Skip to main content
. Author manuscript; available in PMC: 2022 Dec 1.
Published in final edited form as: Health Serv Outcomes Res Methodol. 2022 Jun 6;22(4):435–453. doi: 10.1007/s10742-022-00275-x

Table 2.

Results of top 30 algorithms in MEPS analysis

Algorithma MSEb (108) Relative MSE R2 REc MAE
Two-stage Super Learner + Thresholding 2.1491 1.0000 0.1580 1.0000 5848
Two-stage Super Learner 2.1590 1.0046 0.1558 0.9865 5873
I(P(Y>0)>=0.5) * (S1: RF + S2: RF) 2.1878 1.0180 0.1446 0.9152 5929
Discrete two-stage Learner + Indicator 2.1878 1.0180 0.1446 0.9152 5929
S1: RF + S2: RF 2.1880 1.0181 0.1445 0.9148 5990
Discrete two-stage Learner 2.1880 1.0181 0.1445 0.9148 5990
I(P(Y>0)>=0.25) * (S1: RF + S2: RF) 2.1891 1.0186 0.1441 0.9121 5984
S1: Xgboost + S2: RF 2.1906 1.0193 0.1435 0.9084 6029
I(P(Y>0)>=0.25) * (S1: Xgboost + S2: RF) 2.1907 1.0194 0.1434 0.9081 6022
I(P(Y>0)>=0.5) * (S1: Xgboost + S2: RF) 2.1911 1.0196 0.1433 0.9070 5975
S1: GLM + S2: RF 2.1920 1.0199 0.1429 0.9050 6027
I(P(Y>0)>=0.25) * (S1: GLM + S2: RF) 2.1922 1.0201 0.1428 0.9043 6023
S1: LASSO + S2: RF 2.1925 1.0202 0.1427 0.9036 6026
I(P(Y>0)>=0.25) * (S1: Lasso + S2: RF) 2.1926 1.0202 0.1427 0.9034 6023
I(P(Y>0)>=0.5) * (S1: GLM + S2: RF) 2.1927 1.0203 0.1426 0.9031 5985
I(P(Y>0)>=0.5) * (S1: Lasso + S2: RF) 2.1931 1.0205 0.1425 0.9021 5985
One-stage Super Learner 2.2068 1.0269 0.1371 0.8681 5917
Single: RF 2.2273 1.0364 0.1291 0.8175 6052
S1: NN + S2: RF 2.2356 1.0403 0.1259 0.7968 6034
I(P(Y>0)>=0.25) * (S1: NN + S2: RF) 2.2360 1.0404 0.1257 0.7960 6034
I(P(Y>0)>=0.5) * (S1: NN + S2: RF) 2.2362 1.0405 0.1257 0.7955 6006
S1: SVM + S2: RF 2.2364 1.0406 0.1255 0.7948 6027
I(P(Y>0)>=0.25) * (S1: SVM + S2: RF) 2.2370 1.0409 0.1253 0.7934 6015
I(P(Y>0)>=0.5) * (S1: SVM + S2: RF) 2.2375 1.0411 0.1252 0.7923 6008
Single: Zero-inflated Poisson (ZIP) 2.2571 1.0503 0.1175 0.7436 6106
I(P(Y>0)>=0.5) * (S1: RF + S2: Lasso) 2.2579 1.0506 0.1172 0.7417 6044
S1: RF + S2: LASSO 2.2580 1.0507 0.1171 0.7415 6083
I(P(Y>0)>=0.25) * (S1: RF + S2: Lasso) 2.2582 1.0508 0.1170 0.7410 6081
S1: Xgboost + S2: Lasso 2.2607 1.0519 0.1161 0.7349 6127
I(P(Y>0)>=0.25) * (S1: Xgboost + S2: Lasso) 2.2609 1.0520 0.1160 0.7343 6124
a

Algorithms are presented in ascending order based on MSE.

b

Lower MSE and relative MSE indicate better performance.

c

Greater R2 and RE indicates better performance.

d

S1 refers to stage-1 algorithm

e

S2 refers to stage-2 algorithm

f

RF refers to Random Forest.

g

GLM in S1 refers to logistic regression

h

Lasso in S1 refers to logistic Lasso regression.

i

NN refers to Neural Network.

j

SVM refers to Support Vector Machine.