obsSensCCC: Compute Sensitivity analysis for Observational Studies

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

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.

Usage

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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"))

Arguments

model

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

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.

g0

The slopes on the unmeasured variable when x=0 (on the log scale, not response).

g1

The slopes on the unmeasured variable when x=1, if missing then g1=g0=gamma is assumed.

p0

Probability that U=1 given x=0.

p1

Probability that U=1 given x=1.

logOdds

Should the resulting table be on the log scale or response scale.

log

Should the resulting table be on the log scale or not.

logHaz

Should the resulting table be on the log Hazard ratio scale or Hazard ratio scale.

method

Either "approx" or "sim", only approx is currently implemented.

gamma

Slopes for U (unmeasured variable).

delta

The difference between the mean of U|x=0 and mean of U|x=1.

rho

Correlation coefficient between x and U.

sdx

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).

Details

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.

Value

An obsSens object (S3) stored as a list with the following elements:

beta

A matrix/array with the adjusted slopes for the different conditions.

lcl

A matrix/array with the lower confidence intervals for the slopes.

ucl

A matrix/array with the upper confidence intervals for the slopes.

log

A logical indicating if the values are on the log scale.

xname

The 'name' of the x variable of interest

type

Character field with the type of y variable, can be 'cat', 'surv', or 'num'.

Note

Note: Currently there are no checks on whether the conditions will be appropriate for the approximation to be close. See the first paper below for the conditions when the approximation is good.

Author(s)

Greg Snow [email protected]

References

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.

See Also

print.obsSens, summary.obsSens

Examples

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# 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 )

Example output

Sensitivity analysis on variable 
 on an Odds Ratio scale 

, , Gamma = 2

     P0
P1    0               0.1             0.2             0.3            
  0        23.10           25.41           27.72           30.03     
      ( 6.900, 77.70) ( 7.590, 85.47) ( 8.280, 93.24) ( 8.970,101.01)
  0.2      19.25           21.17           23.10           25.02     
      ( 5.750, 64.75) ( 6.325, 71.22) ( 6.900, 77.70) ( 7.475, 84.17)
  0.4      16.50           18.15           19.80           21.45     
      ( 4.929, 55.50) ( 5.421, 61.05) ( 5.914, 66.60) ( 6.407, 72.15)
  0.6      14.44           15.88           17.32           18.77     
      ( 4.312, 48.56) ( 4.744, 53.42) ( 5.175, 58.27) ( 5.606, 63.13)
  0.8      12.83           14.12           15.40           16.68     
      ( 3.833, 43.17) ( 4.217, 47.48) ( 4.600, 51.80) ( 4.983, 56.12)
  1        11.55           12.71           13.86           15.02     
      ( 3.450, 38.85) ( 3.795, 42.73) ( 4.140, 46.62) ( 4.485, 50.50)
     P0
P1    0.4             0.5            
  0        32.34           34.65     
      ( 9.660,108.78) (10.350,116.55)
  0.2      26.95           28.87     
      ( 8.050, 90.65) ( 8.625, 97.12)
  0.4      23.10           24.75     
      ( 6.900, 77.70) ( 7.393, 83.25)
  0.6      20.21           21.66     
      ( 6.037, 67.99) ( 6.469, 72.84)
  0.8      17.97           19.25     
      ( 5.367, 60.43) ( 5.750, 64.75)
  1        16.17           17.32     
      ( 4.830, 54.39) ( 5.175, 58.27)

, , Gamma = 6

     P0
P1    0               0.1             0.2             0.3            
  0        23.10           34.65           46.20           57.75     
      ( 6.900, 77.70) (10.350,116.55) (13.800,155.40) (17.250,194.25)
  0.2      11.55           17.32           23.10           28.87     
      ( 3.450, 38.85) ( 5.175, 58.27) ( 6.900, 77.70) ( 8.625, 97.12)
  0.4       7.70           11.55           15.40           19.25     
      ( 2.300, 25.90) ( 3.450, 38.85) ( 4.600, 51.80) ( 5.750, 64.75)
  0.6       5.77            8.66           11.55           14.44     
      ( 1.725, 19.42) ( 2.588, 29.14) ( 3.450, 38.85) ( 4.312, 48.56)
  0.8       4.62            6.93            9.24           11.55     
      ( 1.380, 15.54) ( 2.070, 23.31) ( 2.760, 31.08) ( 3.450, 38.85)
  1         3.85            5.77            7.70            9.62     
      ( 1.150, 12.95) ( 1.725, 19.42) ( 2.300, 25.90) ( 2.875, 32.37)
     P0
P1    0.4             0.5            
  0        69.30           80.85     
      (20.700,233.10) (24.150,271.95)
  0.2      34.65           40.42     
      (10.350,116.55) (12.075,135.97)
  0.4      23.10           26.95     
      ( 6.900, 77.70) ( 8.050, 90.65)
  0.6      17.33           20.21     
      ( 5.175, 58.27) ( 6.038, 67.99)
  0.8      13.86           16.17     
      ( 4.140, 46.62) ( 4.830, 54.39)
  1        11.55           13.47     
      ( 3.450, 38.85) ( 4.025, 45.32)

, , Gamma = 10

     P0
P1    0               0.1             0.2             0.3            
  0        23.10           43.89           64.68           85.47     
      ( 6.900, 77.70) (13.110,147.63) (19.320,217.56) (25.530,287.49)
  0.2       8.25           15.67           23.10           30.52     
      ( 2.464, 27.75) ( 4.682, 52.72) ( 6.900, 77.70) ( 9.118,102.67)
  0.4       5.02            9.54           14.06           18.58     
      ( 1.500, 16.89) ( 2.850, 32.09) ( 4.200, 47.30) ( 5.550, 62.50)
  0.6       3.61            6.86           10.11           13.35     
      ( 1.078, 12.14) ( 2.048, 23.07) ( 3.019, 33.99) ( 3.989, 44.92)
  0.8       2.82            5.35            7.89           10.42     
      ( 0.841,  9.48) ( 1.599, 18.00) ( 2.356, 26.53) ( 3.113, 35.06)
  1         2.31            4.39            6.47            8.55     
      ( 0.690,  7.77) ( 1.311, 14.76) ( 1.932, 21.76) ( 2.553, 28.75)
     P0
P1    0.4             0.5            
  0       106.26          127.05     
      (31.740,357.42) (37.950,427.35)
  0.2      37.95           45.38     
      (11.336,127.65) (13.554,152.62)
  0.4      23.10           27.62     
      ( 6.900, 77.70) ( 8.250, 92.90)
  0.6      16.60           19.85     
      ( 4.959, 55.85) ( 5.930, 66.77)
  0.8      12.96           15.49     
      ( 3.871, 43.59) ( 4.628, 52.12)
  1        10.63           12.71     
      ( 3.174, 35.74) ( 3.795, 42.73)

Sensitivity analysis on variable 
 on a Hazard Ratio scale 

, , Gamma = 3

     P0
P1    0             0.1           0.2           0.3           0.4          
  0       1.210         1.452         1.694         1.936         2.178    
      (1.090,1.250) (1.308,1.500) (1.526,1.750) (1.744,2.000) (1.962,2.250)
  0.1     1.008         1.210         1.412         1.613         1.815    
      (0.908,1.042) (1.090,1.250) (1.272,1.458) (1.453,1.667) (1.635,1.875)
  0.2     0.864         1.037         1.210         1.383         1.556    
      (0.779,0.893) (0.934,1.071) (1.090,1.250) (1.246,1.429) (1.401,1.607)
  0.3     0.756         0.907         1.059         1.210         1.361    
      (0.681,0.781) (0.818,0.938) (0.954,1.094) (1.090,1.250) (1.226,1.406)
  0.4     0.672         0.807         0.941         1.076         1.210    
      (0.606,0.694) (0.727,0.833) (0.848,0.972) (0.969,1.111) (1.090,1.250)
  0.5     0.605         0.726         0.847         0.968         1.089    
      (0.545,0.625) (0.654,0.750) (0.763,0.875) (0.872,1.000) (0.981,1.125)
  0.6     0.550         0.660         0.770         0.880         0.990    
      (0.495,0.568) (0.595,0.682) (0.694,0.795) (0.793,0.909) (0.892,1.023)
  0.7     0.504         0.605         0.706         0.807         0.908    
      (0.454,0.521) (0.545,0.625) (0.636,0.729) (0.727,0.833) (0.818,0.938)
  0.8     0.465         0.558         0.652         0.745         0.838    
      (0.419,0.481) (0.503,0.577) (0.587,0.673) (0.671,0.769) (0.755,0.865)
  0.9     0.432         0.519         0.605         0.691         0.778    
      (0.389,0.446) (0.467,0.536) (0.545,0.625) (0.623,0.714) (0.701,0.804)
  1       0.403         0.484         0.565         0.645         0.726    
      (0.363,0.417) (0.436,0.500) (0.509,0.583) (0.581,0.667) (0.654,0.750)
     P0
P1    0.5          
  0       2.420    
      (2.180,2.500)
  0.1     2.017    
      (1.817,2.083)
  0.2     1.729    
      (1.557,1.786)
  0.3     1.512    
      (1.363,1.562)
  0.4     1.344    
      (1.211,1.389)
  0.5     1.210    
      (1.090,1.250)
  0.6     1.100    
      (0.991,1.136)
  0.7     1.008    
      (0.908,1.042)
  0.8     0.931    
      (0.838,0.962)
  0.9     0.864    
      (0.779,0.893)
  1       0.807    
      (0.727,0.833)

Sensitivity analysis on variable 
 on an Odds Ratio scale 

      gamma
rho    0             0.2           0.4           0.6           0.8          
  0        1.140         1.140         1.140         1.140         1.140    
       (1.100,1.180) (1.100,1.180) (1.100,1.180) (1.100,1.180) (1.100,1.180)
  0.5      1.140         1.115         1.090         1.066         1.043    
       (1.100,1.180) (1.076,1.154) (1.052,1.129) (1.029,1.104) (1.006,1.080)
  0.75     1.140         1.103         1.066         1.032         0.998    
       (1.100,1.180) (1.064,1.141) (1.029,1.104) (0.995,1.068) (0.963,1.033)
  0.85     1.140         1.098         1.057         1.018         0.980    
       (1.100,1.180) (1.059,1.136) (1.020,1.094) (0.982,1.054) (0.946,1.015)
  0.9      1.140         1.095         1.052         1.011         0.971    
       (1.100,1.180) (1.057,1.134) (1.015,1.089) (0.976,1.047) (0.937,1.006)
  0.95     1.140         1.093         1.048         1.004         0.963    
       (1.100,1.180) (1.055,1.131) (1.011,1.084) (0.969,1.040) (0.929,0.997)
  0.98     1.140         1.091         1.045         1.000         0.958    
       (1.100,1.180) (1.053,1.130) (1.008,1.082) (0.965,1.035) (0.924,0.991)
  0.99     1.140         1.091         1.044         0.999         0.956    
       (1.100,1.180) (1.053,1.129) (1.007,1.081) (0.964,1.034) (0.922,0.990)
      gamma
rho    1            
  0        1.140    
       (1.100,1.180)
  0.5      1.020    
       (0.984,1.056)
  0.75     0.965    
       (0.931,0.999)
  0.85     0.944    
       (0.911,0.977)
  0.9      0.933    
       (0.901,0.966)
  0.95     0.923    
       (0.891,0.955)
  0.98     0.917    
       (0.885,0.949)
  0.99     0.915    
       (0.883,0.947)

obsSens documentation built on May 29, 2017, 10:39 a.m.