SA4C3 - essay structure

objective - utility maximization
constraint - resources available
method - set of techniques used to assemble evidence on costs and consequences of health care programs - quantify/value health care resource and allocation

1. positively skewed (non-normatively distributed data)
2. missing data
3. censoring

1. opportunity costs
2. potential benefit derived with alternative application of resources
3. comparison with competing alternatives

1. results outcomes
a. clinical trials
b. observational study
c. expert opinion
2. effectiveness = differences in occurence, time to outcomes
a. time to death
b. time to sx
c. time to death adjusted for QoL
3. Duration
a. over observation
b. extrapolation

1. Hypothesis testing
2. Measurement
3. Causality
4. Identification and Estimation

Assumptions
1. conditional distribution of dependent variable
2. functional form of relationship of covariates
Failure
1. biased
2. inconsistent
3. inefficient

- systematic component - determinisitic:
model relationship between E(Y) & X's - (estimation; prediction; counterfactual)
- error (random) component - stochastic:
specify statistical distr of residuals

1. simpler linear regression model
Y = B0 + B1X + E
2. line of means
E(Y) = B0 + B1X
3. fitted line - estimated regression based on observed sample
y = b0 + b1X
4. fitted point
y = b0 + b1x
5. regression residuals
(Yi-yi) = [Yi - (b0+b1xi)]^2
6. sum of square of deviations
summation of 5 from i = 1 to n
OLS estimation: minimize SSE

1. T- Test = bi/std dev bi
2. R^2 - coefficient of determination = SSyy - SSE/SSyy - relating y to x can explain/accoun for (r^2) of the variation in present in the sample of y values
3. F-test multiple hypotheses

1. True model is yi = βxi + εi
2. E(εi) = 0, i = 1, …, n
3. var(εi) = σ^2, ∀i
4. var(εi) = σεi^2 = f(xi)
E(εi εj) = 0, i ≠ j
5. Xi is non-stochastic
6. εi ~ i.i.d. N(0, σ^2)
parameters of interest - b
nuisance parameter - sigma squared

1. linear in the parameters (b) - not necessarily relationship among variables
2. Yi = Bln(Xi) + Ei - Variables could be transformed
3. Interpretation of B depends on the functional form

1. zero mean error in the population
2. implies that, on average, the residual error of the average regression is zero
3. random error term
- include all important variables - excluded variable not individually important
- errors of functional form
- random measurement error
- stochastic processes
Violations --> BIAS
- important omitted variable
- systematic measurement error

Homoscedasticity - constant variance of error terms
non-autocorrelation - no correlation among error terms
Violations:
heteroscedasticity and autocorrelation robust standard error

observations fixed in repeated samples (non-Bayesian)

- fixed across samples
- infer relationship between x and y
- non-Bayesian

error terms are normally distributed - employed for ease of statistical inference; may relax with large samples given Central Limit Theorem, important

1. X = treatment --> Y (controlling for patient characteristics)
2. Measure individual covariate effects --> outcome, given treatment allocation

1. omitted variables: proxy variables (interventing variables)
2. skew in dependent variables: transformation of dependent variables
3. discrete outcome variables:
- non-linear functional form
- two-part models