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keiishima · 3 years ago

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Mon Chéri — Eijiro Kirishima: The Penthouse

Fem-dom!reader x Sub!Kirishima

Warnings and WC : smut 18+ minors dni, fem & dom reader, m.sub, handjob, praising, sugar mommy dynamics, slight breeding kink, unedited | 4k

A/N: This is the first one I’ve written for the ‘mon cheri series’ and the first full smut fic I’ve written for mha.. pls ignore typos I wrote it in one sitting. - sage <3

[Prologue & prompt]

“Dude, are you ever going to stop staring at her?”

Kirishima’s attention was ripped from you just enough for him to realize how long he’d been zoned out. Glancing at the others at the table with him, he could only offer a sheepish smile.

“Sorry. Uh, what were you talking about before?” He offered, still not entirely focused on his friends. It was always like this, and they weren’t surprised anymore.

Whenever you entered the room it was like he went into a completely different world. Quietly replying to whatever part of the conversation he could catch without really trying to listen.

“Do not make him go over that shitty story again, I slam my head into the table if I have to hear one more part of it.” Bakugo groaned loudly, leaning on the table with a bored expression on his face, it was quite obvious he didn’t want to be here.

“It wasn’t that bad! I just.. forgot some parts of it, it’s not that big of a deal.” Kaminari threw his hands up in the air as he spoke before turning to the red-haired man, raising an eyebrow in question. “But Bakugo is right man, aren’t you going to say anything? You’ve been ogling her all night; I get it she’s fuckin hot but like damn.”

“What? No way.” Kirishima couldn’t fight the blush that was creeping over his face now, it was one thing for him to think about you like this, but when other people pointed it out he had a hard time fighting the slight embarrassment. “Don’t say stuff like that.”

He turned to Kaminari, eyebrows furrowing when he saw his friends eyes on you now too. A pang of something lighting up his chest, and before he knew it he had a hand gripping the other man’s shoulder, tugging on him harshly.

“Dude, what the fuck, you know I’m right she’s smokin-“

“Stop talking.” Kirishima cut him off sharply, voice low as he spoke. There was a slight threatening edge to it, and it nearly sent chills through Kaminari’s blood. His grip was tight on the blonde’s shoulder, tight enough to almost hurt.

Kirishima wasn’t sure what had come over him, but he couldn’t fight the building annoyance that sat heavy in his stomach. At the look on Kaminari’s face, Kirishima pulled his hand from him, shaking his head slightly before looking back to you.

It took him a moment to realize you were looking at him, and by the time he did you had taken your eyes away from him. But the slight smile that was sitting on your lips and the glint in your eyes was burned into the forefront of his thoughts.

He couldn’t even hear his friends voices anymore, paying attention to nothing but you once again. This was the first time of the night, and maybe ever, that you had acknowledged him.

The shock only lasted for a minute longer, breaking once you started to move away from the people you were talking to, heading for the exit. This was his least favorite part of the night, every time you left the parties he felt like he had no reason to be there anymore, even if he was one of the pros invited to the banquet tonight.

Without thinking, he pushed away from his chair. Ignoring the questions from his friends as he moved after you, his pace not quite fast enough to catch up to you in the main hall. He slipped out of the doors behind you.

“Ma’am wait!”

He wasn’t sure why he had called out to you all of a sudden, but when you stopped turning around just before you moved onto the first step all of his plans flew from his head. If he even had one to begin with.

“Oh, hello.” Your voice was soft and smooth, even more enticing up close. Kirishima had heard you speak before, catching small bits of your conversations as he passed by, or if the music was quiet enough. But this was the first time your words were directed at him.

“Uh, hi.”

That was all he could say in return, he nearly cringed at the unevenness of his voice. He nearly missed the amused smile your lips turned too, even though his eyes couldn’t leave your face once more.

“Did you need something, sweetheart?” Your question almost shocked him; it was like he wasn’t even expecting you to return anything but hellos.

“Not really..” Kirishima trailed off, not really sure what he even came here for. He had just moved from the table on something similar to instinct.

“Are you sure?” You asked once more, leaning against the railing of the stairs. Your long dress brushing against the ground as you shifted. Kirishima’s eyes flashed to the slit in the dress that your leg shown through.

It was brief before he looked back to meet your gaze, but you caught it. A knowing smile on your face as you pushed your leg out of the slit even further, wanting to see how long he’d be able too keep from looking away.

“Well, if you’re certain. I was just about to leave; my car is here.” You glanced down the stairs, motioning to the car that just pulled up. Raising an eyebrow you waited for a moment longer, you weren’t sure if he was going to say anything else.

Kirishima’s heart was beating faster than it had all night, being this close to you was something he didn’t think he’d be able to do, let alone talk to you. For some reason he felt like this was his only chance, that if you left tonight he wouldn’t be able to ever do anything like this again.

When you started down the stairs, his eyes widened, and his body moved on its own once more. A hand wrapping around your wrist stopping you once more.

“Actually, there is something I wanted to ask, or rather talk to you about?” His voice came out as something more like a question, silently cringing at the way he sounded. It was so different than the usual confidence he held.

“Go on.” You spoke, the tone of your voice the same as before, he felt a little relieved that it held no annoyance.

“Would you want to get some drinks with me? Or dinner? It doesn’t really matter what..” His other hand rubbed the back of his neck softly, trying not to let the soft blush cover his cheeks.

You were quiet for longer than he would’ve liked, and it nearly made him take back his offer. But the gentle expression you still held was inviting.

“Why not? I’ve got nothing else to do for the rest of the night.” You could nearly see his eyes light up when you responded, it was obvious that he thought you were going to turn him down. “How about you come with me? I was just headed home, but I’ve got a pretty nice bar and chef there if you’d like some dinner?”

“That would be wonderful.”

Twenty minutes later after a car ride filled with small talk, Kirishima sat across from you at a small table. He had warmed up now, feeling more comfortable than before now that he wasn’t acting on impulse.

The way he shifted into more of his confidence was a little amusing to you, he was almost different than the man that approached you on the stairs of the banquet hall.

You weren’t a stranger to Kirishima, but you’ve never truly interacted with him. Red Riot was one of the most popular and skilled pro heroes and you knew much of him from interviews and new reports.

He looked out the large windows of the dining room, the night sky was lit up from the cities lights below it. It surprised him a little when you brought him to your place, he wasn’t expecting such a large penthouse. Not that it mattered to him what you had, he just didn’t realize you had that type of money.

You were so intriguing to him, finding out in the car that you were only around ten years older than him. He wasn’t sure of knowing that made him worry more or less. But the kind smile that seemed to always be sitting on your face since he came up to you was comforting.

“So why were you at the banquet? I’ve seen you around at a few of them before, and I was wondering. Are you a hero?” Kirishima asked before taking a drink from the small glass that sat in front of him.

“No, I’m not a hero, not even close. I work for one of the support companies. Actually I own one of them myself, we work more behind the scenes though.” You answered his question after a moment, your attention lingering on the fact that he had said he’s seen you before.

This was the first time he had come up to you, out of all the banquets and parties you had gone to. You were beginning to wonder if he was going to ever reach out to you; you weren’t oblivious to how his eyes seemed to always be on you when you looked his way, and you weren’t naïve. You knew what he wanted, but you wanted to make him come to you for it.

It wouldn’t have been nearly as fun if you stepped in the first time you had bumped into him. Remembering the way his eyes seemed to fall to your lips, his own parted in such a way that you almost knew what he was thinking about.

He was adorable. As big as he was, there was a playful aura around him that you could tell you would like. But you decided that it would be up to him to make any type of move, you could feel the pull between you two. It had just been a matter of when he’d act on it.

“Kirishima, I have a question of my own for you.” You asked after a long moment, breaking the comfortable silence that had fallen over you, finishing your food long ago.

“Yeah?” Kirishima tilted his head slightly, perking up at your voice.

“What took you so long to come find me?”

He wasn’t expecting that. Out of everything you two had talked about that night, he didn’t think you had any idea that he’d been wanting to do this for a while now.

Maybe he hadn’t been that secretive with how he looked for you at every event, trying to find the reason he actually went to them.

For a moment he thought about asking you what you meant, playing dumb now that he had been caught. But the way you were watching him, with such interest gleaming in your eyes, he couldn’t.

“I’m not sure.” He started, dropping his eyes from you to the glass in his hand. “I think I figured you’d think I was too young, or that you were with someone. So, at first I was just trying to figure out if you were taken.”

He paused, bringing his drink to his lips as he reconnected your gaze. It was like the last worry that had been holding him back before was gone. He didn’t know when they all disappeared but, there was nothing standing in his way now.

“Did you miss the way I had my eyes on you as well.” You spoke up before he could continue, pushing away from the table slowly as you walked around to his side. Sliding your hands gently onto his shoulders as you looked down to him. Your voice was low and smooth as you spoke again, just like it had been the first time he heard it. “I’ve been waiting all this time, hun.”

Kirishima’s eyes dropped to your lips again, the same expression on his face as the last time he saw them this close. His heart sped up as you leaned in even closer to him, your breath dancing across his cheek.

“I’m very patient, but.. how much longer can you wait?”

The way you read him like an open book would almost frighten him if he wasn’t so focused on you, just like he had been at all the events. He never expected you to reciprocate what was on his mind, let alone act on it.

You moved your hand to grip his jaw, tilting his chin up to look up at you. Your eyes flicking from his lips only once before closing the distance between them.

His hands wasted no time before touching you, once resting on your cheek, the other gripping your wrist. The kiss was slow, lacking any bit of roughness you would’ve expected from him. You were almost surprised at how soft the rugged man was being, but it only caused you to smile into the kiss.

When the kiss broke, Kirishima pushed away from the table, standing to nearly tower over you. Despite the height difference, you still pulled him in to kiss you again, taking the reigns in your hands.

It was easy. Kirishima basically melted under your touch, following your every move. Like he wanted you to take complete control, you were just so much.

Your hands pushed down his broad chest, slowly trailing down his torso. His hands gripped onto tighter when you hooked a finger into his belt, tugging on it lightly.

“Why don’t we take this to the bedroom, hm? I think you’ve waited long enough already.” You laced your hand in his, pulling him in the direction of the closest bedroom in the house. It was one of the guest rooms, but it would do right now.

Pushing him onto the bed once you entered the room, he sat obediently, waiting for you to close the distance once more. The slit in your dress allowed you to gracefully slip into his lap, threading your fingers in his hair as you kissed him once more.

You could already feel the tightness of his pants under you, it brought a small smile to your lips. Humming into the kiss you pressed your hips down, rolling them once. The low groan that slipped from his lips you swallowed hungrily.

“What were you thinking of sweetheart?” You slipped a hand between your bodies, pressing it to the growing bulge. His breathing was picking up, chest rising and falling a bit faster from both your hand and your lips on his.

“You.” That’s all he could say in response, you were already taking his breath away. Breathy moans pulling from his chest as you palmed him through his pants, pushing his hips up into your hand.

“Hm, so needy already?” You chided, kissing down his jaw before moving to his neck. Keeping the same almost soft movements of your hand on him. Your own arousal was building in your core at the noises that were coming from him.

How easily he reacted to your touch was enticing, you wanted to see more. Pulling back you slipped off his lap quickly undoing his belt sliding down his pants with his help. The large bulge in his underwear made you nearly smirk.

His length slapped against his pelvis once you pulled down his last layer, he sucked in a breath when you wrapped your hand around it loosely. Pumping slowly, you kept your eyes trained on his face.

“You’re being so good, you were worried for nothing, baby. I wouldn’t have ever turned you away.” You spoke low, your other hand moving up and down his inner thigh slowly.

“Sorry..”

The way his voice sounded was adorable, shaky and quiet as you slowly started to speed up your hand. His hands planted flat against the bed, the way he was staring down his cheeks stained in a light pink already, it was addicting.

It didn’t take long for him to start moving his hips with your hand, searching for more than you were giving him.

“Something wrong, baby?” You could tell what he wanted; his hands slowly gripped the sheets when you slowed your hand.

“Can I fuck you?”

“You have such good manners, Kirishima. Thank you for asking.” You pumped him a few more times before standing, slipping down your panties easily before climbing back over his lap. “But you know, I’m the one that’s in charge here so we’ll go at my pace?”

Kirishima nodded quickly, that was fine by him. He didn’t care if you took is slow or not, he was reveling in the feeling of you taking control of him. It was so much easier than he thought to give into you.

“Good, now stay still. I’ll take care of you.”

That was the last thing you said before reaching between you two once more, positioning the tip of his cock and sinking down on him slowly. His hands flew to your hips and a low groan filled the room, it would be hard not to move like you said, but he wanted to listen.

Slowly you started to circle your hips, placing your hands on his shoulders as leverage to help you steady yourself. His breathing was picking up even more, soft moans spilling out mixing with your quiet pants.

“You’re so big, baby. Filling me so well.” You panted out, gripping his jaw with one hand, forcing him to look at you, his eyes were blown out from the pleasure. “You look so beautiful like this, maybe I should take it slow as I can to savor it, hm? What do you think?”

You weren’t really asking, already knowing the answered. He wanted you to move faster, wanted to touch you more than he could right now, but you had already told him to stay still. When he didn’t answer, you slowed your movements even further, your grip tightening on his jaw.

“Fuck don’t stop. Please, I want more.. fuck me faster.” He sounded so pretty already almost begging for you to give him more, you could hardly resist.

“Mm, since you asked me so nicely, and you’re such a good boy how could I say no?”

Closing the distance between your lips once more you started moving your hips faster, bouncing them some as you kissed him. His low groans giving you the chance to push your tongue in his mouth, he didn’t even resist it.

His grip tightened more on your hips before you took one of his hands in your own, slipping it between the two of you.

“Go on, make me feel good. Isn’t that what you wanted this whole time? Be a good boy for me, make me cum on your cock.” You didn’t have to say it twice before his fingers found your clit, rubbing slow circles at first before he sped them up, matching the pace of your hips. “Fuck, just like that-“

The nonstop praises spilling from you were making it easier for him to stay still, especially as you bounced perfectly on his cock, he couldn’t even move his hips if he tried to. You had complete control over him, invading his sense with every time you sank fully on him.

“M’gonna cum soon, fuck don’t stop.” His head fell forward, resting against your shoulder, he was getting pushed closer to the edge with each roll of your hips. His fingers started moving faster, rubbing your clit roughly hoping that you were close too.

Your hands slid up to thread in his hair, tugging harshly pulling a loud whine from his throat. You couldn’t see his face, but you could almost imagine the way it contorted in pleasure with that noise, it was addicting.

“Go on, you can cum baby, fill me up.”

“Ahh, fuck fuck thank you ma’am-“ His words were muffled against your skin, breath hot as he panted into the crook of your neck. You could feel his thighs tense under you, he was close.

A few more rolls of your hips against him he lost the hold he had on himself, pushing his hips up into you, pulling you impossibly closer into him as the hot white pleasure coursed through him. His abs flexed as he came, fingers moving sloppily against your clit.

The muffled moans and whines he let out sent pleasure straight to your core, still moving your hips as he pushed through his high. Despite the slight burn as the pleasure faded, he ground up into you.

His cum dripped out of you with every move of your hips, smearing against his thighs but it only pushed you further towards the edge. You tugged his hair once more, pulling him away from your neck to press your lips against his roughly, teeth clashing some as you kissed him.

He eagerly swallowed your moans as you came, walls clenching around his now aching cock. Your thighs trembled slightly at the intense pleasure that burned through you.

Both of your breathing was heavy as you came down from your high, Kirishima’s arms slipped around your waist tightly, pulling you close to him.

He hummed softly when the quiet praises started leaving your lips, a hand running up and down his back as far as you could reach. Pressing gently kisses down his jaw and neck, the way he held onto you was adorable.

“You with me?”

He nodded opening his eyes to look at you, a soft smile sitting on his lips. It brought one to your own and you slowly pulled yourself off of his lap, slipping out of his grip.

“I’ll be right back, stay here.” You spoke softly, pressing a kiss to his cheek before moving to the attached bathroom. Quickly wetting a towel to clean him up.

You only spent a moment cleaning up your mess, wiping the cum that had spilled onto his thighs, not caring about anything else. Throwing the towel into the bathroom you pulled back the covers on the bed, glancing at the alarm clock as you did, it was nearly past midnight now.

Slipping off your dress quickly you slid into the bed, opening your arms to him. It only took him a moment to crawl under the covers with you, resting his head on your chest gently. You smile softly at how cuddly he was, resting on of your hands in his hair.

“Thank you.” Kirishima breathed out, it was much quieter than before, and you almost missed it. You hummed in response, not expecting him to say anything like that.

“You’re welcome, sweetheart. I did say I’d take care of you.”

It was quiet for a moment, Kirishima’s breathing evened out and you thought he fell asleep. But he turned to look up at you, eyes flicking between yours nervously.

“What is it?” You asked, moving your hand to cup his cheek, gently running your thumb over his soft skin.

“Can I..” He started before pausing to think for a moment, “Um, can I come back here again? Like can I.. I want to be…”

He was having a hard time asking what he wanted, putting his thoughts into words wasn’t easy with something like this, especially not when you were looking at him so sweetly.

“Are you asking if you can be mine?”

Kirishima’s cheeks burned at your question, you had read his mind perfectly. He nodded hoping you wouldn’t make him explain further.

“I’d love to have you as my baby, that’s what you want right? To be spoiled by me, is that what you’ve wanted this whole time?” Your voice was soft and comforting, the embarrassment that was starting to build in him dissipated easily.

“Yeah. I didn’t know how to talk to you…” He trailed off, dropping his gaze from you only to cuddle back into you. His eyes were getting heavier as the slight exhaustion was pulling at them.

“Well, you don’t need to worry about that now, angel. You’re mine until I say you can leave.”

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kiyoors · 3 years ago

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pretty symphony

established relationship! atsumu x reader

word count: 1.9k

warnings: porn not plot, slight edging/teasing, I don't really know if this could count as f.dom/m.sub ?? I doubt it but lets just say it has an air of it, literally this is just almost 2k words of atsumu getting a hand job like a damn high schooler smh, lots of feels too tho, u call atsumu pretty n he cums

synopsis: He's beautiful-- blushy and sweaty and panting-- and he's all yours. God forbid you don't take your time with him, even if he gets a little desperate.

a/n: i just know tsumu would make the absolute prettiest sounds when he’s needy

“Angel, did ya see that serve?”

You lightly hum in response. Honestly, you’re too drowsy right now to coherently respond, but Atsumu sounds too cute and excited. You feel you can’t just leave him to talk to himself and the blue glow of his phone.

He has you curled up to his side, your nose having been nuzzled into the crook of his neck, until now that he spoke, as you tried to sleep. It had been a long day, and ever since Atsumu's volleyball match had ended earlier in the evening, you’ve been craving your boyfriend’s warmth, preferably as you both lay in bed, sleeping.

Atsumu still had too much adrenaline pumping through him, though, so, you’d had to compromise: he’d watch the match reruns on his phone, as he cuddled you in bed, providing you with the warmth you so much desired.

You press a kiss to his jaw as he holds the phone over his face, the arm he has snaked under you to wrap around your waist squeezing you tight in response, “love ya, ma' pretty baby”

You hum again, this time hiding your smile when you press another kiss to his shoulder. Glancing back at his phone screen, you see tiny, video Atsumu serve the ball that had won the set and you smile again, gently patting his chest with the hand you rested over his heart, whispering, now a little more alert, “that was a good serve, baby”

You can practically hear Atsumu's smile as he thanks you, knowing he’s most definitely blushing right now— you just have that effect on him, he tries to tell you not-so-suavely.

You sigh contently as you snuggle deeper onto this human heater’s side, not really bothering to notice how you move your hand from his chest to lay your arm across his whole torso, your hand landing gently at his hip, skimming the band of his underwear that peeks from the hem of his sweats. It’s innocent, really. You're just trying to get more comfortable, looking for the greatest body-to-warmth ratio your boyfriend can provide. Your thumb, now gently tracing the skin exposed by his scrunched up shirt is, also, innocent, you'd like to point out.

But still, Atsumu grows quiet. Gone are all the small, ego-boosting comments and critiques he has to offer your tired figure, and instead he sucks in a shaky breath.

You're not completely aware of his mood change yet, though, too busy savoring his warmth.

"A-angel," his voice is lower, thicker now, a murmur laced with the beginnings of sin.

Blinking, it’s now that you fully begin to register your boyfriend's mood.

"What is it, baby?" you still feign innocence at his side; hoping he'll outright tell you, wanting him to tell you, he needs you.

Atsumu seems to realize this, too, and he whines, the tiny hearts your fingers trace at his v-line driving him insane.

"Ca-can ya touch me? Please, Angel?" his phone suddenly finds itself at the bedside table, and he brings his free hand to tug at the strands of his hair, while the one he has wrapped around you digs a little harsher at the skin of your waist.

"I am touching you, 'Tsumu," you tease, deciding you want to play with him a little, rile him up.

You're so mean, he thinks, you don't even bother hiding the smirk he feels on your lips, still at his neck.

"Babyy"

You chuckle, pressing a kiss to the corner of his mouth, "do you mean here? 'Tsumu?.." you trail off, moving your hand under his shirt, grazing one of his nipples, then the other one, with a feather-light touch. Atsumu mewels at the contact.

"Or- do you mean here?" your hand now, slowly, traces the ridges and grooves along his stomach, taking your time as it makes its way back downward, and stopping at the hem of his underwear again. You toy with the strings of his sweatpants and thumb at the soft trail of hairs that disappear under the material. Your mouth at his neck drives him even crazier.

His voice is whiny now as he nods, "t-there, angel, n lower."

"Lower?" you murmur your question to his neck, soothing the now blooming purple spot with a kiss. You hum and you feel him sucking in a breath. You want to touch him so bad, but you also almost never get to mess with him this way. You know what'll happen if you keep teasing and riling him up, you know he'll do the same to you and take the torture even further, and yet, you can't help it; you love it when he turns to putty in your hands.

"I got you, baby" you assure him, and you do— only just not yet.

Your hand moves lower, over the fabric of his sweatpants, as you trace the outline of his hardening cock. Atsumu groans; he sounds so pretty like this, so needy for you and your touch.

"Yer killin' me, angel,"

You can't help but snicker at his desperation, your mouth still working at his neck. You continue to palm him through his pants, hand gently cupping his girth, and he buckles up to you. He's so fucking hard already. Your mouth watters, and you can only press your thighs together to soothe the ache between them. Gently, you dig your teeth at his shoulder, trying to prevent your own goans from escaping. This is about him, you remind yourself.

It's so crazy, honestly, just how much of an effect you have on each other. You've barely touched him, but the hardness in your palm would have it appear that you've been at it for hours. You're not doing much better, either.

His groans only get louder and sweeter; you want to hear more. He turns to look at you, pleading as he meets your lips halfway in a messy kiss. He's whining into you mouth, and you can't really decipher what he's saying until he pulls away, out of breath, "please, please, please, baby; a need ya,"

And who are you to deny him, really?

You nod, both of your noses nudging messily as you begin to traill kisses from the corner of his mouth, down to his neck.

"My baby," you coo. Atsumu is so worked up right now, sweaty and nodding and desperate for your touch; you love it, love him, "i'll touch you, baby, i got you," you repeat.

Your hand moves back up his sweats, stopping at the hem again. Tracing it, your hand finally, finally, slides under.

Although you already knew this, in that moment, you determine Atsumu to be the most gorgeous man on earth, with the prettiest sounds, too. He's beautiful-- blushy and sweaty and panting-- and he's all yours. He has allowed only you to see him like this, make him feel this way, and that makes a hot, raging fire ignite within your chest and belly. You both moan when your hand finally wraps around the base of his throbbing, hot cock.

Atsumu sighs and groans and moans as you touch him, and you can't decide which is your favorite sound— truthfully, it's all of them, because he makes them only for you to hear.

You prop yourself up on your elbow, continuing to stroke him. You kiss him full on the mouth now, and he moans into the kiss. It's a clash of teeth and bitten lips, and you even giggle a little when you separate from him to brush a couple of strands of his sweaty hair away from his forehead and he moves up to kiss you again, whining in the absence of your lips. It's messy, but it's Atsumu, and you love him nonetheless.

Finally, you take him out of the confines of his briefs and sweats, pushing them just below his hips so you can have better access to his member. Focusing your attention on him, Atsumu continues to kiss down your jaw and neck.

You squeeze him at the base before moving your fist upwards, thumb grazing his pretty, sensitive tip. He bites down at the skin by your earlobe, keeping his moans.

"'Tsumu," your tone is sharp, or as sharp as it can get with him, "i want to hear you, baby. Let me have all of those pretty sounds, okay?"

Atsumu apologizes to the skin of your neck and you hum, gathering the precum at his slit; he whines at the touch.

With his shaft slick, you begin pumping him, gradually building up your pace, and Atsumu gradually gets louder and louder. He's squirming now, biting and nibbling at the skin of your neck, his hand at your waist bruising your skin with his tight grip, and his other hand pulling and messing with his hair.

"A- ah- ngel,"

You flick your wrist at the base of his cock, just the way he likes it.

"Fu- baby, a'm, m'gonna- "

"Go ahead, t'sumu," you're back to kissing his neck, "i got you, pretty boy, my pretty baby."

And it’s then that his release finally hits, spurting thick, hot ropes of his cum onto your hand and his thighs. He’s a moaning, panting mess, but you wouldn’t have it any other way.

Atsumu swears he sees stars. He's not sure if it's because you call him the same thing he calls you (which, he makes a mental note to call you it more often if it makes you cum as hard as it does him), or if it’s because the knot in his chest and lower abdomen finally seems to unravel, or maybe even just the fact that it's you who is making him feel like he never has before, but what he is sure of is that, that night, the secrets of the universe are revealed to him. And it's all you. You are the only thing that matters in this world, in this galaxy, in all of his, and any, existence.

He doesn't realize he's still rutting up to your fist, cock softening, but you gently help him ride his high. He doesn't realize either that he's babbling incoherencies at you, thanking you and kissing you amongst them. You are, and feel, like absolute heaven to him.

You smile down at the man beside you, his eyes still seem to be foggy, off to some distant, post-orgasm bliss. You kiss him again, this time, short and sweet and full of care.

You're finally aware of the death-grip he has on you when you try to move away, trying to get a washcloth to clean him up. He whines at the loss of you by his side.

You talk to him fondly as you untangle yourself from him, brushing the hair away from his forehead, "i'll be right back, 'tumu," you promise with a kiss to his nose.

And you do, of course you come back, settling yourself in between his legs as you take care of him. He shudders at his sensitivity and you plant a kiss to his exposed hip bone, before tucking him back into his sweats. You smile as you lift yourself back up.

Atsumu can't really feel anything from the waist down, but he manages to open his arms to you, beckoning you to come back and lay with him.

He sighs contently once he has you back in his arms, kissing any inch of skin that's available to him, promising to love you forever.

You nuzzle back into his side, welcoming the heat of his skin once more, as you both drift back to sleep, with one last promise of him making you feel just as good tomorrow morning.

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rxseblanche · 8 years ago

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shoves him in here.

FIRST THREE IN MY INBOX GET KISSES

2/3 // @ofwiireiisms

“oh? well – THIS was unexpected to say the less.”

Belle titled her head – but at the same time, a small smile jumped across her face. Grabbing the other’s arm, she pulled him close and inhale for a moment – just a second, before she pulled him closer to her. Moving to slightly be on her tippy toes she leans upwards and places her lips against his.

Leaving it for a moment or so, she pulled away and took a step back from him, and blushed lightly. Tilting her head to the side — while looking away from him, she grinned lightly.

“ – I hope it was alright. I’m not — really good at giving kisses.” M.sub>

#ofwiireiisms #v; to be determined.#♥#wheeeeee for shitty replies at almost 2 am

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persidskiyn6i-blog · 7 years ago

Text

Using moving total mortality counts to obtain improved estimates for the effect of air pollution on mortality.

In many cities of the United States, measurements of ambient particulate matter air pollution (PM) are available only once every 6 days. Time-series studies conducted in these cities that investigate the relationship between mortality and PM are restricted to using a single day's PM as the measure of PM exposure. This is undesirable because current evidence suggests that the effects of PM on mortality are spread over multiple days. And studies have shown that using a single day's PM as the measure of PM exposure can result in estimates that have a large negative bias. In this article, I introduce a new model for estimating the mortality effects of PM when only every-sixth-day PM data are available. This new model uses information available in the daily mortality time series to infer otherwise lost information about the effect of PM on mortality over a period of more than a single day. This new model typically offers an increase in both statistical estimation precision and accuracy compared with existing models. Key words: air pollution, distributed lag model, mortality, particulate matter, time series. doi:10.1289/ehp.7774 available via http://dx.doi.org/[Online 10 May 2005] ********** Numerous time-series studies have investigated the association between daily mortality and some measure of daily ambient particulate matter air pollution (PM) (Chock et al. 2000; Cifuentes et al. 2000; Goldberg et al. 2003; Ito et al. 1995; Kelsall et al. 1997; Klemm et al. 2000; Kwon et al. 2001; Moolgavkar 2000; Ostro et al. 1999; Roemer and van Wijnen 2001; Smith et al. 2000; Stieb et al. 2002; Styer et al. 1995). These studies typically fit a generalized additive model (Hastie and Tibshirani 1990) or generalized linear model (McCullagh and Nelder 1989) to concurrent time series of daily mortality, PM, and meteorologic covariates. The fitted models are then used to quantify the effect of PM on mortality. The general consensus from these studies is that a 2- or 3-day moving average of PM better describes the relationship between PM and mortality than does a single day's PM (Schwartz 2000). In addition, some recent studies have suggested that distributed lag models (DLMs) that allow differential PM mortality effects spread over multiple days may be preferable to single-day or multiple-day moving average PM exposure measures (Schwartz 2000; Smith et al. 2000). The reason is that DLMs do not leave to chance the question of how the mortality effects of PM are distributed over time. Historically, in the United States most monitors that measure PM operate on an every-sixth-day collection schedule (Ito et al. 1995). This is a consequence of the U.S. Environmental Protection Agency often requiring PM concentrations to be collected only every sixth day. For most of the 108 cities contained in the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) database (Peng et al. 2004), measurements of ambient PM The constraint of being able to use only a single day's PM is problematic. Studies have shown that using a single day's PM can result in a large underestimation of the relationship between PM and mortality (Roberts 2005; Schwartz 2000). The reason for this is that if the effects of PM on mortality last for > 1 day, a single-day PM exposure measure will detect the effect of PM only on 1 day's mortality. Even worse, the wrong single-day PM exposure measure may be used. Several PM mortality time-series studies have demonstrated that the effects of PM on mortality last for multiple days (Schwartz 2000; Zanobetti et al. 2003). In addition, toxicologic evidence has shown that the morbidity effects of PM can persist for > 1 day (Clarke et al. 1999). It has been shown that DLMs avoid the problems of underestimation experienced by single-day PM exposure measures. For this reason, it has been suggested that DLMs should be the preferred measure of PM exposure if daily PM measurements are available (Roberts 2005; Schwartz 2000). In this article, I introduce a model that typically improves both the accuracy and precision of the PM mortality effect estimates obtainable from time-series studies where PM measurements are available only every sixth day. This model uses the daily mortality time-series data to create a moving total mortality time series. The moving total mortality time series is then used in place of the current day's mortality time series in the subsequent analysis. Simulation studies will show that for estimating the mortality effects of PM, this model offers a substantial decrease in estimation variance and typically a decrease in estimation bias compared with the standard method of using the current day's mortality time series. With this new model, improved estimates of the effect of PM on mortality will be available for a large number of cities in the United States. This may in turn lead to a better understanding of the public health significance of PM exposure. Materials and Methods Materials The data used in this article were obtained from the publicly available NMMAPS database (Peng et al. 2004). The data extracted consist of concurrent daily time series of mortality, weather, and PM for Cook County, Illinois, and Allegheny County, Pennsylvania, for 1987-2000. The Allegheny County data were subsequently truncated at the end of the year 1998 because PM measurements were unavailable from this time forward. The mortality time-series data, aggregated at the level of county, are nonaccidental daily deaths of individuals [greater than or equal to] 65 years of age. Deaths of nonresidents were excluded from the mortality counts. The weather time-series data are 24-hr averages of temperature and dew point temperature, computed from hourly observations. The measure of PM used was the ambient 24-hr concentration of P[M.sub.10], measured in micrograms per cubic meter. P[M.sub.10] is the most commonly used measure of PM in air pollution mortality time-series studies. The Cook County PM time series of length 5,114 days had 251 days that were missing PM concentrations, and the Allegheny County PM time series of length 4,383 days had 24 days that were missing PM concentrations. The missing PM concentrations were imputed by taking the average of the previous and subsequent day's PM concentration. If either the previous or subsequent day's PM concentration was missing, the average was set equal to the nonmissing value. This method has previously been used to impute missing PM concentrations (Roberts 2004). The missing PM concentrations were imputed because a DLM of PM will be fit to the data, and missing values propagate by up to a factor of 5 when DLMs are used. Methods In many community time-series studies on the effect of PM on mortality, an additive Poisson log-linear model is fit to the time series of observed mortality. Under this model, the daily mortality counts are modeled as independent Poisson random variables with a time-varying mean [[Mu].sub.t] on day t given by log([[Mu].sub.t]) = [confounders.sub.t] + [beta]P[M.sub.t]. [1] Here, [confounders.sub.t] represents other time-varying variables that are related to daily mortality. P[M.sub.t] is the time series containing the PM exposure measure, and [beta] is the effect of this PM exposure measure on mortality. Equation 1 will be referred to as the "standard model." Because of data limitations, the PM exposure measure used in the standard model is typically restricted to be a single day's PM rather than a moving average of PM or a DLM of PM. In this article, I assume that we are in such a situation; that is, only every-sixth-day PM measurements are available. As discussed above, using a single day's PM is undesirable because it can result in estimates that have a large negative bias. And even in the unlikely event that the effect of PM on mortality is concentrated on a single day, it is possible that the wrong single-day PM exposure measure will be used. These problems would be avoided if daily PM measurements were available, making it possible for a DLM of PM to be used. Daily mortality counts are available for cities in the NMMAPS database regardless of the sampling frequency used for PM. The model I introduce takes advantage of this fact by using information available in the daily mortality data to extract information about the effect of PM on mortality over a period of more than a single day, information otherwise unavailable with every-sixth-day PM measurements. To do this, I replace the current day's mortality count used in the standard model with a moving total mortality count. The moving total used is a forward-moving total, meaning that the current day's mortality count is replaced by the sum of the current day's mortality count, the next day's mortality, and so on, for some specified number of days. I use the term "k day moving total" to mean the sum of today's and the subsequent k - 1 days' mortality counts. Under this model, the k-day moving total mortality counts are modeled as independent Poisson random variables with a time varying mean [[Mu].sub.t, k] on day t given by log([[Mu].sub.t,k]) = [confounders.sub.t] + [beta]P[M.sub.t] [2] Here, [confounders.sub.t] has the same specification as in the standard model, and P[M.sub.t] is a single day's PM, as is the case for the standard model. Simulation studies will show that the mortality effect estimates for PM obtained from Equation 2 are typically both more accurate and more precise compared with those obtained from the standard model. Equation 2 will be referred to as the "moving total model." A heuristic argument for why the moving total model may provide more accurate estimates of the mortality effect of PM compared with the standard model is now provided. If the mortality effect of PM lasts for more than a single day, a day of high PM will cause not only the current day's mortality count to be elevated but also the mortality counts on subsequent days. By using a moving total mortality count, we are able to capture the increased mortality on subsequent days, information that is lost if only the current day's mortality count is used. Obviously, if daily PM measurements are available, the best way to capture the effect of PM on mortality is through a DLM of PM. However, in the more common situation where PM measurements are available only every sixth day, using a moving total mortality count provides a "poor person's" substitute for a DLM. Implementing the moving total model is no harder than implementing the standard model. To fit the moving total model instead of using the current day's mortality count ([d.sub.t]) as the response variable, as done in the standard model, a moving total mortality count ([d.sub.t,k]) is used instead, [d.sub.t,k] represents the k-day moving total mortality count for day t; that is, [d.sub.t,k] = [d.sub.t] + [d.sub.t+1] + 4 ... [d.sub.t+k-1]. Simulation Study The simulation study compares the statistical properties of the standard model for estimating the mortality effects of PM with those of the moving total model. In the simulations, the actual weather and PM data from Cook County are used. Although the weather and PM time series are actual, the corresponding mortality time series are generated using models that describe PM mortality effects. Realistic mortality generation. To conduct the simulations, we need a way to generate realistic mortality time series. I used a method previously shown to generate realistic mortality time series (Roberts 2005), which proceeds by estimating the effects of time, temperature, dew point temperature, and day of the week on mortality using the data from Cook County. This was done by fitting the following Poisson log-linear model similar to those used in previous NMMAPS analyses (Daniels et al. 2000) to the actual Cook County mortality and meteorologic time-series data: log([[Mu].sub.t]) = [Mu] + [S.sub.t1] (time, 7 df per year) + [S.sub.t2] ([temp.sub.0], 6 df) + [S.sub.t3] ([temp.sub.1-3, 6 df) + [S.sub.t4] ([dew.sub.0], 3 df) + [S.sub.t5] ([dew.sub.1-3], 3 df) + [gamma] DO[W.sub.t] [3] Here the subscript t refers to the day of the study; [[Mu].sub.t] is the mean number of deaths on day t; the [S.sub.ti]( ) are smooth functions of time, temperature, and dew point temperature with the indicated degrees of freedom (the smooth functions are represented using natural cubic splines); [temp.sub.0] is the current day's mean 24-hr temperature; [temp.sub.1-3] is the average of the previous 3 days' 24-hr mean temperatures; [dew.sub.0] and [dew.sub.1-3] are similarly defined for the 24-hr mean dew point temperature; DO[W.sub.t] is a set of indicator variables for the day of the week. All the models in this article were fit using the glm function in R (version 2.0.0; R Development Core Team 2005). Once Equation 3 was fit, I extracted the estimated mean mortality counts, denoted [u.sub.fit, t]. The effects of PM on mortality were explicitly specified and incorporated in the generated mortality time series. I did this by generating mortality time series that were Poisson distributed with mean [PSI] on day t given by log([[PSI].sub.t]) = log([[Mu].sub.fit, t]) + [theta]([[alpha].sub.0] P[M.sub.t] + [[alpha].sub.1] P[M.sub.t-1], + ... + [[alpha].sub.5] P[M.sub.t-5]). [4] Here P[M.sub.t-i] is the time series of lag i PM concentrations; [theta] is the total mortality effect of a unit increase in PM over time (1,000[theta] is approximately the percentage increase in mean daily mortality for each 10-[micro]g/[m.sup.3] increment in PM), and [theta][[alpha].sub.i] is the mortality effect of a unit increase in PM at lag i. Equation 4 assumes the mortality effects of PM can last for a maximum of 6 days. Mortality time series were generated using various specifications for the "true" effect of PM on mortality in Equation 4. Because previous studies have shown that PM lags of more than a few days have little correlation with daily mortality (Schwartz 2000), the specifications used span a suite of plausible lag structures for the effect of PM on mortality: no effect, PM has no effect on mortality; single-day effect, the effect of PM on mortality is concentrated on a single day [the single days considered were the current day's PM (lag 0), the previous day's PM (lag 1), or the 2 day's previous PM (lag 2)]; moving average effect, the effect of PM on mortality depends on a moving average of PM [the moving averages considered were the average of the current and previous day's PM (lag 0-1), and the average of the current and previous 2 days' PM (lag 0-2)]; distributed lag effect, differential effects of PM on mortality over time were allowed. The distributed lag effects considered were as follows: [[alpha].sub.0] = 6/21, [[alpha].sub.1] = 5/21, [[alpha].sub.2] = 4/21, [[alpha].sub.3] = 3/21, [[alpha].sub.4] = 2/21, [[alpha].sub.5] = 1/21 [DLM 1] [[alpha].sub.0] = 3/6, [[alpha].sub.1] = 2/6, [[alpha].sub.2] = 1/6, [[alpha].sub.3] = 0, [[alpha].sub.4] = 0, [[alpha].sub.5] = 0 [DLM 2] [[alpha].sub.0] = 0, [[alpha].sub.1] = 5/15, [[alpha].sub.2] = 4/15, [[alpha].sub.3] = 3/15, [[alpha].sub.4] = 2/15, [[alpha].sub.5] = 1/15 [DLM 3] [[alpha].sub.0] = 8/15, [[alpha].sub.1] = 4/15, [[alpha].sub.2] = 2/15, [[alpha].sub.3] = 1/15, [[alpha].sub.4] = 0, [[alpha].sub.5] = 0 [DLM 4] For the moving average and distributed lag effects, five [theta] values corresponding to 0.25, 0.5, 1, 2, and 4% increases in mortality for each 10-[micro] g/[m.sup.3] increment in PM were used. For the single-day effects, four [theta] values corresponding to 0.25, 0.5, 1, and 2% increases in mortality for each 10-[micro]g/[m.sup.3] increment in PM were used. These values of [theta] span a plausible range for the total effect of PM on mortality. Fitting models to generated mortality. For each specification of the "true" effect of PM on mortality and [theta] combination 400 mortality time series were generated using Equation 4. Because we are interested in the situation where PM measurements are available only every sixth day, after the mortality time series were generated, I extracted every sixth PM measurement from the PM time series of length 5,114 days that was used to generate mortality. These 852 every-sixth-day PM measurements, assumed to be the only PM measurements available, were then used in both the standard model and moving total model to estimate the effect of PM on mortality ([theta]). The [confounders.sub.t] term in both the standard and moving total models had the same specification as the confounder adjustment used in the mortality generating Equation 4. It is important to remember that in the NMMAPS database daily measurements are available for mortality, temperature, and dew point temperature irrespective of the sampling frequency used for PM. The standard model was fit to each generated mortality, time series using in turn the current day's PM (standard model - lag 0), the previous day's PM (standard model - lag 1), and the 2 day's previous PM (standard model - lag 2) as the PM exposure measure (P[M.sub.t] in Equation l). The moving total model was fit to each generated mortality time series using the current day's PM as the PM exposure measure (P[M.sub.t] in Equation 2) and 2-, 3-, 4-, and 5-day moving total mortality counts (k = 2, 3, 4, 5 in Equation 2). Moving total mortality counts with k > 5 were not considered because the current evidence suggests that mortality counts more than a few days forward have little association with the current day's PM concentration (Schwartz 2000). The standard and moving total models that are being fit to the generated mortality time series are identical except for the specification of the mortality response variable: For the standard models, a single day's mortality count is used, whereas for the moving total models a moving total mortality count is used. This means that for both the standard and moving total models, the same every-sixth-day PM time series is used. Results Tables 1 and 2 contain the results of the simulations. Table 1 contains the results for mortality generated using the no effect, single-day effect, and moving average effect specifications for the "true" effect of PM on mortality. Table 2 contains the results for the distributed lag effect specifications for the "true" effect of PM on mortality. These tables contain the standard deviation and bias of the estimates of the effect of PM on mortality ([theta]) obtained from the three forms of the standard model and the moving total models with k = 2, 3, and 4. A moving total model with k = 5 was also

investigated, but the results for this model were not reported because it performed poorly compared with the moving total models with k = 2, 3, and 4. The reason for this is discussed further below. Tables 1 and 2 show that the moving total models always offer a substantial reduction in estimation variance compared with the standard models. The reduction in estimation variance increases as the number of days used in the moving total mortality count (k) increases. The reason for this is that as the number of days used in the moving total mortality count increases, the estimates for the effect of PM on mortality are based on successively more data. For a given model, the standard deviation remains constant across the simulations because the amount of data used remains constant. Tables 1 and 2 also show that the estimation bias is typically smaller for the moving total models than for the standard models. The smaller bias for the moving total models is a consequence of the moving total mortality counts allowing the moving total models to capture the effect of PM on more than a single day's mortality. This is something that is not possible with the standard models. For a given model, the bias increases as the total PM effect ([theta]) increases because the absolute amount of information lost by not observing the daily PM time series increases as [theta] increases. These results show that the moving total model offers a way to estimate the effect of PM on mortality that is both more precise (smaller variance) and typically more accurate (smaller bias) than the standard model. The results reported in Tables 1 and 2 suggest that a moving total model with k = 2 or k = 3 would be preferred to moving total models with k [greater than or equal to] 4. The reason for this is that k = 2 or k = 3 offers a better compromise between bias and variance. That is, the increased variance of using a moving total model with k = 2 or k = 3, as opposed to k [greater than or equal to] 4, is more than offset by a decrease in bias. This is supported by the fact that in the simulations the mean squared error (for brevity, values are not reported here) for the moving total models with k = 2 or k = 3 was typically smaller than the mean squared error for the moving total models with k = 4 or k = 5. The reason for the poorer performance of the moving total models with k [greater than or equal to] 4 was that in the simulations, because of evidence from previous studies (Schwartz 2000), the effect of PM on mortality was mainly concentrated at lags of up to 2 days. This meant that the last 1 or 2 days of mortality included in the moving total mortality counts when k = 4 or k = 5, respectively, were typically not associated with the measure of PM used in the model. This resulted in a dampening of the estimated effect of PM on mortality for the moving total models with k = 4 or 5, and hence an increase in estimation bias compared with the moving total models with k = 2 or k = 3. Application. In this section 1 compare the results of applying the standard and moving total models to the actual Cook County and Allegheny County mortality time-series data. To do this, I first fit a DLM of PM to the mortality, meteorologic, and PM time-series data from both counties described in "Materials and Methods." The DLM of PM contained PM concentrations lagged for 5 days, and the confounder adjustments used in this model were the same as those used in Equation 3. The effect of PM on mortality obtained from the DLM of PM was then used as a basis for judging the performance of the standard and moving total models. The rationale is that, in the ideal situation where daily PM data are available, a DLM of PM should be the method of choice for estimating the effect of PM on mortality (Roberts 2005; Schwartz 2000; Smith et al. 2000). Hence, in the situation where only every-sixth-day PM data are available, it is desirable that the method used to estimate the effect of PM on mortality return an estimate as close as possible to that obtainable in the ideal situation of daily PM data. After fitting the DLM of PM, an every-sixth-day PM time series was obtained by extracting every-sixth-day PM concentration from the daily PM time series. With the every-sixth-day PM time series, I then estimated the effect of PM on mortality using both the standard and moving total models. The confounder adjustments used in the standard and moving total models were the same as those used in Equation 3. The estimates obtained from the standard and moving total models were then compared with the basis estimates obtained from the DLM of PM. Table 3 contains the estimates obtained from fitting the DLM of PM, the standard models, and the moving total models to the data from both Cook County and Allegheny County. Using the estimates obtained from the DLM of PM as the basis for comparison, we can see that the moving total model with k = 2 provides the "best" estimates for the effect of PM on mortality. In both counties, this model produces an estimate that is closer to the basis value than the estimates obtained from the standard models. In addition, the estimate obtained from the moving total model with k = 2 has smaller variance than the estimates obtained from the standard models. These results reinforce the conclusions from the simulations that the moving total model offers a way to estimate the effect of PM on mortality that is both more precise and more accurate than the standard model. These results also show that the moving total model may provide a more robust estimate of the effect of PM on mortality than that obtained from the standard model. This is illustrated by the moving total models with k = 2, 3, and 4, avoiding the relatively poor estimates obtained from the standard model-lag 2 in Cook County and standard model-lag 1 in Allegheny County. It is important to note the substantially smaller estimates obtained from the moving total models of Cook County data with k = 3 and k = 4 compared with that obtained with k = 2. The reason for this is that the large negative effect of PM on mortality observed for this data at a lag of 2 days (see standard model-lag 2) is incorporated into the estimates obtained from the moving total models with k = 3 and k = 4 but not the moving total model with k = 2. Discussion PM air pollution is an important determinant of community health, and numerous time-series studies in the United States have investigated the association between PM and mortality (Crosignani et al. 2002; Health Effects Institute 2001). One major limitation of these studies is that in most large cities PM measurements are available only every sixth day. Time-series studies conducted in these cities cannot investigate how the effects of PM on mortality are distributed over time; instead, they are forced to examine the mortality effects of PM on a single day only. However, because the current evidence suggests that the mortality effects of PM are spread over multiple days, examining the effect of PM on a single day results in important information about the effect of PM on mortality being lost and estimates that have a large negative bias (Roberts 2005; Schwartz 2000). The moving total model introduced in this article uses information available in the daily mortality time-series data to infer some of this lost information. The results presented here show that, for estimating the total effect of PM on mortality, the moving total model produced estimates that were substantially more precise (smaller variance) compared with those obtained from the standard model. In addition, the moving total model typically produced estimates that were more accurate (smaller bias) compared with those obtained from the standard model. These results indicate that the moving total model should be used in future air pollution mortality time-series studies where only every-sixth-day PM measurements are available. In conclusion, because in most of the largest cities in the United States PM measurements are available only every sixth day, the moving total model has the potential, in a large number of locations, to provide improved estimates of the effect of PM on mortality that have both smaller variance and smaller bias than the estimates that are currently obtainable using existing models. This means that in multicity studies on the health effects of PM, improved estimates could be obtained for the city-specific estimates and hence for the pooled regional and national effect estimates. These improved estimates would allow researchers to better understand the health effects of PM exposure and in turn allow more informed decisions about the public health significance of PM exposure. For these reasons and the ease at which the moving total model can be implemented, I believe that the moving total model is an important contribution to the current air pollution mortality time-series methodology. I thank M. Martin and P. Switzer for their helpful comments. The author declares he has no competing financial interests. Received 20 November 2004: accepted 10 May 2005. REFERENCES Chock DP, Winkler SL, Chen C. 2000. A study of the association between daily mortality and ambient air pollutant concentrations in Pittsburgh, Pennsylvania. J Air Waste Manage Assoc 50:1481-1500. Cifuentes LA, Vega J, Kopfer K, Lave LB. 2000. Effect of the fine fraction of particulate matter versus the coarse mass and other pollutants on daily mortality in Santiago, Chile. J Air Waste Manage Assoc 50:1287-1298. Clarke RW, Catalano PJ, Koutrakis P, Murthy GG, Sioutas C, Paulauskis J, et al. 1999. 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Steven Roberts School of Finance and Applied Statistics, Faculty of Economics and Commerce, Australian National University, Canberra, Australia Address correspondence to S. Roberts, School of Finance and Applied Statistics, Faculty of Economics and Commerce, Australian National University, Canberra ACT 0200, Australia. Telephone: 61-2-6125-3470. Fax: 61-2-6125-0087. E-mail: [email protected] Table 1. Standard deviation and bias for the estimates of the total PM effect ([theta]) obtained from the standard models and the moving total models. Model fit to generated mortality Standard Truth Lag 0 Lag 1 Lag 2 0.00 (a) 0.266 (b) (-0.01) (c) 0.26 (-0.02) 0.28 (-0.01) Lag 0 (d) 0.25 0.27 (0.01) 0.26 (-0.211 0.29 (-0.24) 0.50 0.25 (0.01) 0.28 (-0.38) 0.29 (-0.49) 1.00 0.26 (0.01) 0.28 (-0.78) 0.27 (-1.00) 2.00 0.26 (-0.02) 0.27 (-1.57) 0.29 (-1.971 Lag 1 0.25 0.27 (-0.17) 0.27 (-0.01) 0.29 (-0.19) 0.50 0.26 (-0.37) 0.26 (0.00) 0.30 (-0.35) 1.00 0.27 (-0.79) 0.27 (-0.01) 0.29 (-0.75) 2.00 0.26 (-1.55) 0.26 (0.02) 0.28 (-1.44) Lag 2 0.25 0.28 (-0.26) 0.27 (-0.20) 0.27 (0.00) 0.50 0.27 (-0.49) 0.26 (-0.40) 0.28 (-0.03) 1.00 0.25 (-0.95) 0.26 (-0.73) 0.29 (0.00) 2.00 0.26 (-1.98) 0.26 (-1.50) 0.28 (0.00) Lag 0-1 0.25 0.26 (-0.16) 0.25 (-0.18) 0.26 (-0.19) 0.50 0.25 (-0.33) 0.28 (-0.32) 0.30 (-0.36) 1.00 0.26 (-0.65) 0.28 (-0.66) 0.28 (-0.72) 2.00 0.27 (-1.31) 0.29 (-1.34) 0.28 (-1.44) 4.00 0.27 (-2.59) 0.25 1-2.63) 0.27 (-2.88) Lag 0-2 0.25 0.27 (-0.10) 0.27 (-0.14) 0.29 (-0.18) 0.50 0.28 (-0.21) 0.26 (-0.25) 0.28 (-0.38) 1.00 0.26 1-0.43) 0.25 (-0.52) 0.28 (-0.73) 2.00 0.27 (-0.85) 0.26 (-1.03) 0.27 (-1.46) 4.00 0.26 (-1.68) 0.26 (-2.06) 0.30 (-2.93) Model fit to generated mortality Moving total Truth k = 2 k = 3 k = 4 0.00 (a) 0.19 (0.08) 0.15 (0.11) 0.13 (0.07) Lag 0 (d) 0.25 0.18 (0.01) 0.15 (-0.02) 0.13 (-0.08) 0.50 0.18 (-0.07) 0.15 (-0.14) 0.13 (-0.24) 1.00 0.18 (-0.25) 0.15 (-0.41) 0.13 (-0.56) 2.00 0.18 (-0.60) 0.14 (-0.96) 0.13 (-1.22) Lag 1 0.25 0.18 (0.00) 0.15 (0.00) 0.13 (-0.07) 0.50 0.19 (-0.11) 0.15 (-0.14) 0.13 (-0.22) 1.00 0.18 (-0.33) 0.15 (-0.39) 0.13 (-0.52) 2.00 0.19 (-0.75) 0.15 (-0.89) 0.13 (-1.10) Lag 2 0.25 0.18 (-0.14) 0.15 (-0.05) 0.13 (-0.08) 0.50 0.19 (-0.35) 0.14 (-0.19) 0.12 (-0.22) 1.00 0.19 (-0.78) 0.16 (-0.47) 0.14 (-0.52) 2.00 0.19 (-1.69) 0.16 (-1.08) 0.13 (-1.14) Lag 0-1 0.25 0.18 (-0.08) 0.15 (-0.06) 0.12 (-0.09) 0.50 0.18 (-0.24) 0.14 (-0.22) 0.13 (-0.26) 1.00 0.18 (-0.55) 0.15 (-0.53) 0.14 (-0.59) 2.00 0.19 (-1.19) 0.15 (-1.19) 0.13 (-1.27) 4.00 0.18 (-2.46) 0.14 (-2.49) 0.13 (-2.62) Lag 0-2 0.25 0.18 (-0.01) 0.15 (0.00) 0.13 (-0.07) 0.50 0.18 (-0.14) 0.15 (-0.16) 0.13 (-0.24) 1.00 0.18 (-0.37) 0.15 (-0.42) 0.13 (-0.55) 2.00 0.20 (-0.83) 0.16 (-0.96) 0.14 (-1.17) 4.00 0.19 (-1.73) 0.15 (-2.01) 0.14 (-2.40) Truth is the specification of the "true" effect of PM on mortality and 1,000 times the [theta] value that were used to generate mortality. (a) 1,000 times the total effect of PM on mortality (theta]0) that was used to generate mortality. (b) 1,000 times the standard deviation for the estimate of the total effect of PM on mortality ([theta]). (c) 1,000 times the bias for the estimate of the total effect of PM on mortality ([theta]). (d) The specification of the "true" effect of PM on mortality that was used to generate mortality. Table 2. Standard deviation and bias for the estimates of the total PM effect ([theta]) obtained from the standard models and the moving total models. Model fit to generated mortality Standard &hl=en_US&fs=1&"> &hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="400" height="241"> Truth Lag 0 Lag 1 Lag 2 DLM 1 (a) 0.25 (b) 0.27 (c) (-0.16) (d) 0.26 (-0.11) 0.28 (-0.16) 0.50 0.27 (-0.31) 0.27 (-0.27) 0.28 (-0.27) 1.00 0.26 (-0.61) 0.28 (-0.52) 0.29 (-0.57) 2.00 0.25 (-1.15) 0.27 (-0.99) 0.27 (-1.12) 4.00 0.26 (-2.33) 0.26 (-2.03) 0.28 (-2.29) DLM 2 0.25 0.26 (-0.11) 0.27 (-0.08) 0.27 (-0.22) 0.50 0.27 (-0.22) 0.27 (-0.20) 0.27 (-0.42) 1.00 0.27 (-0.40) 0.26 (-0.39) 0.28 (-0.85) 2.00 0.27 (-0.79) 0.27 (-0.76) 0.29 (-1.70) 4.00 0.26 (-1.56) 0.28 (-1.56) 0.28 (-3.39) DLM 3 0.25 0.25 (-0.22) 0.26 (-0.16) 0.26 (-0.14) 0.50 0.27 (-0.46) 0.27 (-0.31) 0.29 (-0.35) 1.00 0.28 (-0.92) 0.27 (-0.62) 0.27 (-0.63) 2.00 0.27 (-1.81) 0.27 (-1.22) 0.27 (-1.23) 4.00 0.26 (-3.64) 0.25 (-2.48) 0.27 (-2.46) DLM 4 0.25 0.26 (-0.13) 0.26 (-0.15) 0.29 (-0.22) 0.50 0.25 (-0.21) 0.26 (-0.29) 0.27 (-0.41) 1.00 0.27 (-0.40) 0.26 (-0.59) 0.29 (-0.77) 2.00 0.28 (-0.80) 0.26 (-1.16) 0.27 (-1.53) 4.00 0.26 (-1.61) 0.27 (-2.32) 0.29 (-3.11) Model fit to generated mortality Moving total Truth k = 2 k = 3 k = 4 DLM 1 (a) 0.25 (b) 0.19 (-0.06) 0.16 (-0.03) 0.13 (-0.08) 0.50 0.19 (-0.20) 0.16 (-0.17) 0.13 (-0.24) 1.00 0.18 (-0.47) 0.15 (-0.44) 0.13 (-0.55) 2.00 0.18 (-0.99) 0.14 (-0.97) 0.12 (-1.15) 4.00 0.18 (-2.10) 0.15 (-2.07) 0.13 (-2.39) DLM 2 0.25 0.20 (0.00) 0.15 (-0.01) 0.13 (-0.07) 0.50 0.19 (-0.12) 0.16 (-0.15) 0.14 (-0.24) 1.00 0.19 (-0.29) 0.16 (-0.41) 0.14 (-0.54) 2.00 0.18 (-0.68) 0.15 (-0.92) 0.13 (-1.15) 4.00 0.19 (-1.43) 0.15 (-1.96) 0.13 (-2.40) DLM 3 0.25 0.18 (-0.11) 0.15 (-0.07) 0.13 (-0.10) 0.50 0.19 (-0.30) 0.16 (-0.24) 0.14 (-0.26) 1.00 0.19 (-0.66) 0.16 (-0.58) 0.13 (-0.61) 2.00 0.19 (-1.42) 0.15 (-1.27) 0.13 (-1.29) 4.00 0.19 (-2.94) 0.15 (-2.67) 0.13 (-2.66) DLM 4 0.25 0.19 (-0.04) 0.15 (-0.04) 0.13 (-0.08) 0.50 0.18 (-0.16) 0.15 (-0.17) 0.14 (-024) 1.00 0.20 (-0.38) 0.16 (-0.44) 0.14 (-0.55) 2.00 0.19 (-0.86) 0.15 (-1.00) 0.13 (-1.18) 4.00 0.18 (-1.81) 0.16 (-2.11) 0.13 (-2.42) Truth is the specification of the "true" effect of PM on mortality and 1,000 times the [theta] value that were used to generate mortality. (a) The specification of the "true" effect of PM on mortality that was used to generate mortality. (b) 1,000 times the total effect of PM on mortality ([theta]) that was used to generate mortality. (c) 1,000 times the standard deviation for the estimate of the total effect of PM on mortality ([theta]). (d) 1,000 times the bias for the estimate of the total effect of PM on mortality ([theta]). Table 3. Results of fitting both the standard and moving total models to the actual data from Cook County, Illinois, and Allegheny County, Pennsylvania. Model fit to mortality Standard County Lag 0 Lag 1 Lag 2 Cook County 0.127 (a) (0.264) (b) -0.042 (0.249) -0.441 (0.246) Allegheny 0.693 (0.437) 0.356 (0.423) 0.524 (0.415) County Model fit to mortality Moving total County k = 2 k = 3 k = 4 Cook County 0.150 (0.187) -0.047 (0.153) 0.009 (0.133) Allegheny 0.633 (0.310) 0.542 (0.255) 0.528 (0.221) County County Baseline Cook County 0.462 (0.212) Allegheny 0.598 (0.351) County Baseline is the baseline estimate of the total effect of PM on mortality obtained from the OLM of PM fit to the daily data. (a) 1,000 times the estimated effect of PM on mortality. (b) 1,000 times the standard deviation of the estimated effect of PM on mortality. https://www.thefreelibrary.com/Usingmovingtotalmortalitycountstoobtainimprovedestimatesfor...-a0137351361

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