Computes a Sensitivity analysis for a coefficient from a regression model (linear, logistic, Cox) on Observational data. Computes new coefficient estimate and confidence interval for various relationships between the response, predictor of interest, and an unmeasured variable. The last 3 letters of each function refer to the type of the variables in the order Y, X, U with C meaning categorical, N meaning normal (continuous), and S being a survival object.
obsSensCCC(model, which = 2, g0 = c(2, 6, 10), g1, p0 = seq(0, 1, 0.2),
p1 = p0, logOdds = FALSE, method = c("approx", "sim"))obsSensCCN(model, which = 2, gamma = round(seq(0, 2 * bstar,
length = 6), 4), delta = seq(0, 3, 0.5), logOdds = FALSE,
method = c("approx", "sim"))
obsSensCNN(model, which = 2,
gamma = round(seq(0, 2 * bstar, length = 6), 4),
rho = c(0, 0.5, 0.75, 0.85, 0.9, 0.95, 0.98, 0.99), sdx,
logOdds = FALSE, method = c("approx", "sim"))
obsSensNCC(model, which = 2, g0 = c(2, 6, 10), g1, p0 = seq(0, 1, 0.2),
p1 = p0, log = TRUE, method = c("approx", "sim"))
obsSensNCN(model, which = 2, gamma = round(seq(0, 3, length = 6), 4),
delta = seq(0, 3, 0.5), log = TRUE,
method = c("approx", "sim"))
obsSensNNN(model, which = 2,
gamma = round(seq(0, 2 * bstar, length = 6), 4),
rho = c(0, 0.5, 0.75, 0.85, 0.9, 0.95, 0.98, 0.99),
sdx, log = TRUE, method = c("approx", "sim"))
obsSensSCC(model, which = 2, g0 = c(2, 6, 10), g1, p0 = seq(0, 1, 0.2),
p1 = p0, logHaz = FALSE, method = c("approx", "sim"))
obsSensSCN(model, which = 2,
gamma = round(seq(0, 3, length = 6), 4),
delta = seq(0, 3, 0.5), logHaz = FALSE,
method = c("approx", "sim"))
obsSensSNN(model, which = 2, gamma = round(seq(0, 3, length = 6), 4),
rho = c(0, 0.5, 0.75, 0.85, 0.9, 0.95, 0.98, 0.99), sdx,
logHaz = FALSE, method = c("approx", "sim"))
A regression model object (result of lm,
glm, or coxph or
other object with a coef method) or a single numerical value
representing the estimated coefficient from a regression model.
Which coefficient (in the results from
coef(model)) corresponds to the predictor of interest. If
model is a number then this should be a 2 element vector with
the initial confidence interval for model.
The slopes on the unmeasured variable when x=0 (on the log scale, not response).
The slopes on the unmeasured variable when x=1, if missing then g1=g0=gamma is assumed.
Probability that U=1 given x=0.
Probability that U=1 given x=1.
Should the resulting table be on the log scale or response scale.
Should the resulting table be on the log scale or not.
Should the resulting table be on the log Hazard ratio scale or Hazard ratio scale.
Either "approx" or "sim", only approx is currently implemented.
Slopes for U (unmeasured variable).
The difference between the mean of U|x=0 and mean of U|x=1.
Correlation coefficient between x and U.
Standard Deviation of x (default will try to extract this
from model, it will need to be provided if model is a
number rather than a model object).
An obsSens object (S3) stored as a list with the following elements:
A matrix/array with the adjusted slopes for the different conditions.
A matrix/array with the lower confidence intervals for the slopes.
A matrix/array with the upper confidence intervals for the slopes.
A logical indicating if the values are on the log scale.
The 'name' of the x variable of interest
Character field with the type of y variable, can be 'cat', 'surv', or 'num'.
These functions are all used to do sensitivity analysis on regression
models for observational data. Currently it works with linear
regression, logistic regression (using glm), and survival
regressions (using coxph). All models are of the general form:
y = b1*x + gamma*U + Beta*Z
Where y is the response (or function of the response). The first letter in the triplet at the end of each function name corresponds to the type of response variable, N-normal/numeric (continuous), C-Categorical (binary, logistic regression), and S-Survival (coxph models).
The x variable is the coefficient of interest (usually the treatment variable, or primary predictor of interest). The 2nd letter in the triplet can be C-Categorical (x is 0 or 1, usually control vs. treatment) or N-Numeric, a continuous variable.
The U variable is an unmeasured potential confounder that we believe may be related to y and x. The final letter in the final triplet refers to the type of unmeasured variable that we want to correct for: C-Categorical/binary (0-1, present-absent) or N-Numerical/continuous (in this case it is assumed to be normal with mean 0 and sd 1).
The Z represents additional covariates in the model that are not of primary interest in the sensitivity analysis. It is assumed that Z and U are independent of each other.
For all the functions you specify the potential relationships between
U and y (gamma, g0, and g1) and potential
relationships between x and U (p0, p1, delta, and
rho). Then the functions compute a new estimate of b1 (the
slope for x, the variable of interest) and its confidence interval
given each combination of the relationships between U, y, and x.
Currently only the approximation method by Lin et. al. is available. In the future a simulation method will also be implemented.
Lin, DY and Psaty, BM and Kronmal, RA. (1998): Assessing the Sensitivity of Regression Results to Unmeasured Confounders in Observational Studies. Biometrics, 54 (3), Sep, pp. 948-963.
Baer, VL et. als (2007): Do Platelet Transfusions in the NICU Adversely Affect Survival? Analysis of 1600 Thrombocytopenic neonates in a mulihospital healthcare system. Journal of Perinatology, 27, pp. 790-796.
# NOT RUN {
# Recreate tables from above references
obsSensCCC( log(23.1), log(c(6.9, 77.7)), g0=c(2,6,10),
p0=seq(0,.5,.1), p1=seq(0,1,.2) )
obsSensSCC( log(1.21), log(c(1.09,1.25)),
p0=seq(0,.5,.1), p1=seq(0,1,.1), g0=3 )
obsSensCNN( log(1.14), log(c(1.10,1.18)),
rho=c(0,.5, .75, .85, .9, .95, .98, .99),
gamma=seq(0,1,.2), sdx=4.5 )
# }
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