How does Inverse weighted propensity score regression differ from propensity score matching? I understand that in inverse weighted propensity score regression, a set of weights are used to create scoring. In propensity score matching, a propensity score is created for each strata and people are matched off that. Is there a link between the two methods
 A: Propensity score matching or inverse probability weight (IPW) methods etc are used ultimately to balance the characteristics of treatment groups in comparison. Conventional matching finds a comparator group with similar characteristics. However, as the number of confounders increases, it is difficult to find an exact match. 
Propensity score (PS) is the probability of treatment assignment in the presence of given covariates (confounders), which is usually estimated using generalized linear regression. PS reduces the dimensionality, thus making it easier to match. The common methods of PS based analysis are: PS matching, PS weighting (IPW), PS stratification and PS regression adjustment. 
There are no set conditionals about which method is right. You may need to try different methods and see which method balances groups in comparison to the best. 


*

*PS matching might result in the loss of sample size if the characteristics of groups are too different. You could test different types of PS matching methods: nearest neighbour method, optimal matching method etc (also could vary the calliper of matching, or trim extreme PS distributions). I used MatchIt package for PS matching in R.

*Inverse probability weighting: If your sample size is small, you may consider alternate methods for balancing confounders between treatment groups, such as IPW. Firstly, estimate the weights based on PS score: weight for treatment = 1/PS; for control 1/(1-PS). Hence, each patient (ID) receives the weight of the inverse probability of treatment assignment probability. Thus, cases that resemble controls are given more weight, and controls that resemble cases also receive more weight. A chunk of data in the control group will not be discarded. However, patient (ID) with high weight could become unduly influential. In such cases, trim the extreme weights. For IPW, I used ipw package from R.  

*Additional references
step by step guide; PS weighting versus matching.
Good luck!
A: My answer will be more based on my experience of using the two approaches. Both approaches can generate a covariate-balanced pseudo samples, and probably generate similar estimate of treatment effects. For matching, you may discard data points that can not be matched and hence potentially reduce efficiency. For weighting, typically IPTW (inverse probability treatment weight), the main drawback is the extreme weight caused by the very close propensity score that is very close to 0 or 1, which can also lead to unstable treatment effect estimation. The matching can be reviewed as a special case of weighting, in which matched data points receive a weight of 1 and discarded data points get a weight of 0.  However, the theory framework for the two are different. suggest book "Propensity Score Analysis: Statistical Methods and Applications (Advanced Quantitative Techniques in the Social Sciences)".
