML:

## Linear mixed-effects model fit by REML
##  Data: systolic_g
##        AIC      BIC    logLik
##   9247.867 9307.507 -4612.934
##
## Random effects:
##  Formula: ~1 | Hospital_F
##         (Intercept)
## StdDev:   0.2653508
##
##  Formula: ~1 | Doctor_F %in% Hospital_F
##         (Intercept) Residual
## StdDev:   0.2876551 3.752395
##
## Fixed effects: change_systolic ~ Treatment_F

Model 3 — the same model with the variance by treatment grouped under Variance Group #1, fitted by REML:

## Linear mixed-effects model fit by REML
##  Data: systolic_g
##        AIC      BIC    logLik
##   9245.032 9310.093 -4610.516
##
## Random effects:
##  Formula: ~1 | Hospital_F
##         (Intercept)
## StdDev:   0.2829815
##
##  Formula: ~1 | Doctor_F %in% Hospital_F
##         (Intercept) Residual
## StdDev:   0.3081544  3.89183
##
## Variance function:
##  Structure: Different standard deviations per stratum
##  Formula: ~1 | Var_F_G_1
##  Parameter estimates:
##         0         1
## 1.0000000 0.9257221
## Fixed effects: change_systolic ~ Treatment_F

Model Structure XYZ has:

  • All eight treatment options in the fixed effects section of the model
  • A random effect of doctors nested within hospitals
  • An assumption of constant variance across treatment effects

Model Structure STW has:

  • All eight treatment options in the fixed effects section of the model
  • A random effect of doctors nested within hospitals
  • An assumption that the variance by treatment can be grouped under Variance Group #1

The null hypothesis is that variance is constant across all treatment effects.

Determine the level of significance at which one would reject the null hypothesis using a likelihood ratio test.

  • A) Less than .005
  • B) At least .005, but less than .01
  • C) At least .01, but less than .025
  • D) At least .025, but less than .05
  • E) Greater than .05

Answer this question and see the worked solution

Concepts tested

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