An Analysis Of Multi-Treatment Causal Effects Under High-Dimensional Covariates

As the origin of life,the downward trend in the number of births of newborns generally affects social economy,population aging and other issues.At present,the degree of population aging is increasing,the state has introduced a three-child policy to solve this problem,but in the face of the gradual increase in the mother’s age of pregnancy under the third child,the discussion of the mother’s pregnancy age has once again become a research hotspot,because the advanced age of the mother is generally considered to have an impact on the development of the fetus,so it is very valuable to study the impact of the mother’s gestational age on the weight of the baby,to a certain extent,it can avoid the mother’s early pregnancy or too late pregnancy,so that the baby can avoid premature birth,malformation,premature death and other situations as much as possible.However,the small sample size and high-dimensional data are bound to bring challenges to the analysis of survival data,and how to analyze high-dimensional data is a major difficulty faced by existing dimensionality reduction methods.Based on the survival data of relevant people in Pennsylvania,USA,this paper selects "mother’s age of pregnancy" as the treatment variable and "infant birth weight" as the response variable to study the effect of the mother’s gestational age on the baby’s birth weight.Based on this,this paper defines the generalized propensity score function under continuous processing variables on the basis of the generalized propensity score defined by Imbens,and then lays the foundation for the following causal analysis.The research content of this article can be divided into the following steps:Firstly,in order to solve the high-dimensional problem,this paper uses the slice inverse regression dimensionality reduction method to reduce the high-dimensional covariate to a low-dimensional covariate.The slice inverse regression method is used to solve the problem of variable selection under high-dimensional data in a complete way,which lays a foundation for the subsequent estimation of the propensity score function based on the local likelihood method.Slicing can turn continuous processing variables into discrete processing variables,thereby resolving the computational complexity of using integrals to estimate mean causal effects.The processing variables after slicing may no longer be two-dimensional processing variables,but may be three-dimensional or even more than three-dimensional processing variables,which need to be combined with multi-processing treatment plan models for subsequent analysis.Secondly,reviewing the relevant literature,it is found that the causal effect under continuous treatment variables is mostly assumed that the generalized propensity score function follows a normal distribution.However,the assumption of the normal distribution is too strong in the actual situation,and the analysis of age is generally based on the exponential model and the Cox model,so this paper uses the local likelihood method to estimate the generalized propensity score function based on the exponential model and the Cox model,and carries out relevant simulations.Finally,based on the relevant data of Pennsylvania,the causal effect of the mother’s age on the weight of the newborn was studied by inversely weighting the generalized propensity score function,and it was concluded that the causal effect of the mother’s age on the weight of the newborn baby was different at different ages: the causal effect of the mother’s pregnancy age at the age of 13-22 years was greater,that is,the impact on the birth weight of the baby was greater,so it was not recommended for women to become pregnant at this age;The causal effect of the mother’s pregnancy age at the age of 22-26 is less different from the causal effect of the mother’s pregnancy age at the age of 26-27,27-30,30-35 years old,that is,the mother’s pregnancy at the age of22-26 and 26-27,27-30,30-35 years old has little difference in the degree of effect on the baby’s weight,and has better physical function,so pregnancy at the age of 22-35 is the best age group;After the age of 35,with the increase of age,the effect of the mother’s age on the weight of the baby gradually increases,the reason may be that the mother’s physical function begins to decline after the age of 35,at this time the pregnant mother’s nutritional supply to the fetus may have some deficiencies,so it is not recommended for women to become pregnant after the age of 35.In summary,this paper uses the method of sufficient dimensionality reduction to apply the causal effect to multi-processed variables and continuous response variables,thereby expanding the classical causal effect.This paper estimates the generalized propensity score function based on nonparametric methods,so as to effectively solve the problem of parameter estimation in causal inference,and make the application of causal inference more extensive.The results of the case studies show that mothers are recommended to become pregnant in the age group of 22-35 years,and that maternal pregnancy at this age group has a relatively small and stable impact on the birth weight of the baby.The mother’s physical function at this age is relatively stable,can provide the fetus with more sufficient nutrients,to a certain extent can avoid the mother premature or too late pregnancy,so that the baby as much as possible to avoid premature birth,deformity,premature death,etc.,so as to avoid underweight or overweight problems.